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Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…
We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of…
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
Cellular self-assembly and organization are fundamental steps for the development of biological tissues. In this paper, within the framework of a cellular automata model, we address how an ordered tissue pattern spontaneously emerges from a…
We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples for subdiffusive tracer's motion) and concentrate on the intermediate time range, in which the tracer's motion indeed may show…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
We introduce history-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying Hamiltonian of the walker to include couplings with memory-keeping agents. We next numerically study the…
We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…
In recent years the modelling of traffic flow using methods from statistical physics, especially cellular automata models have allowed simulations of large traffic networks faster than real time. In this paper, we study a probabilistic…
Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the…
Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given…
Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. "Collectiveness" can be promoted by cell-cell interactions such as co-attraction and contact…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…