Статті в журналах: "Lattice gas system"

1

Yepez, Jeffrey. "Lattice-Gas Quantum Computation." International Journal of Modern Physics C 09, no. 08 (December 1998): 1587–96. http://dx.doi.org/10.1142/s0129183198001436.

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We present a quantum lattice-gas model for a quantum computer operating with continual wavefunction collapse; entanglement of the wavefunction occurs locally over small spatial regions between nearby qubits for only a short time period. The quantum lattice-gas is a noiseless method that directly models the lattice-gas particle dynamics at the mesoscopic scale. The system behaves like a viscous Navier–Stokes fluid. Numerical simulations indicate the viscosity of the quantum lattice-gas fluid is lower than its classical lattice-gas counterpart's.

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2

Fradkin, Eduardo. "Superfluidity of the Lattice Anyon Gas." International Journal of Modern Physics B 03, no. 12 (December 1989): 1965–95. http://dx.doi.org/10.1142/s0217979289001275.

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I consider a gas of “free” anyons with statistical paremeter δ on a two dimensional lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on a lattice coupled to a Chern-Simons gauge theory with coupling [Formula: see text]. I show that if [Formula: see text] and the density [Formula: see text], with r and q integers, the system is a superfluid. If q is even and the system is half filled the state may be either a superfluid or a Quantum Hall System depending on the dynamics. Similar conclusions apply for other values of ρ and δ. The dynamical stability of the Fetter-Hanna-Laughlin goldstone mode is insured by the topological invariance of the quantized Hall conductance of the fermion problem. This leads to the conclusion that anyon gases are generally superfluids or quantum Hall systems.

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3

SUDO, YASUSHI. "LATTICE GAS TIME DOMAIN METHODS FOR ACOUSTICS WITH REDUCED COMPUTER MEMORY REQUIREMENTS." Journal of Computational Acoustics 09, no. 04 (December 2001): 1239–58. http://dx.doi.org/10.1142/s0218396x0100053x.

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A lattice gas system consists of many particles, which move in a discrete space-time system according to a set of simple motion rules. Lattice gas time domain methods are based on lattice gas systems and have been widely applied to the simulation of complex systems, such as a Navier–Stokes fluid, a dissipation system, and sound propagation. Applying this idea to sound propagation, an excellent simulation model can be obtained, which has no error for one-dimensional system and has small error for multi-dimensional cases. Despite these good characteristics, the amount of computer memories required to perform the simulation depends on the sound speed and that could be extremely large for some sound speed cases. In this article, a new formulation of the lattice gas sound propagation model is explained, in which the memory requirements are independent of the sound speed and can be much smaller than those of the original formulation.

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4

RAMIREZ-PASTOR, ANTONIO J., FEDERICO J. ROMÁ, and JOSÉ L. RICCARDO. "CONFIGURATIONAL ENTROPY IN GENERALIZED LATTICE-GAS MODELS." International Journal of Modern Physics B 23, no. 22 (September 10, 2009): 4589–627. http://dx.doi.org/10.1142/s0217979209053308.

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In this review, we present our recent results concerning accurate calculations of configurational entropy in generalized lattice-gas models. The calculations are based on the use of the thermodynamic integration method. Different applications (or systems) have been considered. Namely, systems in presence of (i) anisotropy, (ii) energetic heterogeneity, (iii) geometric heterogeneity, and (iv) multisite-occupancy adsorption. Total energy is calculated by means of the Monte Carlo simulation. Then the entropy is obtained by using thermodynamic integration starting at a known reference state. In case (iv), the method relies upon the definition of an artificial Hamiltonian associated with the system of interest for which the entropy of a reference state can be exactly known. Thermodynamic integration is then applied to obtain the entropy in a given state of the system of interest. A rich variety of behaviors is found and analyzed in the context of the lattice-gas theory.

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5

Awazu, Akinori. "Complex transport phenomena in a simple lattice gas system." Physica A: Statistical Mechanics and its Applications 373 (January 2007): 425–32. http://dx.doi.org/10.1016/j.physa.2006.05.039.

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6

Wang, Yuanshi, Hong Wu, and Junhao Liang. "Dynamics of a lattice gas system of three species." Communications in Nonlinear Science and Numerical Simulation 39 (October 2016): 38–57. http://dx.doi.org/10.1016/j.cnsns.2016.02.027.

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7

Satulovsky, Javier E., and Tânia Tomé. "Stochastic lattice gas model for a predator-prey system." Physical Review E 49, no. 6 (June 1, 1994): 5073–79. http://dx.doi.org/10.1103/physreve.49.5073.

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8

Schmittmann, B. "CRITICAL BEHAVIOR OF THE DRIVEN DIFFUSIVE LATTICE GAS." International Journal of Modern Physics B 04, no. 15n16 (December 1990): 2269–306. http://dx.doi.org/10.1142/s0217979290001066.

