Lattice Gas Automata Research Articles

Quantum annealing-based algorithm for lattice gas automata

This study proposes a quantum annealing-based algorithm for flow computation based on lattice-gas automata (LGA). Since the state of the lattice gas is determined by Boolean variables, 0 (absence) or 1 (presence), in LGA, it is well suited for implementation in quantum annealing and simulated annealing computers. The quantum annealing-based algorithm proposed in this study is constructed so that conservation of mass and momentum is satisfied at the particle collision process. Verification tests performed with various quantum annealing and simulated annealing computers confirm that the proposed algorithm well replicates a conventional LGA collision model.

From flow to jamming: Lattice Gas Automaton simulations in granular materials

We introduce the first extension of a Lattice Gas Automaton (LGA) model to accurately replicate observed emergent phenomena in granular materials with a special focus on previously unexplored jamming transitions by incorporating gravitational effects, energy dissipation in particle collisions, and wall friction. We successfully reproduce flow rate evolution, density wave formation, and jamming transition observed in experiments. We also explore the critical density at which jamming becomes probable. This research advances our understanding of granular dynamics and offers insights into the jamming behavior of granular materials.

Kinetic modeling of economic markets with heterogeneous saving propensities

The lattice gas automaton (LGA) is proposed for a closed economic market of agents with heterogeneous saving interests. There are two procedures in the standard LGA, i.e. “propagation” + “transaction”. If the propagation step is removed and the transaction is conducted among all agents, the LGA reduces to a more simplified kinetic model. In addition, two dealing rules are imposed on the transaction phase. Under Rule I, the trading volume depends on the average saving propensities of an arbitrary pair of agents in trade. Under Rule II, the exchange is governed by a stochastic parameter between the saving propensities of two traders. Besides, two sampling methods are introduced for the random selection of two agents in the iterative process. Specifically, Sampling I is the sampling with replacement and is easier to program. Sampling II is the sampling without replacement and owns a higher computing efficiency. There are slight differences between the stationary wealth distributions simulated by using the two transaction rules and sampling approaches. In addition, the accuracy, robustness and efficiency of the econophysics models are validated by typical numerical tests. The reduced LGA without the propagation step owns a higher computational efficiency than the standard LGA. Moreover, the impact of saving propensities of agents in two groups on the wealth distributions is studied, and the influence of proportions of agents is investigated as well. To quantitatively measure the wealth inequality, the Gini coefficients, Kolkata indices, and deviation degrees of all agents and two groups are simulated and analyzed in detail. This work is helpful to further analyze and predict the dynamic process of wealth distribution in the realistic economic market.

Prediction Of Two-Phase Relative Permeability In Porqus Media Based On Network Modeling Of Lattice Gas Automata

The displacement of one fluid by another is controlled by the geometry of the pore space. The relative hydrodynamic conductance of each fluid at a given saturation is the relative permeability, while the pressure difference between the phases is the capillary pressure. These two functions determine the macroscopic fluid flow behavior in hydrocarbon reservoir over the scale of centimeters to kilometers.At the pore seale fluids reside in intergranular space of typical sedimentary rocks. The rock type and fluid properties are likely to change drastically through the reservoir, the only sample of rock come from drilling wells, which represents a tiny fraction of the total volume in a reservoir. Furthermore, relative permeability measurements on these samples are difficult and time consuming. To quantify and control uncertainty in recovery estimations, it is necessary to have some theoretical understanding of transport properties. Such understanding would enable us to predict the sensitivity of relative permeability to geological factors such rosity, and the nature of the fluids. This work is a pre- liminary step in this direction. A more important result from this work is that we are now able to quantify the change in the relative permeability to those geological factors.In this paper a pore structure and displacements mechanisms to model two-phase flow in porous media were constructed using lattice gas automata. The void space of the media is represented as a network of large spaces (pores) connected by narrower throats. The aggregation of cell pore volumes is used to calculate the porosity of the network and the fluid saturation when different cells are occupied by different fluids. By judicious choices for the distribution of pore and throat sizes of the network it is possible to predict relative permeability. For predicting the absolute and relative permeability, it is assumed that the viscous pressure drops occur across the throats.

