458 research outputs found
Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update
A multi-species generalization of the asymmetric simple exclusion process
(ASEP) is studied in ordered sequential and sub-lattice parallel updating
schemes. In this model particles hop with their own specific probabilities to
their rightmost empty site and fast particles overtake slow ones with a
definite probability. Using Matrix Product Ansatz (MPA), we obtain the relevant
algebra, and study the uncorrelated stationary state of the model both for an
open system and on a ring. A complete comparison between the physical results
in these updates and those of random sequential introduced in [20,21] is made.Comment: Latex file 36 pages with 10 EPS figure
Multi shocks in Reaction-diffusion models
It is shown, concerning equivalent classes, that on a one-dimensional lattice
with nearest neighbor interaction, there are only four independent models
possessing double-shocks. Evolution of the width of the double-shocks in
different models is investigated. Double-shocks may vanish, and the final state
is a state with no shock. There is a model for which at large times the average
width of double-shocks will become smaller. Although there may exist stationary
single-shocks in nearest neighbor reaction diffusion models, it is seen that in
none of these models, there exist any stationary double-shocks. Models
admitting multi-shocks are classified, and the large time behavior of
multi-shock solutions is also investigated.Comment: 17 pages, LaTeX2e, minor revisio
Finite-dimensional representation of the quadratic algebra of a generalized coagulation-decoagulation model
The steady-state of a generalized coagulation-decoagulation model on a
one-dimensional lattice with reflecting boundaries is studied using a
matrix-product approach. It is shown that the quadratic algebra of the model
has a four-dimensional representation provided that some constraints on the
microscopic reaction rates are fulfilled. The dynamics of a product shock
measure with two shock fronts, generated by the Hamiltonian of this model, is
also studied. It turns out that the shock fronts move on the lattice as two
simple random walkers which repel each other provided that the same constraints
on the microscopic reaction rates are satisfied.Comment: Minor revision
Discontinuous Phase Transition in an Exactly Solvable One-Dimensional Creation-Annihilation System
An exactly solvable reaction-diffusion model consisting of first-class
particles in the presence of a single second-class particle is introduced on a
one-dimensional lattice with periodic boundary condition. The number of
first-class particles can be changed due to creation and annihilation
reactions. It is shown that the system undergoes a discontinuous phase
transition in contrast to the case where the density of the second-class
particles is finite and the phase transition is continuous.Comment: Revised, 8 pages, 1 EPS figure. Accepted for publication in Journal
of Statistical Mechanics: theory and experimen
Exact Solution of an Exclusion Model in the Presence of a moving Impurity
We study a recently introduced model which consists of positive and negative
particles on a ring. The positive (negative) particles hop clockwise
(counter-clockwise) with rate 1 and oppositely charged particles may swap their
positions with asymmetric rates q and 1. In this paper we assume that a finite
density of positively charged particles and only one negative particle
(which plays the role of an impurity) exist on the ring. It turns out that the
canonical partition function of this model can be calculated exactly using
Matrix Product Ansatz (MPA) formalism. In the limit of infinite system size and
infinite number of positive particles, we can also derive exact expressions for
the speed of the positive and negative particles which show a second order
phase transition at . The density profile of the positive particles
on the ring has a shock structure for and an exponential behaviour
with correlation length for . It will be shown that the
mean-field results become exact at q=3 and no phase transition occurs for q>2.Comment: 9 pages,4 EPS figures. To be appear in JP
Double‐spirals offer the development of pre‐programmable modular metastructures
Metamaterials with adjustable, sometimes unusual properties offer advantages over conventional materials with predefined mechanical properties in many technological applications. A group of metamaterials, called modular metamaterials or metastructures, are developed through the arrangement of multiple, mostly similar building blocks. These modular structures can be assembled using prefabricated modules and reconfigured to promote efficiency and functionality. Here, we developed a novel modular metastructure by taking advantage of the high compliance of pre-programmable double-spirals. First, we simulated the mechanical behavior of a four-module metastructure under tension, compression, rotation, and sliding using the finite-element method. Then, we used 3D printing and mechanical testing to illustrate the tunable anisotropic and asymmetric behavior of spiral-based metastructures in practice. Our results show the simple reconfiguration of the presented metastructure toward the desired functions. The mechanical behavior of single double-spirals and the characteristics that can be achieved through their combinations make our modular metastructure suitable for various applications in robotics, aerospace, and medical engineering
The quantum double well anharmonic oscillator in an external field
The aim of this paper is twofold. First of all, we study the behaviour of the
lowest eigenvalues of the quantum anharmonic oscillator under influence of an
external field. We try to understand this behaviour using perturbation theory
and compare the results with numerical calculations. This brings us to the
second aim of selecting the best method to carry out the numerical calculations
accurately.Comment: 9 pages, 6 figure
Relaxation time in a non-conserving driven-diffusive system with parallel dynamics
We introduce a two-state non-conserving driven-diffusive system in
one-dimension under a discrete-time updating scheme. We show that the
steady-state of the system can be obtained using a matrix product approach. On
the other hand, the steady-state of the system can be expressed in terms of a
linear superposition Bernoulli shock measures with random walk dynamics. The
dynamics of a shock position is studied in detail. The spectrum of the transfer
matrix and the relaxation times to the steady-state have also been studied in
the large-system-size limit.Comment: 10 page
First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach
A coagulation-decoagulation model is introduced on a chain of length L with
open boundary. The model consists of one species of particles which diffuse,
coagulate and decoagulate preferentially in the leftward direction. They are
also injected and extracted from the left boundary with different rates. We
will show that on a specific plane in the space of parameters, the steady state
weights can be calculated exactly using a matrix product method. The model
exhibits a first-order phase transition between a low-density and a
high-density phase. The density profile of the particles in each phase is
obtained both analytically and using the Monte Carlo Simulation. The two-point
density-density correlation function in each phase has also been calculated. By
applying the Yang-Lee theory we can predict the same phase diagram for the
model. This model is further evidence for the applicability of the Yang-Lee
theory in the non-equilibrium statistical mechanics context.Comment: 10 Pages, 3 Figures, To appear in Journal of Physics A: Mathematical
and Genera
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