Distribution of a Particle’s Position in the ASEP with the Alternating Initial Condition

In this paper we give the distribution of the position of a particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find ℙ(X _m (t)≤x) where X _m (t) is the position of the particle at time t which was at m=2k−1, k∈ℤ at t=0. As in the ASEP with step initial condition, there arises a new combinatorial identity for the alternating initial condition, and this identity relates the integrand of the integral formula for ℙ(X _m (t)≤x) to a determinantal form together with an extra product.     

A Fredholm Determinant Representation in ASEP

In previous work (Tracy and Widom in Commun. Math. Phys. 279:815–844, 2008) the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice ℤ. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers ℤ⁺ and consider the distribution function for the mth particle from the left. In Tracy and Widom (Commun. Math. Phys. 279:815–844, 2008) an infinite series of multiple integrals was derived for the distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.     

On ASEP with Step Bernoulli Initial Condition

This paper extends earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)     

Current Moments of 1D ASEP by Duality

We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Schütz. For the ASEP on the infinite lattice we show that the nth moment is reduced to the problem of the ASEP with less than or equal to n particles.     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is z=1 rather than the KPZ exponent z=3/2 which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.     

Applicability of the Hydrodynamic Approach to the Electron Component in Plasmachemical Reactors of a Beam Plasma Type

In the present work the question of the possible use of the hydrodynamic approach for describing a plasma beam discharge is investigated. It is shown that the condition ν_ei > (ν_ei + ν_en) X W/nT is the Maxwelliazation criterion of moderate energy particles in a plasma beam discharge. In this case the value of moderate energy is less than 3÷4 values of plasma electrons thermal ernergy. The influence of the tail of the distribution function on electron heating is considered qualitatively.     

The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line

In this paper we find explicit formulas for: (1) Green’s function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for the one-dimensional asymmetric simple exclusion process (ASEP) with particles confined to the nonnegative integers. These are both for systems with a finite number of particles. The formulas are analogous to ones obtained earlier for the Bose gas and ASEP on the line and integers, respectively. We use coordinate Bethe Ansatz appropriately modified to account for confinement of the particles to the half-line. As in the earlier work, the proof for the ASEP is less straightforward than for the Bose gas.     

Fatigue in precipitation hardened materials: a three-dimensional discrete dislocation dynamics modelling of the early cycles

Three-dimensional dislocation dynamics (DD) fatigue simulations in precipitation hardened metals is a major challenge in terms of numerical development. Several precipitate configurations have been investigated with an original treatment of precipitate–dislocation interactions and a parallelized DD code. In grains containing single-sized shearable particles (r _p?=?160?nm), strain is localized in clear bands where the precipitates are totally sheared-off. The fatigue behaviour involves an initial hardening followed by severe cyclic softening and significant surface slip irreversibility. In the presence of large single-sized particles (r _p?=?400?nm), the persistent slip band (PSB) structure is accompanied by highly reversible surface displacements. Slip dispersion originates from Orowan loops that have little effect on the mechanical response. The mechanical behaviour of a bimodal distribution is intermediate between the two above cases with the above microstructural features coexisting within the same grain. Unlike in the monomodal large-particle case, where all the particles retain their initial strength, some of the large particles of the bimodal distribution undergo a significant strength reduction.     

Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile

We show how to apply the macroscopic fluctuation theory (MFT) of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim to study the current fluctuations of diffusive systems with a step initial condition. We argue that one has to distinguish between two ways of averaging (the annealed and the quenched cases) depending on whether we let the initial condition fluctuate or not. Although the initial condition is not a steady state, the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem. We show how the equations of the MFT can be solved in the case of non-interacting particles. The symmetry of these equations can be used to deduce the distribution of the current for several other models, from its knowledge (Derrida and Gerschenfeld in J. Stat. Phys. 136, 1–15, 2009) for the symmetric simple exclusion process. In the range where the integrated current $Q_{t}\sim\sqrt{t}$ , we show that the non-Gaussian decay exp?[?Q _t ³ /t] of the distribution of Q _t is generic.     

