Nearest-neighbor Exclusion Research Articles

Hydrodynamic Limit for a Type of Exclusion Process with Slow Bonds in Dimension d ≥ 2

Let Λ be a connected closed region with smooth boundary contained in the d-dimensional continuous torus Td. In the discrete torus N-1TdN, we consider a nearest-neighbor symmetric exclusion process where occupancies of neighboring sites are exchanged at rates depending on Λ in the following way: if both sites are in Λ or Λc, the exchange rate is 1; if one site is in Λ and the other site is in Λc, and the direction of the bond connecting the sites is ej, then the exchange rate is defined as N-1 times the absolute value of the inner product between ej and the normal exterior vector to ∂Λ. We show that this exclusion-type process has a nontrivial hydrodynamical behavior under diffusive scaling and, in the continuum limit, particles are not blocked or reflected by ∂Λ. Thus, the model represents a system of particles under hard-core interaction in the presence of a permeable membrane which slows down the passage of particles between two complementary regions.

Critical behavior of hard-core lattice gases: Wang–Landau sampling with adaptive windows

Critical properties of lattice gases with nearest-neighbor exclusion are investigated via adaptive-window Wang–Landau sampling (WLS) on the square and simple cubic lattices, for which the model is known to exhibit an Ising-like phase transition. We study the particle density, order parameter, compressibility, Binder cumulant and susceptibility, in efforts to test WLS, which has been used quite widely in recent years, in the context of lattice gases. Of considerable interest is whether it is possible to estimate critical exponents reliably using WLS with adaptive windows. We find that the method yields results in fair agreement with exact values (in two dimensions) and numerical estimates (in three dimensions).

Solution Structure and Thermodynamics of 2′,5′ RNA Intercalation

As a means to explore the influence of the nucleic acid backbone on the intercalative binding of ligands to DNA and RNA, we have determined the solution structure of a proflavine-bound 2',5'-linked octamer duplex with the sequence GCCGCGGC. This structure represents the first NMR structure of an intercalated RNA duplex, of either backbone structural isomer. By comparison with X-ray crystal structures, we have identified similarities and differences between intercalated 3',5' and 2',5'-linked RNA duplexes. First, the two forms of RNA have different sugar pucker geometries at the intercalated nucleotide steps, yet have the same interphosphate distances. Second, as in intercalated 3',5' RNA, the phosphate backbone angle zeta at the 2',5' RNA intercalation site prefers to be in the trans conformation, whereas unintercalated 2',5' and 3',5' RNA prefer the -gauche conformation. These observations provide new insights regarding the transitions required for intercalation of a phosphodiester-ribose backbone and suggest a possible contribution of the backbone to the origin of the nearest-neighbor exclusion principle. Thermodynamic studies presented for intercalation of both structural RNA isomers also reveal a surprising sensitivity of intercalator binding enthalpy and entropy to the details of RNA backbone structure.

Quenched non-equilibrium central limit theorem for a tagged particle in the exclusion process with bond disorder

For a sequence of i.i.d. random variables $\{\xi_x : x\in \bb Z\}$ bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at $x$ (resp. $x+1$) jumps to $x+1$ (resp. $x$) at rate $\xi_x$. We examine a quenched nonequilibrium central limit theorem for the position of a tagged particle in the exclusion process with bond disorder $\{\xi_x : x\in \bb Z\}$. We prove that the position of the tagged particle converges under diffusive scaling to a Gaussian process if the other particles are initially distributed according to a Bernoulli product measure associated to a smooth profile $\rho_0:\bb R\to [0,1]$.

One Dimensional Nearest Neighbor Exclusion Processes in Inhomogeneous and Random Environments

The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of, nonreversible stationary distributions. In the case of an i.i.d. environment, these combine to give a necessary and sufficient condition for the existence of nonreversible stationary distributions.

Antitumor Activity, X-ray Crystal Structure, and DNA Binding Properties of Thiocoraline A, a Natural Bisintercalating Thiodepsipeptide

The marine natural product thiocoraline A displayed approximately equal cytotoxic activity at nanomolar concentrations in a panel of 12 human cancer cell lines. X-ray diffraction analyses of orthorhombic crystals of this DNA-binding drug revealed arrays of docked pairs of staple-shaped molecules in which one pendent hydroxyquinoline chromophore from each cysteine-rich molecule appears intercalated between the two chromophores of a facing molecule. This arrangement is in contrast to the proposed mode of binding to DNA that shows the two drug chromophores clamping two stacked base pairs, in agreement with the nearest-neighbor exclusion principle. Proof of DNA sequence recognition was obtained from both classical DNase I footprinting experiments and determination of the melting temperatures of several custom-designed fluorescently labeled oligonucleotides. A rationale for the DNA-binding behavior was gained when models of thiocoraline clamping a central step embedded in several octanucleotides were built and studied by means of unrestrained molecular dynamics simulations in aqueous solution.

