Related papers: Wave front propagation in the Active Coagulation M…
We study motion of a phase transition front at a constant temperature between stable and metastable states in fluids with the universal Van der Waals equation of state (which is valid sufficiently close to the fluid's critical point). We…
We analyze the late-time relaxation dynamics for a general contagion model. In this model, nodes are either active or failed. Active nodes can fail either "spontaneously" at any time or "externally" if their neighborhoods are sufficiently…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and…
We extend the Rouse model of polymer dynamics to situations of non-stationary chain growth. For a dragged polymer chain of length $N(t) = t^\alpha$, we find two transitions in conformational dynamics. At $\alpha= 1/2$, the propagation of…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass and rigidity interface parameters are modulated in time.…
A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
The movement of motor particles consisting of one or several molecular motors bound to a cargo particle is studied theoretically. The particles move on patterns of immobilized filaments. Several patterns are described for which the motor…
We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame…
In this paper we investigate the long-term behaviour of solutions to the discrete Allen-Cahn equation posed on a two-dimensional lattice. We show that front-like initial conditions evolve towards a planar travelling wave modulated by a…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain…
The diffusion of active microscopic organisms in complex environments plays an important role in a wide range of biological phenomena from cell colony growth to single organism transport. Here, we investigate theoretically and…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…