Lattice gas model for O on Ni(110)

We consider the unusual behavior of the chemisorption system O on Ni(110). At a coverage of about$\text{1}\text{3}$, as the temperature is increased from room temperature to about 300°C, a wellordered (3 × 1) structure changes reversibly into a poorly organized (2 × 1) structure. This has been observed for a Ni crystal saturated with oxygen in the interior. We propose a two-dimensional lattice gas model with anisotropic and competing interactions between the adsorbed atoms to explain this behavior. Monte Carlo calculations on a 30 × 30 lattice show a transition of this type for coverages near$\text{1}\text{3}$.     

Lattice gas simulations of osmosis

An analysis of the phenomenon of osmosis within the lattice gas model is presented. The model considered is a two-species version of the Frisch-Hasslacher-Pomeau model with rest particles and a semipermeable membrane which is implemented as a boundary that blocks one species, but lets the other pass freely. In this way the equilibrium between a pure and a mixed subsystem can be studied. Analytic expressions for both the pressure difference and the fluctuations of this quantity are obtained from the entropy function for the lattice gas, and we find that these results are in good agreement with those obtained from simulation. The osmotic flow across the membrane is also studied. We characterize the concentration boundary layer, and an analytic expression for the osmotic permeability as a function of porosity is compared with results from simulations.     

Lattice gas automata for simple and complex fluids

We review some recent applications of lattice gas automata, including flow through porous media, phase transitions, thermodydrodynamics, and magnetohydrodynamics.     

Lattice gas generalization of the hard hexagon model. III.q-Trinomial coefficients

In the first two papers in this series we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites, and we described the local densities in terms of elliptic theta functions. Here we present the mathematical theory behind our derivation of the local densities. Our work centers onq-analogs of trinomial coefficients.     

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ _m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.     

Lattice model for colloidal gels and glasses

We study a lattice model of attractive colloids. It is exactly solvable on sparse random graphs. As the pressure and temperature are varied, it reproduces many characteristic phenomena of liquids, glasses, and colloidal systems such as ideal gel formation, liquid-glass phase coexistence, jamming, or the re-entrance of the glass transition.     

Deuteron NMR study of monolayer thick films of nematogenic molecules

We present a deuteron NMR study of molecular thickness films of a nematogenic material in cylindrical pores. Compared to liquid crystal in bulk or completely filling the pores, a reduced quadrupole splitting is found. It strongly depends on thickness, but only weakly on temperature, even crossing the bulk nematic-isotropic transition. This demonstrates the presence of a 2D-like film that eventually coexists with a bulklike phase suggesting a dewetting behavior. Motionally averaged angular patterns with biaxiallike features reveal unexpectedly fast surface molecular diffusion.     

Lattice gas models with competing interactions

The phase diagrams of lattice gas models on square and centred rectangular lattices with short range competing pair interactions and three-body forces are studied using Monte Carlo techniques and the transfer matrix method. A variety of commensurate (C) phases can be described as observed experimentally for adsorbed monolayers like H on Pd(100), O on W (110) and especially H on Fe(110). In addition, due to the competition between different C phases incommensurate (IC) structures may occur. Their properties and related aspects (C-IC transitions, disorder lines) are discussed in connection with the widely studied ANNNI model, and general concepts on two-dimensional C and IC phases and experiments. Also dynamic properties — such as the self-diffusion of the adsorbate at the surface — are briefly mentioned.     

Phase-field model for the morphology of monolayer lipid domains

Phase-separated domains exist in multicomponent lipid monolayers and bilayers. We present here a phase-field model that takes into account the competition between lipid dipole-dipole interactions and line tension to define the domain morphology. A dynamic equation for the phase-field is solved numerically showing stationary non-circular shapes like starfish shapes. This phase-field model could be applied to study the dynamic properties of complex problems like phase segregation in pulmonary surfactant membranes and films.     

Lattice tube model of proteins

We present a new lattice model for proteins that incorporates a tubelike anisotropy by introducing a preference for mutually parallel alignments in the conformations. The model is demonstrated to capture many aspects of real proteins.     

Lattice Boltzmann model for anisotropic liquid-solid phase transition

We develop a simple reaction model for the liquid-solid phase transition in the context of the lattice Boltzmann method with enhanced collisions. Calculations for a two-dimensional test problem of Ga melting and for a two-dimensional anisotropic growth of dendrites are presented and commented on.     

Lattice gas activity series from secular equations

The secular equations for finite tori of lattice sites are obtained by computer expansion of determinants for a hard-particle lattice gas. The secular equations yield all of the thermodynamic functions for finite systems and the beginning terms of activity expansions for all of the eigenvalues of the infinite system. The same secular equation that yields the low-density series for the equation of state of the infinite-circumference system also yields the beginning terms in the highdensity expansion. As examples we treat two hard-particle lattice gases in two dimensions, the lattice gas with nearest-neighbor exclusion (which has a secondorder transition), and the case of dimers (which is analytic all the way to close packing).     

Lattice gas with “interaction potential”

We present an extension of a simple automaton model to incorporate nonlocal interactions extending over a spatial range in lattice gases. From the viewpoint of statistical mechanics, the lattice gas with interaction range may serve as a prototype for non-ideal-gas behavior. From the density fluctuations correlation function, we obtain a quantity which is identified as a potential of mean force. Equilibrium and transport properties are computed theoretically and by numerical simulations to establish the validity of the model at macroscropic scale.     

Single- and multigrain nanojunctions with a self-assembled monolayer of conjugated molecules

Systematic conductivity measurements in nanoscale junctions containing a self-assembled monolayer of conjugated molecules are reported. Different conductivity mechanisms are identified depending on the granularity of the metal used as a substrate for assembling the monolayer. Unexpectedly, the energy scale controlling the dominant conductance channels is quite low in comparison with the molecular level spacing. In single-grain junctions, the dominant conductance mechanism is hopping with an energy scale of the order of 10-100 meV determined by the nature of the metal contacts. In the case of multigrain junctions, additional tunnel conductance is observed with low-energy Coulomb-blockade features.