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Linear stability analysis of systems with Preisach memory | We consider differential equations coupled with the input-output memory relation defined by the Preisach operator. ::: The differential equation relates an instant value of the rate of change of the output of the Preisach operator ::: with an instant value of its input. We propose an algorithm for the linearisation of the evolution operator of the system ::: and apply it to define the characteristic multiplier of periodic solutions, which determines their stability. ::: Examples of the system considered include models of terrestrial hydrology and electronic oscillators with hysteresis. | We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented. | eng_Latn | 11,000 |
Inference of Schr\"odinger's Equation from Classical-Mechanical Solution | We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field $V$ in a susceptible vacuum. The waves are Doppler-displaced upon the source motion, and superpose into a total, traveling- and in turn a standing- beat wave, or de Broglie phase wave, described by a corresponding total classical wave equation. By back-substitution of the explicitly known total, standing beat wave function and upon appropriate reductions at classic-velocity limit, we separate out from the total a component wave equation describing the kinetic motion of particle, which is equivalent to the Schr\"odinger equation. The Schr\"odinger wave function follows to be the envelope function of the standing beat wave at classic-velocity limit. | Motivated by a recently proposed local refinement strategy for immersed interface problems, in this work we aim at dealing with the behavior of mixed finite elements for the Stokes problem in (strongly) anisotropic mesh situations, leading to severely distorted elements. In fact, the majority of the theoretical results present in the finite element literature has been carried out under the assumption of well-shaped elements. In the case such a condition is not satisfied, the inf-sup constant may degenerate, thus leading to the instability of the system. | eng_Latn | 11,001 |
Stochastic evaluation of supply chains and replenishment policies with Petri net components | The outbound logistics deals with the transportation and storage of finished goods. It is one of the most complex and expensive activity of the supply chain management and is decisive for the Quality of Service (QoS). This paper proposes the use of pre-defined Petri net components to model and evaluate this activity. The model that represents an outbound logistics scenario is obtained with a bottom-up approach, guaranteeing some expected Petri nets properties. Furthermore, the use of pre-defined, validated components allows modelling and evaluating the supply chain entities and processes through a systematic procedure. In the end of this paper, results related to a real case study, conducted by considering the proposed models, is depicted. | O. Introduction This lecture will unfortunately not be a systematic review of the subject of rigorous results in non-equilibrium statistical mechanics. A preliminary attempt to outline such a review led me quickly to the conclusion that the field is too diverse to be summarized in a single lecture. I have therefore decided instead to discuss a few related.works in depth. The works I have chosen are: 1. The paper of J. Fritz and R. L. Dobrushin[5] on two-dimensional dynamics. 2. The paper of W. Braun and K. Hepp[3] on classical mechanics in the Vlasov limit. 3. A recent preprint by H. van Beijeren, J. L. Lebowitz, H. Spohn, and myself[2] on autocorrelations and fluctuations in the dilute equilibrium hard-sphere gas. | eng_Latn | 11,002 |
Selected Works Dynamical Theory And Quantum And Classical Statistical Mechanics | Thank you very much for reading selected works dynamical theory and quantum and classical statistical mechanics. As you may know, people have search numerous times for their chosen books like this selected works dynamical theory and quantum and classical statistical mechanics, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some harmful bugs inside their computer. | This chapter contains sections titled: Introduction Identification of the Best Linear Approximation Using Random Excitations Generation of Uncertainty Bounds? Identification of the Best Linear Approximation Using Periodic Excitations Advises and Conclusions ]]> | yue_Hant | 11,003 |
Possibility of restoring chiral symmetry in quantum chromodynamics | The effective potential is found for scalar and pseudoscalar fields, both in the low-energy domain and in the domain of asymptotic freedom. Using the properties of this potential the mechanism of restoration of chiral symmetry is given as well as a description of the formation of a quark-gluon “bubble” with finite radius. | A new class of high order, implicit, three time step schemes for semi-discretized wave equations is introduced and studied. These schemes are constructed using the modified equation approach, generalizing the @q-scheme. Their stability properties are investigated via an energy analysis, which enables us to design super-convergent schemes and also optimal stable schemes in terms of consistency errors. Specific numerical algorithms for the fully discrete problem are tested and discussed, showing the efficiency of our approach compared to second order @q-schemes. | eng_Latn | 11,004 |
Solitons supported by spatially inhomogeneous nonlinear losses. | We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate η (in one dimension) faster than |η|. The spatially-inhomogeneous absorption also supports new types of solitons, that do not exist in uniform dissipative media. In particular, single-well absorption profiles give rise to spontaneous symmetry breaking of fundamental solitons in the presence of uniform focusing nonlinearity, while stable dipoles are supported by double-well absorption landscapes. Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity. | Stress vs. strain fluctuations in athermal amorphous solids are an example of `crackling noise' of the type studied extensively in the context of elastic membranes moving through random potentials. Contrary to the latter, we do not have a stochastic equation whose statistics agree with the measured ones. On the other hand we show in this Letter that the statistics of the former exhibit 'density scaling' when the interparticle potential can be well approximated by a power law. The distributions of sizes of dissipative events for a wide range of densities and system sizes follow a single scaling function. We find that both the system-size scaling of energy drops and the entire strain interval statistics are invariant to changes in density. We use this to determine accurately the exponents in the scaling laws, establishing that the present crackling noise belongs to a different universality class. | eng_Latn | 11,005 |
Cohomology and deformations for the Heisenberg Hom-Lie algebras | ABSTRACTIn this work, we consider the Heisenberg Lie algebra with all its Hom-Lie structures. We completely characterize the cohomology and deformations of any order of all Heisenberg Hom-Lie algeb... | We show how to extend the formalism of infinitesimal differential diffusion quantum Monte Carlo to the case of higher derivatives of the ground‐state energy of a molecule with respect to the molecular geometry. We use LiH as an example, but the technique can be extended to more complicated, nonliner molecules as well. We obtain good agreement with experimental values for the energy derivatives and for the harmonic and anharmonic frequencies of LiH and LiD, despite using a compact single‐determinant wave function. | eng_Latn | 11,006 |
On the Nonlinear Effects in Focused Ultrasound Beams with Frequency Power Law Attenuation | When finite amplitude ultrasound propagation is considered, changes in spatial features of focused ultrasound beams can be observed. These nonlinear effects typically appear in thermoviscous fluids as focal displacements, beam-width variations or gain changes. However, in soft-tissue media, the frequency dependence of the attenuation doesn’t obey a squared law. In this way, these complex media response leads to weak dispersion that prevents the cumulative processes of energy transfer to higher harmonics. In this work we explore the influence of different frequency power law attenuation responses and its influence on the self-defocusing effects in focused ultrasound beams. Thus, we numerically explore the spatial field distributions produced by low-Fresnel number devices and High Intensity Focused Ultrasound (HIFU) radiating trough different soft-tissue media. | Abstract In this paper, we study the long-time behavior of solutions for a non-autonomous strongly damped wave equation. We first prove the existence of a uniform attractor for the equation with a translation compact driving force and then obtain an upper estimate for the Kolmogorov e -entropy of the uniform attractor. Finally we obtain an upper bound of the fractal dimension of the uniform attractor with quasiperiodic force. | eng_Latn | 11,007 |
Vortex lattices in Bose-Einstein condensates with dipolar interactions beyond the weak-interaction limit | We study the ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions. | Abstract We discuss random matrix-model representations of D = 1 string theory, with particular emphasis on the case in which the target space is a circle of finite radius. The duality properties of discretized strings are analyzed and shown to depend on the dynamics of vortices. In the representation in terms of a continuous circle of matrices we find an exact expression for the free energy, neglecting non-singlet states, as a function of the string coupling and the radius which exhibits exact duality. In a second version, based on a discrete chain of matrices, we find that vortices induce, for a finite radius, a Kosterlitz-Thouless phase transition that takes us to a c = 0 theory. | eng_Latn | 11,008 |
Scaling of energy spreading in a disordered Ding-Dong lattice | We study numerically propagation of energy in a one dimensional Ding-Ding lattice, composed of linear oscillators with ellastic collisions. Wave propagation is suppressed by breaking translational symmetry, we consider three way to do this: a position disorder, a mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to appearance of chaos, and subdiffusive. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence on energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder. | We investigate the OLS-based estimator s2 of the disturbance variance in the standard linear regression model with cross section data when the disturbances are homoskedastic, but spatially correlated. For the most popular model of spatially autoregressive disturbances, we show that s2 can be severely biased in finite samples, but is asymptotically unbiased and consistent for most types of spatial weighting matrices as sample size increases. | eng_Latn | 11,009 |
Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain | The novel stable “soliton islands” in a “sea of solitary waves” of the nonlinear Schrodinger equation model with varying dispersion, nonlinearity, and gain or absorption are discovered. Different soliton management regimes are predicted. | Compact differencing can deliver high-order accuracy using only a limited span of stencils, but incurring a costly matrix in version. Hence, use of a stable implicit time discretizaton becomes favorable in order to offset the computation cost by allowing a large time step. A practical way to reduce the burden of inverting a large matrix from multidimensional problems is to split the implicit operator into a series of smaller operators. Undesirable consequences can surface, such as (1) loss of stability, and/or (2) loss of accuracy. Here, we propose a consistent implicit compact method and study the stability and accuracy of steady and unsteady solutions. | eng_Latn | 11,010 |
Effect of Timing Jitter on Sigma Delta ADC for SDR Mobile Receiver | Jitter is the limiting effect for high speed analog-to-digital converters with high resolution and wide digitization bandwidth, which are required in receivers in order to support high data rates. The rapid development of digital wireless system has led to a need of high resolution and high speed analog to digital converter. The performance of a data converter is dependent upon the accuracy and stability of the clock supplied to the circuits. When data converter employ a high sampling rate, clocking issues become magnified and significant distortion can be result. This paper describes minimizing the effect of Timing error such as aperture jitter and clock jitter on the performance of sigma delta ADC Model and Present analytical evaluation of the performance in terms of achievable signal to noise ratio and also draw mean error power spectrum due to aperture jitter and clock jitter. | We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn–Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on a... | eng_Latn | 11,011 |