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This paper reviews simulational and theoretical investigations of critical behavior in a stochastic, interacting lattice gas under the influence of a uniform external driving field. By studying this model system one wishes to gain a deeper understanding of steady states far from thermal equilibrium, and their dynamic universality classes. The major result in the case of attractive particle-particle interactions is the emergence of a novel non-equilibrium fixed point, different from the Wilson-Fisher fixed point of the equilibrium system. The fluctuations of internal energy, the structure factor and the two-point correlations all display surprising features associated with the non-equilibrium nature of the system. For repulsive interactions and small driving forces, one finds a continuous, Ising-like transition which turns first order for larger fields until it is completely destroyed.

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9

Wang, Yuanshi, and Hong Wu. "Population dynamics of intraguild predation in a lattice gas system." Mathematical Biosciences 259 (January 2015): 1–11. http://dx.doi.org/10.1016/j.mbs.2014.11.001.

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10

Szász, A. "The exact solution of the real square-lattice-gas system." physica status solidi (b) 140, no. 2 (April 1, 1987): 415–20. http://dx.doi.org/10.1002/pssb.2221400212.

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11

SLAVIN, V., and A. SLUTSKIN. "THERMODYNAMICS OF LOW-DENSITY ELECTRON GAS ON HIGHLY DISORDERED ONE-DIMENSIONAL HOST LATTICE." International Journal of Modern Physics B 18, no. 20n21 (August 30, 2004): 2863–76. http://dx.doi.org/10.1142/s0217979204026287.

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The low-temperature thermodynamics of a one-dimensional electron gas on a disordered lattice, which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the partition function as a product of random transfer-matrixes, has been developed for calculations of thermodynamic characteristics of the system under consideration. The lattice structures were varied from completely chaotic up to the strictly regular one. It has been established that for any degree of disorder the entropy and heat capacity of the system tend to zero linearly as the temperature is reduced. The conclusion about the gapless character of the elementary excitations spectrum has been made. An instability of one-dimensional electron gas on a disordered lattice has been revealed: under conditions of vanishingly small disordering of the lattice, the long-range order in the systems under consideration is broken by frustrations that are one-dimensional analogues of the frustrations in two- and three-dimensional spin glasses.

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12

PANDEY, R. B., WARREN T. WOOD, and J. F. GETTRUST. "GRADIENT DRIVEN FLOW: LATTICE GAS, DIFFUSION EQUATION AND MEASUREMENT SCALES." International Journal of Modern Physics C 12, no. 02 (February 2001): 273–79. http://dx.doi.org/10.1142/s0129183101001687.

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Tracer diffusion and fluid transport are studied in a model for a geomarine system in which fluid constituents move from regions of high to low concentration. An interacting lattice gas is used to model the system. Collective diffusion of fluid particles in lattice gas is consistent with the solution of the continuum diffusion equation for the concentration profile. Comparison of these results validates the applicability and provides a calibration for arbitrary (time and length) units of the lattice gas. Unlike diffusive motion in an unsteady-state regime, both fluid and tracer exhibit a drift-like transport in a steady-state regime. The transverse components of fluid and tracer displacements differ significantly. While the average tracer motion becomes nondiffusive in the long time regime, the collective motion exhibits an onset of oscillation.

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13

YEPEZ, JEFFREY. "QUANTUM LATTICE-GAS MODEL FOR THE DIFFUSION EQUATION." International Journal of Modern Physics C 12, no. 09 (November 2001): 1285–303. http://dx.doi.org/10.1142/s0129183101002656.

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Presented is a factorized quantum lattice-gas algorithm to model the diffusion equation. It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor classical communication channels. The quantum lattice-gas system is described at the mesoscopic scale by a lattice-Boltzmann equation whose collision term is unconditionally stable and obeys the principle of detailed balance. An analytical treatment of the model is given to predict a macroscopic effective field theory. The numerical simulations are in excellent agreement with the analytical results. In particular, numerical simulations confirm the value of the analytically calculated diffusion constant. The algorithm is time-explicit with numerical convergence that is first-order accurate in time and second-order accurate in space.

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14

Groda, Yaroslav G., and Ruslan N. Lasovsky. "Transport properties of lattice fluid with SALR-potential on a simple square lattice." Journal of the Belarusian State University. Physics, no. 1 (February 9, 2021): 90–101. http://dx.doi.org/10.33581/2520-2243-2021-1-90-101.

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The transport properties of the lattice fluid with the attraction interaction between the nearest and repulsion interaction between the next-next-nearest neighbours on the square lattice are investigated. Computer simulation by the Monte Carlo method of the diffusion process in the specified system has been realised. The jump and tracer diffusion coefficients were determined. The dependence of the diffusion coefficients versus the concentration of adparticles and the interaction parameter of the model is investigated. The activation energy of jump and tracer diffusion determined. The possibility of estimating the jump diffusion coefficient of the lattice fluid with competing interactions using the Zhdanov’s relation on the base of information on the equilibrium properties of the system and the diffusion coefficient of a Langmuir (non-interacting) lattice gas is shown. In the future, it is planned to use the obtained results to study transport processes in 3D lattice systems which is suitable for describing the processes of mass or charge transfer in the volumes of solids.

