具有物理背景的高维Painlevé可积模型

提出了一种求解任意维数非线性模型的“M?bious”变换下不变的渐进展开方法,并可同时获得许多新的与原模型有着相同维数的Painlevé可积模型.取(2+1)维KdV-Burgers(KdVB)方程和Kadomtsev-Petviashvili(KP)方程为具体例子,获得了一些新的具有Painlevé性质的高维“M?bious”变换下不变的方程及原模型的近似解.在某些特殊情况下,某些近似解可以成为精确解 关键词： 高维可积模型 “M?bious”不变 近似方法     

Non-equilibrium statistical mechanics in the general theory of relativity: II. Linear fields in a kinetic approximation

The first paper in this series introduced a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. The object of this second paper is to apply that formalism to the evolution of a collection of particles that interact via linear fields in a fixed curved background spacetime. Given the viewpoint adopted here, the fundamental objects of the theory are a many-particle distribution function, which lives in a many-particle phase space, and a many-particle conservation equation which this distribution satisfies. By viewing a composite N-particle system as interacting one- and (N ? 1)-particle subsystems, one can derive exact coupled equations for appropriately defined reduced one- and (N ? 1)-particle distribution functions. Alternatively, by treating all the particles on an identical footing, one can extract an exact closed equation involving only the one-particle distribution. The implementation of plausible assumptions, which constitute straightforward generalizations of standard non-relativistic “kinetic approximations”, then permits the formulation of an approximate kinetic equation for the one-particle distribution function. In the obvious non-relativistic limit, one recovers the well-known Vlasov-Landau equation. The explicit form for the relativistic expression is obtained for three concrete examples, namely, interactions via an electromagnetic field, a massive scalar field, and a symmetric second rank tensor field. For a large class of interactions, of which these three examples are representative, the kinetic equation will admit a relativistic Maxwellian distribution as an exact stationary solution; and, for these interactions, an H-theorem may be proved.     

Entropy in heavy ion collisions — A two-fluid scenario

Entropy balance is very important at ultra-high energy HIC’s, because there is not even approximate thermalisation there. Only a minor fragment of the incoming kinetic energy will be turned into “heat”, so internal energy, while the thermodynamic state variable is internal energy, not the total one. Here an approach is discussed calculating entropy directly, in a continuum physics scenario.     

Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the “fractional centered derivative” approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank–Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank–Nicolson method for the fractional diffusion equation with using fractional centered difference approach.     

Nonequilibrium statistical mechanics in the general theory of relativity I. A general formalism

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. by mapping the true physics onto a fictitious “background” spacetime, which may be chosen to satisfy some “average” field equations, one then obtains a useful covariant notion of “evolution” in response to a fluctuating “gravitational force.” For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as “localized” in space and time, one obtains a tractable kinetic equation which reduces, in the newtonian limit, to the standard Landau equation.     

色交叉关联噪声对基因转录调节系统的影响

研究了受色交叉关联噪声驱动的基因转录调节系统的瞬态性质(平均首通时间).据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,求出稳态概率分布函数的表达式.在此基础上运用最快下降法得到平均首通时间的近似表达式.经过数值计算,结果表明：在强关联,小关联时间条件下,蛋白质的浓度经历了开→关→开;在弱关联,大关联时间条件下,蛋白质的浓度经历了开→关.在基因转录过程中出现了重入现象. 关键词： 色交叉关联噪声 基因转录调节系统 平均首通时间     

A comment on the early onset of semi-inclusive scaling in proton-proton collisions

The present experimental evidence for the scaling of multiplicity distributions predicted by Koba, Nielsen and Olesen is examined critically. Our results indicate that the approximate scaling observed experimentally is not necessarily connected with an “early” approach to the asymptotic limit. Some simple models are shown to predict an extremely slow approach to scaling. The possibility of distinguishing between “early” scaling ang the “quasi-scaling” exhibited by these models with experiments at ISR is discussed.     

Dynamics of and radiation from superconducting strings and springs

We present a detailed study of the dynamics of and radiation from superconducting strings. We derive an approximate local action for a current-carrying vortex line and present some exact solutions to its equation of motion. These include stable static “springs” and oscillating “kinky” loops. For one of these “kinky” loops we are able to calculate the radiation exactly, and find (in contrast to previous work) the result is finite. We also argue that the non-local electromagnetic self-interaction of a loop causes the kinks to slowly straighten out. Finally, we discuss the loss of current at “cusp-like” regions and show that the shrinking of loops generally leads to current loss rather than gain.     

On the Stability Behaviour of Boltzmann's Equation

The Boltzmann equation for an “isolated” gas system is assumed to form a “dynamical system” in a compact subset of the space of continuous distribution functions (existence assumption). Then the asymptotic stability in the sense of Lyapunov of the total Maxwell distribution is investigated (“approach to equilibrium”). Further the influence of persistent perturbations on the stability behaviour of Boltzmann's equation is considered (“structural stability”).     