A sufficient condition for the Hamiltonian evolution | We give a sufficient condition for the time evolution of a finite quantum system to be a Hamiltonian one. We use the semigroup formalism recently developed by Kossakowski, Gorini, Sudarshan et al. | The main objective of this article is to study dynamic of the ::: three-dimensional Boussinesq equations with the periodic boundary ::: condition.We prove that when the Rayleigh number $R$ crosses the ::: first critical Rayleigh number $R_c$, the Rayleigh-Benard problem ::: bifurcates from the basic state to an global attractor $\Sigma$, which is homeomorphic to $S^3$. | eng_Latn | 11,012 |
Dynamics of multifrequency oscillator communities | We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The simplest situation of three resonantly interacting groups is analyzed in detail. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations and present examples where the interaction between communities leads to their synchrony or to a partially asynchronous state or to a chaotic dynamics of order parameters. | An asymptotic solution of the frequency equation of an infinite, monoclinic crystal plate is derived. Formulas are given which describe the variation of frequency with wavelength at high frequencies and long wavelengths. | eng_Latn | 11,013 |
Kelvin-Helmholtz instability of AB interface in superfluid 3He | The Kelvin-Helmholtz instability is well-known in classical hydrodynamics, where it explains the sudden emergence of interfacial surface waves as a function of the velocity of flow parallel to the interface. It can be carried over to the inviscid two-fluid dynamics of superfluids, to study different types of interfaces and phase boundaries in quantum fluids. We report measurements on the stability of the phase boundary separating the two bulk phases of superfluid 3He in rotating flow, while the boundary is localized with the gradient of the magnetic field to a position perpendicular to the rotation axis. The results demonstrate that the classic stability condition, when modified for the superfluid environment, is obeyed down to 0.4 Tc, if a large fraction of the magnetic polarization of the B-phase is attributed to a parabolic reduction of the interfacial surface tension with increasing magnetic field. | A computational modification of the Heidemann-Khalil method for calculating the critical temperatures and pressures for general phase-equilibrium problems greatly reduced the computing time for simple two-constant cubic equations of state. For systems where the unlike binary interaction parameters can be derived from the pure-component parameters using the geometric mean values, a further simplification lowers the computing times to a few milliseconds, regardless of the number of components. | eng_Latn | 11,014 |
Several recent results in nonlinear geometric optics | Many recent works are devoted to the study of high frequency oscillatory nonlinear waves, and to nonlinear geometric optics. Typical questions are the existence, the propagation, the interaction and the reflection of waves of the form ::: ::: $$ {u^\varepsilon }\left( {t,x} \right) \sim \underline u \left( {t,x} \right) + {\varepsilon ^\alpha }\sum\limits_{n0} {{\varepsilon ^n}} {U_n}\left( {t,x,\varphi \left( {t,x} \right)/\varepsilon } \right). $$ ::: ::: (1.1) | 4 pages.-- PACS numbers: 05.45.Xt, 87.10.+e.-- ArXiv pre-print: http://arxiv.org/abs/nlin.CD/0512009.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.73.055202. | eng_Latn | 11,015 |
LDA-Investigations of the Separated Flow over Slender Wings | The flowfield over inclined slender delta wings has been investigated using a 3D-Laser-Doppler Anemometer. Preliminary tests led to the result that a sufficient distribution of scattering particles in the whole vortex flowfield can be achieved by a proper combination of particle diameter and free stream Reynoldsnumber. The available 3D-LDA system with three counters leads to reliable results for all three components of the mean velocity but for two components of the velocity fluctuations only. It is demonstrated that the reliability of the third component of the velocity fluctuations can also be achieved by the application of burst spectrum analyzers (BSA) as signal processors. | We show how to extend the formalism of infinitesimal differential diffusion quantum Monte Carlo to the case of higher derivatives of the ground‐state energy of a molecule with respect to the molecular geometry. We use LiH as an example, but the technique can be extended to more complicated, nonliner molecules as well. We obtain good agreement with experimental values for the energy derivatives and for the harmonic and anharmonic frequencies of LiH and LiD, despite using a compact single‐determinant wave function. | eng_Latn | 11,016 |
Hot tube semiconductor thermal electric refrigerator | The utility model provides a hot tube semiconductor thermal electric refrigerator with a hot tube as the main heat transferring component, and is mainly characterized in that the utility model is assembled by a plurality of hot tubes whose one end is equipped with a fin tail and metal blocks with excellent heat-conducting property to become one or two general heat transferring components. The cold and hot ends of the semiconductor refrigeration plate are respectively combined with two heat transferring components according to different application requests. The utility model provides a hot tube semiconductor thermoelectric refrigerating air-conditioning box and a hot tube semiconductor thermoelectric refrigerating fresh keeping box, and has the advantages of simple structure, strong universal property, convenient operation and maintenance, short settle time and high refrigerating efficiency. | Preface Bose-Einstein Condensation in Nonlinear System New Aspects of Relaxation Processes in Cryogenic Solids Induction Transformer Coupled Discharges: Investigation & Application P-Type InGaAs/AlGaAs Quantum Well Structures for Infrared Photodetection A D-3He Spherical Tokamak Reactor with the Plasma Current Ramp-Up by Vertical Field 5-Dimension Space-Time Field Theory & Realization of Matter Chemical Physics of Phonons & Superconductivity: A Heuristic Approach Description of the Ultraslow Light Phenomenon in Atomic Bose Condensates in the Framework of the Microscopic Approach Energy Decay Mechanism of Quantum Grid Turbulence in He II Below 1 K Dark Matter Haloes as Fruits of Merger Trees in a CDM Garden Application of GEANT4 Code in Gamma Irradiation Processing Stochastic Dynamic Systems with Long-Range Correlations: Basic Notions & Applications Index. | eng_Latn | 11,017 |
An Expected Utility-Based Optimization of Slow Steaming in Sulphur Emission Control Areas by Applying Big Data Analytics | This paper analyses the operator’s risk-based decision (RBD) company for slow steaming, and creates a sailing speed optimization model for slow steaming (SSOM-SS), aiming to balance the expected utility-based objectives (EUO) of fuel consumption, SOx emissions and delivery delay. Considering the limitations of existing theoretical fuel consumption functions under uncertainties in voyages, the authors applies big data analytics (BDA) techniques like data fusion and feature selection to provide the SSOM-SS with accurate and suitable data on fuel consumption. In addition, a solver is built based on the genetic algorithm (GA) to solve the SSOM-SS. The effectiveness of the SSOM-SS is verified through a case study on the RBD for slow steaming of an Orient Overseas Container Line (OOCL) containership sailing across the sulphur emission control areas (SECAs) in Chinese coastal regions. The results show that the SSOM-SS can facilitate the RBD for slow steaming, and provide a novel tool for sailing speed optimization. | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | eng_Latn | 11,018 |
On the stochastic nonlinear neutron transport equation | The probability that a neutron leads to a divergent chain reaction in a nuclear reactor is governed by a nonlinear integro-partial-differential equation [ 1 ]. A model case of this equation was completely analysed by Pazy and Rabinowitz [ 2,3 ]. The purpose of this paper is to extend their results to the general case and to tackle some related topics. | O. Introduction This lecture will unfortunately not be a systematic review of the subject of rigorous results in non-equilibrium statistical mechanics. A preliminary attempt to outline such a review led me quickly to the conclusion that the field is too diverse to be summarized in a single lecture. I have therefore decided instead to discuss a few related.works in depth. The works I have chosen are: 1. The paper of J. Fritz and R. L. Dobrushin[5] on two-dimensional dynamics. 2. The paper of W. Braun and K. Hepp[3] on classical mechanics in the Vlasov limit. 3. A recent preprint by H. van Beijeren, J. L. Lebowitz, H. Spohn, and myself[2] on autocorrelations and fluctuations in the dilute equilibrium hard-sphere gas. | eng_Latn | 11,019 |
Reply to ''Comments on alternate formulations for preequilibrium decay'' | Blann's criticisms of the exciton model formulation are found to originate mainly in misunderstandings. An attempt is made to support the contention that the exciton model uses a correct quantum statistical approach to the problem of preequilibrium decay. | We present and analyze different splitting algorithms for numerical ::: solution of the both classical and generalized nonlinear Schrodinger ::: equations describing propagation of wave packets with ::: special emphasis on applications to nonlinear fiber-optics. ::: The considered generalizations take into account ::: the higher-order corrections of the linear differential ::: dispersion operator as well as ::: the saturation of nonlinearity ::: and the self-steepening of the field envelope function. ::: For stabilization of the pseudo-spectral splitting schemes for generalized ::: Schrodinger equations a regularization ::: based on the approximation of the derivatives by the low number of ::: Fourier modes is proposed. ::: To illustrate the theoretically predicted performance of these schemes several numerical ::: experiments have been done. In particular, we compute real-world examples of extreme ::: pulses propagating in silica fibers. | eng_Latn | 11,020 |
Loads induced by terminal-shock boundary-layer interaction on cone-cylinder bodies | An analysis is described that can define the loads induced by shock-induced separation at high subsonic speeds. The supersonic flow region aft of the cone-cylinder shoulder is terminated by a normal shock that causes the boundary layer to separate. At increasing angle-ofattack the leeward side boundary layer is thickened due to crossflow effects and is more easily separated, resulting in a forward movement of the shock. On the windward side, opposite effects occur, and a negative forebody load is generated. When the angle-of-attack exceeds a critical value, the leeward side boundary layer can nowhere support the shock due to the steepening adverse pressure gradient near the shoulder. As a consequence, complete flow separation occurs on the leeward side with an associated large discontinuous change of the forebody load. | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | eng_Latn | 11,021 |
Designing Langevin microdynamics in macrocosm | Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von Neumann) equation for its statistical operator. Can one reformulate the theory in terms of stochastic ``Langevin equations'' for its variables? Here it is shown that in case of classical Hamiltonian underlying dynamics the answer is principally positive, and general explicit method of constructing such equations is described. | Using the divergence term appearing in the Lagrangian of the teleparallel equivalent of general relativity (TEGR), we calculate the thermodynamic quantities of four tetrads’ spacetime reproducing Lense–Thirring (LT) metric. We also investigate the first law of thermodynamics and the quantum statistical relation. | eng_Latn | 11,022 |
Quantum theory of phase correlations in optical frequency combs generated by stimulated Raman scattering | We explore theoretically the phase correlation between multiple generated sidebands in a Raman optical frequency comb under conditions of spontaneous initiation from quantum zero-point noise. We show that there is a near-deterministic correlation between sideband phases in each laser shot which may lead to synthesis of attosecond pulse trains. | Abstract The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the latter is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite pol... | eng_Latn | 11,023 |
VORTEX FORMATION IN DILUTE INHOMOGENEOUS BOSE-EINSTEIN CONDENSATES | A valve regulates the pressure of secondary air discharged from a pump to a constant value. A second valve then meters the flow in accordance with the amount of air taken into the engine. | This paper is concerned with the Free boundary problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. A local (in time) existence result is established when the initial density is of compact support and connects to the vacuum continuously. (C) 2002 Elsevier Science (USA). | yue_Hant | 11,024 |