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15

Rozenfeld, A. F., and E. V. Albano. "Study of a lattice-gas model for a prey–predator system." Physica A: Statistical Mechanics and its Applications 266, no. 1-4 (April 1999): 322–29. http://dx.doi.org/10.1016/s0378-4371(98)00612-8.

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16

Dhaundiyal, Alok, and Suraj Bhan Singh. "Mathematical Modelling of Volatile Gas Using Lattice Boltzmann Method." Environmental and Climate Technologies 24, no. 1 (January 1, 2020): 483–500. http://dx.doi.org/10.2478/rtuect-2020-0030.

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AbstractThis study investigates the behaviour of pyrolysis gas, generated by the thermal decomposing of biomass, in a pilot size reactor. The discreet mathematical model, Lattice Boltzmann, has adopted for mathematical simulation of flow of pyrolysis gas across a porous bed of biomass. The effect of permeability, pressure gradient, voidage of bed, density, temperature, and the dynamic viscosity on the mass flow rate of gas is examined by simulating the gas flow across the fixed bed of hardwood. The Darcy equation is used to estimate the flow rate of gas across the fixed bed of hardwood chips. The temperature in the reactor varies from 32 °C to 600 °C. The reactor has an external diameter of 220 mm and the vertical height of 320 mm. Rockwool insulation is used to prevent heat loss across the reactor. The external heating element of 2 kWe was provided to trigger the pyrolysis reaction. The properties of the system have been recorded by the pressure and temperature sensors, which are retrofitted along the periphery of the reactor. The temperature sensors are located at 80 mm apart from each other; whereas the pressure sensor, placed at the bottom circumference of the reactor. The effect of input parameters on the flow properties of gas is also examined to add up the qualitative assessment of the system to biomass pyrolysis. The polytropic equation of gas is found to be PV2.051 = C, whereas the compressibility of gas varies from 0.0025–0.042 m2·N–1.

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17

GULMINELLI, FRANCESCA, and PHILIPPE CHOMAZ. "PHASE TRANSITION AND FRAGMENT PRODUCTION IN THE LATTICE GAS MODEL." International Journal of Modern Physics E 08, no. 06 (December 1999): 527–44. http://dx.doi.org/10.1142/s0218301399000367.

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The critical behavior of fragment production is studied within a Lattice Gas Model in the canonical ensemble. Finite size effects on the liquid-gas phase transition are analyzed by a direct calculation of the partition function, and it is shown that phase coexistence and phase transition are relevant concepts even for systems of a few tens of particles. Critical exponents are extracted from the behavior of the fragment production yield as a function of temperature by means of a finite size scaling. The result is that in a finite system well defined critical signals can be found at supercritical (Kertész line) as well as subcritical densities inside the coexistence zone.

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18

Hashimoto, Yasuhiro, Yu Chen, and Hirotada Ohashi. "Boundary Conditions in Lattice Gas with Continuous Velocity." International Journal of Modern Physics C 09, no. 08 (December 1998): 1263–69. http://dx.doi.org/10.1142/s0129183198001138.

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The model we have adopted is called "Hydrodynamic Lattice Gases", that is, a kind of lattice gas with continuous velocity. This model describes the conservation of energy naturally, using innovative collision and propagation schemes. As a result, operations of particles on the boundary become more flexible and complicated as compared with those of the FHP model. And we need to pay attention to the way of treating individual particles. Focusing on the velocity and the coordinates of particles that will return from the boundary to the system, we introduce a reasonable operation that can set temperature and flow velocity of any value required as boundary conditions. Numerical calculations show that those parameters are well controlled using a new boundary scheme.

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19

Danani, A., R. Ferrando, E. Scalas, and M. Torri. "Lattice-Gas Theory of Collective Diffusion in Adsorbed Layers." International Journal of Modern Physics B 11, no. 19 (July 30, 1997): 2217–79. http://dx.doi.org/10.1142/s0217979297001155.

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A general theory for collective diffusion in interacting lattice-gas models is presented. The theory is based on the description of the kinetics in the lattice gas by a master equation. A formal solution of the master equation is obtained using the projection-operator technique, which gives an expression for the relevant correlation functions in terms of continued fractions. In particular, an expression for the collective dynamic structure factor S c is derived. The collective diffusion coefficient D c is obtained from S c by the Kubo hydrodynamic limit. If memory effects are neglected (Darken approximation), it turns out that D c can be expressed as the ratio of the average jump rate <w> and of the zero-wavevector static structure factor S(0). The latter is directly proportional to the isothermal compressibility of the system, whereas <w> is expressed in terms of the multisite static correlation functions gn. The theory is applied to two-dimensional lattice systems as models of adsorbates on crystal surfaces. Three examples are considered. First, the case of nearest-neighbour interactions on a square lattice (both repulsive and attractive). Here, the theoretical results for D c are compared to those of Monte Carlo simulations. Second, a model with repulsive interactions on the triangular lattice. This model is applied to NH 3 adsorbed on Re(0001) and the calculations are compared to experimental data. Third, a model for oxygen on W(110). In this case, the complete dynamic structure factor is calculated and the width of the quasi-elastic peak is studied. In the third example the gn are calculated by means of the discretized version of a classical equation for the structure of liquids (the Crossover Integral Equation), whereas in the other examples they are computed using the Cluster Variation Method.

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20

Agranov, Tal, Michael E. Cates, and Robert L. Jack. "Entropy production and its large deviations in an active lattice gas." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 12 (December 1, 2022): 123201. http://dx.doi.org/10.1088/1742-5468/aca0eb.

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Abstract Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase separation. Exploiting a recent formulation of the exact fluctuating hydrodynamics for this model, we provide analytical results for its entropy production statistics in both typical and atypical (biased) regimes. This complements previous studies of the large deviation statistics of entropy production in off-lattice active particle models that could only be addressed numerically. Our analysis uncovers an unexpectedly intricate phase diagram, with five different phases arising (under bias) within the parameter regime where the unbiased system is in its homogeneous state. Notably, we find the concurrence of first order and second order nonequilibrium phase transition curves at a bias-induced tricritical point, a feature not yet reported in previous studies of active systems.

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21

Briant, A. J. "Lattice Boltzmann simulations of contact line motion in a liquid-gas system." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 360, no. 1792 (March 15, 2002): 485–95. http://dx.doi.org/10.1098/rsta.2001.0943.

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22

Gonz�lez-Miranda, J. M., and J. Marro. "Monte Carlo study of the generalized reaction-diffusion lattice-gas model system." Journal of Statistical Physics 61, no. 5-6 (December 1990): 1283–93. http://dx.doi.org/10.1007/bf01014375.

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23

BOGOLUBOV, Jr., N. N., and D. P. SANKOVICH. "UPPER BOUND ON THE TWO-POINT CORRELATION FUNCTION OF A SYSTEM OF COUPLED ANHARMONIC OSCILLATORS." Modern Physics Letters B 05, no. 01 (January 10, 1991): 51–56. http://dx.doi.org/10.1142/s0217984991000071.

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A quantum system of coupled anharmonic oscillators on v-dimensional hypercubic lattice is considered. The upper bound on the pair correlator is obtained. For the representation of creation-annihilation operators this system corresponds to a lattice boson gas model with δ-type repulsion. We prove the existence of Bose condensation at sufficiently low temperatures, and hence of a phase transition in three or more dimensions. An estimate of the critical temperature is obtained.

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24

ROMANO, S. "COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL." International Journal of Modern Physics B 14, no. 11 (May 10, 2000): 1195–207. http://dx.doi.org/10.1142/s0217979200001448.

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We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearest-neighbouring sites interact via the nematogenic potential [Formula: see text] here P2(τ) denotes the second Legendre polynomial, νj=0,1 are occupation numbers, uj are the unit vectors (classical spins), and ∊ is a positive quantity setting energy and temperature scales (i.e. T*=k B T/∊); the total Hamiltonian is given by [Formula: see text] where ∑{j<k} denotes sum over all distinct nearest-neighbouring pairs of lattice sites. The saturated-lattice version of this model defines the extensively studied Lebwohl–Lasher model, possessing a transition to an orientationally ordered phase at low temperature; according to available rigorous results, there exists a μ0<0, such that, for all μ>μ0, the system supports an ordering transition at a finite, μ-dependent, temperature. We have studied here the case μ=0, and found evidence of a transition, taking place at a lower temperature, and possessing a more pronounced first-order character than its Lebwohl–Lasher counterpart; a Mean Field treatment has also been worked out, and found to yield results in qualitative agreement with simulation.

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25

Ponce, F. A., R. L. Thornton, and G. B. Anderson. "Structural aspects of silicon diffusion in quaternary III-V thin-film semiconductors." Proceedings, annual meeting, Electron Microscopy Society of America 49 (August 1991): 850–51. http://dx.doi.org/10.1017/s0424820100088567.

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The InGaAlP quaternary system allows the production of semiconductor lasers emitting light in the visible range of the spectrum. Recent advances in the visible semiconductor diode laser art have established the viability of diode structures with emission wavelengths comparable to the He-Ne gas laser. There has been much interest in the growth of wide bandgap quaternary thin films on GaAs, a substrate most commonly used in optoelectronic applications. There is particular interest in compositions which are lattice matched to GaAs, thus avoiding misfit dislocations which can be detrimental to the lifetime of these materials. As observed in Figure 1, the (AlxGa1-x)0.5In0.5P system has a very close lattice match to GaAs and is favored for these applications.In this work, we have studied the effect of silicon diffusion in GaAs/InGaAlP structures. Silicon diffusion in III-V semiconductor alloys has been found to have an disordering effect which is associated with removal of fine structures introduced during growth. Due to the variety of species available for interdiffusion, the disordering effect of silicon can have severe consequences on the lattice match at GaAs/InGaAlP interfaces.

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26

Ebihara, Kenichi, Tadashi Watanabe, and Hideo Kaburaki. "Surface of Dense Phase in Lattice-Gas Fluid with Long-Range Interaction." International Journal of Modern Physics C 09, no. 08 (December 1998): 1417–27. http://dx.doi.org/10.1142/s012918319800128x.

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A lattice gas with long-range interaction can simulate phase separation in the system consisting of one kind of component particle like the liquid-vapor theory of van der Waals. The generated phases are distinguished from each other by their particle density. In lattice-gas fluid with long-range interaction, the phase with high density can be observed in the phase with low density like the droplet in vapor. In this paper, the surface of the droplet in lattice-gas fluid with the long-range interaction is determined from the local density and its position is compared with that of Gibbs's dividing surface. The inside region and the outside region of the droplet are defined on the basis of the mean free path in each region. The surface tension is calculated through Laplace's formula using the droplet radius and the pressures in both regions. It is shown that the surface thickness becomes 4r where r is the distance of the long-range interaction.

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27

Kaehler, Goetz, and Alexander Wagner. "Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations." Communications in Computational Physics 9, no. 5 (May 2011): 1315–22. http://dx.doi.org/10.4208/cicp.151109.161110s.

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AbstractWe analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al. [Europhys. Lett., 71 (2005), 473-479] and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered. This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths. In particular cross correlators vanish to less than 0.5%. For larger mean velocities, however, Galilean invariance violations manifest themselves.

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28

Chen, Shuyong, Bo Fu, Xigang Yuan, Huishu Zhang, Wei Chen, and Kuotsung Yu. "Lattice Boltzmann Method for Simulation of Solutal Interfacial Convection in Gas–Liquid System." Industrial & Engineering Chemistry Research 51, no. 33 (August 13, 2012): 10955–67. http://dx.doi.org/10.1021/ie3018912.

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29

Almarza, Noé G., José A. Capitán, José A. Cuesta, and Enrique Lomba. "Phase diagram of a two-dimensional lattice gas model of a ramp system." Journal of Chemical Physics 131, no. 12 (September 28, 2009): 124506. http://dx.doi.org/10.1063/1.3223999.

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30

ROMANO, S. "COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL WITH FOURTH-RANK INTERACTIONS." International Journal of Modern Physics B 16, no. 19 (July 30, 2002): 2901–15. http://dx.doi.org/10.1142/s0217979202009986.

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We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearestneighboring sites interact via the nematogenic potential [Formula: see text] here P4(τ) denotes the fourth Legendre polynomial, nuj=0,1 are occupation numbers, uj are unit vectors (classical spins), and ∊ is a positive quantity setting the energy and temperature scales (i.e. T* =k B T / ∊). The total Hamiltonian is given by [Formula: see text] where ∑{j < k} denotes sum over all distinct nearest-neighboring pairs of lattice sites. The saturated-lattice version of this model defines a nematogenic lattice model, already studied in the literature, and found to possess a transition to an orientationally ordered phase at low temperature; moreover, according to available rigorous results, there exists a μ0<0, such that, for all μ>μ0, the system supports an ordering transition at a finite, μ-dependent, temperature. We present here a detailed study of the case μ=0, and characterize it by means of Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.

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31

REBENKO, ALEXEI L. "CELL GAS MODEL OF CLASSICAL STATISTICAL SYSTEMS." Reviews in Mathematical Physics 25, no. 04 (May 2013): 1330006. http://dx.doi.org/10.1142/s0129055x13300069.

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The work is a brief review of articles by the author and his young colleagues to describe the classical statistical systems with the use of properties of integrals with respect to Poisson measure on configuration space. A variant of cell gas model which is an approximation of the continuous classical gas is proposed. Cell gas (CG) model for continuous classical system of interacting point particles is defined as follows. For a given partition [Formula: see text] of the space ℝd into an infinite set of mutually disjoint hypercubes with edges a, every point of a phase space of an infinite particle system is a configuration in which every hypercube [Formula: see text] contains no more than one particle. We present a structure of measurable sets of the configuration space and show that for strong superstable interaction the pressure and correlation functions of the system pointwise converge to the corresponding values of the conventional continuous system if the edges a of cubes [Formula: see text] tend to zero. We also define lattice gas (LG) model which approximates the CG model and thus provides a continuous transition LG model in the model of continuous gas.

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32

MONETTI, ROBERTO A., and EZEQUIEL V. ALBANO. "STUDY OF THE CROSSOVER FROM NON-EQUILIBRIUM STATIONARY STATES TO QUASI-EQUILIBRIUM STATES IN A DRIVEN DIFFUSIVE SYSTEM UNDER THE INFLUENCE OF AN OSCILLATORY FIELD." International Journal of Modern Physics B 16, no. 27 (October 30, 2002): 4165–74. http://dx.doi.org/10.1142/s0217979202013079.

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A driven diffusive system (DDS) is a lattice-gas in contact with a thermal bath in the presence of an external field. Such DDS constantly gains (losses) energy from (to) the driving field (thermal bath) and therefore, for long enough time, it reaches a non-equilibrium steady-state (NESS) with a generally unknown statistical distribution. It is found that if the constant driving is replaced by an oscillatory field of magnitude E and period τ, the system exhibits a crossover from NESS to a quasi-equilibrium state (QES) driven by τ. The crossover behavior is characterized by a typical crossover time which is proportional to the lattice side and consequently relevant to confined systems.

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33

HUANG, KERSON. "FIFTY YEARS OF HARD-SPHERE BOSE GAS: 1957–2007." International Journal of Modern Physics B 21, no. 30 (December 10, 2007): 5059–73. http://dx.doi.org/10.1142/s0217979207038204.

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Fifty years ago, Yang and I worked on the dilute hard-sphere Bose gas, which has been experimentally realized only relatively recently. I recount the background of that work, subsequent developments, and fresh understanding. In the original work, we had to rearrange the perturbation series, which was equivalent to the Bogoliubov transformation. A deeper reason for the rearrangement has been a puzzle. I can now explain it as a crossover from ideal gas to interacting gas behavior, a phenonmenon arising from Bose statistics. The crossover region is infinitesimally small for a macroscopic system, and thus unobservable. However, it is experimentally relevant in mesoscopic systems, such as a Bose gas trapped in an external potential, or on an optical lattice.

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34

Derzhko, Oleg, Johannes Richter, and Mykola Maksymenko. "Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons." International Journal of Modern Physics B 29, no. 12 (May 10, 2015): 1530007. http://dx.doi.org/10.1142/s0217979215300078.

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On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki–Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

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35

KHOTIMAH, SITI NURUL, IDAM ARIF, and THE HOUW LIONG. "LATTICE-GAS AUTOMATA FOR THE PROBLEM OF KINETIC THEORY OF GAS DURING FREE EXPANSION." International Journal of Modern Physics C 13, no. 08 (October 2002): 1033–45. http://dx.doi.org/10.1142/s0129183102003772.

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The lattice-gas method has been applied to solve the problem of kinetic theory of gas in the Gay–Lussac–Joule experiment. Numerical experiments for a two-dimensional gas were carried out to determine the number of molecules in one vessel (Nr), the ratio between the mean square values of the components of molecule velocity [Formula: see text], and the change in internal energy (ΔU) as a function of time during free expansion. These experiments were repeated for different sizes of an aperture in the partition between the two vessels. After puncturing the partition, the curve for the particle number in one vessel shows a damped oscillation for about half of the total number. The oscillations do not vanish after a sampling over different initial configurations. The system is in nonequilibrium due to the pressure equilibration, and here the flow is actually compressible. The equilibration time (in time steps) decreases with decreased size of aperture in the partition. For very small apertures (equal or less than [Formula: see text] lattice units), the number of molecules in one vessel changes with time in a smooth way until it reaches half of the total number; their curves obey the analytical solution for quasi-static processes. The calculations on [Formula: see text] and ΔU also support the results that the equilibration time decreases with decreased size of aperture in the partition.

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36

Ren, Junjie, Shengzhen Wang, and Xiaoxue Liu. "A modified lattice Boltzmann model for microcylindrical Couette gas flows." Physica Scripta 97, no. 8 (June 27, 2022): 085201. http://dx.doi.org/10.1088/1402-4896/ac7910.

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Abstract We develop an axisymmetric lattice Boltzmann (LB) model to simulate microcylindrical Couette gas flows (MCGF) in the slip regime and transition regime, respectively. A kinetic boundary scheme in the cylindrical coordinate system is proposed to fulfill the second-order slip boundary condition at the cylindrical wall. To consider the effect of the Knudsen layers for transition flows, local effective Knudsen numbers are introduced into the kinetic boundary scheme and relaxation time. Numerical tests are executed to acquire the velocity distributions of the time-independent and time-dependent MCGF. Comparisons with the analytical solution and direct Monte Carlo data are also implemented. The simulation results demonstrate that the developed LB model can successfully acquire the velocity distribution of the MCGF with an intermediate Knudsen number in the transition regime.

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37

Buckley, C. E., H. K. Birnbaum, J. S. Lin, S. Spooner, D. Bellmann, P. Staron, T. J. Udovic, and E. Hollar. "Characterization of H defects in the aluminium–hydrogen system using small-angle scattering techniques." Journal of Applied Crystallography 34, no. 2 (April 1, 2001): 119–29. http://dx.doi.org/10.1107/s0021889800018239.