Edge-to-site reduction of Bethe-Peierls approximation for nearest neighbor exclusion cubic lattice particle systems and thermodynamic modeling of liquid silicates

We study an interacting particle system on the simple cubic lattice satisfying the nearest neighbor exclusion (NNE) which forbids any two nearest sites to be simultaneously occupied. Under the constraint, we develop an edge-to-site reduction of the Bethe-Peierls entropy approximation of the cluster variation method. The resulting NNE-corrected Bragg-Williams approximation is applied to statistical mechanical modeling of a liquid silicate formed by silica and a univalent network modifier, for which we derive the molar Gibbs energy of mixing and enthalpy of mixing and compare the predictions with available thermodynamic data.

On the similarities and differences between lattice and off–lattice models of driven fluids

Microscopic modeling of complex systems by cellular automata, which deal with particles at lattice sites interacting via simple local rules, involves some arbitrariness besides a drastic simplification of nature. Here we briefly report on some recent work on the influence of dynamic details on the morphological and critical properties of one of such model systems. In particular, we discuss on the similarities and differences between a kinetic nonequilibrium Ising model-which is a prototype for nonequilibrium anisotropic phase transitions-and its off-lattice counterpart, namely, an analogue in which the spatial coordinates of the particles vary continuously. We also pay attention to a related driven lattice model with nearest-neighbor exclusion.

Lattice gas with nearest-neighbor exclusion in a shear-like field

We present Monte Carlo simulations of the lattice gas with nearest-neighbor exclusion and Kawasaki (hopping) dynamics (hard square lattice gas), under the influence of a nonuniform drive, on the square lattice. The drive, which favors motion along the +x axis and inhibits motion in the opposite direction, varies linearly in the y direction. Our lattice has rigid walls at the end points in the y direction and periodic boundaries along the drive. We find that this model has transition to a sublattice-ordered phase at a density of about 0:298, lower than in equilibrium (rc ’ 0:37), but somewhat higher than in the uniformly driven case at maximal bias (rc ’ 0:272). For smaller global densities (r • 0:33), the ordering occurs with particle accumulation in the low-drive region. Above this density we observe a surprising reversal in the density profile, with particles migrating to the high-drive region.

Driven lattice gas with nearest-neighbor exclusion: shear-like drive

We present Monte Carlo simulations of the lattice gas with nearest-neighbor exclusion and Kawasaki (hopping) dynamics, under the influence of a nonuniform drive, on the square lattice. The drive, which favors motion along the +$x$ and inhibits motion in the opposite direction, varies linearly with $y$, mimicking the velocity profile of laminar flow between parallel plates with distinct velocities. We study two drive configurations and associated boundary conditions: (1) a linear drive profile, with rigid walls at the layers with zero and maximum bias, and (2) a symmetric (piecewise linear) profile with periodic boundaries. The transition to a sublattice-ordered phase occurs at a density of about 0.298, lower than in equilibrium ($\rho_c \simeq 0.37$), but somewhat higher than in the uniformly driven case at maximal bias ($\rho_c \simeq 0.272$). For smaller global densities ($\rho \leq 0.33$), particles tend to accumulate in the low-drive region. Above this density we observe a surprising reversal in the density profile, with particles migrating to the high-drive region and forming structures similar to force chains in granular systems.

Phase behavior of the lattice restricted primitive model with nearest neighbor exclusion

The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density rho*(max)= sqrt 2 and reduced temperature T* approximately equal to 0.29. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered, and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.

Thermodynamic properties of lattice hard-sphere models

Thermodynamic properties of several lattice hard-sphere models were obtained from grand canonical histogram- reweighting Monte Carlo simulations. Sphere centers occupy positions on a simple cubic lattice of unit spacing and exclude neighboring sites up to a distance sigma. The nearestneighbor exclusion model, sigma = radical2, was previously found to have a second-order transition. Models with integer values of sigma = 1 or 2 do not have any transitions. Models with sigma = radical3 and sigma = 3 have weak first-order fluid-solid transitions while those with sigma = 2 radical2, 2 radical3, and 3 radical2 have strong fluid-solid transitions. Pressure, chemical potential, and density are reported for all models and compared to the results for the continuum, theoretical predictions, and prior simulations when available.