On Nonlocal Normal Forms of Linear Second Order Mixed Type PDEs on the Plane | Here we propose the nonlocal normal form of main symbol of linear second order mixed type PDEs on the plane for Cibrario-Tricomi case with periodic coefficients. In particular that provides the normal form for equation, which describes an infinitesimal bending of typical rotation surface or sufficiently close to the one near its parabolic line. | Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von Neumann) equation for its statistical operator. Can one reformulate the theory in terms of stochastic ``Langevin equations'' for its variables? Here it is shown that in case of classical Hamiltonian underlying dynamics the answer is principally positive, and general explicit method of constructing such equations is described. | eng_Latn | 11,025 |
Stability of standing waves for a nonlinear Schrödinger equation under an external magnetic field | In this paper we study the existence and orbital stability of ground states for logarithmic Schrodinger equation under a constant magnetic field. For this purpose we establish the well-posedness of the Cauchy Problem in a magnetic Sobolev space and an appropriate Orlicz space. Then we show the existence of ground state solutions via a constrained minimization on the Nehari manifold. We also show that the ground state is orbitally stable. | The matrix formalism previously introduced for the discussion of polymer dynamics is rendered more tractable by the introduction of an explicit operator representation satisfying boson commutation rules. Techniques are devised by which singular functions of segment coordinates may be expanded in a fluctuation series (containing ordered products of boson operators) around an equilibrium or nonequilibrium average. The techniques are here applied to equilibrium excluded‐volume expansions, and are shown to give good results. The detailed numerical results are presented in the following paper. The Gaussian potential is adopted for polymer chains in a theta solvent, but methods for its improvement are considered. | eng_Latn | 11,026 |
Combinations of Independent Normal Random Variables | Summary ::: ::: There are several well known approaches to proving that a linear combination of a pair of independent random variables is itself normal. Here the author offers a simple proof, based on analytical geometry, which can be used early in a statistics course. | The Moyal *-deformed noncommutative version of Burgers' equation is considered. Using the *-analog of the Cole-Hopf transformation, the linearization of the model in terms of the linear heat equation is found. Noncommutative q-deformations of shock soliton solutions and their interaction are described | eng_Latn | 11,027 |
The air disc brake in commercial vehicles - field experiences | The air disc brake is established as standard equipment for heavy commercial vehicles in Europe. The utilisation spectrum, applications, design, function, field monitoring, and further technical developments are described. For the covering abstract see ITRD E136300 | We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the sub-diffusive continuous time random walk model. When the fluctuations become normal we recover usual ergodic statistical mechanics. Examples of a particle undergoing fractional dynamics in a binding force field are worked out in detail. We briefly discuss possible physical applications in single particle experiments. | eng_Latn | 11,028 |
Effect of a novel nonlinearity, viz., electron temperature dependence of electron-ion recombination on electromagnetic wave. Plasma interaction: Nonlinear propagation in the E-layer | In this paper, we consider the nonlinearity in the propagation of electromagnetic (e.m.) waves in a plasma caused by the electron temperature dependence of the coefficient of recombination of electrons with ions; specifically, the ionospheric E layer has been investigated. The enhancement in electron temperature by an intense electromagnetic wave causes reduction of the electron-ion recombination coefficient and thereby enhancement of electron density, the electron collision frequency also gets enhanced. The equations for number and energy balance of electrons and the wave equation have been used to predict the dependence of electron density/collision frequency and the nonlinear refractive index and absorption coefficient on αE02 (proportional to wave irradiance). The dependence of the propagation parameters on αE02 has been used to investigate the nonlinear electromagnetic wave propagation in the ionosphere. The study concludes that the electron temperature dependence of the recombination coefficient sho... | We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement. | eng_Latn | 11,029 |
Quantum Monte Carlo study of a 1D phase-fluctuating condensate | We study numerically the low temperature behaviour of a 1D Bose gas trapped in an optical lattice. For a sufficient number of particles and weak repulsive interactions, we find a clear regime of temperatures where density fluctuations are negligible but phase fluctuations are considerable, i.e., a quasicondensate. In the weakly interacting limit, our results are in very good agreement with those obtained using a mean-field approximation. In coupling regimes beyond the validity of mean-field approaches, a phase-fluctuating condensate also appears, but the phase-correlation properties are qualitatively different. It is shown that quantum depletion plays an important role. | ABSTRACTThis paper aims to develop, assess, and numerically implement analytical models for the newly introduced Quintuple Friction Pendulum Isolator (QFPI) which can identically capture its real e... | eng_Latn | 11,030 |
Low lying spectrum of weak-disorder quantum waveguides | We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain a so-called ‘initial length scale decay estimate’ as they are employed in the proof of spectral localization using the multiscale analysis method. | Abstract A self-consistent quasilinear model of the interaction between VLF emissions and geomagnetic pulsation is set forth. As a result an explicit expression of a modulation frequency dependence can be obtained. | eng_Latn | 11,031 |
Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space | We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted ::: tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a ::: robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl ::: fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in ::: condensed matter physics due to their unusual properties such as the topologically protected “Fermi arc” ::: surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is ::: well within experimental reach with an extension of techniques recently used in ultracold gases. | We deal with linear parabolic (in the sense ::: of Petrovskii) systems of order $2b$ with discontinuous principal ::: coefficients. A priori estimates in Sobolev and ::: Sobolev--Morrey spaces are proved for the strong solutions by ::: means of potential analysis and boundedness of certain singular ::: integral operators with kernels of mixed homogeneity. As a ::: byproduct, precise characterization of the Morrey, $BMO$ and ::: Holder regularity is given for the solutions and their ::: derivatives up to order $2b-1.$ | eng_Latn | 11,032 |
Resonant and weakly-bound one-particle levels in quadrupole-deformed potentials | Both positive-energy and weakly-bound one-particle levels for neutrons in Y20 deformed Woods-Saxon potentials are examined in comparison with those in spherical Woods-Saxon potentials. While s1/2 levels play a unique role in spherical drip-line nuclei, the Ωπ = 1/2+ levels in Y20 deformed potentials, which always contain some amount of s1/2 component, exhibit an important role in deformed drip-line nuclei. As the potential strength becomes weaker, some weakly-bound Ωπ = 1/2+ levels continue to the positive-energy region as one-particle resonant levels, while others have no such continuation. Among an infinite number of one-particle levels at a given positive-energy and in a given deformed potential, only some selected levels expressed in terms of eigenphase are found to be important in the pair-correlated ground state of neutron-drip-line nuclei. | The main objective of this article is to study dynamic of the ::: three-dimensional Boussinesq equations with the periodic boundary ::: condition.We prove that when the Rayleigh number $R$ crosses the ::: first critical Rayleigh number $R_c$, the Rayleigh-Benard problem ::: bifurcates from the basic state to an global attractor $\Sigma$, which is homeomorphic to $S^3$. | eng_Latn | 11,033 |
Frequency pressure regulation in water supply systems | In water supply systems, pressure management in most cases is proven to be the most cost-effective activity related to water loss control. As an advanced method of pressure control, it is possible to use variable frequency drives for centrifugal pump control. Pressure regulation can be performed with constant pressure or with proportional pressure control. The application of proportional pressure control is particularly applicable in water supply systems as the operating pump performance is constantly adapting the pressure to the actual demand. Along with lower leakage losses, it also results in lower energy consumption and the elimination of non-stationary phenomena, thereby extending the pump lifetime. Therefore, the paper presents a theoretical discussion of the proportional pressure control. Possible savings are shown on the numerical example of water supply system of the city of Velika Gorica. | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | eng_Latn | 11,034 |
Soliton solution of nonlinear schrodinger equation with application to bosezeinstein condensation using the FD method | In this paper, we discussed the behavior of bright soliton solutions to the NLS equation and their interactions then investigated dark solitons and their formation within an attractive potential and applied them to Bose-Einstein condensation using fast and efficient finite difference scheme. | A spectroscopic method to determine in-cylinder flame temperature and soot concentration was combined with in-cylinder NOx-modelling to study the influence of operating conditions and combustion system parameters on the formation of soot and NOx in a low-emission single- cylinder direct-injection diesel engine. Fuel consumption and emissions are compared with time-resolved combustion analysis data. (A) For the covering abstract see IRRD 869246. | eng_Latn | 11,035 |
Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations. | We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn–Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on a... | The differential equations of the continuous time LQ control problem are discretized, then the mixed-energy condensation algorithm is established for the continuous time and linear equality constraint LQ control problem, the above algorithm can be used to solve Riccati equation with the linear constraint effectively. An example is given. | eng_Latn | 11,036 |
A generalised Green-Julg theorem for proper groupoids and Banach algebras | The Green-Julg theorem states that K_0^G(B) is isomorphic to K_0(L^1(G,B)) for every compact group G and every G-C*-algebra B. We formulate a generalisation of this result to proper groupoids and Banach algebras and deduce that the Bost assembly map is surjective for proper Banach algebras. On the way, we show that the spectral radius of an element in a C_0(X)-Banach algebra can be calculated from the spectral radius in the fibres. | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | eng_Latn | 11,037 |
The Fractional Schrodinger-Klein-Gordon Equation and Intermediate Relativism | By considering a random walk model compounded in Einstein’s evolution equation, we show that both the classical Schr¨odinger and Klein-Gordon equations can be viewed as a consequence of introducing a memory function given by −iδ and δ (1), respectively. For a memory function of the type −i 1+αδ (α) where 0 < α < 1 we derive a fractional Schr¨odinger-Klein-Gordon equation whose corresponding propagator (free space Green’s function) is then evaluated. The purpose of this is to derive a wave equation that, on a phenomenological basis at least, describes the transitional characteristics of wave functions for spin-less particles that may exist in the intermediate or ‘semirelativistic’ regime. On the basis of the phenomenology considered, it is shown that such wave functions are self-affine functions of time t with a probability density that scales as 1/t1−α for mass-less particles. | We discuss a paradox which appears in EPR experiments when the collapse of the wave function is analyzed in moving reference frames: the collapse can occur before the actual measurement of the spin component (or polarization) of one of the particles. We show that the paradox can be solved using the instantaneity of the reduction process in all reference frames. Using the same concept, we illustrate with an example the impossibility of defining, in certain circumstances, a covariant state vector in all regions of space-time. | eng_Latn | 11,038 |