Shock profiles for the asymmetric simple exclusion process in one dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at ratesp and 1-p (herep > 1/2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers’ equation; the latter has shock solutions with a discontinuous jump from left density ρ- to right density ρ+, ρ-< ρ +, which travel with velocity (2p−1 )(1−ρ₊−p ₋). In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time-invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice siten, measured from this particle, approachesp _± at an exponential rate asn→ ±∞, witha characteristic length which becomes independent ofp when . For a special value of the asymmetry, given byp/(1−p)=p ₊(1−p ₋)/p ₋(1−p ₊), the measure is Bernoulli, with densityρ ₋ on the left andp ₊ on the right. In the weakly asymmetric limit, 2p−1 → 0, the microscopic width of the shock diverges as (2p+1)^-1. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.     

On the asymptotical normality of statistical solutions for harmonic crystals in half-space

We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial date is a random function with zero-mean, finite-mean energy density which also satisfies a mixing condition of Rosenblatt or Ibragimov type. We study the distribution μ _t of the solution at time t ∈ ℝ. The main result is the convergence of μ _t as t → ∞ to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian in general). Supported partly by research grant of RFBR (06-01-00096).     

An optimised molecular model for ammonia

Based on molecular dynamics (MD) computer simulations we investigate the dynamic behaviour of a model complex fluid suspension consisting of large (A) particles (the ‘solute’) immersed in a bath of smaller ‘solvent’ (B) particles. The goal is to identify the effect of systematic simplifications (coarse-graining) of the solvent on typical microscopic time correlation functions characterizing the single-particle and collective dynamics of the solute. As a reference system we employ a binary Lennard–Jones mixture of spherical particles with significant differences in particle sizes (σ_A>σ_B) and masses (m _A>m _B). We then replace the original B particles step by step by a reduced number of larger and heavier particles such that the mass and volume fraction of B particles is kept constant. At each step of coarse-graining, the intermolecular interactions between A particles are chosen such that the static A–A structure of the reference system is preserved. Our MD results indicate that coarse-graining has a profound influence on both the single-particle dynamics as reflected by the self-diffusion constant and the collective dynamics represented by the distinct part of the van Hove time correlation function. The latter holds only at intermediate packing fractions, whereas the collective dynamics turns out to be essentially insensitive to coarse-graining at high packing fractions.     

Diffusion-annihilation and the kinetics of the Ising model in one dimension

The relationship between the one-dimensional kinetic Ising model at zero temperature and diffusion-annihilation in one dimension is studied. Explicit asymptotic results for the average domain size, average magnetization squared, and pair-correlation function are derived for the Ising model, for arbitrary initial magnetization. For the case of zero initial magnetization (m ₀=0, a number of recent exact results for diffusion-annihilation with random initial conditions are obtained. However, for the casem ₀ not equal to zero, the asymptotic behavior turns out to be different from diffusion-annihilation with random initial conditions and at a finite density. In addition, in contrast to the case of diffusion-annihilation, the domain-size distribution scaling functionh(x) is found to depend nontrivially on the initial magnetization. The origin of these differences is clarified and the existence of nontrivial correlations in the initial wall distribution for finite initial magnetization is found to be responsible for these differences. Results of Monte Carlo simulations for the domain size distribution function for different initial magnetizations are also presented.This paper is dedicated to George Weiss on the occasion of his 60th birthday.     

