Nonlinear evolution equations andH theorems

We prove a structure theorem for evolution equations in the state space of a discrete classical system fulfilling a class ofH theorems. TheseH theorems are proved to give strong implications on the time behavior of the solutions. All the results are demonstrated by examples (Boltzmann-like equations, for example).     

Effect of initial rotational distribution and softness of surface on inelastic scattering of heteropolar rotor by surfaces

It is shown that the presence of two rotational rainbow peaks and a smearing effect due to the initial rotational distributions explain Boltzmann-like distributions in the low excitation region. and that softness of the surface makes gentle the slope of the decrease of the rotational state distribution near the cut-off energy.     

Adiabatic and isothermal elastic constants for highly anharmonic crystals

The mass operator of the phonon Green function for a highly anharmonic crystal in the ladder approximation is derived. In order to calculate the mass operator in the collision-dominated regime it is necessary to solve the Boltzmann-like equations. These solutions allow us to find the thermal conductivity coefficient and to prove that the thermodynamic relation between adiabatic and isothermal elastic constants is satisfied.     

Time-relaxation approach in far from equilibrium semiconductor plasma

The dynamics of evolution of the LO-phonon population in semiconductors under high levels of optical excitation is determined. Collision operators are written in a Boltzmann-like form, with the relaxation-times being a functional of the nonequilibrium thermodynamic parameters which describe the instantaneous macroscopic state of the whole system. The expected behavior of the relaxation channels under different experimental constraints is discussed.     

Pre-equilibrium decay in the exciton model

A new closed-form formulation of the statistical exciton model which gives results very similar to the total pre-equilibrium spectrum obtained by solving a set of Boltzmann-like master equations that describe the nuclear equilibration process, is suggested. The effect of including the loss of strength from each exciton state of a composite nucleus due to the transitions of Δn = 0 (Δp = Δh = 0) in both the master equations and closed-form formalisms is discussed.     

Moment Equations for a Granular Material in a Thermal Bath

We compute the moment equations for a granular material under the simplifying assumption of pseudo-Maxwellian particles approximating dissipative hard spheres. We obtain the general moment equations of second and third order and the isotropic moment equations of any order. Our equations describe, in the space homogeneous case, the granular system described by a Boltzmann-like collision term and subject to a Brownian motion due to the interaction with a bath, described by a Fokker–Planck term. The trend to equilibrium is studied in detail.     

Transitions from coherent to incoherent state induced by anharmonic interaction

A non-linear stochastic oscillator driven by a coherent radiation field is studied. Analog simulation is shown to support the arguments of theory on the specific role of the fluctuation-dissipation process and/or anharmonic interaction in making valid a treatment in terms of a Boltzmann-like distribution of energy. The results of analog simulation show that at certain values of the excitation frequency a superimposition of a coherent and an incoherent state may appear thereby opening the way to a more exhaustive theoretical treatment of this problem.     

Maximum-entropy closures for kinetic theories of neuronal network dynamics

We analyze (1 + 1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order, kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.     

A Bhatnagar-Gross-Krook kinetic approach to fast reactive mixtures: Relaxation problems

The paper deals with a consistent BGK-type approximation for the Boltzmann-like equations which govern the evolution of a gas undergoing bimolecular chemical reactions. In particular, model equations, specifically devised for physical situations in which chemical relaxation is as fast as mechanical relaxation, are discussed in comparison to previous models. This BGK approach preserves the main features of the reactive Boltzmann equations, including law of mass action and H-theorem. Numerical results illustrating the effects of the several varying parameters on the relaxation to equilibrium are presented and commented on.     

激光与近相对论临界密度薄层相互作用产生大电量高能电子束

研究了激光与近相对论临界密度等离子体薄层相互作用时所产生的高能电子束的主要特征,包括平均有效温度以及截止能量等.实验结果表明,电子束的电量超过nC量级,平均有效温度可达8 MeV以上.PIC数值模拟证明,近相对论临界密度等离子体内,相对论自透明效应和激光钻孔效应共同形成一条磁化等离子体通道,电子与激光将在角向磁场的协助下发生Betatron共振.激光可将电子直接加速到很高能量,因此电子束平均有效温度("斜坡温度")远远超过Wilks定标率预计的平均温度.该研究为产生高亮度X射线源提供了一种新的可能途径.     

Resonant tunneling in weakly coupled GaAs/AlGaAs superlattices in a transverse magnetic field: A probe of electronic distribution function

A method is proposed to get information about carrier distribution function in superlattices and multiple quantum-well structures from the analysis of the vertical transport experiments in a transverse magnetic field. The method was applied to the GaAs/AlGaAs superlattices with wide quantum wells in strong (B=0–7 T) magnetic fields. It was shown that the distribution function of electron is nonequilibrium Boltzmann-like, with electronic temperature T=10–20 K.     