Modeling and Simulation of Non-Uniform Electrolytic Machining Based on Cellular Automata

Porous microstructure is a common surface morphology that is widely used in antifouling, drag reduction, adsorption, and other applications. In this paper, the lattice gas automata (LGA) method was used to simulate the non-uniform electrochemical machining of porous structure at the mesoscopic level. In a cellular space, the metal and the electrolyte were separated into orderly grids, the migration of corrosive particles was determined by an electric field, and the influences of the concentration gradient and corrosion products were considered. It was found that different pore morphologies were formed due to the competition between dissolution and diffusion. When the voltage was low, diffusion was sufficient, and no deposit was formed at the bottom of the pore. The pore grew faster along the depth and attained a cylindrical shape with a large depth-to-diameter ratio. As the voltage increased, the dissolution rates in all directions were the same; therefore, the pore became approximately spherical. When the voltage continued to increase, corrosion products were not discharged in time due to the rapid dissolution rate. Consequently, a sedimentary layer was formed at the bottom of the pore and hindered further dissolution. In turn, a disc-shaped pore with secondary pores was formed. The obtained simulation results were verified by experimental findings. This study revealed the causes of different morphologies of pores, which has certain guiding significance for non-uniform electrochemical machining.

Simulation Study of Fluid Flow and Estimation of a Heterogeneous Porous Media Properties Using Lattice Gas Automata Method

Most models used in reservoir simulation studies are on the scale of meters to hundreds of meters. However, increasing resolution in geological measurements results in finer geological models. Simulations study of particle movements provide an alternative to conventional reservoir simulation by allowing the study of microscopic and/or macroscopic fluid flow, which is close to the scale of geological models. In this paper, the FHP-II (Frisch, Hasslacher and Pomeau - FHP) model of lattice gas automata were developed to study fluid flow in order to estimate the properties of heterogeneous porous media. Heterogeneity simulated by placing solid obstacles randomly in a two-dimensional test volume. Properties of the heterogeneous porous media were estimated by the shape, size, number of the obstacles and by the distribution of the obstacles within the volume. Results of the effects of grain sizes and shapes, and its distribution in the porous media on the tortuosity, effective porosity, permeability and displacement efficiency were obtained. An investigation of fluid flow and comparison with laboratory experiment were also presented. Reasonably good agreement between the lattice gas automata simulation and laboratory experiment results were achieved.

A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton

The dynamics of wealth distribution plays a critical role in the economic market, hence an understanding of its nonequilibrium statistical mechanics is of great importance to human society. For this aim, a simple and efficient one-dimensional (1D) lattice gas automaton (LGA) is presented for wealth distribution of agents with or without saving propensity. The LGA comprises two stages, i.e., random propagation and economic transaction. During the former phase, an agent either remains motionless or travels to one of its neighboring empty sites with a certain probability. In the subsequent procedure, an economic transaction takes place between a pair of neighboring agents randomly. It requires at least 4 neighbors to present correct simulation results. The LGA reduces to the simplest model with only random economic transaction if all agents are neighbors and no empty sites exist. The 1D-LGA has a higher computational efficiency than the 2D-LGA and the famous Chakraborti–Chakrabarti economic model. Finally, the LGA is validated with two benchmarks, i.e., the wealth distributions of individual agents and dual-earner families. With the increasing saving fraction, both the Gini coefficient and Kolkata index (for individual agents or two-earner families) reduce, while the deviation degree (defined to measure the difference between the probability distributions with and without saving propensities) increases. It is demonstrated that the wealth distribution is changed significantly by the saving propensity which alleviates wealth inequality.

Lattice-Gas-Automaton Modeling of Income Distribution.

A simple and effective lattice–gas–automaton (LGA) economic model is proposed for the income distribution. It consists of four stages: random propagation, economic transaction, income tax, and charity. Two types of discrete models are introduced: two-dimensional four-neighbor model (D2N4) and D2N8. For the former, an agent either remains motionless or travels to one of its four neighboring empty sites randomly. For the latter, the agent may travel to one of its nearest four sites or the four diagonal sites. Afterwards, an economic transaction takes place randomly when two agents are located in the nearest (plus the diagonal) neighboring sites for the D2N4 (D2N8). During the exchange, the Matthew effect could be taken into account in the way that the rich own a higher probability of earning money than the poor. Moreover, two kinds of income tax models are incorporated. One is the detailed taxable income brackets and rates, and the other is a simplified tax model based on a fitting power function. Meanwhile, charity is considered with the assumption that a richer agent donates a part of his income to charity with a certain probability. Finally, the LGA economic model is validated by using two kinds of benchmarks. One is the income distributions of individual agents and two-earner families in a free market. The other is the shares of total income in the USA and UK, respectively. Besides, impacts of the Matthew effect, income tax and charity upon the redistribution of income are investigated. It is confirmed that the model has the potential to offer valuable references for formulating financial laws and regulations.