Hereditary differential systems with constant delays. I. General case | Abstract : The paper presents a discussion of the structure of hereditary differential systems defined on a Banach space with initial data in the space of p-integrable maps. Both finite and infinite time histories are allowed. A unified approach to Global and Local Cauchy problems on finite or infinite time intervals is presented. An existence theorem for Caratheodory systems and an existence and uniqueness theorem for Lipschitz systems are derived. In both cases continuity of a solution with respect to the initial data is established. (Author) | Preface Bose-Einstein Condensation in Nonlinear System New Aspects of Relaxation Processes in Cryogenic Solids Induction Transformer Coupled Discharges: Investigation & Application P-Type InGaAs/AlGaAs Quantum Well Structures for Infrared Photodetection A D-3He Spherical Tokamak Reactor with the Plasma Current Ramp-Up by Vertical Field 5-Dimension Space-Time Field Theory & Realization of Matter Chemical Physics of Phonons & Superconductivity: A Heuristic Approach Description of the Ultraslow Light Phenomenon in Atomic Bose Condensates in the Framework of the Microscopic Approach Energy Decay Mechanism of Quantum Grid Turbulence in He II Below 1 K Dark Matter Haloes as Fruits of Merger Trees in a CDM Garden Application of GEANT4 Code in Gamma Irradiation Processing Stochastic Dynamic Systems with Long-Range Correlations: Basic Notions & Applications Index. | eng_Latn | 11,039 |
Theory and method for accelerating the convergence of self-consistent electronic structure calculations☆ | Abstract In this paper, we present a method which accelerates the iterative process of self-consistent calculations of the electronic structure of atoms, molecules, and crystals. The theory is based on the behavior of potential parameters during the iterative process. A criterion of convergence is established. The convergence of the iterative process is fastest when, at the beginning of each iteration, the potential is a linear combination of the potentials of previous iterations. As many previous iterations should be combined as there are parameters describing the potential; the theory and method are applied in the test case of the molecules N 2 and CO with very good results. | Abstract This paper is a concluding review exposition of the investigations aimed at the construction of a general cosmological solution of the Einstein equations with a singularity in time; thus it is a direct continuation of the previous (1970) paper by the authors in this Journal. A detailed description is given of the analysis which leads to the construction of such a solution, and of its properties. | eng_Latn | 11,040 |
Approximate any l-state solutions of the Dirac equation for modified deformed Hylleraas potential by using the Nikiforov?Uvarov method | We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov—Uvarov technique. A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail. The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included. | A new computer simulation method based on stochastic integration of the Langevin equations of dislocation motion is proposed for the investigation of the dynamic properties of a system of parallel straight dislocations. The stochastic approach developed for weakly correlated dislocation systems allows for more than dislocations in the simulation area. Relaxation of a system of parallel edge dislocations is presented. | eng_Latn | 11,041 |
Bootstrap in nonstationary autoregression | The first-order autoregression model with heteroskedastic innovations is considered and it is shown that the classical bootstrap procedure based on estimated residuals fails for the least-squares estimator of the autoregression coefficient. A different procedure called wild bootstrap, respectively its modification is considered and its consistency in the strong sense is established under very mild moment conditions. | The Moyal *-deformed noncommutative version of Burgers' equation is considered. Using the *-analog of the Cole-Hopf transformation, the linearization of the model in terms of the linear heat equation is found. Noncommutative q-deformations of shock soliton solutions and their interaction are described | deu_Latn | 11,042 |
Scalar wave theory : Green's functions and applications | This monograph is an introduction to the mathematical techniques used to describe the scattering and propagation of scalar waves, in particular sound waves. The scalar wave equations and Green's functions are developed from fundamental principles and applied to the following main problems: plane wave and spherical wave scattering from flat interfaces, and propagation in a two-layer liquid half-space (Pekeris waveguide). The detailed discussion facilitates extension of the techniques to real situations. | Let 0 o , has the same behavior as the sequence sup |£Q|'/I 0. In other words, if we know all "far points" of supp Ff, we can wholly describe this behavior without any concrete calculation of ||Z)a/||p , a > 0 . A Paley-Wiener-Schwartz theorem for a nonconvex case, which is a consequence of the result, is given. | eng_Latn | 11,043 |
Integral-antenna-type electronic clock | To improve space-use efficiency and reduce noise entering an antenna body, an electronic clock (100) is provided with: a cylindrical outer case (80); a cover glass (84) for blocking one of the two openings in the outer case (80); a ring-shaped antenna body (40) provided along the inner circumference of the outer case (80); a circuit substrate (25) having a shield pattern (G) formed thereon, and positioned beneath the antenna body (40) when viewed from the cover glass (84); and a GPS receiving unit (26) for amplifying and processing a signal received by the antenna body (40), and positioned on a circuit-substrate (25) surface that is opposite the antenna body (40) with the shield pattern (G) interposed as a boundary therebetween. | We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the sub-diffusive continuous time random walk model. When the fluctuations become normal we recover usual ergodic statistical mechanics. Examples of a particle undergoing fractional dynamics in a binding force field are worked out in detail. We briefly discuss possible physical applications in single particle experiments. | eng_Latn | 11,044 |
A Generalised Wick Transform for Gravity | Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue within ``connection-dynamics'' where one can work, throughout, only with real variables. The resulting quantum theory would then be free of complicated reality conditions. Ramifications of this development to the canonical quantization program are discussed. | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | eng_Latn | 11,045 |
Stable isotopes of the water vapour in the Atmospheric boundary layer from five Atlantic Ocean cruises in 2012-2015 | The marine boundary layer atmospheric water vapour isotopic composition (oxygen 18 and deuterium) has been measured above the Atlantic Ocean from 5 research vessels between 2012 and 2015. Using laser spectroscopy analysers, measurements have been carried out semi-continuously on samples collected 10-20 meter above sea level. | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | eng_Latn | 11,046 |
Spectral Energy Density in a Kerr Nonlinear Blackbody | In a Kerr nonlinear blackbody, bare photons with opposite wave vectors and helicities are bound into pairs and unpaired photons are transformed into a new kind of quasiparticle, the nonpolariton. The nonpolariton system constitutes free thermal radiation in the blackbody. The present paper investigates the spectral energy density of the thermal radiation. It is found that the spectral energy density of a Kerr nonlinear blackbody is larger than that of a normal blackbody. | In this paper, by using the atomic decomposition of the weighted weakHardy space WH1w （Rn）, the authors discuss a class of multilinear oscillatory singularintegrals and obtain their boundedness from the weighted weak Hardy spaceWH1w （Rn） to the weighted weak Lebesgue spaceWL1w（Rn） for w∈ A1（Rn）. | eng_Latn | 11,047 |
Mathematical Analysis of a Bohr Atom Model | Bohr proposed in 1913 a model for atoms and molecules by synthesizing Planck’s quantum hypothesis with classical mechanics. When the atom number Z is small, his model provides good accuracy for the ground-state energy. When Z is large, his model is not as accurate in comparison with the experimental data but still provides a good trend agreeing with the experimental values of the ground-state energy of atoms. The main objective of this paper is to provide a rigorous mathematical analysis for the Bohr atom model. We have established the following: (1) An existence proof of the global minimizer of the ground-state energy through scaling. (2) A careful study of the critical points of the energy function. Such critical points include both the stable steady-state electron configurations as well as unstable saddle-type configurations. (3) Coplanarity of certain electron configurations. Numerical examples and graphics are also illustrated. | Simple form of Boltzmann equation will be proposed after introducing a three-dimensional closed Lie group to simplify its collision term. | kor_Hang | 11,048 |
Time‐evolved numerical simulation of a two‐dimensional electron wave packet through a quantum double slit | We performed time‐evolved numerical simulation of a two‐dimensional electron wave packet through a double slit by solving the time‐dependent Schrodinger equation using the finite difference method to simulate the electron interference phenomenon of a single electron. The propagating directions of interference peaks show that the starting point of electron interference is the center between the two slit exits. The number of interference peaks and their angles are found to be independent of potential barrier thickness. These results are compared with the results of our previous calculation of electron diffraction through a single slit. | Abstract We discuss random matrix-model representations of D = 1 string theory, with particular emphasis on the case in which the target space is a circle of finite radius. The duality properties of discretized strings are analyzed and shown to depend on the dynamics of vortices. In the representation in terms of a continuous circle of matrices we find an exact expression for the free energy, neglecting non-singlet states, as a function of the string coupling and the radius which exhibits exact duality. In a second version, based on a discrete chain of matrices, we find that vortices induce, for a finite radius, a Kosterlitz-Thouless phase transition that takes us to a c = 0 theory. | eng_Latn | 11,049 |
Purge needs in absorption chillers | Absorption chillers are regaining a significant share of large tonnage chiller sales, such as they had 20 years ago. Gas-fired chillers are now available that have a base energy (ultimate fuel usage) consumption rate per ton comparable to that in electric units. Effective purging in an absorption chiller is an absolute necessity to achieve the low chilled water temperature needed for dehumidification and to fully benefit from the energy savings offered by double-effect cycles. Although the purge system is usually not shown on the typical cycle schematic, its proper functioning is a key requirement for satisfactory machine operation. This article discusses the effect of noncondensible (N/C) gases on the absorption cooling process and the basics of purge systems. In addition, the article discusses the rationale for the important design step of selecting the location of the N/C probe, and discusses purge systems applicable to the direct-fired, double-effect machines now entering the marketplace. | Preface Bose-Einstein Condensation in Nonlinear System New Aspects of Relaxation Processes in Cryogenic Solids Induction Transformer Coupled Discharges: Investigation & Application P-Type InGaAs/AlGaAs Quantum Well Structures for Infrared Photodetection A D-3He Spherical Tokamak Reactor with the Plasma Current Ramp-Up by Vertical Field 5-Dimension Space-Time Field Theory & Realization of Matter Chemical Physics of Phonons & Superconductivity: A Heuristic Approach Description of the Ultraslow Light Phenomenon in Atomic Bose Condensates in the Framework of the Microscopic Approach Energy Decay Mechanism of Quantum Grid Turbulence in He II Below 1 K Dark Matter Haloes as Fruits of Merger Trees in a CDM Garden Application of GEANT4 Code in Gamma Irradiation Processing Stochastic Dynamic Systems with Long-Range Correlations: Basic Notions & Applications Index. | eng_Latn | 11,050 |
