Nonequilibrium lattice models: Series analysis of steady states

A perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state. The expansion is expressed directly in terms of the kinetic parameter (creation rate), rather than in powers of the interaction. An algorithm for generating series expansions for local properties is described. Order parameter series (16 terms) and precise estimates of critical properties are presented for the one-dimensional contact process and several related models.     

Collision of spinning particles near BTZ black holes

We study the collision property of spinning particles near a Ba?ados-Teitelboim-Zanelli(BTZ)black hole.Our results show that although the center-of-mass energy of two ingoing particles diverges if one of the particles possesses a critical angular momentum,the particle with critical angular momentum cannot exist outside of the horizon due to violation of the timelike constraint.Further detailed investigation indicates that only a particle with a subcritical angular momentum is allowed to exist near an extremal rotating BTZ black hole,and the corresponding collision center-of-mass energy can be arbitrarily large in a critical angular momentum limit.     

The kinetics of adsorption to a one-dimensional lattice with nearest-neighbor exclusion: A series expansion study

Exact 15-term series expansions are given for the cooperative kinetics of adsorption of particles to a one-dimensional lattice with nearest-neighbor exclusion. Padé approximants to various forms of the series accurately describe the relaxation process, which is found to be well-approximated by assuming instantaneous internal equilibrium on the lattice. The series do not describe the very last stages of decay to equilibrium well and it has not been possible to extract from them the limiting relaxation parameters. The series show that the rate of change of the particle density on the lattice is not analytic in the density when expanded about the equilibrium state.     

Probing a subcritical instability with an amplitude expansion: An exploration of how far one can get

We explore methods to locate subcritical branches of spatially periodic solutions in pattern forming systems with a nonlinear finite-wavelength instability. We do so by means of a direct expansion in the amplitude of the linearly least stable mode about the appropriate reference state which one considers. This is motivated by the observation that for some equations fully nonlinear chaotic dynamics has been found to be organized around periodic solutions that do not simply bifurcate from the basic (laminar) state. We apply the method to two model equations, a subcritical generalization of the Swift–Hohenberg equation and a novel extension of the Kuramoto–Sivashinsky equation that we introduce to illustrate the abovementioned scenario in which weakly chaotic subcritical dynamics is organized around periodic states that bifurcate “from infinity” and that can nevertheless be probed perturbatively. We explore the reliability and robustness of such an expansion, with a particular focus on the use of these methods for determining the existence and approximate properties of finite-amplitude stationary solutions. Such methods obviously are to be used with caution: the expansions are often only asymptotic approximations, and if they converge their radius of convergence may be small. Nevertheless, expansions to higher order in the amplitude can be a useful tool to obtain qualitatively reliable results.     

Efficient simulation of chemical potentials and phase equilibria in associating fluids: monomer/dimer insertion versus gradual particle insertion in primitive water models

Widom's test particle method for simulation of chemical potentials fails for associating (network forming) fluids. Therefore we study more sophisticated insertion methods, such as gradual particle insertion and the recent unbonded particle insertion of Tripathi and Chapman. We model strongly associating fluids by short-ranged primitive models (PMs) due to Nezbeda and co-workers. Recently, we showed that gradual insertion, in principle, is applicable to PM water. Here, we study systematically subcritical chemical potential isotherms, determine vapour–liquid coexistence densities and estimate the critical point density and temperature. For comparison we implement two variants of the Tripathi–Chapman algorithm. In the first case we use as unbonded test particles only particles which remain single molecules (monomers), when inserted and in the second case such test particles which remain as single molecules or form a two-particle cluster with an existing free molecule (monomer/dimer), when inserted. While monomer insertion improves Widom's method slightly, monomer/dimer insertion extends substantially the range of application to the subcritical temperatures studied by gradual insertion. But, for low temperatures monomer/dimer insertion requires extremely long Markov chains and significantly more computer time than gradual insertion. The Tripathi–Chapman algorithm—a direct extension of Widom's method—is much simpler than gradual insertion and therefore should be preferred at supercritical and critical conditions.     