Current status of Lattice Boltzmann Methods applied to aerodynamic, aeroacoustic, and thermal flows

We present a review of the evolutionary advancement of the lattice Boltzmann methods (LBM) and current status of their applications in dealing with diverse flow problems such as advection-diffusion, forced convection, natural convection, conjugate heat transfer, radiative heat transfer, thermal flow through porous media, phase transition and phase separation, aerodynamics and aeroacoustics, and thermal jet flows. We analyze and discuss various thermal LBM frameworks and methodologies since the time of Lattice Gas Automata (LGA) to recently developed methods to model simple and complex aerodynamic, aeroacoustic and thermal flow problems. Multi-speed (M-S) models, hybrid LBM models, and double distribution function LBM (DDF-LBM) models, along with their applications and improvements are discussed in details. Moreover, the recent developments in addressing various applications such as energy storage devices, systems with electro-thermo convection, aerodynamic flows, simulations of noise profiles in nozzles with and without chevrons, and thermal simulations of jet flow with LBM are presented in great detail.

Lattice Gas Automata Applications to Estimate Effective Porosity and Permeability Barrier Model of the Triangle with a Height Variation

Penelitian ini bertujuan untuk menghitung porositas efektif (фeff) dan permeabilitas (k) menggunakan model segitiga dengan variasi tinggi yaitu 3, 4, 5, 6 dan 7 cm. Perhitungan porositas dan permeabilitas yang efektif dilakukan dengan menggunakan model Lattice Gas Automata (LGA), yang diimplementasikan dengan bahasa pemrograman Delphi 7.0. Untuk model segitiga penghalang dengan tinggi 3, 4, 5, 6 dan 7 cm, nilai porositas efektif dan permeabilitas, masing-masing: фeff (T1) = 0,1690, k (T1) = 0 , 001339 pixel2; фeff (T2) = 0,1841, k (T2) = 0,001904 pixel2; фeff (T3) = 0,1885, k (T3) = 0,001904 pixel2; фeff (T4) = 0,1938, k (T4) = 0001925 pixel2; dan фeff (T5) = 0,2053, k (T5) = 0,002400 pixel2. Dari hasil simulasi, diperoleh tinggi segitiga akan berpengaruh signifikan terhadap nilai porositas efektif dan permeabilitas. Pada segitiga lebih tinggi, menyebabkan tabrakan model aliran fluida LGA mengalami lebih banyak hambatan untuk penghalang, sehingga porositas efektif dan permeabilitas menurun. Sebaliknya, jika segitiga lebih rendah, menyebabkan tabrakan model aliran fluida LGA mengalami lebih sedikit hambatan untuk penghalang, sehingga porositas efektif dan permeabilitas meningkat.This research purposed to calculate the effective porosity (feff) and permeability (k) using the barrier model of the triangle with a high varying are 3, 4, 5, 6 and 7 cm. Effective porosity and permeability calculations performed using the model Lattice Gas Automata (LGA), which is implemented with Delphi 7.0 programming language. For model the barrier triangle with a high of 3, 4, 5, 6 and 7 cm, the value of effective porosity and permeability, respectively: feff(T1)=0,1690, k(T1)=0,001339 pixel2; feff(T2)=0,1841, k(T2)=0,001904 pixel2; feff(T3)=0,1885, k(T3)=0,001904 pixel2; feff(T4)=0,1938, k(T4)= 0001925 pixel2; and feff(T5)=0,2053, k(T5)=0,002400 pixel2. From the simulation results, obtained by the high of the triangle will be a significant effect on the value of effective porosity and permeability. If the triangle highest, causing the collision of fluid flow models LGA experience more obstacles to the barrier, so that the effective porosity and permeability decrease. Conversely, if the triangle lower, causing the collision of fluid flow models LGA experience less obstacles to the barrier, so that the effective porosity and permeability increases.Keywords: Effective porosity, permeability, model triangle, model LGA

Pore‐Scale Explanation of the Archie's Cementation Exponent: Microstructure, Electrical Anisotropy, and Numerical Experiments

AbstractElectrical anisotropy of rock is a key parameter in geophysical research. In this paper, digital rocks were constructed by aligning elliptic grains to create samples with anisotropic pore connectivities. Lattice gas automata are used to research electrical transport properties for revealing the anisotropy and physical meaning of Archie's cementation exponent. Simulated results indicate that the relationship between formation factor and porosity is of anisotropy with the exponent corresponding to the change rate of pore complexity with porosity, instead of pore complexity itself, confirming previous theoretical studies. Besides, the results reveal that anisotropy of pore structure is a main factor leading to the anisotropic relation. Under the effects of fracture, there is a U‐shape transition zone over a range of porosity for anisotropy exponent. Moreover, the simulated data are in good agreement with the laboratory experiments, which can further verify the validity of the results.