Different thermodynamic pathways to the solvation free energy of a spherical cavity in a hard sphere fluid | This paper determines the excess free energy associated with the formation of a spherical cavity in a hard sphere fluid. The solvation free energy can be calculated by integration of the structural changes induced by inserting the cavity using a number of different exact thermodynamic pathways. We consider three such pathways, including a new density route derived here. Structural information about the nonuniform hard sphere fluid in the presence of a general external field is given by the recently developed hydrostatic linear response (HLR) integral equation. Use of the HLR results in the different pathways gives a generally accurate determination of the solvation free energy for cavities over a wide range of sizes, from zero to infinity. Results for a related method, the Gaussian field model, are also discussed. | In this paper the physical meaning of a nonlinear partial differential equation (nPDE) of the fourth order relating to wave theory is deduced to the first time. The equation under consideration belongs to a class of less studied nPDEs and an explicit physical meaning is not known until now. This paper however bridges the gap between some known results and a concrete application concerning wave theory. We show how one can derive locally supercritical solitary waves as well as locally and nonlocally forced supercritical waves and analytical solutions are given explicitly. ::: ::: Keywords: Nonlinear partial differential equations, evolution equations, supercritical solitary waves, locally supercritical waves, non-locally supercritical waves. | eng_Latn | 11,051 |
Spectroscopy and lasing performance of a new solid state laser crystal--Nd:GdLiF4 | Laser action of Nd3+ doped GdLiF4 (GLF) has been demonstrated for the first time for both pulsed and CW laser pumped operation. A slope efficiency of 60% was obtained in either manner of operation. Detailed comparison studies show that the spectroscopic properties and laser performance of Nd:GLF are very similar to those of Nd:YLF. GLF, on the other hand, can be doped with much higher Nd3+ concentration.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. | We present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we demonstrate that the SDW order parameter obeys a generalized Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method, our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables dynamical SDW simulations with $N \simeq 10^5$ lattice sites. Our real-space formulation can be used to compute dynamical responses, such as dynamical structure factor, of complex and even inhomogeneous SDW configurations at zero or finite temperatures. Applying the QLLD to study the relaxation of a noncoplanar topological SDW under the excitation of a short pulse, we further demonstrate the crucial role of spatial correlations and fluctuations in the SDW dynamics. | eng_Latn | 11,052 |
Measurement of charged particles and cavitation bubble expansion velocities in laser induced breakdown in water | The measurement of charged particles and cavitation bubble expansion velocity is reported in a laser induced breakdown in water using beam deflection set-up. Effect of laser power on charged particles, cavitation bubble velocities and higher order bubble oscillations is also studied. | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | eng_Latn | 11,053 |
Quantum gases: Atomic superfluids see the light | A method for measuring the excitation spectrum in atomic gases confined to optical lattices reveals the band structure of these systems, and should facilitate the comparison of quantum gas phases with their condensed-matter counterparts. | In a previous paper, we adapted Nitsche's method for the approximation of the linear elastodynamic unilateral contact problem. The space semi-discrete problem was analyzed and some schemes (theta-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed under appropriate CFL conditons. In the present paper we look at the stability properties of the above-mentioned schemes and we achieve the corresponding numerical experiments. In particular we prove and illustrate numerically some interesting stability and (almost) energy conservation properties of Nitsche's semi-discretization combined to the new hybrid scheme. | eng_Latn | 11,054 |
Optical nonuniformities of nonequilibrium turbulent gas flow in fast-axial-flow CO2 laser | The luminescence method and the method of dual-beam shear interferometry were used to perform the measurements of spatial and time characteristics of molecular gas subsonic turbulent flow fluctuations under strong vibrational non- equilibrium. Gas-discharge tubes of fast-axial-flow CO2 laser served as the investigation object. A turbulent component of gas density fluctuations has been separated by method of frequency selection of the registered signal. The spectrum of density pulsation has been determined, as well as the amplitude dependence of small-scale inhomogeneities on energy input has been specified. A degree of cross correlation of fluctuations of wave-front phase incursion in the turbulent flow has been evaluated under non-equilibrium conditions of electric discharge.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. | Abstract In this paper, we delve into the dynamics of a barothropic relaxing medium under pressure perturbations originating from blast wave explosions in the milieu. Analyzing the problem within the viewpoint of the Lyakhov formalism of geodynamic systems, we derive a complex-valued nonlinear evolution equation which models the wave propagation of the pressure perturbations within the barothropic medium. As a result, we find that the previous system can be circularly polarized and hence support traveling rotating pressure excitations which profiles strongly depend upon their angular momenta. In the wake of these results, we address some physical implications of the findings alongside their potential applications. | eng_Latn | 11,055 |
Enigmatic E-Cat of Andrea Rossi and the Unitary Quantum Theory | In this article we are discussing the nature and mechanism of the huge ::: amount of heat generation in Megawatts Energy Catalyzers (E-cat) of Andrea ::: Rossi that are able to change the energetics of our civilization in general. ::: These processes are new effects of Unitary Quantum Theory and do not relate to ::: either chemical or nuclear reactions or phase transfer. | Abstract In this note, we obtain some results for the Riccati differential equations u′=A(z)+u2 with nonentire meromorphic functions A(z). Some examples are given to illustrate our some results are sharp. | eng_Latn | 11,056 |
Spectral Properties of Non-Unitary Band Matrices | We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure results about the location and nature of the spectrum of such non-normal operators as a function of their parameters. We relate these results to the analysis of certain random quantum walks, the dynamics of which can be studied by means of iterates of such random non-unitary contraction operators. | We generalize the algebraic multiplicity of the eigenvalues of nonlinear eigenvalue problems (NEPs) to the rational form and give the extension of the argument principle. In addition, we propose a novel numerical method to determine the algebraic multiplicity of the eigenvalues of the NEPs in a given region by the contour integral method. Finally, some numerical experiments are reported to illustrate the effectiveness of our method. | eng_Latn | 11,057 |
Some Aspects of Lagrangian Dynamics of Turbulence | This chapter is dedicated to fundamental properties of Lagrangian transport in turbulence, emphasizing the role of anisotropy and 2D turbulence which are relevant for geophysical considerations. The focus is on three main aspects of Lagrangian turbulence: (i) the role of small-scale anisotropy on the Lagrangian energy spectrum, (ii) the role of Lagrangian intermittency and (iii) the relative dispersion of tracer particles. | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | eng_Latn | 11,058 |
SHORT COMMUNICATION On Flame Propagation Through Periodic Flow Fields | Abstract Flame propagation through a periodic system or time independent eddies is studied. It is shown that at sufficiently low amplitudes of the velocity spatial variation, the effective speed of a passive flame has a global dependence on the underlying flow. However, at high amplitudes, the effective flame speed is determined by the local features of the flow. Simultaneously, the shape of the flame undergoes a transition from a smooth configuration to a cusped one. | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | kor_Hang | 11,059 |
Quantization of static domains in slim superlattices | We have calculated dc I - V curves of the semiconductor superlattices of a very small (practically, submicron) cross-section. The I - V curves exhibit periodic oscillations with a voltage period e/C. These oscillations are caused by quantization of electric charge Q of the walls of static high-field domains.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. | We review a new formalism based on Orlicz spaces for the description of large regular statistical systems. Our presentation includes both classical and quantum systems. This approach has the advantage that statistical mechanics is much better settled. | eng_Latn | 11,060 |
An Investigation on Vortex Breakdown Phenomena in a Vertical Cylindrical Tube | ������� ��������� ��� � ����� �� � �������� ���� � ����� ���� ���� ���� ���� * ����� ���� ����� ** ���� ��� ����� ������� *** ������ ��� ���� ���� � ��� � ������� ������ ������ � � * ������� ������� ��� � � ** ������ ������ ������ � � *** ������ ������ ������ � ������ ������� – ��!�"�� � ������ ��� ������ . ������ ���� ��� � ������ ����� �� �� ��� ��� ������ �� ������ � ���!� �� ��� �� ������� ������ ���" ��� � ���"� ���!��� ������ ��� . #$%& ��%� ������� '��("� )�&�* +�!� ����� �� ������� . � �� ����"��� ) ( | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | eng_Latn | 11,061 |
The Ground State Properties of Polaron in Spherical Quantum Dot in Finite Potential Well | The ground state properties of polaron in spherical quantum dot in finite potential well are studied by using expand the potential function as plane waves, solve precisely energy eigen-equation, variation method and LLP unitary.The numerical results indicate that the ground state energy of polaron increase with increasing the width or height of the potential barrier and decrease with increasing the coupling strength or quantum dot 's radius. | A self-similar solution, for the equatorial propagation of axisymmetric point explosion into an inhomogeneous ideal gas permeated by a current-free azimuthal magnetic field, are obtained. The model has been considered here in which the magnetic field is proportional tor−1, but the total energy of the wave is of the increasing order, not constant. | eng_Latn | 11,062 |
Global attractor for the initial–boundary value problems for Ginzburg–Landau equations for atomic Fermi gases near the BCS–BEC crossover☆ | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | The local interaction between strings with intrinsic spin and an external scalar field is considered as an interaction through a virtual state of a closed string compressed to a point. The amplitude for the interaction of this state with an arbitrary number of open strings in their ground states is constructed. The asymptotic behavior 1/q/sup 2/ at large momentum transfers is obtained for the scalar form factor of the ground state. The properties of the 2..-->..2 elastic amplitude with emission of a single scalar closed string into the vacuum are studied and, in particular, a power-law decrease is obtained in the region of large-angle scattering. | eng_Latn | 11,063 |
Optimal decay of extremals for the fractional Sobolev inequality | We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding. | We present and analyze different splitting algorithms for numerical ::: solution of the both classical and generalized nonlinear Schrodinger ::: equations describing propagation of wave packets with ::: special emphasis on applications to nonlinear fiber-optics. ::: The considered generalizations take into account ::: the higher-order corrections of the linear differential ::: dispersion operator as well as ::: the saturation of nonlinearity ::: and the self-steepening of the field envelope function. ::: For stabilization of the pseudo-spectral splitting schemes for generalized ::: Schrodinger equations a regularization ::: based on the approximation of the derivatives by the low number of ::: Fourier modes is proposed. ::: To illustrate the theoretically predicted performance of these schemes several numerical ::: experiments have been done. In particular, we compute real-world examples of extreme ::: pulses propagating in silica fibers. | eng_Latn | 11,064 |
