EXTENDED MEAN FIELD APPROACH TO ANALYZING PATTERN FORMATION IN SURFACE CHEMICAL REACTIONS

2004 ◽  
Vol 11 (01) ◽  
pp. 57-70 ◽  
Author(s):  
E. E. MOLA ◽  
D. A. KING ◽  
I. M. IRURZUN ◽  
M. RAFTI ◽  
J. L. VICENTE
Keyword(s):  
Pattern Formation ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
M Cells ◽  
Surface Chemical ◽  
Partial Pressures ◽  
Global Coupling ◽  
Surface Chemical Reactions

In this paper we apply a model of surface chemical reactions to describe pattern formation in the CO oxidation on Pt(100). The model is an extended mean field approximation (EMFA), where two coupling processes are included: gas global coupling (to take into account the mass chemical reaction balance) and CO diffusion. The surface is divided into M×M cells; inside each of them the mean field approximation (MFA) is fulfilled. Anisotropic diffusion between nearest neighbor cells and gas coupling among all cells are also allowed. The EMFA goes beyond the traditional reaction–diffusion approaches with Fickian terms, in favor of a more general mass balance equation that consistently incorporates the coupling between CO diffusion and the nonlinear phase transition of the substrate. In this paper we study three different cases: (a) homogeneous coverage oscillations — when CO and O 2 partial pressures are kept constant and the whole set of M×M cells have the same value of partial coverages and phase fractions; in this case the system exhibits self-oscillations, such as those experimentally observed; (b) inhomogeneous coverage oscillations — when CO and O 2 partial pressures are kept constant and inhomogeneities of coverage are present; the system evolves by CO diffusion between nearest neighbor cells; (c) gas global coupling — when gas global coupling is allowed and inhomogeneities of coverage are present, there are oscillations in the gas phase that follow the surface evolution.

scholarly journals ISOSPIN LATTICE GAS MODEL AND NUCLEAR-MATTER PHASE DIAGRAM AND PRESSURE-VOLUME ISOTHERMS

1996 ◽  
Vol 05 (02) ◽  
pp. 303-311 ◽  
Author(s):  
T.T.S. KUO ◽  
S. RAY ◽  
J. SHAMANNA ◽  
R.K. SU
Keyword(s):  
Nuclear Matter ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Lattice Gas Model ◽  
Mean Field Approximation ◽  
Kinetic Energy Term ◽  
Phase Liquid ◽  
Matter Phase

We study a cubic lattice gas model for nuclear matter where each lattice site can be either occupied, by one proton or one neutron, or unoccupied. A nearest-neighbor interaction of the form - ∑<ij>Jijτziτzj is assumed. Our model is an isospin-1 Ising model, with τz= (1, 0, –1) representing respectively (proton, vacancy, neutron). A kinetic-energy term has been included in our model. Under the Bragg-Williams mean-field approximation our model exhibits the existence of a dense phase (liquid-like) and a rare phase (gas-like). The nuclear-matter p−v isotherms given by our model are discussed.

PHASE TRANSITIONS OF THE MIXED-SPIN ISING MODEL ON A DECORATED LATTICE WITH THE NEAREST-NEIGHBOR INTERACTION BETWEEN DECORATING SPINS

2009 ◽  
Vol 23 (24) ◽  
pp. 4963-4976 ◽  
Author(s):  
A. BENYOUSSEF ◽  
A. EL KENZ ◽  
M. EL YADARI ◽  
M. LOULIDI
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Phase Diagrams ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nearest Neighbors ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Neighbor Interaction ◽  
Mixed Spin

A mean-field approximation is developed for a decorated ferrimagnetic Ising model, in which the two magnetic atoms A and B have spins σ=1/2 and S=1, respectively. In this system, the exchange interaction between nearest-neighbors of atom B is taken into account. Some interesting phenomena, such as the appearance of three types of phase diagrams and the existence of one and two compensation points are found. Phase diagrams and temperature dependence of the magnetizations of the system are investigated in detail.

