Related papers: Resonantly Forced Inhomogeneous Reaction-Diffusion…
We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the…
We analyze experimentally chemical waves propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity which drastically depends on the mean flow direction and rate. The fronts may propagate…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
We study synchronization and rhythmic patterns generated in the heterogeneous cluster of FitzHugh$-$Nagumo oscillators with transition between self-oscillating and excitable elements. Such cluster models the sinoatrial node of the heart,…
We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive {\it master equations} for the dynamics of the expected power in the discrete modes. In…
The generalized Swift--Hohenberg equation with a quadratic-cubic nonlinearity is used to study the persistence and decay of localized patterns in the presence of time-periodic parametric forcing. A novel resonance phenomenon between the…
We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent…
The effect of increasing structural disorder on the distribution of contact forces P(f), inside three dimensional particle assemblies is systematically studied using computer simulations of model granular packings. Starting from a…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
In this paper we present the results of parallel numerical computations of the long-term dynamics of linked vortex filaments in a three-dimensional FitzHugh-Nagumo excitable medium. In particular, we study all torus links with no more than…
We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
Three-dimensional turbulence is usually studied experimentally by using a spatially localized forcing at large scales (e.g. via rotating blades or oscillating grids), often in a deterministic way. Here, we report an original technique where…
Spatial scale separation often leads to sharp interfaces that can be fully localized pulses or transition layer fronts connecting different states. This paper concerns the asymptotic interaction laws of pulses and fronts in the so-called…