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We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844), Goldbeter and Koshland mathematically analyzed a reversible covalent modification system which is highly sensitive to the concentration of effectors. Its…
The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex…
The evolution of the two-point functions of autonomous one-dimensional single-species reaction-diffusion systems with nearest-neighbor interaction and translationally-invariant initial conditions is investigated. It is shown that the…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
By identifying potential composite states that occur in the Sel'kov-Gray-Scott (GS) model, we show that it can be considered as an effective theory at large spatio-temporal scales, arising from a more \textit{fundamental} theory (which…
We study the dynamics of a single-photon pulse travelling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubit amplitudes and for…
A simple model is studied for the chemotactic movement of biological cells in the presence of a periodic chemical wave. It incorporates the feature of adaptation that may play an important role in allowing for ``rectified" chemotaxis:…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between…
The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
Wave phenomena in vibrofluidized dry and partially wet granular materials confined in a quasi-two-dimensional geometry are investigated with numerical simulations considering individual particles as hard spheres. Short ranged cohesive…
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of…
In a two species reaction diffusion system,we show that it is possible to generate a set of wavelength doubling bifuractions leading to spatially chaotic state.The wavelength doubling bifurcations are preceded by a symmetry breaking…
We consider the spontaneous formation of striped structures in a holographic model which possesses explicit translational symmetry breaking, dual to an ionic lattice with spatially modulated chemical potential. We focus on the perturbative…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
Cell signaling, gene expression, and metabolism are affected by cell-cell heterogeneity and random changes in the environment. The effects of such fluctuations on cell signaling and gene expression have recently been studied intensively…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…