Related papers: Predictability of the large relaxations in a cellu…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
Numerical data on the probability distribution of the equilibrium relaxation time of the Sherrington-Kirkpatrick model are obtained by means of dynamical Monte Carlo simulation, for several values of the system size $N$ and temperature $T$.…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the…
We propose a model of the Earth's torqueless precession, the "Chandler wobble", as a self-oscillation driven by positive feedback between the wobble and the centrifugal deformation of the portion of the Earth's mass contained in circulating…
The jamming transition in the stochastic cellular automaton model (Nagel-Schreckenberg model) of highway traffic is analyzed in detail, by studying the relaxation time, a mapping to surface growth problems and the investigation of…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) theory within the minimal subtraction scheme in two loop…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
The evolution of correlations in the \emph{exactly} solvable Luttinger model (a model of interacting fermions in one dimension) after a sudden interaction switch-on is \emph{analytically} studied. When the model is defined on a finite-size…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
We test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative seismic strain release increases as a power-law…
We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties…
We study the critical dynamics of hyper-cubic finite size system in the presence of quenched short-range correlated disorder. By using the random $T_c$ model A for the critical dynamics and the renormalization group method in the vicinity…