TiO2/ZnO纳米薄膜界面热导率的分子动力学模拟

采用平衡分子动力学方法及Buckingham势研究了金红石型TiO₂薄膜与闪锌矿型ZnO薄膜构筑的纳米薄膜界面沿晶面[0001](z轴方向)的热导率.通过优化分子模拟初始条件中的截断半径r_c和时间步后,计算并分析了平衡温度、薄膜厚度、薄膜截面大小对热导率的影响.研究表明,薄膜热导率受薄膜温度和厚度的影响很大,当温度由300 K升高600 K时,薄膜的热导率逐渐减小;当薄膜厚度由1.8 nm增大到5 nm时,热导率会逐渐增大;并在此基础 关键词： 热导率 分子动力学 2/ZnO纳米薄膜界面')" href="#">TiO₂/ZnO纳米薄膜界面 数值模拟     

Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity

In deformed or doubly special relativity (DSR) the action of the lorentz group on momentum eigenstates is deformed to preserve a maximal momenta or minimal length, supposed equal to the Planck length, l_p = ?{(^h/_2p) G}{l_p = \sqrt{\hbar G}}. The classical and quantum dynamics of a particle propagating in κ-Minkowski spacetime is discussed in order to examine an apparent paradox of locality which arises in the classical dynamics. This is due to the fact that the lorentz transformations of spacetime positions of particles depend on their energies, so whether or not a local event, defined by the coincidence of two or more particles, takes place appears to depend on the frame of reference of the observer. Here it is proposed that the paradox arises only in the classical picture, and may be resolved when the quantum dynamics is taken into account. If so, the apparent paradoxes arise because it is inconsistent to study physics in which (^h/_2p) = 0{\hbar =0} but l_p = ?{(^h/_2p) G} 1 0{l_p = \sqrt{\hbar G}\neq 0}. This may be relevant for phenomenology such as observations by FERMI, because at leading order in l _p × distance there is both a direct and a stochastic dependence of arrival time on energy, due to an additional spreading of wavepackets.     

Quantum Equilibrium Distributions of Displacements and Momenta of Particles in Molecules and Solids

The quantum equilibrium distribution, ?Qm, of an arbitrary number, m, of momentum or displacement components is determined for atoms that are part of a polyatomic molecule or a solid. This is shown to be a multidimensional Gaussian distribution. Two cases are considered: (1) the motion of the system as a whole is given, (2) it is in itself determined by the statistical equilibrium conditions. In the first case we obtain distributions for the vibrational momenta and displacements and in the second for the total momenta, including the momenta of vibrational, translational and rotational motions. The distributions for momenta and displacements of one particle and for the maximum number of linearly independent components of momenta and displacements of all particles of the system are considered as particular cases. It is shown that the averaging of any function, F_m, depending on an arbitrary number, m, of components of displacements or momenta of particles, over the canonical ensemble is reduced to the integration of this function weighted by ?Qm over all its arguments between infinite limits.     

Multiply connected Fermi sphere and fermion condensation

We examine the structure of the ground state of a homogeneous Fermi liquid beyond the instability point of the Fermi-like quasiparticle momentum distribution in the effective-functional method with a strong repulsive effective interaction. A numerical study of the initial stage of rearrangement of the ground state, based on a simple effective functional, showed that there exists a temperature T ₀, above which the behavior of the system is the same as in the theory of fermion condensation, and for T<T ₀ the scenario of rearrangement of the ground state is different. At low temperatures an intermediate structure arises, with a multiply connected quasiparticle momentum distribution. The transition of this structure with growth of the coupling constant to a state with a fermion condensate is discussed. Zh. éksp. Teor. Fiz. 114, 2078–2088 (December 1998)     

Universal Large-Deviation Function of the Kardar–Parisi–Zhang Equation in One Dimension

Using the Bethe ansatz, we calculate the whole large-deviation function of the displacement of particles in the asymmetric simple exclusion process (ASEP) on a ring. When the size of the ring is large, the central part of this large deviation function takes a scaling form independent of the density of particles. We suggest that this scaling function found for the ASEP is universal and should be characteristic of all the systems described by the Kardar–Parisi–Zhang equation in 1+1 dimension. Simulations done on two simple growth models are in reasonable agreement with this conjecture.