Kinetics of nucleation of the solid phase in supercooled solutions or liquids under heat-insulating conditions: Intensive nucleation stage

The kinetics of decomposition of a supercooled melt or a viscous fluid under heat-insulating conditions during intensive nucleation has been investigated. Particles of a new phase have been studied, whose size is larger than the critical value, and for which the times are longer than the settling time of the classical quasi-steady state, which is characteristic of subcritical nuclei. The heat removal from the phase boundary is assumed to be the key process in the vicinity of a growing particle. The estimates of the duration of the stage of intensive nucleation, the maximum number of nucleated particles, and their average “size” have been obtained. Numerical simulations have been performed for nickel.     

Kawasaki Dynamics with Two Types of Particles: Critical Droplets

This is the third in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and are interested in the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. In the first paper we identified the parameter range for which the system is metastable, showed that the first entrance distribution on the set of critical droplets is uniform, computed the expected transition time up to and including a multiplicative factor of order one, and proved that the nucleation time divided by its expectation is exponentially distributed, all in the limit of low temperature. These results were proved under three hypotheses, and involved three model-dependent quantities: the energy, the shape and the number of critical droplets. In the second paper we proved the first and the second hypothesis and identified the energy of critical droplets. In the third paper we prove the third hypothesis and identify the shape and the number of critical droplets, thereby completing our analysis. Both the second and the third paper deal with understanding the geometric properties of subcritical, critical and supercritical droplets, which are crucial in determining the metastable behavior of the system, as explained in the first paper. The geometry turns out to be considerably more complex than for Kawasaki dynamics with one type of particle, for which an extensive literature exists. The main motivation behind our work is to understand metastability of multi-type particle systems.     

Conservative ensembles for nonequilibrium lattice-gas systems

We show how to set up a constant particle ensemble for the steady state of nonequilibrium lattice-gas systems which originally are defined on a constant rate ensemble. We focus on nonequilibrium systems in which particles are created and annihilated on the sites of a lattice and described by a master equation. We consider also the case in which a quantity other than the number of particle is conserved. The conservative ensembles can be useful in the study of phase transitions and critical phenomena particularly discontinuous phase transitions.     

Algebra for fermions with a new exclusion principle

We construct the algebra of the creation and destruction operators for spin 1/2 particles obeying a new exclusion principle which is “more exclusive” than Pauli’s exclusion principle: an orbital state shall not contain more than one particle, whether spin up or spin down. The consequences of this algebra are studied and applications to the Hubbard model in condensed matter physics are indicated. An erratum to this article is available at .     

二粒子部分纠缠未知态的量子受控传递

提出了二粒子部分纠缠态的量子隐形传递控制方案.在该方案中,以四个二能级粒子GHZ态作为量子通道,把量子通道中的一个粒子作为控制粒子.在传递者和控制者进行一系列的量子操作和测量之后,根据他们的测量结果,接收者再进行适当的变换就能得到待传递粒子的量子态.     

Structure of supercritical water: The concept of critical isotherm as a percolation threshold

Computer simulations are used to study the rearrangements of hydrogen-bonded structures of water upon transition to the supercritical state. It is shown that the destruction of the infinite hydrogen-bonded cluster, i.e., crossing the percolation threshold occurs in the subcritical region and that, at the critical temperature, structural variations reach the point where the fluid acquires the properties of a system with two types of ordering. The existence of tetrahedral clusters in supercritical water is confirmed only at high pressure.     

双分散颗粒体系在临界堵塞态的结构特征

堵塞行为是颗粒体系中一种常见的现象,其力学性质与堆积结构的关联非常复杂.本文采用离散元法研究了由两种不同半径颗粒组成的二维双分散无摩擦球形颗粒体系在临界堵塞态所呈现的结构特征,讨论了大小颗粒粒径比与大颗粒百分比对临界堵塞态的影响.数值模拟结果表明,当粒径比小于1.4时,临界平均接触数与大颗粒百分比关系不大,当粒径比大于1.4时随着大颗粒百分比的增大临界平均接触数先减小再增大.而临界体积分数在粒径比小于1.8时随着大颗粒百分比的增加先减小后增大,大于1.8时又基本不随大颗粒百分比而变化.大颗粒百分比在接近0或1时,系统近似为单分散体系,临界平均接触数与体积分数基本不随半径比的增大而变化;在接近0.5时,临界平均接触数随着半径比的增大逐渐减小,而临界体积分数则是先减小后增大.文中对大-小颗粒这一接触类型的百分比也进行了探讨,其值随着大颗粒百分比的增大呈二次函数的变化趋势,粒径比对这一变化趋势只有较小的影响.     

