scholarly journals Space-like dynamics in a reversible cellular automaton

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Katja Klobas ◽  
Tomaz Prosen
Keyword(s):  
Cellular Automaton ◽  
Lattice Gas ◽  
Time Correlation ◽  
Matrix Product ◽  
Product Representation ◽  
Circuit Representation ◽  
Reversible Cellular Automaton ◽  
The Matrix ◽  
Local Space ◽  
Local Observables

In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

scholarly journals Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Marko Medenjak ◽  
Vladislav Popkov ◽  
Tomaz Prosen ◽  
Eric Ragoucy ◽  
Matthieu Vanicat
Keyword(s):  
Cellular Automaton ◽  
Time Evolution ◽  
Stationary State ◽  
Finite Lattice ◽  
Matrix Product ◽  
Density Profiles ◽  
Reversible Cellular Automaton ◽  
Product Expression ◽  
Particle Current ◽  
Exact Matrix

In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and the local quench. Our main result is an exact matrix product expression of the time evolution of the probability distribution, which we use to determine the time evolution of the density profiles analytically. In the second part we study the model on a finite lattice coupled with stochastic boundaries. Once again we derive an exact matrix product expression of the stationary distribution, as well as the particle current and density profiles in the stationary state. The exact expressions reveal the existence of different phases with either ballistic or diffusive transport depending on the boundary parameters.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

Diffusion in tight confinement: A lattice-gas cellular automaton approach. II. Transport properties

2007 ◽  
Vol 126 (19) ◽  
pp. 194710 ◽  
Author(s):  
Pierfranco Demontis ◽  
Federico G. Pazzona ◽  
Giuseppe B. Suffritti
Keyword(s):  
Cellular Automaton ◽  
Transport Properties ◽  
Lattice Gas

scholarly journals 2D DOA Estimation with a Two-Parallel Array Consisting of Two Uniform Large-Spacing Linear Arrays

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Sheng Liu ◽  
Jing Zhao ◽  
Yu Zhang
Keyword(s):  
Mutual Coupling ◽  
Elevation Angle ◽  
Doa Estimation ◽  
Matrix Product ◽  
Linear Arrays ◽  
Parallel Array ◽  
Propagator Method ◽  
The Matrix ◽  
2D Doa Estimation ◽  
Estimation Precision

In this paper, an improved propagator method (PM) is proposed by using a two-parallel array consisting of two uniform large-spacing linear arrays. Because of the increase of element spacing, the mutual coupling between two sensors can be reduced. Firstly, two matrices containing elevation angle information are obtained by PM. Then, by performing EVD of the product of the two matrices, the elevation angles of incident signals can be estimated without direction ambiguity. At last, the matrix product is used again to obtain the estimations of azimuth angles. Compared with the existed PM algorithms based on conventional uniform two-parallel linear array, the proposed PM algorithm based on the large-spacing linear arrays has higher estimation precision. Many simulation experiments are presented to verify the effect of proposed scheme in reducing the mutual coupling and improving estimation precision.

A Lattice-Gas Cellular Automaton to Model Diffusion in Restricted Geometries

2006 ◽  
Vol 110 (27) ◽  
pp. 13554-13559 ◽  
Author(s):  
P. Demontis ◽  
F. G. Pazzona ◽  
G. B. Suffritti
Keyword(s):  
Cellular Automaton ◽  
Lattice Gas ◽  
Model Diffusion

scholarly journals IMPROVEMENT AND ANALYSIS OF A PSEUDO-RANDOM BIT GENERATOR BY MEANS OF CELLULAR AUTOMATA

2010 ◽  
Vol 21 (06) ◽  
pp. 741-756 ◽  
Author(s):  
J. S. MURGUÍA ◽  
M. MEJÍA CARLOS ◽  
H. C. ROSU ◽  
G. FLORES-ERAÑA
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Statistical Tests ◽  
Random Sequences ◽  
Multifractal Formalism ◽  
Random Generator ◽  
Random Bit Generator ◽  
The Matrix ◽  
Randomization Process

In this paper, we implement a revised pseudo-random bit generator based on a rule-90 cellular automaton. For this purpose, we introduce a sequence matrix HNwith the aim of calculating the pseudo-random sequences of N bits employing the algorithm related to the automaton backward evolution. In addition, a multifractal structure of the matrix HNis revealed and quantified according to the multifractal formalism. The latter analysis could help to disentangle what kind of automaton rule is used in the randomization process and therefore it could be useful in cryptanalysis. Moreover, the conditions are found under which this pseudo-random generator passes all the statistical tests provided by the National Institute of Standards and Technology (NIST).

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