Cellular automaton models for time-correlated random walks: derivation and analysis
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In this article, a non-Markovian lattice-gas cellular automata model for moving agents with memory is proposed, where the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect their approach is ''data-driven''.Citations
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BIO-LGCA: a cellular automaton modelling class for analysing collective cell migration
Andreas Deutsch,Josué Manik Nava-Sedeño,Josué Manik Nava-Sedeño,Simon Syga,Haralampos Hatzikirou,Haralampos Hatzikirou +5 more
TL;DR: A novel on-lattice, agent-based modelling class for collective cell migration, called biological lattice-gas cellular automaton (BIO-LGCA), which allows for rigorous derivation of rules from biophysical laws and/or experimental data, mathematical analysis of the resulting dynamics, and computational efficiency.
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A least microenvironmental uncertainty principle (LEUP) as a generative model of collective cell migration mechanisms.
TL;DR: The least microenvironmental uncertainty principle (LEUP) is proposed that serves as a generative model of collective migration without incorporation of full mechanistic details and is applied to quantitatively study of the collective behavior of spherical Serratia marcescens bacteria.
Journal ArticleDOI
Search efficiency of fractional Brownian motion in a random distribution of targets
TL;DR: Fractional Brownian motion as a search process, which under parameter variation generates all three basic types of diffusion, from sub- to normal to superdiffusion, is studied, finding that different search scenarios favour different modes of motion for optimising search success, defying a universality across all search situations.
Book ChapterDOI
A Lattice-Gas Cellular Automaton Model for Discrete Excitable Media
TL;DR: This cellular automaton model includes a parameter which defines the maximum local number of individuals and influences the onset of spiral waves, and it is found that small values of this parameter allow spiral pattern formation even in situations where the corresponding deterministic PDE model predicts that no spirals are formed, reminiscent of stochastic resonance effects.
References
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Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Book
Fundamentals of Statistical and Thermal Physics
TL;DR: In this article, a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars is presented for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum.
Journal ArticleDOI
Anomalous transit-time dispersion in amorphous solids
Harvey Scher,Elliott W. Montroll +1 more
TL;DR: In this paper, the authors developed a stochastic transport model for the transient photocurrent, which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface.
Journal ArticleDOI
The scaling laws of human travel
TL;DR: It is shown that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two-parameter continuous-time random walk model to a surprising accuracy, and concluded that human travel on geographical scales is an ambivalent and effectively superdiffusive process.
Journal ArticleDOI
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.