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Aluminium foils (99.99% purity) and single crystals (99.999% purity) were charged with hydrogen using a gas plasma method and electrochemical methods, resulting in the introduction of a large amount of hydrogen. X-ray diffraction measurements indicated that within experimental error there was a zero change in lattice parameter after plasma charging. This result is contradictory to almost all other face-centred cubic (f.c.c.) materials, which exhibit a lattice expansion when the hydrogen enters the lattice interstitially. It is hypothesized that the hydrogen does not enter the lattice as an interstitial solute, but instead forms an H–vacancy complex at the surface that diffuses into the volume and then clusters to form H2bubbles. Small- and ultra-small-angle neutron scattering (SANS, USANS) and small-angle X-ray scattering (SAXS) were primarily employed to study the nature and agglomeration of the H–vacancy complexes in the Al–H system. The SAXS results were ambiguous owing to double Bragg scattering, but the SANS and USANS investigation, coupled with results from inelastic neutron scattering, and transmission and scanning electron microscopy, revealed the existence of a large size distribution of hydrogen bubbles on the surface and in the bulk of the Al–H system. The relative change in lattice parameter is calculated from the pressure in a bubble of average volume and is compared with the experimentally determined value.

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38

Tribel, Olivier, and Jean Pierre Boon. "Entropy and Correlations in Lattice-Gas Automata Without Detailed Balance." International Journal of Modern Physics C 08, no. 04 (August 1997): 641–52. http://dx.doi.org/10.1142/s0129183197000552.

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We consider lattice-gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas properties and can undergo phase transitions. For this class of automata, mean-field theory provides a correct evaluation of properties such as compressibility and viscosity (away from the phase transition), despite the fact that no H-theorem strictly holds. We introduce the notion of locality — necessary to define quantities accessible to measurements — by treating the coupling between nonlocal bits as a perturbation. Then if we define operationally "local" states of the automaton — whether the system is in a homogeneous or in an inhomogeneous state — we can compute an estimator of the entropy and measure the local channel occupation correlations. These considerations are applied to a simple model with nonlocal interactions.

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39

MATSUKUMA, Yosuke, Yuichi OTSUKA, and Masaki MINEMOTO. "Basic Numerical Study on Recovery System of Methane Hydrate by Lattice Gas Automata method." Proceedings of the JSME annual meeting 2002.3 (2002): 209–10. http://dx.doi.org/10.1299/jsmemecjo.2002.3.0_209.

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40

MASUDA, Shinnosuke, Yu CHEN, and Hirotada OHASHI. "Numerical Simulation of the Colloidal System by using the Real-coded Lattice Gas Method." Proceedings of The Computational Mechanics Conference 2003.16 (2003): 129–30. http://dx.doi.org/10.1299/jsmecmd.2003.16.129.

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41

Prestipino, Santi, and Gabriele Costa. "Condensation and Crystal Nucleation in a Lattice Gas with a Realistic Phase Diagram." Entropy 24, no. 3 (March 17, 2022): 419. http://dx.doi.org/10.3390/e24030419.

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We reconsider model II of Orban et al. (J. Chem. Phys. 1968, 49, 1778–1783), a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: Upon closer inspection, the alleged liquid–vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier relative to crystal nucleation from the “liquid”.

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42

ROMANO, S. "MEAN FIELD, TWO-SITE CLUSTER, AND COMPUTER SIMULATION STUDY OF A NEMATOGENIC LATTICE-GAS MODEL." International Journal of Modern Physics B 15, no. 03 (January 30, 2001): 259–80. http://dx.doi.org/10.1142/s0217979201003545.

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We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearest-neighbouring sites interact via the nematogenic potential [Formula: see text] here P2(τ) denotes the second Legendre polynomial, νj = 0, 1 are occupation numbers, uj are unit vectors (classical spins), and ∊ is a positive quantity setting energy and temperature scales (i.e. T* = k B T/∊); the total Hamiltonian is given by [Formula: see text] where ∑{j<k} denotes sum over all distinct nearest-neighbouring pairs of lattice sites. The saturated-lattice version of this model defines the extensively studied Lebwohl–Lasher model, possessing a transition to an orientationally ordered phase at low temperature; according to available rigorous results, there exists a μ0 < 0, such that, for all μ > μ0, the system supports an ordering transition at a finite, μ-dependent, temperature. Continuing along the lines of our previous communication [S. Romano, Int. J. Mod. Phys.B14, 1195 (2000)], we present here a detailed study of the case μ = 0, using Monte Carlo simulation, Mean Field and Two Site Cluster treatments; the latter significantly improves the agreement with simulation results.

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43

Holder, Jacob, Ralf Schmid, and Peter Nielaba. "Two-step nucleation in confined geometry: Phase diagram of finite particles on a lattice gas model." Journal of Chemical Physics 156, no. 12 (March 28, 2022): 124504. http://dx.doi.org/10.1063/5.0073043.

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We use a degenerated Ising model to describe nucleation and crystallization from solution in a confined two-component system. The free energy is calculated using metadynamics simulation with coordination numbers as the reaction coordinates. We deploy nudged elastic band simulation to determine the minimum energy path and give properties of the crystallization path. In this confined system, depletion effects, which could also be caused by slow material transport in the solution, prevent the post-critical cluster from further growth, and the crystalline state would only be stable at larger cluster sizes. Fluctuation of the higher coupling strength of the crystalline state enables further growth until the crystalline cluster is in equilibrium with the solvent, and this way, a second barrier is crossed. From the parameters and setup, we find necessary conditions for the occurrence of two-step nucleation in our system. These findings can be adapted to real systems as biomineralization, colloidal crystallization, and the solidification of metals.

