scholarly journals Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models

2010 ◽  
Vol 74 (2) ◽  
pp. 159-164 ◽  
Author(s):  
A. Aghamohammadi ◽  
M. Khorrami
Keyword(s):  
Nearest Neighbor ◽  
Reaction Diffusion ◽  
Diffusion Models ◽  
One Dimensional

scholarly journals Effective dynamics of a conditioned generalized linear Glauber model

2018 ◽  
Vol 32 (22) ◽  
pp. 1850243
Author(s):  
Sara Kaviani ◽  
Farhad H. Jafarpour
Keyword(s):  
Nearest Neighbor ◽  
Reaction Diffusion ◽  
Glauber Model ◽  
Transition Rates ◽  
Original Process ◽  
One Dimensional ◽  
Effective Dynamics ◽  
Physical Observable ◽  
Constants Of Motion ◽  
Classical Particles

In order to study the stochastic Markov processes conditioned on a specific value of a time-integrated observable, the concept of ensembles of trajectories has been recently used extensively. In this paper, we consider a generic reaction–diffusion process consisting of classical particles with nearest-neighbor interactions on a one-dimensional lattice with periodic boundary conditions. By introducing a time-integrated current as a physical observable, we have found certain constraints on the microscopic transition rates of the process under which the effective process contains local interactions; however, with rescaled transition rates comparing to the original process. A generalization of the linear Glauber model is then introduced and studied in detail as an example. Associated effective dynamics of this model is investigated and constants of motion are obtained.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

Study of the one-dimensional Holstein model with next-nearest-neighbor hopping

2010 ◽  
Vol 23 (2) ◽  
pp. 025601 ◽  
Author(s):  
Monodeep Chakraborty ◽  
A N Das ◽  
Atisdipankar Chakrabarti
Keyword(s):  
Nearest Neighbor ◽  
One Dimensional ◽  
Holstein Model ◽  
The One

scholarly journals The interplay between phenotypic and ontogenetic plasticities can be assessed using reaction-diffusion models

2017 ◽  
Vol 43 (2) ◽  
pp. 247-264 ◽  
Author(s):  
Aldo Ledesma-Durán ◽  
Lorenzo-Héctor Juárez-Valencia ◽  
Juan-Bibiano Morales-Malacara ◽  
Iván Santamaría-Holek
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Models

scholarly journals Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

2016 ◽  
Vol 30 (03) ◽  
pp. 1550260 ◽  
Author(s):  
I. Grusha ◽  
M. Menteshashvili ◽  
G. I. Japaridze
Keyword(s):  
Magnetic Field ◽  
Nearest Neighbor ◽  
Effective Hamiltonian ◽  
Heisenberg Chain ◽  
Spin Hamiltonian ◽  
Effective Spin ◽  
One Dimensional ◽  
The One ◽  
Strong Repulsion ◽  
Ionic Hubbard Model

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.

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

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
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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