Related papers: Arnold diffusion in multidimensional a priori unst…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or…
We consider models given by Hamiltonians of the form $$H(I,\phi,p,q,t;\epsilon) = h(I) + \sum_{j = 1}^n \pm(\frac{1}{2} p_j^2 + V_j(q_j)) + \epsilon Q(I,\phi,p,q,t;\epsilon)$$ where $I,\phi$ are d-dimensional actions and angles, $p,q$ are…
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
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 consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…
Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this…
We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It…
Over the past 15 years, several groups have engineered media that are both strongly dispersive and roughly transparent for some finite bandwidth. Relationships and intuitive models that are satisfactory when it is reasonable to neglect…
We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong…
Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially…
We consider the flow of a generalized Newtonian fluid through a thin porous medium of height $h_\varepsilon$ perforated with $\varepsilon$-periodically distributed solid cylinders of very small diameter $\varepsilon\delta_\varepsilon$,…
As a fundamental astrophysical process, the scattering of particles by turbulent magnetic fields has its physical foundation laid by the magnetohydrodynamic (MHD) turbulence theory. In the framework of the modern theory of MHD turbulence,…
We consider coupled diffusions in $n$-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalisation of the Ornstein-Uhlenbeck process with a random force which depends on position as well…
The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the…
A two-field Hamiltonian gyrofluid model for kinetic Alfv\'en waves retaining ion finite Larmor radius corrections, parallel magnetic field fluctuations and electron inertia, is used to study turbulent cascades from the MHD to the sub-ion…