Related papers: Time-dependent rescalings and Lyapunov functionals…
We change a previous time-stepping algorithm for solving a multi-scale Vlasov-Poisson system within a Particle-In-Cell method, in order to do accurate long time simulations. As an exponential integrator, the new scheme allows to use large…
An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force.…
We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that…
The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrodinger equation in 1 and 3 dimensions for a one-body soft Coulomb potential in a…
A fundamental two-fluid model for describing dynamics of a plasma is the Euler-Poisson system, in which compressible ion and electron fluids interact with their self-consistent electrostatic force. Global smooth electron dynamics were…
We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively-charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modeled by a…
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…
We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…
Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Levy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is…
When particle speeds are large the motion of a collisionless plasma is modeled by the relativistic Vlasov Maxwell system. Large time behavior of solutions which depend on one position variable and two momentum variables is considered. In…
The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle…
We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. In particular, we construct solutions that initially possess arbitrarily small charge…
In the present research, a variational technique to modifying the Poisson equation is presented, expanding its modelling capabilities to include a wider range of physical processes and resonant structures. The study examines the…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamical systems a number of the numerical technics have been developed to obtain the spectrum of…
Time dependent mode structure for the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra and its relation to the momentum auto-correlation function are discussed in quasi-one-dimensional many-hard-disk systems.…
A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…
We study the linearized Vlasov-Poisson system around suitably stable homogeneous equilibria on $\mathbb{R}^d\times \mathbb{R}^d$ (for any $d \geq 1$) and establish dispersive $L^\infty$ decay estimates in the physical space.
Numerical diffusion is introduced by any numerical scheme as soon as small scales fluctuations, generated during the dynamical evolution of a collisionless plasma, become comparable to the grid size. Here we investigate the role of…
Kinetic equations of Vlasov type are in widespread use as models in plasma physics. A well known example is the Vlasov-Poisson system for collisionless, unmagnetised plasma. In these notes, we discuss recent progress on the quasineutral…