Related papers: Causal Dynamics of Discrete Surfaces
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…
We show how permutability of transforms of smooth surfaces with particular characteristics leads to discrete surfaces with discrete analogues of the same characteristics.
We present simulations of a hard disc system and analyze the time evolution of the dynamic heterogeneities. We characterize the time evolution of slow regions and slow particles individually. The motion of slow clusters turns out to be very…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
Color naming in natural languages is not arbitrary: it reflects efficient partitions of perceptual color space modulated by the relative needs to communicate about different colors. These psychophysical and communicative constraints help…
Dispersal is a well recognized driver of ecological and evolutionary dynamics, and simultaneously an evolving trait. Dispersal evolution has traditionally been studied in single-species metapopulations so that it remains unclear how…
We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the…
We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete…
In this paper we consider a layer of incompressible viscous fluid lying above a flat periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and evolves in time. We assume that a mass of surfactants…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Because human cognition is creative and socially situated, knowledge accumulates, diffuses, and gets applied in new contexts, generating cultural analogs of phenomena observed in population genetics such as adaptation and drift. It is…
We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is…
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
Conformal field theories with central charge $c\le1$ on random surfaces have been extensively studied in the past. Here, this discussion is extended from their equilibrium distribution to their critical dynamics. This is motivated by the…