Recurrence properties of Lorentz lattice gas cellular automata

Recurrence properties of a point particle moving on a regular lattice randomly occupied with scatterers are studied for strictly deterministic, nondeterministic, and purely random scattering rules.On leave from Institute of Oceanology, USSR Academy of Sciences, 117218 Moscow, USSR     

Long-time behavior of the Lorentz electron gas in a constant,uniform electric field

The long-time behavior of the Lorentz electron gas is studied in the presence of a uniform external field. A discussion of the rigorous solution of the one-dimensional Boltzmann equation is followed by the derivation of the asymptotic form of the velocity distribution in an arbitrary number of dimensions. The system is shown to absorb energy from the field without bounds, which excludes the usually assumed steady state with finite thermal energy density.Supported by the Polish Ministry of Higher Education, Science and Technology, Project MR.I.7.The authors are very grateful to Dr. Y. Pomeau for many valuable comments.     

Statistical properties of the periodic Lorentz gas. Multidimensional case

In 1981 Bunimovich and Sinai established the statistical properties of the planar periodic Lorentz gas with finite horizon. Our aim is to extend their theory to the multidimensional Lorentz gas. In that case the Markov partitions of the Bunimovich-Sinai type, the main tool of their theory, are not available. We use a crude approximation to such partitions, which we call Markov sieves. Their construction in many dimensions is essentially different from that in two dimensions; it requires more routine calculations and intricate arguments. We try to avoid technical details and outline the construction of the Markov sieves in mostly qualitative, heuristic terms, hoping to carry out our plan in full detail elsewhere. Modulo that construction, our proofs are conclusive. In the end, we obtain a stretched-exponential bound for the decay of correlations, the central limit theorem, and Donsker's Invariance Principle for multidimensional periodic Lorentz gases with finite horizon.     

Molecular dynamical simulation of the canonical ensemble

We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltzmann distribution. A good approximation to the Boltzmann distribution is achieved in computationally accessible time for some model systems including the one-dimensional jellium.     

An approximate formula for the diffusion coefficient for the periodic Lorentz gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.     

Topological dynamics of flipping Lorentz lattice gas models

We study the topological dynamics of the flipping mirror model of Ruijgrok and Cohen with one or an infinite number of particles. In particular we prove the topological transitivity and topological mixing up to a natural first integral for the one-particle model.     

Decay of correlations in the regular Lorentz gas

The regular Lorentz gas on triangular lattice is studied numerically and analytically. The velocity correlation function is shown to decay exponentially in the number of collisions with a decay rate which vanishes as the scatterers approach close packing. The crossover to power law decay at close packing is described by a scaling function.     

The computational complexity of the Lorentz lattice gas

The Lorentz lattice gas is studied from the perspective of computational complexity theory. It is shown that using massive parallelism, particle trajectories can be simulated in a time that scales logarithmically in the length of the trajectory. This result characterizes the logical depth of the Lorentz lattice gas and allows us to compare it to other models in statistical physics.     

Example of diffusion in a disordered Lorentz gas

We prove a diffusion law for a disordered Lorentz gas obtained by modification of a model of Gates, Gerst, Kac in Ref. 1, even though the motion is not a Markovian one in the technical sense of the word.     

Measures with infinite Lyapunov exponents for the periodic Lorentz gas

We study invariant measures for the periodic Lorentz gas which are supported on the set of points with infinite Lyapunov exponents. We construct examples of such measures which are measures of maximal entropy and ones which are not.     

On localization of vorticity in Lorentz lattice gases

We study the generalized deterministic Lorentz lattice gases, in a fixed as well as in varying environments, in lattices with dimensionsd3. We show that bounded orbits (vortices) in these models are often contained in some lower dimensional subsets (vortex sheets) of these lattices.     

Dynamical chaos in the Lorentz lattice gas

This paper provides an introduction to the applications of dynamical systems theory to nonequilibrium statistical mechanics, in particular to a study of nonequilibrium phenomena in Lorentz lattice gases with stochastic collision rules. Using simple arguments, based upon discussions in the mathematical literature, we show that such lattice gases belong to the category of dynamical systems with positive Lyapunov exponents. This is accomplished by showing how such systems can be expressed in terms of continuous phase space variables. Expressions for the Lyapunov exponent of a one-dimensional Lorentz lattice gas with periodic boundaries are derived. Other quantities of interest for the theory of irreversible processes are discussed.     