A Three State Hard-Core Model on a Cayley Tree

We consider a nearest-neighbor hard-core model, with three states , on a homogeneous Cayley tree of order k (with k + 1 neighbors). This model arises as a simple example of a loss network with nearest-neighbor exclusion. The state σ(x) at each node x of the Cayley tree can be 0, 1 and 2. We have Poisson flow of calls of rate λ at each site x, each call has an exponential duration of mean 1. If a call finds the node in state 1 or 2 it is lost. If it finds the node in state 0 then things depend on the state of the neighboring sites. If all neighbors are in state 0, the call is accepted and the state of the node becomes 1 or 2 with equal probability 1/2. If at least one neighbor is in state 1, and there is no neighbor in state 2 then the state of the node becomes 1. If at least one neighbor is in state 2 the call is lost. We focus on ‘splitting’ Gibbs measures for this model, which are reversible equilibrium distributions for the above process. We prove that in this model, ∀ λ > 0 and k ≥ 1, there exists a unique translationinvariant splitting Gibbs measure *. We also study periodic splitting Gibbs measures and show that the above model admits only translation - invariant and periodic with period two (chess-board) Gibbs measures. We discuss some open problems and state several related conjectures.

From Atomic Scale Ordering to Mesoscale Spatial Patterns in Surface Reactions: A Heterogeneous Coupled Lattice-Gas Simulation Approach

A current challenge in the modeling of surface reaction-diffusion systems is to connect the length scales from a realistic atomistic treatment of local ordering of adsorbed reactants and of reaction kinetics to an "exact" description of mesoscale spatial pattern formation. We discuss a heterogeneous coupled lattice-gas approach which utilizes parallel kinetic Monte Carlo simulations of lattice-gas models to simultaneously determine the local reaction kinetics and diffusive transport properties at various macroscopic "points" distributed across the surface. These simulations are periodically coupled to reflect macroscopic mass transport via surface diffusion. We place particular emphasis on the key issue of correctly describing the associated chemical or collective diffusion flux. This method is general, but it is discussed here only in the context of simple models for the bistable CO oxidation reaction on surfaces, where macroscopic mass transport involves only diffusion of adsorbed CO. Detailed analysis is presented for a canonical model of CO oxidation which incorporates nearest-neighbor exclusion between adsorbed oxygen, leading to superlattice ordering of this reactant. In this model, interactions of adsorbed CO with other adspecies are ignored. This reduces CO surface transport from a many-particle to a single-particle problem, although one with the complexity of "ant-in-the-labyrinth"-type percolative diffusion (the labyrinth being formed by coadsorbed oxygen).

Adsorption of gases on SnS 2: trace of order–disorder phase transition of a honeycomb lattice gas

We have made volumetric measurements of adsorption isotherm of Ar, Kr, O 2 and N 2 on a powder sample of tin disulfide SnS 2 in the temperature range of 77–90 K. Ar, Kr and O 2 exhibited pressure isotherms unusually bending at the coverage of 0.3–0.4 monolayer, while N 2 did not. The isotherms are analyzed by a quasi-chemical approximation theory developed for a honeycomb lattice gas with first nearest neighbor exclusion and with a small adsorption potential difference between the two (1 × 1)-1/2 sublattices. The unusual bending of the pressure isotherms is successfully explained as a trace of the order–disorder phase transition of second order that would take place in the honeycomb lattice gas if the two sublattices had the same adsorption potential. The adsorption potential difference is found to be at most of order of magnitude of the second nearest neighbor interaction energy.

Pair Correlation Function Realizability: Lattice Model Implications

Despite their long history in experiment, simulation, and analytical theory, pair correlation functions that describe local order in many-body systems still retain a legacy of mathematical mysteries. One such open question concerns “realizability” of a given candidate pair correlation function, namely whether it actually represents the pair correlation for some spatial distribution of particles at number densityρ >0. Several necessary conditions that must be satisfied by the candidate are known, including nonnegativity of the function and its associated structure factor, as well as constraints on implied local density fluctuations. However, general conditions sufficient to ensure realizability are not known. To clarify this situation, we have examined realizability for a simple one-dimensional lattice model, with single-site occupancy, and nearest-neighbor exclusion. By virtue of exhaustive enumeration for systems of 15 or fewer sites subject to periodic boundary conditions, several conclusions have been formulated for the case of a constant pair correlation beyond the exclusion range. These include (a) pair correlation realizability over a nonzero density range, (b) violation of the Kirkwood superposition approximation for many such realizations, and (c) inappropriateness of the so-called “reverse Monte Carlo” method that uses a candidate pair correlation function as a means to suggest typical many-body configurations.

