121 research outputs found
A family of discrete-time exactly-solvable exclusion processes on a one-dimensional lattice
A two-parameter family of discrete-time exactly-solvable exclusion processes
on a one-dimensional lattice is introduced, which contains the asymmetric
simple exclusion process and the drop-push model as particular cases. The
process is rewritten in terms of boundary conditions, and the conditional
probabilities are calculated using the Bethe-ansatz. This is the discrete-time
version of the continuous-time processes already investigated in [1-3]. The
drift- and diffusion-rates of the particles are also calculated for the
two-particle sector.Comment: 10 page
Exactly solvable models through the generalized empty interval method: multi-species and more-than-two-site interactions
Multi-species reaction-diffusion systems, with more-than-two-site interaction
on a one-dimensional lattice are considered. Necessary and sufficient
constraints on the interaction rates are obtained, that guarantee the
closedness of the time evolution equation for 's, the
expectation value of the product of certain linear combination of the number
operators on consecutive sites at time .Comment: 10 pages, LaTe
Exclusion Processes and boundary conditions
A family of boundary conditions corresponding to exclusion processes is
introduced. This family is a generalization of the boundary conditions
corresponding to the simple exclusion process, the drop-push model, and the
one-parameter solvable family of pushing processes with certain rates on the
continuum [1-3]. The conditional probabilities are calculated using the Bethe
ansatz, and it is shown that at large times they behave like the corresponding
conditional probabilities of the family of diffusion-pushing processes
introduced in [1-3].Comment: 11 pages, LaTeX2
Design and Construction of Zana Robot for Modeling Human Player in Rock-paper-scissors Game using Multilayer Perceptron, Radial basis Functions and Markov Algorithms
In this paper, the implementation of artificial neural networks (multilayer perceptron [MLP] and radial base functions [RBF]) and the upgraded Markov chain model have been studied and performed to identify the human behavior patterns during rock, paper, and scissors game. The main motivation of this research is the design and construction of an intelligent robot with the ability to defeat a human opponent. MATLAB software has been used to implement intelligent algorithms. After implementing the algorithms, their effectiveness in detecting human behavior pattern has been investigated. To ensure the ideal performance of the implemented model, each player played with the desired algorithms in three different stages. The results showed that the percentage of winning computer with MLP and RBF neural networks and upgraded Markov model, on average in men and women is 59%, 76.66%, and 75%, respectively. Obtained results clearly indicate a very good performance of the RBF neural network and the upgraded Markov model in the mental modeling of the human opponent in the game of rock, paper, and scissors. In the end, the designed game has been employed in both hardware and software which include the Zana intelligent robot and a digital version with a graphical user interface design on the stand. To the best knowledge of the authors, the precision of novel presented method for determining human behavior patterns was the highest precision among all of the previous studies
On the solvable multi-species reaction-diffusion processes
A family of one-dimensional multi-species reaction-diffusion processes on a
lattice is introduced. It is shown that these processes are exactly solvable,
provided a nonspectral matrix equation is satisfied. Some general remarks on
the solutions to this equation, and some special solutions are given. The
large-time behavior of the conditional probabilities of such systems are also
investigated.Comment: 13 pages, LaTeX2
Static- and dynamical-phase transition in multidimensional voting models on continua
A voting model (or a generalization of the Glauber model at zero temperature)
on a multidimensional lattice is defined as a system composed of a lattice each
site of which is either empty or occupied by a single particle. The reactions
of the system are such that two adjacent sites, one empty the other occupied,
may evolve to a state where both of these sites are either empty or occupied.
The continuum version of this model in a Ddimensional region with boundary is
studied, and two general behaviors of such systems are investigated. The
stationary behavior of the system, and the dominant way of the relaxation of
the system toward its stationary state. Based on the first behavior, the static
phase transition (discontinuous changes in the stationary profiles of the
system) is studied. Based on the second behavior, the dynamical phase
transition (discontinuous changes in the relaxation-times of the system) is
studied. It is shown that the static phase transition is induced by the bulk
reactions only, while the dynamical phase transition is a result of both bulk
reactions and boundary conditions.Comment: 10 pages, LaTeX2
Exactly solvable models through the empty interval method
The most general one dimensional reaction-diffusion model with
nearest-neighbor interactions, which is exactly-solvable through the empty
interval method, has been introduced. Assuming translationally-invariant
initial conditions, the probability that consecutive sites are empty
(), has been exactly obtained. In the thermodynamic limit, the large-time
behavior of the system has also been investigated. Releasing the translational
invariance of the initial conditions, the evolution equation for the
probability that consecutive sites, starting from the site , are empty
() is obtained. In the thermodynamic limit, the large time behavior of
the system is also considered. Finally, the continuum limit of the model is
considered, and the empty-interval probability function is obtained.Comment: 12 pages, LaTeX2
Phase transition in an asymmetric generalization of the zero-temperature q-state Potts model
An asymmetric generalization of the zero-temperature q-state Potts model on a
one dimensional lattice, with and without boundaries, has been studied. The
dynamics of the particle number, and specially the large time behavior of the
system has been analyzed. In the thermodynamic limit, the system exhibits two
kinds of phase transitions, a static and a dynamic phase transition.Comment: 11 pages, LaTeX2
Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions
Autonomous multispecies systems with more-than-two-neighbor interactions are
studied. Conditions necessary and sufficient for closedness of the evolution
equations of the -point functions are obtained. The average number of the
particles at each site for one species and three-site interactions, and its
generalization to the more-than-three-site interactions is explicitly obtained.
Generalizations of the Glauber model in different directions, using generalized
rates, generalized number of states at each site, and generalized number of
interacting sites, are also investigated.Comment: 9 pages, LaTeX2
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