Entropy Analysis of a Nearest-Neighbor Attractive/Repulsive Exclusion Process on One-Dimensional Lattices

We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model (IHM) with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin S = 1/2 anisotropic XXZ Heisenberg chain with alternating next-nearest-neighbor (NNN) and three-spin couplings in the presence of a uniform and a staggered magnetic field.

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EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

International Journal of Modern Physics B ◽

10.1142/s0217979296001847 ◽

1996 ◽

Vol 10 (25) ◽

pp. 3451-3459 ◽

Cited By ~ 2

Author(s):

ANTÓNIO M.R. CADILHE ◽

VLADIMIR PRIVMAN

Keyword(s):

Exact Solution ◽

Domain Wall ◽

Nearest Neighbor ◽

Spin Exchange ◽

Initial Conditions ◽

Strong Dependence ◽

Zero Temperature ◽

Dimensional Model ◽

One Dimensional ◽

Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

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Negative Thermal Expansion of the One-Dimensional Lattice Gas with Next-Nearest-Neighbor Interaction

Progress of Theoretical Physics ◽

10.1143/ptp/90.6.1355 ◽

1993 ◽

Vol 90 (6) ◽

pp. 1355-1360

Author(s):

K. Nisizima

Keyword(s):

Thermal Expansion ◽

Lattice Gas ◽

Nearest Neighbor ◽

Negative Thermal Expansion ◽

Neighbor Interaction ◽

Dimensional Lattice ◽

One Dimensional ◽

The One

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A stochastic airplane boarding model in a framework of ASEP with distinguishable particles

International Journal of Modern Physics C ◽

10.1142/s0129183118500936 ◽

2018 ◽

Vol 29 (10) ◽

pp. 1850093

Author(s):

ShengJie Qiang ◽

Bin Jia ◽

QingXia Huang

Keyword(s):

Removal Rate ◽

Exclusion Process ◽

System Size ◽

Nonequilibrium Systems ◽

One Dimensional ◽

Simple Exclusion Process ◽

Maximum Current ◽

Asymmetric Simple Exclusion ◽

Simple Exclusion ◽

The Difference

The asymmetric simple exclusion process (ASEP) is a paradigmatic model for nonequilibrium systems and has been used in many applications. Airplane boarding provides another interesting example where this framework can be applied. We propose a simple model for boarding process, in which a particle moves along a one-dimensional aisle after being injected, and finally is removed at a reserved site. Different from the typical ASEP model, particles are removed in a disorderly or a parallel way. Detailed calculations and discussions of some related characteristics, such as mean boarding time and parallelism indicator, are provided based on Monte-Carlo simulations. Results show that three phases exist in the boarding process: free-flow, jamming and maximum current. Transitions between these phases are governed by the difference between the injection and removal rate. Further analysis shows how the scaling behavior depends on the system size and the boarding conditions. Those results emphasize the importance of utilizing the whole length of the aisle to reduce the boarding time when designing an efficient boarding strategy.

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ROBUSTNESS OF COMPLETE STABILITY FOR 1-D CIRCULAR CNNs

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406015994 ◽

2006 ◽

Vol 16 (08) ◽

pp. 2177-2190

Author(s):

MAURO DI MARCO ◽

CHIARA GHILARDI

Keyword(s):

Neural Networks ◽

Equilibrium Point ◽

Nearest Neighbor ◽

Perturbation Parameter ◽

Relative Magnitude ◽

Loss Of Stability ◽

Unique Equilibrium ◽

Small Perturbations ◽

Structure Preserving ◽

One Dimensional

This paper investigates the issue of robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominally symmetric interconnections. More specifically, a class of circular one-dimensional (1-D) CNNs with nearest-neighbor interconnections only, is considered. The class has sparse interconnections and is subject to perturbations which preserve the interconnecting structure. Conditions assuring that the perturbed CNN has a unique equilibrium point at the origin, which is unstable, are provided in terms of relative magnitude of the perturbations with respect to the nominal interconnection weights. These conditions allow one to characterize regions in the perturbation parameter space where there is loss of stability for the perturbed CNN. In turn, this shows that even for sparse interconnections and structure preserving perturbations, robustness of complete stability is not guaranteed in the general case.

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