Relativistic properties and invariants of the Du Fort–Frankel scheme for the one-dimensional Schrödinger equation

The Du Fort–Frankel scheme for the one-dimensional Schrödinger equation is shown to be equivalent, under a time-dependent unitary transformation, to the Ablowitz–Kruskal–Ladik scheme for the Klein–Gordon equation. The Schrödinger equation describes a non-relativistic quantum particle, while the Klein–Gordon equation describes a relativistic particle. The conditional convergence of the Du Fort–Frankel scheme to solutions of the Schrödinger equation arises because solutions of the Klein–Gordon equation only approximate solutions of the Schrödinger equation in the non-relativistic limit. The time-dependent unitary transformation is the discrete analog of the transformation that arises from seeking a non-relativistic limit using the interaction picture of quantum mechanics to decompose the Klein–Gordon Hamiltonian into the relativistic rest energy and a remainder. The Ablowitz–Kruskal–Ladik scheme is in turn decomposed into a quantum lattice gas automaton for the one-dimensional Dirac equation, which is also the one-dimensional discrete time quantum walk. This relativistic interpretation clarifies the origin of the known discrete invariant of the Du Fort–Frankel scheme as expressing conservation of probability for the 2-component wavefunction in the one-dimensional Dirac equation under discrete unitary evolution. It also leads to a second invariant, the matrix element of the evolution operator, whose imaginary part gives a discrete approximation to the expectation of the non-relativistic Schrödinger Hamiltonian.

Derivation of lattice Boltzmann equation via analytical characteristic integral**Project supported by the National Science and Technology Major Project, China (Grant No. 2017ZX06002002).

A lattice Boltzmann (LB) theory, the analytical characteristic integral (ACI) LB theory, is proposed in this paper. ACI LB theory takes the Bhatnagar–Gross–Krook (BGK)-Boltzmann equation as the exact kinetic equation behind Navier–Stokes continuum and momentum equations and constructs an LB equation by rigorously integrating the BGK-Boltzmann equation along characteristics. It is a general theory, supporting most existing LB equations including the standard lattice BGK (LBGK) equation inherited from lattice-gas automata, whose theoretical foundation had been questioned. ACI LB theory also indicates that the characteristic parameter of an LB equation is collision number, depicting the particle-interaction intensity in the time span of the LB equation, instead of the traditionally assumed relaxation time, and the over-relaxation time problem is merely a manifestation of the temporal evolution of equilibrium distribution along characteristics under high collision number, irrelevant to particle kinetics. In ACI LB theory, the temporal evolution of equilibrium distribution along characteristics is the determinant of LB method accuracy and we numerically prove this.

3D simulations of the metal passivation process in potentiostatic conditions using discrete lattice gas automaton

A cellular automaton model is used for 3D simulations of metal corrosion in electrolyte solutions in potentiostatic conditions. The focus of this research is the formation of the passive layer on the metal surface. A general, mesoscopic-scale model is used. It contains only the elements necessary to reproduce the most important features of passivation. It is a 3D version of the 2D model presented in our previous papers. The simulations are run on graphics processing units which allow an effective operation on large 3D lattices. We consider the influence of three factors: the rate of corrosion (related to the electric potential), solubility of the corrosion products and their adhesion or absence of adhesion to the metal surface. For each set of the parameters we wait in the simulation run for the system to attain the steady state. Then we collect data characterizing steady-state properties such as electric current density, passive layer thickness, its roughness and overall morphology. The qualitative properties of passivation are reproduced in our 3D simulations confirming the conclusions based on earlier, 2D simulations.

Emergent dynamic structures and statistical law in spherical lattice gas automata.

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Dissipative particle dynamics simulation of biomagnetic fluid flow and heat transfer

