TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

INTERFACE INSTABILITY IN DRIVEN LATTICE GASES

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 954-958 ◽  
Author(s):  
G. SZABÓ ◽  
A. SZOLNOKI ◽  
T. ANTAL ◽  
I. BORSOS
Keyword(s):  
Lattice Gas ◽  
Nearest Neighbor ◽  
Interfacial Instability ◽  
Lattice Gases ◽  
Square Lattice ◽  
Wave Number ◽  
Material Transport ◽  
Interface Instability ◽  
Amplification Rate ◽  
Lattice Gas Models

In driven lattice-gas models, the enhanced material transport along the interfaces results in an instability of the planar interfaces and leads to the formation of multistrip states. To study the interfacial instability, Monte Carlo simulations are performed on different square lattice-gas models. The amplification rate of a periodic perturbation depends on the wave number k; it has a positive maximum at a characteristic value of k on the analogy of the Mullins-Sekerka instability. Significant differences have been found in the dependence of amplification rate on k when comparing the systems with nearest neighbor repulsive and nearest and next-nearest neighbor attractive interactions. The results agree qualitatively with theories neglecting the fluctuations.

Fractional Propagation and the Elimination of Staggered Invariants in Lattice-BGK Models

1997 ◽  
Vol 08 (04) ◽  
pp. 753-761 ◽  
Author(s):  
Yue-Hong Qian
Keyword(s):  
Complex Systems ◽  
Numerical Simulations ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Lattice Gas ◽  
Dynamical Equations ◽  
Lattice Gas Models ◽  
Lattice Boltzmann Models

Lattice-based models have been attracting much interest in recent years and have been applied to many complex systems. The derivation of large scale dynamical equations of lattice-gas models as well as lattice-Boltzmann models was based on the belief that only the physically interesting quantities (mass, momentum and energy) are conserved. Staggered invariants in lattice-gas models were found in 1988 and there have been no efficient methods to eliminate these invariants. In this paper, we will first discuss the existence of staggered invariants, then we propose to use fractional propagation as an effective way of suppressing these undesired invariants. Numerical simulations will be used to confirm the theory and to show the improvement of computations.

Phase transitions in centered-rectangular- and square-lattice-gas models

1983 ◽  
Vol 27 (11) ◽  
pp. 6777-6786 ◽  
Author(s):  
K. Kaski ◽  
W. Kinzel ◽  
J. D. Gunton
Keyword(s):  
Phase Transitions ◽  
Lattice Gas ◽  
Square Lattice ◽  
Lattice Gas Models

The Equation of State for a one-component System

1974 ◽  
Vol 29 (1) ◽  
pp. 65-74 ◽  
Author(s):  
H. P. Neumann
Keyword(s):  
Long Range ◽  
Lattice Gas ◽  
Particle Interaction ◽  
Hard Core ◽  
State Diagram ◽  
Phase Changes ◽  
Square Lattice ◽  
Temperature Phase ◽  
Density State ◽  
Transcendental Equations

The cooperative problem for a lattice gas on a plane, square lattice and on a simple cubic lattice is solved by a system of two coupled, transcendental equations, derived by a combinatorial method, which describes a homogeneous or periodical particle density on the lattice as a function of the temperature and the chemical potential of the lattice-gas.For the particle interaction a Hard-Core potential (nearest neighbour exclusion) with a soft long-range tail is assumed. The zero-component of the Fourier-transform of this long-range interaction part can be positive or negative. The system of transcendental equations is solved by a graphic method. As a result, the complete pressure-density state diagram and the pressure-temperature phase diagram can be drawn. The lattice-gas exists in three stable phases: gas, liquid and solid. Three phase changes are possible: condensation, crystallization and sublimation. Critical points of condensation and freezing are examined. The number of possible phases and phase changes at a fixed temperature depends on the geometric structure of the particle interaction.

scholarly journals Simulation of continuous flows with discrete models

Vestnik IGEU ◽  
2019 ◽  
pp. 68-75
Author(s):  
S.P. Bobkov ◽  
A.S. Chernjavskaja
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Dynamic Models ◽  
Physical Nature ◽  
Flow Regimes ◽  
Discrete Analogue ◽  
Discrete Models ◽  
Lattice Gases ◽  
Spatial Lattice ◽  
Lattice Gas Models

The vast majority of heat and power processes include the motion of significant amounts of gases and liq-uids. This makes it important and quite urgent to develop approaches for computer simulation and visualiza-tion of continuum flows in technological devices and pipelines. A whole set of new approaches to mathematical modelling of continuum flows has been recently developed. The most common one is using discrete mathematical models for these purposes. Discrete approaches can simplify modeling procedures in cases where traditional methods require complex time-consuming calculations. At the same time, correct-ness of description of various flow regimes by the discrete methods is often questioned. The second problem of the mentioned models is a large-scale transition from model discrete parameters to generally accepted macroscopic characteristics of flows. The purpose of this work is to determine continuous flow regimes that can be correctly described by certain models. The paper considers discrete dynamic models in the form of lattice gases. A continuum in this case is represented by a set of particles moving only in allowed directions. Despite certain limitations, there is solid evidence that lattice gases quite successfully describe a whole range of hydrodynamic phenomena, and the obtained results do not contradict the generally accepted views on the physical nature of continuum motion processes. The paper describes approaches that allow estimating flow parameters using generally accepted macroscopic indicators. It also studies possible application areas of lattice gas models using the motion of virtual particles on a spatial lattice (HPP and FHP models) and the model based on the discrete analogue of the Boltzmann equation (LBM model) to simulate and visualize continuum flows. The obtained data are in good agreement with the generally accepted results and do not contradict the provisions of classical hydrodynamics. The paper shows that the models considering particle collisions (HPP and FHP) are applicable to describing gas flows in laminar regimes. The LBM model should be considered to be more correct for simulation and visualization of real fluid flows.

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