How chlorides affect FGD design | Chlorides enter scrubber systems from both fuel and makeup water. Chloride buildup in the recirculating liquor of an FGD system probably is the main contributor to corrosion failures in the piping, tanks, and system internals. The proper choice of alloys for these systems can preclude costly maintenance and repairs over the lifetime of the fossil-fuel generating plants. Options to limit chloride effects are discussed. | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | eng_Latn | 11,065 |
Computations of Turbulent Recirculating Flows with Fully Coupled Solution of Momentum and Continuity Equations | A fully coupled solution algorithm for pressure-linked fluid flow equations earlier found to be rapidly convergent in laminar flows has been extended to calculate turbulent flows. The governing mean flow equations are solved in conjunction with a two-equation (k - epsilon) turbulence model. A number of two-dimensional recirculating flows have been computed and it is shown that the calculation procedure is rapidly convergent in all the cases. The calculations have been compared with published experimental data; their agreement is in accord with other published experiences with the (k - epsilon) model in similar flows. | We investigated a Bose system confined in one-dimensional channel by using quantum Monte Carlo simulations. We observed temperature dependences of the superfluid density and two correlation functions along the tubal and the circumferential directions of the channel. As temperature is lowered, first the correlation develops along the circumference, and then it develops along the tubal and the Kosterlitz-Thouless (KT) phase appears at the temperature depending on the confining potential and the ratio of the circumferential length to the length of the channel. We found that the onset temperature of the superfluidity observed by a torsional oscillator measurement depends on the direction of the torsion in this system. | eng_Latn | 11,066 |
Waves in almost-periodic particle chains | Almost periodic particle chains exhibit peculiar propagation properties that are not observed in perfectly periodic ones. Furthermore, since they inherently support non-negligible long-range interactions and radiation through the surrounding free-space, nearest-neighbor approximations cannot be invoked. Hence the governing operator is fundamentally different than that used in traditional analysis of almost periodic structures, e.g. Harper's model and Almost-Mathieu difference equations. We present a mathematical framework for the analysis of almost periodic particle chains, and study their electrodynamic properties. We show that they support guided modes that exhibit a complex interaction mechanism with the light-cone. These modes possess a two-dimensional fractal-like structure in the frequency-wavenumber space, such that a modal phase-velocity cannot be uniquely defined. However, a well defined \emph{group velocity} is revealed due to the fractal's inner-structure. | Abstract A self-consistent quasilinear model of the interaction between VLF emissions and geomagnetic pulsation is set forth. As a result an explicit expression of a modulation frequency dependence can be obtained. | eng_Latn | 11,067 |
The Properties of weakly collapsing solutions to the nonlinear Schrödinger equation at Large values of the free parameters. | It is shown that there exists an infinite set of weakly collapsing solutions with zero energy. Zero energy solutions are distributed along two lines in the space of parameters (A, C1). At large values of C1 (C1→∞), the distance between the nearest points on every line tends to a finite limit. Along each of the lines, the amplitude of the oscillating terms is exponentially small with respect to the parameter C1. | Let 0 o , has the same behavior as the sequence sup |£Q|'/I 0. In other words, if we know all "far points" of supp Ff, we can wholly describe this behavior without any concrete calculation of ||Z)a/||p , a > 0 . A Paley-Wiener-Schwartz theorem for a nonconvex case, which is a consequence of the result, is given. | eng_Latn | 11,068 |
Maxwellian distribution versus Rayleigh distribution | The inverse problem of deducing the molecular velocity distribution from a given density function is solved analytically. The results corresponding to two physically interesting systems viz. Maxwellian and Rayleigh gases are compared. | 4 pages.-- PACS numbers: 05.45.Xt, 87.10.+e.-- ArXiv pre-print: http://arxiv.org/abs/nlin.CD/0512009.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.73.055202. | eng_Latn | 11,069 |
The effect of a super-normal phase transition on the collective mass parameter | We derive an expression for the temperature-dependent collective masses for the general collective motion. It is an application of the time dependent BCS approximation, which is usually used for the ground state, to finite temperature. The resulting masses show a very prominent structure, that is, it changes discontinuously across the critical temperature. | A method of solving the eikonal equation, in either flat or curved space–times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front singularities that are associated with their level surfaces (the characteristic surfaces or “big wave fronts”). | eng_Latn | 11,070 |
One Method to Fit Biexponential Curve by Using Fourier Transform | Many physical phenomena can be described by biexponential curve. To study the physical phenomena, there is a need to obtain their mathematical expressions. Generally, the expressions are acquired based on the fitting of experimental data, and the general method to fit exponential curve is nonlinear least squares (NLLS). In the NLLS method, it is crucial to choose good enough starting values for the parameters, otherwise, the fitting might fail to converge. In this paper, one new method is proposed to solve the problem, which utilizes the Fourier transform to transform the non-linear exponential fitting model into a linear one. It makes the estimation of the parameters independent of the initial values and easy to converge. The fitting result shows that the proposed method can be used to fit the curve expressed by difference of double exponentials. | We perform a Variational Quantum Monte Carlo simulation of an interacting ::: Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based in the results of two-body calculations for trapped atoms, we propose a family of variational many-body wave functions that takes into account the qualitative different nature of the BCS and BEC regimes as a function of the scattering length. Energies, densities and correlations functions are calculated and compared with previous results for homogeneous gases. Universality tests at the unitarity limit are also performed. | eng_Latn | 11,071 |
Ten years of Nature Physics: Frozen motion | Cooling the motion of mechanical resonators to the ground state and subsequent advances in cavity optomechanics have been made possible by resolved-sideband cooling — an atomic-physics-inspired technique — first demonstrated in a 2008 Nature Physics paper. | O. Introduction This lecture will unfortunately not be a systematic review of the subject of rigorous results in non-equilibrium statistical mechanics. A preliminary attempt to outline such a review led me quickly to the conclusion that the field is too diverse to be summarized in a single lecture. I have therefore decided instead to discuss a few related.works in depth. The works I have chosen are: 1. The paper of J. Fritz and R. L. Dobrushin[5] on two-dimensional dynamics. 2. The paper of W. Braun and K. Hepp[3] on classical mechanics in the Vlasov limit. 3. A recent preprint by H. van Beijeren, J. L. Lebowitz, H. Spohn, and myself[2] on autocorrelations and fluctuations in the dilute equilibrium hard-sphere gas. | eng_Latn | 11,072 |
An Integrable Three Particle System Related to Intrinsic Localized Modes in Fermi–Pasta–Ulam-β Chain | In this paper, a ring of three particles interacting via nearest-neighbor harmonic and quartic potentials is investigated for the study of intrinsic localized modes (ILMs) in Fermi–Pasta–Ulam (FPU) atomic chain. In spite of the fact that above Hamiltonian system has been shown to be integrable by Hietaniata [Phys. Rep. 147 (1987) 87], Yoshida and Ramani [Physica D 30 (1988) 151], respectively, we approve its integrability in a more straightforward way. Moreover, we obtain exact periodic solutions in terms of the Jacobi elliptic functions for both the zero and nonzero third first integral. The significance of these findings lies in the fact that analytical stationary and moving ILMs solutions are obtained, and a close relationship between the movability of ILMs and the third first integral is clarified. | In this paper, a numerical method is given for solving fuzzy Fredholm integral equations of the second kind, by using Bernstein piecewise polynomial, whose coefficients determined through solving dual fuzzy linear system. Numerical examples are presented to illustrate the proposed method, whose calculations were implemented by using the Computer software MathCadV.14. | eng_Latn | 11,073 |
Monitoring the growth of tension in a liquid contained in a Berthelot tube | A new method of measuring the critical tension which a liquid contained in a steel Berthelot tube can sustain is described which enables one to monitor the growth of this tension prior to its critical value at which the enclosed liquid breaks. The pressure and tension changes in the liquid inside the cylindrical Berthelot tube are measured by attaching a pressure transducer to the tube in such a way that the diaphragm of the transducer forms one of the end walls of the tube. Earlier methods used for the calculation of the critical tension are discussed and compared with the new method. | Abstract In this paper, we investigate the time-dependent Ginzburg–Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion–boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS–BEC crossover. | eng_Latn | 11,074 |
Bose-einstein condensation in quasi-2D trapped gases | We discuss Bose-Einstein condensation (BEC) in quasi-2D trapped gases and find that well below the transition temperature T(c) the equilibrium state is a true condensate, whereas at intermediate temperatures T<T(c) one has a quasicondensate (condensate with fluctuating phase). The mean-field interaction in a quasi-2D gas is sensitive to the frequency omega(0) of the (tight) confinement in the "frozen" direction, and one can switch the sign of the interaction by changing omega(0). Variation of omega(0) can also reduce the rates of inelastic processes. This offers promising prospects for tunable BEC in trapped quasi-2D gases. | In this paper, we consider the density-dependent incompressible Navier–Stokes equations in with linearly growing initial velocity at infinity. We obtain a blow-up criterion and global well-posedness of the two-dimensional system. It generalized the local well-posedness results due to the recent work by the first and third authors to the global well-posedness in . Copyright © 2012 John Wiley & Sons, Ltd. | eng_Latn | 11,075 |
Simulations of Parametric Resonance Ionization Cooling of Muon Beams | Parametric-resonance ionization cooling (PIC) is being developed to create small beams so that high muon collider luminosity can be achieved with fewer muons. In the linear channel that is studied in this effort, a half integer resonance is induced such that the normal elliptical motion of particles in x − x′ phase space becomes hyperbolic, with particles moving to smaller x and larger x′ as they pass down the channel. Thin absorbers placed at the focal points of the channel then cool the angular divergence of the beam by the usual ionization cooling mechanism where each absorber is followed by RF cavities. Thus the phase space of the beam is compressed in transverse position by the dynamics of the resonance and its angular divergence is compressed by the ionization cooling mechanism. We report the first results of simulations of this process, a study of the compensation of chromatic aberration by using synchrotron oscillations. | We consider the approximation of the ground state of the one-dimensional cubic nonlinear Schrodinger equation by a normalized gradient algorithm combined with linearly implicit time integrator, and finite difference space approximation. We show that this method, also called imaginary time evolution method in the physics literature, is con-vergent, and we provide error estimates: the algorithm converges exponentially towards a modified solitons that is a space discretization of the exact soliton, with error estimates depending on the discretization parameters. | eng_Latn | 11,076 |
Squeezing in a three-level Jaynes-Cummings model | Abstract The evolution of the state vector of a system composed of a cascade three-level atom and a single-mode field with arbitrary detuning and initial condition has been obtained. The quantum fluctuations of the field are presented. The contribution of single- and two-photon transitions to the squeezing of the field is discussed. The dependence of the squeezing on initial intensities of the field and detuning are given. | The main objective of this article is to study dynamic of the ::: three-dimensional Boussinesq equations with the periodic boundary ::: condition.We prove that when the Rayleigh number $R$ crosses the ::: first critical Rayleigh number $R_c$, the Rayleigh-Benard problem ::: bifurcates from the basic state to an global attractor $\Sigma$, which is homeomorphic to $S^3$. | eng_Latn | 11,077 |