Small Mass Ratio Limit of Boltzmann Equations in the Context of the Study of Evolution of Dust Particles in a Rarefied Atmosphere

We propose a model based on the coupling of two Boltzmann-like equations for the study of the evolution of dust particles in a rarefied atmosphere, such as it can be found in the context of safety studies for the ITER project of nuclear fusion. When the typical size of a dust speck becomes too large, the numerical simulation of the system under study becomes too expensive, and one needs to introduce an asymptotic model in which the mass ratio between molecules and dust specks tends to 0. This model is constituted of a coupling (by a drag force term) between a Boltzmann equation and a Vlasov equation.     

SOME PROGRESS IN THE LATTICE BOLTZMANN MODEL

A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell－Boltzmann-like form, which is third order in fluid velocity u_α. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and Chapman－Enskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.     

Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution

The present Note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker–Planck-like differential equation in the phase space. The limiting equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. In the longitudinal case, the Fokker–Planck-like equation can be solved exactly. To cite this article: A.C. Fannjiang, C. R. Physique 8 (2007).     

Reconstruction of hadronization stage in Pb+Pb collisions at 158 A GeV/c

Recent data on hadron multiplicities in central Pb+Pb collisions at 158 A GeV/c at mid-rapidity are analyzed within the concept of chemical freeze-out. A non-uniformity of the baryon chemical potential along the beam axis is taken into account. An approximate analytical solution of the hydrodynamic equations for a chemically frozen Boltzmann-like gas is found. The Cauchy conditions for hydrodynamic evolution of the hadron resonance gas are fixed at the thermal freeze-out hypersurface from analysis of one-particle momentum spectra and HBT correlations. The proper time of chemical freeze-out and physical conditions at the hadronization stage, such as energy density and averaged transverse velocity, are found.     

On the kinetic theory of vehicular traffic flow: Chapman–Enskog expansion versus Grad’s moment method

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier–Stokes equations for viscous fluids by applying two well-known methods of gas-kinetic theory, namely the Chapman–Enskog method and the method of moments of Grad. The viscosity coefficient appearing in our macroscopic traffic model is not introduced in an ad hoc way–as in other second-order traffic flow models–but comes into play through the derivation of a first-order constitutive relation for the traffic pressure. Numerical simulation shows that our Navier–Stokes-like traffic model satisfies the anisotropy condition and produces numerical results which are consistent with our daily experiences in real traffic.     

Density-Dependent Diffusion in the Periodic Lorentz Gas

We study the deterministic diffusion coefficient of the two-dimensional periodic Lorentz gas as a function of the density of scatterers. Based on computer simulations, and by applying straightforward analytical arguments, we systematically improve the Machta–Zwanzig random walk approximation [Phys. Rev. Lett. 50:1959 (1983)] by including microscopic correlations. We furthermore, show that, on a fine scale, the diffusion coefficient is a non-trivial function of the density. On a coarse scale and for lower densities, the diffusion coefficient exhibits a Boltzmann-like behavior, whereas for very high densities it crosses over to a regime which can be understood qualitatively by the Machta–Zwanzig approximation.     

Convergence of general decompositions of exponential operators

A general theorem is proved concerning the convergence of decompositions of exponential operators in a Banach space (or normed space). As a corollary, the convergence of fractal decompositions is proved. The convergence of generalized. Trotter-like formulas is also shown to result from the general theorem.     

Origin of Anisotropy in Gadolinium Crystal Using a New Spin Hamiltonian

Single crystal rare-earth magnets,such as hexagonal-close-packed gadolinium,usually have a large second order anisotropy K_2 and a negative first order anisotropy K_1 at low temperatures,which are difficult to explain using microscopic theories.An atomic scale effective spin Hamiltonian F|{S_i}] is proposed,which,apart from the usual isotropic nearest neighbor coupling J,consists of two new terms that are different for in-plane and out-of-plane neighbors and which are characterized by two new couplings C_1 and C_2,respectively.The hybrid Monte-Carlo method is utilized to sample this system to the desired Boltzmann-like distribution exp(-F/k_BT).It is found that K_2 and K_1 are compatible with the experimental values and arise naturally from the exchange anisotropy C_1 and C_2,which are less than 0.01% in magnitude of the isotropic exchange energy J.This new model spin Hamiltonian can also be applied to study other magnetic properties.