The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model

1997 ◽  
Vol 11 (13) ◽  
pp. 565-570
Author(s):  
G. L. S. Paula ◽  
W. Figueiredo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Stationary States ◽  
Transition Rates ◽  
The Mean ◽  
The One

We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

Modulated Phases on the FCC(110) Surfaces with Adsorbate-Induced Reconstructions

2003 ◽  
Vol 10 (02n03) ◽  
pp. 189-194
Author(s):  
Min Kang ◽  
Makoto Kaburagi
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Correlation Function ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Modulated Phases ◽  
The Mean ◽  
Beg Model

We theoretically investigate the fcc(110) surfaces with missing row reconstructions induced by adatoms using the Blume–Emmery–Griffith (BEG) model. In the model, Kij is introduced to denote interactions between surface atoms and Jij to describe interactions between dipoles. The investigation by the mean field approximation has predicted that there appear modulated phases on the surfaces as the next-nearest-neighbor (NNN) and the nearest-neighbor (NN) interactions along the [001] direction become competitive. In this study, Monte Carlo simulations are performed to confirm the prediction. A correlation function defined by concentration operators in wave vector q space is calculated. The results show that the concentration modulations appear. The temperature versus the ratio of the NNN interaction K2 to the NN interaction K1 phase diagram is obtained. The possible features of the modulated phases in experiments are discussed.

scholarly journals The Role of Extended Range of Interactions in the Dynamics of Interacting Molecular Motors

2021 ◽  
Author(s):  
Cade Spaulding ◽  
Hamid Teimouri ◽  
S.L. Narasimha ◽  
Anatoly B. Kolomeisky
Keyword(s):  
Computer Simulations ◽  
Molecular Motors ◽  
Nearest Neighbor ◽  
Theoretical Calculations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Experimental Investigations ◽  
Cellular Transport ◽  
Fundamental Diagram

Motor proteins, also known as biological molecular motors, play important roles in various intracellular processes. Experimental investigations suggest that molecular motors interact with each other during the cellular transport, but the nature of such interactions remains not well understood. Stimulated by these observations, we present a theoretical study aimed to understand the effect of the range of interactions on dynamics of interacting molecular motors. For this purpose, we develop a new version of the totally asymmetric simple exclusion processes in which nearest-neighbor as well as the next nearest-neighbor interactions are taken into account in a thermodynamically consistent way. A theoretical framework based on a cluster mean-field approximation, which partially takes correlations into account, is developed to evaluate the stationary properties of the system. It is found that fundamental current-density relations in the system strongly depend on the strength and the sign of interactions, as well as on the range of interactions. For repulsive interactions stronger than some critical value, increasing the range of interactions leads to a change from unimodal to trimodal dependence in the flux-density fundamental diagram. Theoretical calculations are tested with extensive Monte Carlo computer simulations. Although in most ranges of parameters excellent agreement between theoretical predictions and computer simulations is observed, there are situations when the cluster mean-field approach fails to describe properly the dynamics in the system. Theoretical arguments to explain these observations are presented. Our theoretical analysis clarifies the microscopic picture of how the range of interactions influences the dynamics of interacting molecular motors.

scholarly journals Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 58
Author(s):  
Zlatko Koinov
Keyword(s):  
Phase Diagram ◽  
Optical Lattices ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Recent Developments ◽  
Topological States ◽  
Half Filling ◽  
The Mean

Motivated by recent developments in the experimental study of ultracold atoms in graphene-like honeycomb optical lattices, we investigate superconductivity of the attractive Kane-Mele-Habbard (KMH) model with the next-nearest-neighbor (NNN) hoping at half filling. The mean-field approximation is used to study the phase diagram which interpolates the trivial and the non-trivial topological states. It is shown that: (a) when the NNN hoping is taken into account, one has to introduce two mean-field gap equations for the two sublattices, instead of a single gap when the NNN hopping is neglected, and (b) in the non-trivial topological region the phase diagram with the NNN hopping is significantly different compared to the phase diagram calculated previously, but without the NNN term. We also discuss the superconducting instability of the attractive KMH model that is driven by condensation of Cooperons.

