Related papers: Compact Waves in Microscopic Nonlinear Diffusion
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
The time-asymptotic behavior of undamped, nonlinear oscillators with a random frequency is investigated analytically and numerically. We find that averaged quantities of physical interest, such as the oscillator's mechanical energy,…
The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and…
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature…
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate.…
In the decay region around the centreline of three qualitatively different turbulent plane wakes, the turbulence is non-homogeneous and two-point turbulent diffusion counteracts the turbulence cascade all the way down to scales smaller than…
The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interests. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure (CM), we…
We investigate the stabilization mechanisms of the invasion front in two-dimensional drainage displacement in porous media by using a network simulator. We focus on the process when the front stabilizes due to the viscous forces in the…
We consider the properties of the diffusion controlled reaction A+B->0 in the steady state, where fixed currents of A and B particles are maintained at opposite edges of the system. Using renormalisation group methods, we explicitly…
This work investigates the evolution of the distribution of charged particles due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a…
We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…
We predict the development and propagation of the fluctuations in a perturbed ideally-expanded air jet. A non-propagating harmonic perturbation in the density, axial velocity, and pressure is introduced at the inflow with different…
We follow the dynamics of nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. In the absence of nonlinear terms Anderson localization traps the packet in space. For the nonlinear case a destruction of Anderson…
We investigate analytically the propagation of linear waves in a three-dimensional, nonmagnetic, isothermal atmosphere stratified in plane-parallel layers. The motivation is to study oscillations in the non-magnetic chromosphere and to…
We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the…
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…
Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport…
Propagation of waves through Cantor-set media is investigated by renormalization-group analysis. For specific values of wave numbers, transmission coefficients are shown to be governed by the logistic map, and in the chaotic region, they…