Behavior dominated by slow particles in a disordered asymmetric exclusion process

We study the large space and time scale behavior of a totally asymmetric, nearest-neighbor exclusion process in one dimension with random jump rates attached to the particles. When slow particles are sufficiently rare, the system has a phase transition. At low densities there are no equilibrium distributions, and on the hydrodynamic scale the initial profile is transported rigidly. We elaborate this situation further by finding the correct order of the correction from the hydrodynamic limit, together with distributional bounds averaged over the disorder. We consider two settings, a macroscopically constant low density profile and the outflow from a large jam.

Lattice-gas modeling of the formation and ordering of oxygen adlayers on Pd(100)

Abstract We construct a lattice-gas (LG) model to describe not just the ordering of equilibrated adlayers of chemisorbed oxygen on Pd(1 0 0), but also the non-equilibrium ordering observed during dissociative adsorption of molecular oxygen on Pd(1 0 0). First, by combining transfer matrix analysis and Monte Carlo simulations, we determine the equilibrium phase diagrams for candidate LG models with pairwise-additive interactions including nearest-neighbor (NN) exclusion, second NN repulsion, third NN attraction, and possibly fourth NN repulsion. These interactions are selected so as to recover the p(2×2) and c(2×2) ordering observed in experiment. Interaction strengths are assessed by matching simulated and experimental phase diagrams. Second, a kinetic model is constructed to describe dissociative adsorption of molecular oxygen on second NN empty sites (consistent with NN exclusion), as well as subsequent thermally activated surface diffusion, and adlayer formation. Hopping rates for the latter reflect the selected adspecies interactions through detailed-balance constraints. By comparing simulated diffracted intensities for non-equilibrium adlayer structure during adsorption with experimental data for various temperatures and pressures, we demonstrate the existence of transient mobility for dissociative adsorption in this system, and also determine the magnitude of the thermal diffusion barrier.

Order?disorder phase transitions in a honeycomb lattice gas with first nearest neighbor exclusion: comparison between different approximations and a Monte Carlo simulation

The order–disorder phase transitions in a honeycomb lattice gas have been studied in the Bragg–Williams (BW) and the quasi-chemical (QC) approximations as well as by means of Monte Carlo simulations. The model system, which is the same as studied by the cluster variation method (CVM) in a previous paper, contains the first nearest neighbor exclusion and the second nearest neighbor attraction. Simple analytical expressions of thermodynamic functions have been derived in the BW and QC approximations, which will provide a useful tool for semi-quantitative analysis of experimental observations. In every method the lattice gas has been found to undergo both the phase transition of the first order and that of the second order to give rise to the tricritical point. However, the second order transition has been found to be limited to within a finite temperature in the BW approximation, while the other methods including CVM allow the phase transition to occur at infinitely high temperature. The tricritical temperatures calculated by BW and QC are about two times higher than the MC simulations. The previous CVM calculation has been found to give the tricritical temperature only a little lower than in BW and QC. The reason why the previous CVM is not so accurate as expected is discussed on the basis of the network arrangement of clusters at the limit where one of the two (1 × 1)-1/2 triangular sublattices can be neglected.

Order–disorder phase transitions in a honeycomb lattice gas with first nearest neighbor exclusion: comparison between different approximations and a Monte Carlo simulation

The order–disorder phase transitions in a honeycomb lattice gas have been studied in the Bragg–Williams (BW) and the quasi-chemical (QC) approximations as well as by means of Monte Carlo simulations. The model system, which is the same as studied by the cluster variation method (CVM) in a previous paper, contains the first nearest neighbor exclusion and the second nearest neighbor attraction. Simple analytical expressions of thermodynamic functions have been derived in the BW and QC approximations, which will provide a useful tool for semi-quantitative analysis of experimental observations. In every method the lattice gas has been found to undergo both the phase transition of the first order and that of the second order to give rise to the tricritical point. However, the second order transition has been found to be limited to within a finite temperature in the BW approximation, while the other methods including CVM allow the phase transition to occur at infinitely high temperature. The tricritical temperatures calculated by BW and QC are about two times higher than the MC simulations. The previous CVM calculation has been found to give the tricritical temperature only a little lower than in BW and QC. The reason why the previous CVM is not so accurate as expected is discussed on the basis of the network arrangement of clusters at the limit where one of the two (1 × 1)-1/2 triangular sublattices can be neglected.