Related papers: Diffusive wave dynamics beyond the continuum limit
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been…
Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…
Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large scales characterized by few variables such as the particle number density, temperature and pressure obeying a set of hydrodynamic (or macroscopic) equations. Does…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
The diffusion model is used to calculate the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered…
Elastic wave dispersion is studied in an octet truss lattice and compared with a designed rib lattice known to exhibit strong Cosserat elastic effects. Dispersion entails variation of wave speed with frequency. The phenomenon is…
On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide…
We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between…
The statistics of the field structure in the vortex core surrounding phase singularities in random wave fields are measured and calculated for diffusive and localized waves. Excellent agreement is found between experiment and theory. The…
Propagation of acoustic waves in an one-dimensional water duct containing many air filled blocks is studied by the transfer matrix formalism. Energy distribution and interface vibration of the air blocks are computed. For periodic…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…