Related papers: Growth Exponent in the Domany-Kinzel Cellular Auto…
Consider the quadratic form $\beta = {\bf y}^* ({\bf YY}^* + \rho {\bf I})^{-1} {\bf y}$ where $\rho$ is a positive number, where ${\bf y}$ is a random vector and ${\bf Y}$ is a $N \times K$ random matrix both having independent elements…
Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's…
We have previously reported that a universal growth law, as proposed by West and collaborators for all living organisms, appears to be able to describe also the growth of tumors in vivo. In contrast to the assumption of a fixed power…
By considering corrections to the asymptotic scaling functions of the photon and electron in quantum electrodynamics with $\Nf$ flavours, we solve the skeleton Dyson equations at $O(1/\Nf)$ in the large $\Nf$ expansion at the…
In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
We redefine the transition function of elementary cellular automata (ECA) in terms of discrete operators. The operator representation provides a clear hint about the way systems behave both at the local and the global scale. We show that…
We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with $m$ random interactions to older ones. Each constitutive element in the model stays either active or is temporarily…
We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular,…
It is argued that the dielectric-breakdown model has an upper critical $\eta_c$ equal to 4, for which the clusters become one-dimensional. A renormalization group treatment of the model is presented near the critical $\eta$.
Transition rates and dynamic spin structure factor at zero temperature for the spin-1/2 XXZ chain at critical regime in a magnetic field are numerically evaluated in terms of the exact determinant representations for the form factors and…
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial…
Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\propto \exp-(k/k_{\beta})^{\beta }$. An asymptotic theory has been developed…
In Ising model on the simple cubic lattice, we describe the inverse temperature \beta in terms of the bare-mass M and study its critical behavior by the use of delta expansion from high temperature or large M side. In the vicinity of…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
We study the asymptotic shape of the occupied region for monotone deterministic dynamics in d-dimensional Euclidean space parametrized by a threshold theta, and a Borel set N with positive and finite Lebesgue measure. If A_n denotes the…
The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments…
From the works of Rauzy and Thurston, we know how to construct (multiple) tilings of some Euclidean space using the conjugates of a Pisot unit $\beta$ and the greedy $\beta$-transformation. In this paper, we consider different…
We investigate critical properties of a class of number-conserving cellular automata (CA) which can be interpreted as deterministic models of traffic flow with anticipatory driving. These rules are among the only known CA rules for which…