Related papers: Motion representation of one-dimensional cellular …
For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration…
This paper presents a novel method for introducing time into discrete and continuous spatial representations used in mobile robotics, by modelling long-term, pseudo-periodic variations caused by human activities. Unlike previous approaches,…
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and…
In this paper, we consider a series of events observed at spaced time intervals and present a method of representation of the series. To explain an idea, by dealing with a set of gene expression data, which could be obtained from…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
We present a universal motion representation that encompasses a comprehensive range of motor skills for physics-based humanoid control. Due to the high dimensionality of humanoids and the inherent difficulties in reinforcement learning,…
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
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…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
In this paper we address the problem of representing solutions of a system of scalar linear partial difference equations akin to state space equations of 1-D systems theory. We first obtain a representation formula for a special class of…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…
We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation…