Related papers: Time Evolution of Cosmic-Ray Modified Plane Shocks
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
Galactic cosmic rays (CRs) play a crucial role in galaxy formation and evolution by altering gas dynamics and chemistry across multiple scales. Typical numerical simulations of CR transport assume a constant diffusion coefficient for the…
The linear theory of shock acceleration predicts the maximum particle energy to be limited only by the acceleration time and the size of the shock. We study the combined effect of acceleration nonlinearity (shock modification by accelerated…
Dynamical simulations are a fundamental tool for studying the secular evolution of disc galaxies. Even at their maximum resolution, they still follow a limited number of particles and typically resolve scales of the order of a few tens of…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
Galactic cosmic rays (GCRs) are affected by solar modulation while they propagate through the heliosphere. The study of the time variation of GCR spectra observed at Earth can shed light on the underlying physical processes, specifically…
For the numerical simulation of time-dependent problems, recent works suggest the use of a time marching scheme based on a tensorial decomposition of the time axis. This time-separated representation is straightforwardly introduced in the…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
Shock acceleration is considered one of the most important mechanisms for the acceleration of astrophysical energetic particles. In this work, we calculate the trajectories of a large number of test charged particles accurately in a…
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It…
In this thesis different numerical methods, as well as applications of the methods to a number of current problems in relativistic astrophysics, are presented. In the first part the theoretical foundation and numerical implementation of a…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
We develop a self-consistent nonlinear extension of diffusive shock acceleration that incorporates cosmic ray (CR) backreaction on the shock precursor together with a physically motivated upstream-escape mechanism that produces an…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
We performed a series of three-dimensional numerical simulations of supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 1024^3 zones. Our experiments describe non-magnetized driven…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
We present in this Letter the first global comparison between traditional line-tied steady state magnetohydrodynamic models and a new, fully time-dependent thermodynamic magnetohydrodynamic simulation of the global corona. The maps are…
In-situ spacecraft observations recently suggested that the transport of energetic particles accelerated at heliospheric shocks can be anomalous, i.e. the mean square displacement can grow non-linearly in time. In particular, a new analysis…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…