Statistical mechanics of systems nonlinearly displaced from equilibrium I

A graphical approach is used to extend the response theory expression for nonequilibrium averages to any arbitrry order in deviations from equilibrium. Various ways in which the perturbation series about equilibrium can be resummed into gradient or Chapman-Enskog like expansions are presented. As a matter of illustration, examples from the hydrodynamics of simple fluids and the motion of a Brownian particle are considered. Specifically the normal stresses, shear dependent viscosity and velocity dependent friction constant are examined.     

A new solution to the problem of scattering of a plane wave by a multilayer confocal spheroid

We have constructed a solution to the problem of scattering by a nonconfocal multilayer particle. The main difficulty was to join expansions constructed in two spheroidal systems on either side of each boundary. As a result of a detailed consideration of relations between scalar wave spheroidal and spherical functions, we have succeeded in finding a representation of the former in terms of the latter and vice versa. In the final form, the joining of solutions is described by only one matrix, which depends on coefficients of representations of angle spheroidal functions in terms of associated Legendre functions of the first kind. Since the problem has been solved using an approach that involves the method of extended boundary conditions, the dimension of the system for numerical determining unknown coefficients is equal to the number of terms that are taken into account in field expansions and does not depend on the number of particle layers. Previously performed numerical calculations for confocal particles have shown a very high efficiency of the algorithm not only for particles that are close to spheres in shape, but also for strongly prolate and strongly oblate spheroids. In addition, the algorithm makes it possible to calculate optical properties of particles that have dozens of layers.     

Cluster formation in dispersion systems: Oil and micellar systems

Solutions of hydrated reversed micelles and mixtures of distillate cracking residue and light catalytic gas oil are studied by the methods of correlation spectroscopy of scattered light and polarized fluorescence, respectively. The temperature dependences of the particle size of the disperse phase are obtained. It is found that the particle size increases with temperature in the range from room temperature to the critical temperature, which depends on the composition of the system under investigation, at temperatures above the critical temperature, the particle size decreases. These dependences can be explained by the formation of clusters from particles of the disperse phase at temperatures below the critical temperature and subsequent destruction of these clusters. Therefore, the structures of model (micellar) and natural (oil) disperse systems are compared for the first time, and the correlation between their behavior upon heating is revealed.     

Ion specificity and the theory of stability of colloidal suspensions

A theory is presented which allows us to accurately calculate the critical coagulation concentration of hydrophobic colloidal suspensions. For positively charged particles, the critical coagulation concentrations follow the Hofmeister (lyotropic) series. For negatively charged particles, the series is reversed. We find that strongly polarizable chaotropic anions are driven towards the colloidal surface by electrostatic and hydrophobic forces. Within approximately one ionic radius from the surface, the chaotropic anions lose part of their hydration sheath and become strongly adsorbed. The kosmotropic anions, on the other hand, are repelled from the hydrophobic surface. The theory is quantitatively accurate without any adjustable parameters. We speculate that the same mechanism is responsible for the Hofmeister series that governs stability of protein solutions.     

Cluster size distribution and scaling for spherical particles and red blood cells in pressure-driven flows at small Reynolds number

The clustering characteristic of purely hydrodynamically interacting particles suspended in pressure-driven flow in a circular cylinder is studied using direct numerical simulation based on the solution of the lattice-Boltzmann equation. We find a universal scaling relation for the cluster size distribution in the subcritical regime for all of the cases considered in this study. This scaling relation is independent of particle shape and concentration.     

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequilibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such a system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.     

A Purely Probabilistic Representation for the Dynamics of a Gas of Particles

The aim of the present paper is to give a purely probabilistic account for the approach to equilibrium of classical and quantum gas. The probability function used is classical. The probabilistic dynamics describes the evolution of the state of the gas due to unary and binary collisions. A state change amounts to a destruction in a state and the creation in another state. Transitions probabilities are splittled into destructions terms, denoting the random choice of the colliding particle(s), and creation terms, describing the allocation of the same particle(s) on the final state(s). While the destruction term is the same for all types of particles, the creation one depends upon a parameter bound to the interpraticle correlation. The transition probabilities give rise to a homogeneous Markov chain. The equilibrium distributions satisfy the principle of detailed balance. Relaxation times depend upon the interparticle correlation. Relationships with the Ehrenfest urn model, Brillouin unified method, ensemble interpretation, and quantum H-theorem are considered too.