Related papers: Two-dimensional Burgers Cellular Automaton
In this paper we are extending the well known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example we apply the theory to the case of a differential-difference…
A representation of the solid angle and the Burgers formula as line integral is derived in the framework of the theory of gradient elasticity of Helmholtz type. The gradient version of the Eshelby-deWit representation of the Burgers formula…
We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of…
We analyze the score field of a diffusion generative model through a Burgers-type evolution law. For VE diffusion, the heat-evolved data density implies that the score obeys viscous Burgers in one dimension and the corresponding…
We consider a nonhomogeneous Burgers equation with time variable coefficients, and obtain an explicit solution of the general initial value problem in terms of solution to a corresponding linear ODE. Special exact solutions such as…
If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum…
In Isliker et al. (2000b), an extended cellular automaton (X-CA) model for solar flares was introduced. In this model, the interpretation of the model's grid-variable is specified, and the magnetic field, the current, and an approximation…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
We propose new type of $q$-diffusive heat equation with nonsymmetric $q$-extension of the diffusion term. Written in relative gradient variables this system appears as the $q$- viscous Burgers' equation. Exact solutions of this equation in…
The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more…
We investigate generalizations of the Burgers and Burgers-Huxley equations. The investigations we offer focus attention mainly on presenting explict analytical solutions by means of relating these generalized equations to relativistic 1+1…
Herein, we present a polylogarithmic decomposition method to load the matrix from the linearized 1-dimensional Burgers' equation onto a quantum computer. First, we use the Carleman linearization method to map the nonlinear Burgers' equation…
Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
We discuss the mode spectrum in both the deterministic and noisy Burgers equations in one dimension. Similar to recent investigations of vortex depinning in superconductors, the spectrum is given by a non-Hermitian eigenvalue problem which…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…