Application of the Difference Gaussian Rules to Solution of Hyperbolic Problems: II. Global Expansion

This work is the sequel to S. Asvadurov et al. (2000, J. Comput. Phys.158, 116), where we considered a grid refinement approach for second-order finite-difference time domain schemes. This approach permits one to compute solutions of certain wave equations with exponential superconvergence. An algorithm was presented that generates a special sequence of grid steps, called “optimal”, such that a standard finite-difference discretization that uses this grid produces an accurate approximation to the Neumann-to-Dirichlet map. It was demonstrated that the application of this approach to some problems in, e.g., elastodynamics results in a computational cost that is an order of magnitude lower than that of the standard scheme with equally spaced gridnodes, which produces the same accuracy. The main drawback of the presented approach was that the accurate solution could be obtained only at some a priori selected points (receivers). Here we present an algorithm that, given a solution on the coarse “optimal” grid, accurately reconstructs the solution of the corresponding fine equidistant grid with steps that are approximately equal to the minimal step of the optimal (strongly nonuniform) grid. This “expansion” algorithm is based on postprocessing of the approximate solution, is local in time (but not in space), and has a cost comparable to that of the discrete Fourier transform. An approximate inverse to the “expansion” procedure—the “reduction” algorithm—is also presented. We show different applications of the developed procedures, including refinement of a nonmatching grid. Numerical examples for scalar wave propagation and 2.5D cylindrical elasticity are presented.     

Kinetic equations within the formalism of non-equilibrium thermo field dynamics

After reviewing the real-time formalism of dissipative quantum field theory, i.e. non-equilibrium thermo field dynamics (NETFD), a kinetic equation, a self-consistent equation for the dissipation coefficient and a “mass” or “chemical potential” renormalization equation for non-equilibrium transient situations are extracted out of the two-point Green's function of the Heisenberg field, in their most general forms upon the basic requirements of NETFD. The formulation is applied to the electron-phonon system, as an example, where the gradient expansion and the quasi-particle approximation are performed. The formalism of NETFD is reinvestigated in connection with the kinetic equations.     

Sound generation and transmission in flow ducts with axial temperature gradients

This article describes a one-dimensional, linearized, analysis of fundamental mode sound generation and propagation in rigid-walled flow ducts with axial temperature variation. An acoustic wave equation, including damping effects and volume sources, is derived and its solution (in the absence of sources) by a numerical technique and an approximate analytical method is discussed. The “forced” wave equation is then solved (the existence of an oscillating solution to the “unforced” equation being assumed) for sound generation by a side-branch volume source in an infinite duct, and the results are applied to a duct of finite length. Reasonably good agreement is obtained between measurements and predictions of the sound pressure field in a flow duct, away from the source region.     

A nonperturbative treatment of radiative decays and the relativistic kinetic energy in heavy quarkonia

Using a “regularized potential” we solve the Schrödinger equation including all spin dependent interactions nonperturbatively and calculate the radiative decays of heavy quarkonia. The influence ofS-D mixing due to the tensor term is discussed. Applying the variational approach we investigate the influence of the relativistic kinetic energy on the bound state masses.     

On a kinetic equation for and the dynamical friction of a particle in a plasma-a phenomenological approach

Based on phenomenological considerations, a one particle distribution function consisting of two parts accounting for the effects of “distant” particles and the “nearest” neighbors is suggested. Employing the above distribution function and the Liouville theorem, dynamical friction of a particle in, and a kinetic equation for a plasma are demonstrated.     

Phase factors in bases for solutions of time-dependent schrödinger equations

The time-dependent Schrödinger equation is formulated within a model space by means of a finite set of coupled, linear differential equations. The basis is spanned by a set of orthogonal and well-defined many body wave-functions, which are solutions of a model Hamiltonian in a “moving frame”. As a by-product one is able to separate approximatively collective potential, collective kinetic, and intrinsic excitation energy for arbitrary collective motion. For the two types of motion discussed in greater details (i.e. center of mass and quadrupole motion), the expressions for the collective kinetic energy approach their correct asymptotic values.     

Thermodynamic properties of rotating trapped ideal Bose gases

Ultracold atomic gases can be spined up either by confining them in rotating frame, or by introducing “synthetic” magnetic field. In this paper, thermodynamics of rotating ideal Bose gases are investigated within truncated-summation approach which keeps to take into account the discrete nature of energy levels, rather than to approximate the summation over single-particle energy levels by an integral as it does in semi-classical approximation. Our results show that Bose gases in rotating frame exhibit much stronger dependence on rotation frequency than those in “synthetic” magnetic field. Consequently, BEC can be more easily suppressed in rotating frame than in “synthetic” magnetic field.     

Estimation of accuracy of an asymptotic solution of the generalized Cauchy problem for the Boussinesq equation as applied to the potential model of tsunami with a “simple” source

Statement of the hydrodynamic problem in the framework of the potential tsunami model with “simple” source whose solution is chosen as the reference one. Generalized Cauchy problem for the Boussinesq equation and its reduction to the classical one. Analytical solution of the Cauchy problem for the Boussinesq equation. An explanation of the incorrectness of the formulation of the problem. Derivation of an approximate equation for the correct setting of the Cauchy problem. The known reference solution of the problem. An analytical solution of the correct problem and the derivation of its asymptotic representation in the “far zone.” Comparison of the graphs of the temporal history of wave height calculated by the formulas of the asymptotic and reference solutions. Estimation of the accuracy of the asymptotic solution by a three-level scale. Discussion. A remark concerning the referees.     

Strongly interacting parton matter equilibration

We study the kinetic and chemical equilibration in “infinite” parton matter within the Parton-Hadron-String Dynamics transport approach. The “infinite” matter is simulated within a cubic box with periodic boundary conditions initialized at different energy densities. Particle abundances, kinetic energy distributions, and the detailed balance of the off-shell quarks and gluons in the strongly-interacting quarkgluon plasma are addressed and discussed.