Related papers: Is Arnold diffusion relevant to global diffusion?

Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to…

We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.

The chaotic interaction between electrons and whistler mode waves has been shown to provide a mechanism for enhanced diffusion in phase space. Pitch angle diffusion is relevant for the scattering of electrons into the loss cones, thus…

A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…

We describe a topological mechanism for the existence of diffusing orbits in a dynamical system satisfying the following assumptions: (i) the phase space contains a normally hyperbolic invariant manifold diffeomorphic to a two-dimensional…

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…

First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of an ABC magnetic field. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of…

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…

We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…

Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to…

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For…

In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…

The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…

We present two complementary simulations that lead to an exploration of Anderson localization, a phenomenon in which wave diffusion is suppressed in disordered media by interference from multiple scattering. To build intuition, the first…

A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational…

We present a Molecular Dynamics study of large Lennard-Jones clusters evolving on a crystalline surface. The static and the dynamic properties of the cluster are described. We find that large clusters can diffuse rapidly, as experimentally…

Constant flux atom deposition into a porous medium is shown to generate a dense overlayer and a diffusion profile. Scaling analysis shows that the overlayer acts as a dynamic control for atomic diffusion in the porous substrate. This is…