Dissipative particle dynamics is a Lagrangian particle-based mesoscopic technique with higher computation efficiency than microscopic numerical methods, originally conceived as a hybrid of lattice gas automata (LGA), Brownian dynamics (BD) and molecular dynamics (MD). As an improved version of this method, the energy-conservative dissipative particle dynamics (eDPD or DPD+E) allows for temperature-variation in fluid system and has great potential to solve hydrodynamics problem involving heat transfer in complex fluids such as biomagnetic fluid, ferrofluid, eletrorheological fluid and so on. Considering the both effects of ferrohydrodynamic and magnetohydrodynamic, the hydrodynamics behavior of biomagnetic fluid is rather complicated and has received considerable attention from various researchers. In this work, the fluid flow and heat transfer in a semi-annulus filled with biomagnetic fluid in presence of an external magnetic field is investigated systematically by the eDPD method for different conditions. The flow is steady, two-dimensional, laminar and incompressible. To begin with, a simple and practicable strategy is proposed to matchup the mesoscopic parameters in eDPD model with the transport coefficients of real fluid because the eDPD formlation has no direct relation to transport coefficients. In detail, the viscosity and thermal diffusivity for the eDPD fluid are calculated by numerically simulating the isothermal Poiseuille flow and two-dimensional heat conduct with uniform heat generation, respectively. To study the magnetostatic interactions regardless of the induced magnetic field, a model concerned with the magnetic field is introduced. The Kelvin force and Lorentz force on DPD particles are computed in the same way as the buoyance force; the heat source induced by the external magnetic is replaced by imposing an external heat flux on the DPD particles. Then the eDPD model is first validated against the finite volume method (FVM) results for the natural convection at a given Rayleigh number and Prandtl number to access the accuracy of the eDPD simulations and it is found that the eDPD model predict the temperature and flow fields throughout the convection domains properly. Finally the effects of Magnetic number and Hartmann number, which arise from ferrohydrodynamics and magnetohydrodynamics respectively, have been examined and presented via temperature isotherms and streamlines. The obtained results simply reveal that the thermomagnetic convection is very different from buoyance-driven natural convection. Three thermal plume and four vortexes appears over the hot wall and heat transfer drop a lot near the middle zone as Magnetic number increases. It can be also found that the local Nusselt number near the hot wall significantly decrease as Hartmann number increases.

A Lattice Gas Automata Model for the Coupled Heat Transfer and Chemical Reaction of Gas Flow Around and Through a Porous Circular Cylinder

Coupled heat transfer and chemical reaction of fluid flow in complex boundaries are explored by introducing two additional properties, i.e. particle type and energy state into the Lattice gas automata (LGA) Frisch–Hasslacher–Pomeau (FHP-II) model. A mix-redistribute of energy and type of particles is also applied on top of collision rules to ensure randomness while maintaining the conservation of mass, momentum and energy. Simulations of heat transfer and heterogeneous reaction of gas flow passing a circular porous cylinder in a channel are presented. The effects of porosity of cylinder, gas inlet velocity, and reaction probability on the reaction process are further analyzed with respect to the characteristics of solid morphology, product concentration, and temperature profile. Numerical results indicate that the reaction rate increases with increasing reaction probability as well as gas inlet velocity. Cylinders with a higher value of porosity and more homogeneous structure also react with gas particles faster. These results agree well with the basic theories of gas–solid reactions, indicating the present model provides a method for describing gas–solid reactions in complex boundaries at mesoscopic level.

Simulation of flow and heat transfer around a heated stationary circular cylinder by lattice gas automata

A two-dimensional (2D) lattice gas automata model was developed to describe the behavior of flow and heat transfer around a heated stationary circular cylinder. To validate the feasibility of this model, heat transfer of a heated stationary circular cylinder, which is concentrically placed in a square enclosure, was simulated and compared with analytical results. Further investigations on flow and heat transfer past a heated stationary cylinder in a channel at Reynolds number of 100–200 were then carried out. The flow and heat characteristics were presented by streamlines and thermal nephograms. The dependences of drag coefficient and Nusselt number on the Reynolds number were further studied and compared to literature data. Simulation results of the heat transfer in the enclosure agree with the solution of the diffusive heat transfer equation. For the investigated Reynolds number range, time averaged drag coefficient decreases as Reynolds number increases, while Nusselt number increases with increasing Reynolds number. Reasonable agreements with previous investigations were achieved, demonstrating that the presented model provides an alternate method to simulate flow and heat transfer problems.

Moisture Flow as Driving Force behind Drying Shrinkage and Microcracking in Interfacial Transition Zone in Concrete

In order to determine drying shrinkage in early age cementitious paste and ITZ, prior to a calculation of shrinkage coefficient and further complex coupling, experimental methods at micro-level and numerical methods at meso-level are separately performed as the initial steps. Digital images of a small-size 1-mm thick cement paste specimen with an embedded obstacle as a concrete model are captured at different magnifications and analyzed in drying experiments with Environmental Scanning Electron Microscope (ESEM) and Vic-2D. The drying shrinkage shows the dependence on image magnification, chosen Area of Interest (AOI) and RH variations. Numerical moisture flow/ drying simulations by Lattice Gas Automata (LGA) show the difference in a moisture gradient depending on the heterogeneity of the LGA domain (population with smaller and/ or larger solids). Expected higher moisture gradient around larger solids is confirmed in the LGA simulations, which could be an initial sign of gaps/microcracks in real ITZ.

History dependent quantum random walks as quantum lattice gas automata

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.