Free chattering and finite time in a high order system by terminal back-stepping and terminal sliding mode control techniques | Nowadays, finite Time stability of systems is popular for control engineering designers. In this paper, two control inputs will be designed for a typical high order system with using of Nonsingular Terminal Sliding Mode Control (NTSMC) and Back-Stepping methods, which clearly and completely remove chattering phenomena, also as finite time cause system stability. The control inputs are robust against of disturbance and uncertainties. The high order system that is used in this paper is a general sample and the most systems are compatible on it. | We study, both classically and quantum mechanically, the problem of a neutral particle with a spin angular momentum S, mass m, and magnetic moment μ, moving in one dimension in an inhomogeneous magnetic field given by B=B0ẑ+B⊥′xŷ. This problem serves for us as a toy model to study the trapping of neutral particles. We identify K≡[S2(B⊥′)2/μmB03], which is the ratio between the precessional frequency of the particle and its vibrational frequency, as the relevant parameter of the problem. Classically, we find that when μ is antiparallel to B, the particle is trapped provided that K<0.5. We also find that viscous friction, be it translational or precessional, destabilizes the system. Quantum mechanically, we study the problem of a spin S=ℏ/2 particle in the same field. Treating K as a small parameter for the perturbation from the adiabatic Hamiltonian, we find that the lifetime Tesc of the particle in its trapped ground state is Tesc=(Tvib/2π)(1/8πK)exp(2/K), where Tvib=2πmB0/μ(B⊥′)2 is the classical period ... | eng_Latn | 11,078 |
Band structures of a dipolar Bose-Einstein condensate in one-dimensional lattices | We derive the effective Gross-Pitaevskii equation for a cigar-shaped dipolar Bose-Einstein condensate in one-dimensional lattices and investigate the band structures numerically. Due to the anisotropic and the longranged dipole-dipole interaction in addition to the known contact interaction, we elucidate the possibility of modifying the band structures by changing the alignment of the dipoles with the axial direction. With the considerations of the transverse parts and the practical physical parameters of a cigar-shaped trap, we show the possibility to stabilize an attractive condensate simply by adjusting the orientation angle of dipoles. Some interesting Bloch waves at several particle current densities are identified for possible experimental observations. | Abstract We discuss random matrix-model representations of D = 1 string theory, with particular emphasis on the case in which the target space is a circle of finite radius. The duality properties of discretized strings are analyzed and shown to depend on the dynamics of vortices. In the representation in terms of a continuous circle of matrices we find an exact expression for the free energy, neglecting non-singlet states, as a function of the string coupling and the radius which exhibits exact duality. In a second version, based on a discrete chain of matrices, we find that vortices induce, for a finite radius, a Kosterlitz-Thouless phase transition that takes us to a c = 0 theory. | eng_Latn | 11,079 |
Low-dimensional semi-classical treatment of the dissipation problem | Abstract The interaction between two harmonic oscillators, a classical and a quantum one, coupled through a linear term, is analyzed by recourse to Ehrenfest's theorem. This model is able to mimic dissipative behaviour for the quantum harmonic oscillator, without violating any quantum rule. | A statistical analysis has been made of the distribution functions for residence time of a liquid in different flow formulations. The region of application of the different models of longitudinal dispersion is discussed. | eng_Latn | 11,080 |
A hierarchy of Liouville integrable lattice equations and its integrable coupling systems | Abstract A new discrete two-by-two matrix spectral problem with two potentials is introduced, followed by a hierarchy of integrable lattice equations obtained through discrete zero curvature equations. It is shown that the Hamiltonian structures of the resulting integrable lattice equations are established by virtue of the trace identity. Furthermore, based on a discrete four-by-four matrix spectral problem, the discrete integrable coupling systems of the resulting hierarchy are obtained. Then, with the variational identity, the Hamiltonian structures of the obtained integrable coupling systems are established. Finally, the resulting Hamiltonian systems are proved to be all Liouville integrable. | We have studied the dynamic regimes of an autonomous chaotic system (a modified oscillator with inertial nonlinearity) and found a chaotic attractor of a new type. The autocorrelation function, power spectrum, and Lyapunov exponents of this attractor have been calculated. Some of these characteristics resemble the behavior of a strange nonchaotic attractor. | eng_Latn | 11,081 |
Validation of a nonlinear HEMT model by power spectrum characteristics | The experimental bias dependence of the power output spectrum from various types of HEMT at large signal excitation was studied and compared with predicted values obtained from a newly proposed HEMT model. Good agreement between simulated and measured power spectrum up to at least the fourth harmonic was demonstrated for HEMT devices from different manufacturers. An extension of the existing model is also proposed, which models the V/sub ds/ dependence of the transconductance peak in the region where the drain current is unsaturated and at negative drain voltage. > | Previously developed ``stochastic representation of deterministic interactions`` enables exact treatment of an open system without leaving its native phase space (Hilbert space) due to peculiar stochastic extension of the Liouville (von Neumann) equation for its statistical operator. Can one reformulate the theory in terms of stochastic ``Langevin equations'' for its variables? Here it is shown that in case of classical Hamiltonian underlying dynamics the answer is principally positive, and general explicit method of constructing such equations is described. | eng_Latn | 11,082 |
Time dependent phenomena in statistical mechanics | O. Introduction This lecture will unfortunately not be a systematic review of the subject of rigorous results in non-equilibrium statistical mechanics. A preliminary attempt to outline such a review led me quickly to the conclusion that the field is too diverse to be summarized in a single lecture. I have therefore decided instead to discuss a few related.works in depth. The works I have chosen are: 1. The paper of J. Fritz and R. L. Dobrushin[5] on two-dimensional dynamics. 2. The paper of W. Braun and K. Hepp[3] on classical mechanics in the Vlasov limit. 3. A recent preprint by H. van Beijeren, J. L. Lebowitz, H. Spohn, and myself[2] on autocorrelations and fluctuations in the dilute equilibrium hard-sphere gas. | ABSTRACTLong-term travel behavior is difficult to observe and explain and even more difficult to forecast. This paper proposes an approach based on stochastic state equations to describe the gradua... | eng_Latn | 11,083 |
Is there a proof of the time-dependent Schrödinger equation? In many books, we find the proof of the time-independent Schrödinger equation which can be derived from the wave equation and the expression of de Broglie wavelength. But what about the time-dependent equation? In ion-atom collisions, there is a way to prove the eikonal equation which is similar to the TDSE where the starting point is TISE, if we consider that the projectile ion does linear trajectories, time can be embedded and we prove the eikonal equation that very known in a semiclassical treatment of ion-atom collisions. Is there a similar proof for example, and how time is introduced? | How can one derive Schrödinger equation? The is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his experiments. My question is, can one derive the Schrödinger equation mathematically? | In the Landau theory of phase transitions, is the order parameter a thermodynamic variable of state? In the Landau theory of phase transitions, one typically considers a "free energy" $F$ as a function of the temperature $T$ and the "order parameter" $\psi$: $F(T, \psi)$. For the sake of clarity, let's consider the liquid-gas transition, in which the order parameter is usually taken to be the difference of densities between the ordered phase and the disordered phase. In this case, it looks that the order parameter $\psi$ is closely related to the the volume $V$, a global variable of state. What is the correct interpretation of $\psi$ as a thermodynamic variable? I consider several logical possibilities, but all interpretations look troublesome to me: $\psi$ is a variable of state replacing the volume. In this case I have a few related concerns: Is the "free energy" $F$ the Helmholtz or the Gibbs free energy? If $F$ is the Gibbs free energy, $F$ should depend on the temperature $T$ and the pressure $p$ (the conjugate variable of the volume), so it shouldn't depend on $\psi$. If it is the Helmholtz free energy, it's ok that it depends on $\psi$, but the experiments are usually carried out at constant pressure, not constant volume. Usually, state variables are something one can select at will [for instance, think of the phase diagram $(p, T)$]. However, the order parameter $\psi$ is not selected at will, but it is selected by the system as a result of the minimization process according to the Landau theory. $\psi$ is yet another variable of state in addition to volume and temperature. Why the pressure is not usually taken into account as a variable of state, and only the temperature is considered? What is the conjugate variable to $\psi$? Can really $\psi$ and $V$ be taken as independent? $\psi$ is not a variable of state, is something else. What else can $\psi$ be from the thermodynamic point of view? Same question as above, why is pressure not usually taken into account in Landau theory? | eng_Latn | 11,084 |
Momentum of electron problem Recently, my friend bemused me with a question related to the momentum of an electron. The confusing logic is stated below: Since an electron is a particle and according to classical physics, we know that it's momentum equals to: $p_e=mv$ However, by looking from a different perspective, we found that, From de Broglie's hypothesis: $p=\frac{h}{\lambda} $ And since de Broglie proposed that particles also obey the Einstein relation: $E=hf$ Then, $p_e=\frac{hf}{c}=\frac{E_e}{v}$ Since the only energy of the electron is Kinetic energy, then $E_e=\frac{1}{2}mv^2$ and $p_e=\frac{1}{2}mv$ We thus arrive at a contradiction: $mv \neq \frac{1}{2}mv $ What is the flaw in this logic? | $\lambda=\frac{2h}{p}$ instead of $\lambda=\frac{h}{p}$? I am studying quantum physics and there is something I don't understand: I know that for any particle $E=hf$ (Einstein relation) and $v=\lambda f$ ($v$ is the speed of the particle). I also know that the kinetic energy is $E_k=\frac{mv^2}{2}$. Solving those 3 equations for $\lambda$: $$h\frac{v}{\lambda}=\frac{mv^2}{2},$$ I finally find $$\lambda=\frac{2h}{mv}=\frac{2h}{p},$$ which is not consistent with the De Broglie relation $$\lambda=\frac{h}{p}.$$ Where am I wrong in my development? | How is the Schroedinger equation a wave equation? Wave equations take the form: $$\frac{ \partial^2 f} {\partial t^2} = c^2 \nabla ^2f$$ But the Schroedinger equation takes the form: $$i \hbar \frac{ \partial f} {\partial t} = - \frac{\hbar ^2}{2m}\nabla ^2f + U(x) f$$ The partials with respect to time are not the same order. How can Schroedinger's equation be regarded as a wave equation? And why are interference patterns (e.g in the double-slit experiment) so similar for water waves and quantum wavefunctions? | eng_Latn | 11,085 |
Schrodinger Equation | Variational Derivation of Schrodinger Equation | How can one derive Schrödinger equation? | deu_Latn | 11,086 |
