Random anisotropy in lattice gas model

We consider a lattice-gas model with infinite-range interaction with site dependent random anisotropy distributed with a Gaussian distribution. The random anisotropy lattice-gas analogous of the random field Ising model is solved exactly using a replica theory. We show that, at finite temperature, the introduction of disorder eliminates completely the phase transition, and destroy the equivalence between real gases and Ising magnets. Whereas at T = 0, the density of occupied sites has a step-like behavior as function of the random anisotropy.     

Phase shift and attenuation characteristics of acoustic waves in a flowing gas confined by cylindrical walls

Wave propagation in flowing ideal gases confined by cylindrical waveguides is described in the low-frequency range using an iterative Frobenius series expansion method. The primary concern is to present a mathematical model enabling any radial-dependent flow profile to be analyzed. In contrast to previous analytical results, the present model is applicable in the general case where cubic and higher order terms in the axial acoustic velocity become important and to examine the influence of a non-vanishing radial velocity term. As a numerical test case, it is found that a gas flow velocity w(r)—for simplifying reasons assumed to be a linear combination of a flat flow profile and a parabolic flow profile corresponding to a mean flow equal to —is well approximated by a flat flow profile of the same mean flow value at low shear wavenumbers and at higher shear wavenumbers (calculations were done for shear wavenumbers up to 8). In actual fact, the error introduced by making this mean flow approximation is smaller than the error introduced by neglecting the radial velocity term.     

Three-phase equation of state by the lattice gas model

A rigid lattice gas model of solid-liquid, liquid-gas, and solid-gas transformations is proposed. The total free energy is separated into a lattice part and a vibrational correction part. It is reported that the vibrational part plays an important role in obtaining the gas, liquid and solid phases and the correct phase transitions. A method of combining the two lowest order approximations (single site, two-site) in the cluster variation method is suggested in describing the lattice free energy. The critical point and the triple point of argon are reproduced fairly well. Results are compared with the expandable lattice theory demonstrating the appropriateness of the present model in the vicinity of the triple point.     

A lattice gas model for thermohydrodynamics

The lattice gas model is extended to include a temperature variable in order to study thermohydrodynamics, the combination of fluid dynamics and heat transfer. The compressible Navier-Stokes equations are derived using a Chapman-Enskog expansion. Heat conduction and convection problems are investigated, including Bénard convection. It is shown that the usual rescaling procedure can be avoided by controlling the temperature.     

Damage spreading in a driven lattice gas model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T$T$, the magnitude of the external driving field E$E$, and the lattice size. The DLG model undergoes an order–disorder second-order phase transition at the critical temperature _Tc(E)$T_c\left(E\right)$, such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value _Dsat$D_{sat}$ that depends only on T$T$. _Dsat$D_{sat}$ increases for T<_Tc(E=∞)$T<T_c(E=\infty )$, decreases for T>_Tc(E=∞)$T>T_c(E=\infty )$ and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T$T$. Also, we investigated damage spreading for a range of finite fields as a function of T$T$, finding a behavior similar to that of the case with E=∞$E=\infty$.     

Multilayer lattice gas model in the quasichemical approximation

The multilayer lattice gas model is dealt with in the quasichemical approximation. A restriction on the atomic stacking is also introduced in the system so that an atom can occupy only a lattice site whose underlying nearest neighbor lattice sites are all occupied by atoms. The critical condensation of atoms is investigated as the substrate potential is varied. The theory is also applied to the surface roughening of the crystalline bulk.     

Slow quench dynamics of a one-dimensional Bose gas confined to an optical lattice

We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.     

Layered lattice gas model for the metal-electrolyte interface

Several models of the diffuse double layer in liquid electrolytes are discussed. These models all involve partitioning the space charge region into a number of planar layers parallel to the metal electrode, with ionic liquid lattice gas, as opposed to idea gas, response in each layer. Each layer may contain both ions and solvent molecules. Several difficulties implicit in the earlier work of Liu on such a model are pointed out. These problems seem to have caused the appearance of an initial charge-free region in Liu's results. A layer model involving Liu's original assumptions of point ionic charges and point dipoles is discussed in detail and is shown to be electrostatically inconsistent. It is replaced by a layer model in which ionic charge resides on each basic layer, with each such layer surrounded symmetrically by charge layers representing the effect of finite-extent permanent dipoles. This model leads, as it should, to Gouy-Chapman behavior in the continuum limit. Finally, a method of including ion hydration effects explicitly in such a model is proposed.     