Molecular dynamics simulation of a graphite-supported copper nanocluster: thermodynamic properties and gas adsorption

Molecular dynamics simulations were conducted for a cubic Cu cluster supported on a graphite bilayer. The Sutten–Chen and Lennard–Jones potentials were used for metal–metal and metal–graphite interactions, respectively. Heating and cooling processes were performed by NVT simulations at different temperatures in the range 200 to 1800?K. The melting point was identified on the basis of caloric and heat capacity curves. The calculated melting point was 770?K, far below the bulk melting point of crystalline copper. Several phenomena such as the appearance of a hysteresis (irreversibility) in caloric curves, surface melting, and cluster-induced surface wetting were justified from the results. The simulation of cluster in the presence of gas atmosphere showed that the CO gas is adsorbed more than H₂ and it has a greater impact on the cluster's structure.     

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.     

Correlation dimension of the sheared hard-disk Lorentz gas

The correlation dimension for the isokinetic Lorentz gas is calculated for hard disks using nonequilibrium molecular dynamics simulation. The trajectories are confined to a strange attractor embedded in a four-dimensional phase space—the additional degree of freedom having not been included properly until this work. This degree of freedom accounts for the explicit time dependence of the system (as quantified by the moving periodic cells under shear) and is significant because the collisions tend to synchronize with the periodic change of symmetry of the lattice at high shear rates.     

Deviations from Fick's law in Lorentz gases

We have calculated the self-dynamic structure factorF(k,t) for tagged particle motion in hopping Lorentz gases. We find evidence that, even at long times, the probability distribution function for the displacement of the particles is highly non-Gaussian. At very small values of the wave vector this manifests itself as the divergence of the Burnett coefficient (the fourth moment of the distribution never approaching a value characteristic of a Gaussian). At somewhat larger wave vectors we find thatF(k,t) decays algebraically, rather than exponentially as one would expect for a Gaussian. The precise form of this power-law decay depends on the nature of the scatterers making up the Lorentz gas. We find different power-law exponents for scatterers which exclude certain sites and scatterers which do not.     

Exact solutions to the time-dependent Lorentz gas Boltzmann Equation: The approach to hydrodynamics

New exact solutions to the time-dependent Lorentz gas Boltzmann equation are presented for two classes of nonequilibrium initial value problems: thedecay of localized disturbances and theresponse to applied electric fields. These exact results are used to gain some insight into the crossover of the nonequilibrium state from the early-timekinetic regime to the late-timehydrodynamic regime.     

Dynamical properties of water in living cells

With the aim of studying the effect of water dynamics on the properties of biological systems, in this paper, we present a quasi-elastic neutron scattering study on three different types of living cells, differing both in their morphological and tumor properties. The measured scattering signal, which essentially originates from hydrogen atoms present in the investigated systems, has been analyzed using a global fitting strategy using an optimized theoretical model that considers various classes of hydrogen atoms and allows disentangling diffusive and rotational motions. The approach has been carefully validated by checking the reliability of the calculation of parameters and their 99% confidence intervals. We demonstrate that quasi-elastic neutron scattering is a suitable experimental technique to characterize the dynamics of intracellular water in the angstrom/picosecond space/time scale and to investigate the effect of water dynamics on cellular biodiversity.     

铜原子纳米团簇热力学性质的分子动力学模拟研究

利用分子动力学模拟方法,研究了CuN(N=80,140,216,312,408,500,628和736)纳米团簇在热化和冷凝过程中结构和热力学性质的变化,模型采用的是Johnson的EAM作用势.模拟结果表明:铜团簇的熔点和凝固点随其尺寸线性增加,并逐渐向大块晶体靠拢;所有团簇的凝固点都低于熔点,出现凝固过程中的滞后现象;在熔点和凝固点附近,团簇都具有负热容特性,负热容是由相变前后团簇内部结构突变引起的.     

洛伦兹光束的传输特性研究

运用光束传输的二阶矩理论,对洛伦兹光束的传输特性进行了研究,给出了束腰、横向发散角和光束传输因子的表达式.横向束腰仅取决于对应方向上的光束参数;而横向发散角和光束传输因子却取决于两横向上的光束参数.给出了光束传输因子随两横向光束参数的变化关系曲线.结果表明,两横向上的光束传输因子随两光束参数的变化规律是不相同的,而整体的光束传输因子随两光束参数的变化是前两者的综合体现;但在傍轴情形下,光束传输因子趋向于常数141,因此,对于相同束腰,其傍轴条件下的发散性为对应高斯光束的141倍.所以,洛伦兹光束适合用于描述某些发散程度较大的激光光源. 关键词： 洛伦兹光束 光束传输 二阶矩