Inverse proportional to cosmological scale factor How can I show using calculation that the temperature of the universe is inversely proportional to the cosmological scale factor? I am just curious, as my textbook states this fact but does not show the calculations, and so I was thinking how one could show this? I would appreciate the help. EDIT: so I know for a fact that the equation: $$z+1=\frac{R}{R_0}$$ Where $z$ is the Doppler shift and $R$ is the cosmological scale factor in the present and the $R_0$ is the scale factor at $t_0$. but we also know that: $$\frac{R}{R_0}=\frac{\lambda}{\lambda_0}$$ But we know from Wien's Law that: $$\lambda T=2.9\times 10^{-3}$$ Hence we have: $$\frac{R}{R_0}=\frac{\lambda}{\lambda_0}=\frac{T_0}{T}=z+1$$ This is all I can extract at this point the relationship between temperature and the scale factor, I do not know if I am on the right track, or if this is correct at all? I would appreciate if someone can help me check and help me go further from here to show that the relationship between $T$ and $R$ is inversely proportional. | Why is scale factor inversely proprotional to temperature? In all lectures, books and papers I have read about, the scale factor of the universe is inversely proportional to temperature $$a \propto \frac{1}{T}$$ What is the reasoning behind this relation? People did mention stretching of wavelength proportional to scale factor and wavelength being inversely proportional to temperature by Wein's law, but somehow this argument doesn't seem convincing to me. How did we initially come about to this relation? | About the complex nature of the wave function? 1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an explanation that I need some help with: that the de Broglie wavelength and the wavelength of an elastic wave do not show similar properties under a Galilean transformation. He basically says that both are equivalent under a gauge transform and also, separately by Lorentz transforms. This, accompanied with the observation that $\psi$ is not observable, so there is no "reason for it being real". Can someone give me an intuitive prelude by what is a gauge transform and why does it give the same result as a Lorentz tranformation in a non-relativistic setting? And eventually how in this "grand scheme" the complex nature of the wave function becomes evident.. in a way that a dummy like me can understand. 2. A wavefunction can be thought of as a scalar field (has a scalar value in every point ($r,t$) given by $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{C}$ and also as a ray in Hilbert space (a vector). How are these two perspectives the same (this is possibly something elementary that I am missing out, or getting confused by definitions and terminology, if that is the case I am desperate for help ;) 3. One way I have thought about the above question is that the wave function can be equivalently written in $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{R}^2 $ i.e, Since a wave function is complex, the Schroedinger equation could in principle be written equivalently as coupled differential equations in two real functions which staisfy the Cauchy-Riemann conditions. ie, if $$\psi(x,t) = u(x,t) + i v(x,t)$$ and $u_x=v_t$ ; $u_t = -v_x$ and we get $$\hbar \partial_t u = -\frac{\hbar^2}{2m} \partial_x^2v + V v$$ $$\hbar \partial_t v = \frac{\hbar^2}{2m} \partial_x^2u - V u$$ (..in 1-D) If this is correct what are the interpretations of the $u,v$.. and why isn't it useful. (I am assuming that physical problems always have an analytic $\psi(r,t)$). | eng_Latn | 11,087 |
In solving finite square well problem, we solve the TISE inside and outside the well, and we match the wave function at the boundary, by the continuity of wave function. Now this bugs me, since the wavefunction is only assume to be square-integrable, why we can use the continuity of wavefunction? Edit: There is no problem for this bound state solution to hold, but will we miss other non-continuous solutions? | Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention anything. | There is a bar of chocolate of size $N$ x $M$. Little square $(x, y)$ is poisoned. There are 2 players taking turns. In each move they can cut the bar along any of the horizontal or vertical lines, then the part which does not contain $(x, y)$ is being eaten. The player who is left only with square $(x, y)$ loses (beacause it is poisoned). Which player has the winning strategy? I guess that this game is equivalent to game of Nim due to Sprauge-Grundy theorem, but I don't know how. | eng_Latn | 11,088 |
Why can quantum tunnelling be handled as a static problem? Quantum tunnelling is a process that can happen in quantum mechanics but is forbidden in classical mechanics. Roughly speaking, a particle can possibly escape from a potential well or penetrate into a potential barrier. Obviously, the probability for a trapped particle to escape from a potential well should be handled with the time-dependent Schrödinger equation. But in most cases, we simply solve the static Schrödinger equation with proper boundary conditions (and match conditions around the turning points). I wonder, how can a time-dependent process be handled as a static problem? | Why can we treat quantum scattering problems as time-independent? From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger equation to find the energy eigenstates. There will be a continuous spectrum of energy eigenvalues. In the region to the left of the potential, identify a piece of the wavefunction that looks like $Ae^{i(kx - \omega t)}$ as the incoming wave. Ensure that to the right of the potential, there is not piece of the wavefunction that looks like $Be^{-i(kx + \omega t)}$, because we only want to have a wave coming in from the left. Identify a piece of the wavefunction to the left of the potential that looks like $R e^{-i(kx + \omega t)}$ as a reflected wave. Identify a piece of the wavefunction to the right of the potential that looks like $T e^{i(kx - \omega t)}$ as a transmitted wave. Show that $|R|^2 + |T|^2 = |A|^2$. Interpret $\frac{|R|^2}{|A|^2}$ as the probability for reflection and $\frac{|T|^2}{|A|^2}$ as the probability for transmission. This entire process doesn't seem to have anything to do with a real scattering event - where a real particle is scattered by a scattering potential - we do all our analysis on a stationary waves. Why should such a naive procedure produce reasonable results for something like Rutherford's foil experiment, in which alpha particles are in motion as they collide with nuclei, and in which the wavefunction of the alpha particle is typically localized in a (moving) volume much smaller than the scattering region? | In the Landau theory of phase transitions, is the order parameter a thermodynamic variable of state? In the Landau theory of phase transitions, one typically considers a "free energy" $F$ as a function of the temperature $T$ and the "order parameter" $\psi$: $F(T, \psi)$. For the sake of clarity, let's consider the liquid-gas transition, in which the order parameter is usually taken to be the difference of densities between the ordered phase and the disordered phase. In this case, it looks that the order parameter $\psi$ is closely related to the the volume $V$, a global variable of state. What is the correct interpretation of $\psi$ as a thermodynamic variable? I consider several logical possibilities, but all interpretations look troublesome to me: $\psi$ is a variable of state replacing the volume. In this case I have a few related concerns: Is the "free energy" $F$ the Helmholtz or the Gibbs free energy? If $F$ is the Gibbs free energy, $F$ should depend on the temperature $T$ and the pressure $p$ (the conjugate variable of the volume), so it shouldn't depend on $\psi$. If it is the Helmholtz free energy, it's ok that it depends on $\psi$, but the experiments are usually carried out at constant pressure, not constant volume. Usually, state variables are something one can select at will [for instance, think of the phase diagram $(p, T)$]. However, the order parameter $\psi$ is not selected at will, but it is selected by the system as a result of the minimization process according to the Landau theory. $\psi$ is yet another variable of state in addition to volume and temperature. Why the pressure is not usually taken into account as a variable of state, and only the temperature is considered? What is the conjugate variable to $\psi$? Can really $\psi$ and $V$ be taken as independent? $\psi$ is not a variable of state, is something else. What else can $\psi$ be from the thermodynamic point of view? Same question as above, why is pressure not usually taken into account in Landau theory? | eng_Latn | 11,089 |
Expectation value of $\frac{1}{r^2}$ of hydrogen atom | The average of inverse square radius $r^{-2}$ for any state quantum $|n\ell\rangle$ using the radial Schrödinger equation | Proving a graph has no Hamiltonian cycle | eng_Latn | 11,090 |
Connection between Group of Schrodinger equation and energy level degeneracy | What is the relationship between symmetry and degeneracy in quantum mechanics? | Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate? | eng_Latn | 11,091 |
Derive Entropy of an Ideal Gas of Photons | This article shows the details of the derivation of the entropy of an ideal gas of photons based on the equation of forces that govern the motion of photons. | Projection operators are defined below, given an arbitrary state | ψ ⟩ . {\displaystyle |\psi \rangle .}
| kor_Hang | 11,092 |
Are the Weeping Angels really trapped? | What exactly happens when a Weeping Angel is quantum locked? | Direct proof that nilpotent matrix has zero trace | eng_Latn | 11,093 |
Expectation value of momentum in any bound state How do we prove that the expectation value of momentum operator in any bound state is zero ? $$ \langle \hat{P} \rangle_{\text{bound state}}=0 $$ and what about the position expectation value ? How do we prove it for a general case. How do we get a physical intuition from the corresponding wavefunctions ? | Expectation of momentum in the bound state Is it logically correct to assert that the expectation of the momentum $$\langle \hat p \rangle=0$$ for any bound state because it is bound to some finite region? What is the physical interpretation of the fact that $$\langle \hat p \rangle=0$$ in an energy eigenstate $\psi_n(x,t)$ but $$\langle \hat p \rangle\neq0$$ in some superposition state $$\psi(x,t)=c_m\psi_m(x,t)+c_n\psi_n(x,t)~?$$ Here $\psi_n(x,t)$ the eigenstates of the Hamiltonian, for example, in the problem of particle in a box (say). | Why can we treat quantum scattering problems as time-independent? From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger equation to find the energy eigenstates. There will be a continuous spectrum of energy eigenvalues. In the region to the left of the potential, identify a piece of the wavefunction that looks like $Ae^{i(kx - \omega t)}$ as the incoming wave. Ensure that to the right of the potential, there is not piece of the wavefunction that looks like $Be^{-i(kx + \omega t)}$, because we only want to have a wave coming in from the left. Identify a piece of the wavefunction to the left of the potential that looks like $R e^{-i(kx + \omega t)}$ as a reflected wave. Identify a piece of the wavefunction to the right of the potential that looks like $T e^{i(kx - \omega t)}$ as a transmitted wave. Show that $|R|^2 + |T|^2 = |A|^2$. Interpret $\frac{|R|^2}{|A|^2}$ as the probability for reflection and $\frac{|T|^2}{|A|^2}$ as the probability for transmission. This entire process doesn't seem to have anything to do with a real scattering event - where a real particle is scattered by a scattering potential - we do all our analysis on a stationary waves. Why should such a naive procedure produce reasonable results for something like Rutherford's foil experiment, in which alpha particles are in motion as they collide with nuclei, and in which the wavefunction of the alpha particle is typically localized in a (moving) volume much smaller than the scattering region? | eng_Latn | 11,094 |
What is a Bose-Einstein condensate? | What is a Bose–Einstein condensate? What is the use of it? | How would space-time be bent at the middle of the double slit experiment when a single particle passes through the device? | eng_Latn | 11,095 |
What are some examples of Bose-Einstein condensate state of matter? | What are some examples of a Bose-Einstein condensate? | Is it possible to stop time by cooling a closed system down to 0 Kelvin? | eng_Latn | 11,096 |
What is a quarter-wave plate? | What is a Quarter wave plate? | If it's impossible to have zero (no) energy how it is then quantized and non continous? | eng_Latn | 11,097 |
Does a transition matrix have to be square? | Does a transition matrix have to be square? Why? | Is thinking the particle doesn't always travel through a single slit in a double slit experiment the biggest incorrect notion in physics? | eng_Latn | 11,098 |
A bound state is: given a potential vanishing at infinity, negative-energy states must be bound. How can I distinguish between a bound state and a resonance state in particles physics? | I still do not understand what a precisely is. Is it exactly the same as a particle? Or only an excited state? And why does it make a peak in some diagrams? And which diagrams? | Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like this:$$V(r)=-V_0\quad(r<a)$$$$ V(r)=0\quad(r>a)$$ and found that there is no bound state when $V_0a^2<\pi^2\hbar^2/8m$. So what's the condition that we have at least one bound state for 3D and 2D? | eng_Latn | 11,099 |
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