Gauge-invariant lattice gas for the microcanonical Ising model

We introduce a lattice gas for particles with discrete momenta (1, 0, –1) and local deterministic microdynamics, which exactly reproduces Creutz's microcanonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.     

Critical behavior of two-dimensional magnetic lattice gas model

Using Monte Carlo simulations and finite-size scaling, we investigate the critical behavior of two-dimensional magnetic lattice gas at densities ρ = 0.90, 0.95, 1.0. There is a ferromagnetic phase transition at each density. As expected, the critical temperature T _c depends on system density ρ. Unexpectedly, there is a density dependence of the critical exponent of correlation length ν. For densities ρ = 0.90,0.95,1.0, we obtain the inverse of critical exponent 1/ν = 0.835(5), 0.905(5), 1.00(1) respectively. It is found that the ratios of critical exponent β/ν and γ/ν of magnetization and susceptibility are independent of density.     

Critical point field mixing in an asymmetric lattice gas model

The field mixing that manifests broken particlehole symmetry, is studied for a 2-D asymmetric lattice gas model having tunable field mixing properties. Monte Carlo simulations within the grand canonical ensemble are used to obtain the critical density distribution for different degrees of particle-hole asymmetry. Except in the special case when this asymmetry vanishes, the density distributions exhibit an antisymmetric correction to the limiting scale-invariant form. The presence of this correction reflects the mixing of the critical energy density into the ordering operator. Its functional form is found to be in excellent agreement with that predicted by the mixed-fied finite-size-scaling theory of Bruce and Wilding. A computational procedure for measuring the signiffcant field mixing parameter is also described, and its accuracy gauged by comparing the results with exact values obtained analytically.     

Random walk and diffusion in a stochastic lattice gas model

The time evolution of the stochastic lattice gas with simple exclusion interaction is shown to converge in the thermodynamic limit and it is studied in the asymptotic regime of large time. The diffusion equation applies to the bulk transport of matter in an appropriate scaling limit. As regards the one-dimensional model, a conjecture by Spitzer is proved, stating that the distance travelled by a tagged particle is of the order of the fourth root of the elapsed time.Asymptotic exponents β and α are defined for more general models as giving the power law in time for the distances travelled by density fluctuations and tagged particles respectively. It is argued that α = β/2 should be valid for all one-dimensional models with exclusion.     

Domain walls confined in magnetic nanotubes with uniaxial anisotropy

We present calculations of the different domain wall structures confined in magnetic nanotubes, such as transverse wall, asymmetric vortex wall, branch fashion wall, and horse-saddle wall. The wall structures were calculated by micromagnetic simulations. The tube radii R=50 nm and 100 nm, and aspect ratios length/radius L/R≤15 were considered. The magnetic phase diagrams of the stability of different kinds of the domain walls were plotted as function of the tube aspect ratio L/R and the tube thickness (difference of the outer and inner tube radii).     

A heterogeneous lattice gas model for simulating pedestrian evacuation

Based on the cellular automata method (CA model) and the mobile lattice gas model (MLG model), we have developed a heterogeneous lattice gas model for simulating pedestrian evacuation processes in an emergency. A local population density concept is introduced first. The update rule in the new model depends on the local population density and the exit crowded degree factor. The drift D, which is one of the key parameters influencing the evacuation process, is allowed to change according to the local population density of the pedestrians. Interactions including attraction, repulsion, and friction between every two pedestrians and those between a pedestrian and the building wall are described by a nonlinear function of the corresponding distance, and the repulsion forces increase sharply as the distances get small. A critical force of injury is introduced into the model, and its effects on the evacuation process are investigated. The model proposed has heterogeneous features as compared to the MLG model or the basic CA model. Numerical examples show that the model proposed can capture the basic features of pedestrian evacuation, such as clogging and arching phenomena.     

The lattice gas model of fractional quantum hall effect

The two-dimensional interacting electron gas under a strong homogeneous magnetic field is approximated by the one-dimensional classical lattice gas. We show that in our model the eigenstates of the system approach single-particle Slater determinants in the large particle number limit. Cusps in the energy of our model are found at simple fractional occupations.     

Nuclear liquid-gas phase transition within the lattice gas model

We study the nuclear liquid-gas phase transition on the basis of a two-component lattice gas model. A Metropolis type of sampling method is used to generate microscopic states in the canonical ensemble. The effective equation of state and fragment mass distributions are evaluated in a wide range of temperatures and densities. A definition of the phase coexistence region appropriate for small systems is proposed. The caloric curve resulting from different types of freeze-out conditions are presented.