SPONTANEOUS SYMMETRY BREAKING IN A MICROTUBULE-LIKE SYSTEM

2010 ◽  
Vol 21 (06) ◽  
pp. 825-837 ◽  
Author(s):  
MINGZHE LIU ◽  
RUILI WANG ◽  
RUI JIANG
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Low Density ◽  
Channel System ◽  
Multiple Channel ◽  
Proposed Model

This paper studies asymmetric exclusion processes on a microtubule-like system with two species of particles. The model is motivated by the structure of microtubules and kinesins and dyneins moving along microtubules in opposite directions. The proposed model is similar to that in J. Phys. A40, 2275 (2007) in which two-channel TASEPs with narrow entrances and parallel update are studied. This paper extended the above-mentioned work to a multiple-channel hollow cylinder case. Thus, each channel has two nearest neighbors in our model. The corresponding rule for narrow entrances is that particles cannot enter the system if either of two nearest-neighbor sites on neighboring channels is occupied by the other species of particles. The phase diagram of the model is obtained from a mean-field approximation and verified by computer simulations. It is shown that the spontaneous symmetry breaking exists with two asymmetric phases: high/low density and low/low density. The flipping process of particles is observed. Bulk density and particle currents are computed. Monte Carlo simulation results deviate from the mean-field prediction when entrance rate α is high, which is due to neglecting correlations among particles in mean-field calculations. The results are also compared with that obtained from two-channel system with one neighbor narrow entrance in parallel update.

PHASE DIAGRAM OF STRIPE ORDER IN THE EXTENDED HUBBARD MODEL

2000 ◽  
Vol 14 (29n31) ◽  
pp. 3508-3513 ◽  
Author(s):  
MASARU KATO
Keyword(s):  
Hubbard Model ◽  
Coulomb Interaction ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Square Lattice ◽  
Mean Field Approximation ◽  
Extended Hubbard Model ◽  
Stable States ◽  
Stripe Order

The extended Hubbard model with the nearest-neighbor Coulomb interaction on the square lattice is studied within the mean-field approximation. The stable states for 8×8 sites lattice with the periodic boundary condition and the electron filling n=0.875, as well as for 10×10 lattice and n=0.80, are obtained. For 8×8 lattice where quarter-filled straight stripe is expected because of the long-range Coulomb interaction, the cross stripe phases become stable.

A MEAN-FIELD APPROACH TO A DISCRETE DIPOLAR SPIN MODEL WITH UNIAXIAL MAGNETIC ANISOTROPY

2009 ◽  
Vol 20 (09) ◽  
pp. 1335-1343
Author(s):  
YUSUKE TOMITA ◽  
SHUNSUKE YANAI ◽  
HAJIME TAKAYAMA
Keyword(s):  
Magnetic Anisotropy ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Dipolar Interaction ◽  
Field Approximation ◽  
Spin Model ◽  
Lattice Points ◽  
Mean Field Approximation ◽  
Hypercubic Lattice ◽  
Dipolar System

Using the mean-field approximation, we study the reorientation transition in a discrete dipolar spin model. We array the d-dimensional spins in the d-1-dimensional hypercubic lattice points, and apply the magnetic anisotropy in the dth direction. Even though the long-range dipolar interaction is truncated to the nearest-neighbor interaction, the model exhibits the reorientation transition. The effects of the exchange interaction on the dipolar system are also studied.

Scaling of Reaction Fronts in the Presence of Disorder

1994 ◽  
Vol 366 ◽  
Author(s):  
Mariela Araujo
Keyword(s):  
Reaction Front ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Diffusion Reaction ◽  
Mean Field Approximation ◽  
Disorder Strength ◽  
Reaction Systems ◽  
Reaction Fronts ◽  
The Mean

ABSTRACTA study of the dynamics of the reaction front that appears in diffusion-reaction systems of the form A + B → C with initially separated reactants in the presence of quenched disorder is presented. The scaling of the width of the front w is analyzed as a function of the “disorder strength” and the dimensionality of the system. It is shown that disorder strongly affects the width exponent α, ω tα even for d ≥ 2, where the mean field approximation is known to be valid. The scaling of the nearest neighbor distance, midpoint fluctuations and concentration profiles near the center of the front, are also studied.

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