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44

YU. KHLEBNIKOV, S. "LOW DENSITY HUBBARD MODEL IN TWO AND THREE DIMENSIONS." Modern Physics Letters B 06, no. 12 (May 20, 1992): 753–60. http://dx.doi.org/10.1142/s0217984992000831.

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We consider two- and three-dimensional repulsive Hubbard models at low density, using the gas approximation. The large-U three-dimensional model is shown to behave as a Fermi liquid and the corresponding two-particle scattering length is found. In the two-dimensional case we find that the gas approximation is inconsistent, as indicated by an isolated pole of the two-particle Green function below the occupied states in the upper half-plane. This behaviour is specific to the lattice system as opposed to the continuum two-dimensional Fermi gas with short-range repulsion.

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45

LaBella, V. P., D. W. Bullock, M. Anser, Z. Ding, C. Emery, L. Bellaiche, and P. M. Thibado. "Microscopic View of a Two-Dimensional Lattice-Gas Ising System within the Grand Canonical Ensemble." Physical Review Letters 84, no. 18 (May 1, 2000): 4152–55. http://dx.doi.org/10.1103/physrevlett.84.4152.

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46

Pandey, R. B., and J. F. Gettrust. "Eruptive flow response in a multi-component driven system by an interacting lattice gas simulation." Physica A: Statistical Mechanics and its Applications 368, no. 2 (August 2006): 416–24. http://dx.doi.org/10.1016/j.physa.2006.01.086.

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47

Fritz, József, and Bálint Tóth. "Derivation of the Leroux System as the Hydrodynamic Limit of a Two-Component Lattice Gas." Communications in Mathematical Physics 249, no. 1 (May 20, 2004): 1–27. http://dx.doi.org/10.1007/s00220-004-1103-x.

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48

Awazu, Akinori. "Forward and Backward Drift Motions and Inversion of Drift Directions in Small Lattice Gas System." Journal of the Physical Society of Japan 74, no. 12 (December 2005): 3127–30. http://dx.doi.org/10.1143/jpsj.74.3127.

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49

Ujita, Hiroshi, Satoru Nagata, Minoru Akiyama, Masanori Naitoh, and Hirotada Ohashi. "Development of LGA & LBE 2D Parallel Programs." International Journal of Modern Physics C 09, no. 08 (December 1998): 1203–20. http://dx.doi.org/10.1142/s0129183198001096.

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A lattice-gas Automata two-dimensional program was developed for analysis of single and two-phase flow behaviors, to support the development of integrated software modules for Nuclear Power Plant mechanistic simulations. The program has single-color, which includes FHP I, II, and III models, two-color (Immiscible lattice gas), and two-velocity methods including a gravity effect model. Parameter surveys have been performed for Karman vortex street, two-phase separation for understanding flow regimes, and natural circulation flow for demonstrating passive reactor safety due to the chimney structure vessel. In addition, lattice-Boltzmann Equation two-dimensional programs were also developed. For analyzing single-phase flow behavior, a lattice-Boltzmann-BGK program was developed, which has multi-block treatments. A Finite Differential lattice-Boltzmann Equation program of parallelized version was introduced to analyze boiling two-phase flow behaviors. Parameter surveys have been performed for backward facing flow, Karman vortex street, bent piping flow with/without obstacles for piping system applications, flow in the porous media for demonstrating porous debris coolability, Couette flow, and spinodal decomposition to understand basic phase separation mechanisms. Parallelization was completed by using a domain decomposition method for all of the programs. An increase in calculation speed of at least 25 times, by parallel processing on 32 processors, demonstrated high parallelization efficiency. Application fields for microscopic model simulation to hypothetical severe conditions in large plants were also discussed.

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50

LaBELLA, V. P., Z. DING, D. W. BULLOCK, C. EMERY, and P. M. THIBADO. "A UNION OF THE REAL-SPACE AND RECIPROCAL-SPACE VIEW OF THE GaAs(001) SURFACE." International Journal of Modern Physics B 15, no. 17 (July 10, 2001): 2301–33. http://dx.doi.org/10.1142/s0217979201005647.

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A union of the real-space and reciprocal space view of the GaAs(001) surface is presented. An optical transmission temperature measurement system allowed fast and accurate temperature determinations of the GaAs(001) substrate. The atomic features of the Ga A s (001)-(2×4) reconstructed surface are resolved with scanning tunneling microscopy and first principles density functional theory. In addition, the 2D lattice-gas Ising model within the grand canonical ensemble can be applied to this surface to understand the thermodynamics. An algorithm for using electron diffraction on the GaAs(001) surface to determine the substrate temperature and tune the nanoscale surface roughness is presented.

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