Related papers: Fast Arnold Diffusion in three time scale systems
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…
We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coefficient is a fixed bounded monotone profile that is shifted at…
We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection…
We study large deviations for the time average of the Ornstein-Uhlenbeck process raised to an arbitrary power. We prove that beyond a critical value, large deviations are subexponential in time, with a non-convex rate function whose main…
We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the…
We study a chain of non-linear, interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
We study the electron dynamics in a 2D waveguide bounded by a periodically rippled surface in the presence of the time-periodic electric field. The main attention is paid to a possibility of a weak quantum diffusion along the coupling…
Anomalous short- and long-time self-diffusion of non-overlapping fractal particles on a percolation cluster with spreading dimension $1.67(2)$ is studied by dynamic Monte Carlo simulations. As reported in Phys. Rev. Lett. 115, 097801…
We study the time asymptotic propagation of solutions to the reaction-diffusion cooperative systems with fractional diffusion. We prove that the propagation speed is exponential in time, and we find the precise exponent of propagation. This…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but…
A major question in dynamical systems is to understand the mechanisms driving global instability in the 3 Body Problem (3BP), which models the motion of three bodies under Newtonian gravitational interaction. The 3BP is called restricted if…
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are…
Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the long range coulomb repulsion between protons, the system has structural inhomogeneities. These structural inhomogeneities arise…
We consider a typical class of systems with delayed nonlinearity, which we show to exhibit chaotic diffusion. It is demonstrated that a periodic modulation of the time-lag can lead to an enhancement of the diffusion constant by several…
Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when…
We consider the dynamics of a small trojan companion of a hypothetical giant exoplanet under the secular perturbations of additional planets. By a suitable choice of action-angle variables, the problem is amenable to the study of the slow…
We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e.~the speed of light of the system,…
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…