Related papers: A C++ Code to Solve the DGLAP Equations Applied to…
We present a collection of MATLAB routines using discontinuous Galerkin finite elements method (DGFEM) for solving steady-state diffusion-convection-reaction equations. The code employs the sparse matrix facilities of MATLAB with…
We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize…
In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to the convection dominated non-linear, quasi-stationary diffusion-convection-reaction equations. We propose an efficient preconditioner using a matrix reordering…
We have developed a model which aims to reproduce observational data of many kinds related to cosmic-ray (CR) origin and propagation: direct measurements of nuclei, antiprotons, electrons and positrons, gamma-rays, and synchrotron…
Several explanations for the existence of Ultra High Energy Cosmic Rays invoke the idea that they originate from the decay of massive particles created in the reheating following inflation. It has been suggested that the decay products can…
A computer code is described for the simulation of gravitational lensing data. The code incorporates adaptive mesh refinement in choosing which rays to shoot based on the requirements of the source size, location and surface brightness…
We compare two techniques for simulation of Ultra High Energy Cosmic Rays (UHECR) propagation, the Monte Carlo approach and method based on solving transport equations in one dimension. For the former we adopt publicly available tool…
The pulsar light curves and energy spectra are explored in dissipative pulsar magnetospheres with the Aristotelian electrodynamics (AE), where particle acceleration is fully balanced with radiation reaction. The AE magnetospheres with…
We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute…
The topic of this paper is a semi-linear, defocusing wave equation $u_{t t}-\Delta u=-|u|^{p-1} u$ in sub-conformal case in the higher dimensional space whose initial data are radical and come with a finite energy. We prove some decay…
The numerical approximation of high-dimensional evolution equations poses significant computational challenges, particularly in kinetic theory and radiative transfer. In this work, we introduce the Galerkin Alternating Projection (GAP)…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
In this paper we briefly discuss the problem of the origin of Ultra High Energy Cosmic Rays in the framework of Top-Down models. We show that, for high energy of decays and in a wide range of spectra of injected protons, their extragalactic…
Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order…
We show that ``top-down'' mechanisms of Ultra-High Energy Cosmic Rays which involve heavy relic particle-like objects predict Galactic anisotropy of highest energy cosmic rays at the level of minimum $\sim 20%$. This anisotropy is large…
We present \textsc{Mathpop}, a novel method to infer the globular cluster (GC) counts in ultra-diffuse galaxies (UDGs) and low-surface brightness galaxies (LSBGs). Many known UDGs have a surprisingly high ratio of GC number to surface…
In this talk, I present the last and more precise results obtained in the computation of the final spectra of stable particles issued from the decay of super-heavy X particles (M_X ~ 10^21 to 10^25 eV). Such very energetic decay products,…
We explore scenarios where the highest energy cosmic rays (HECR) are produced by new particle physics near the grand unification scale. Using detailed numerical simulations of extragalactic cosmic and gamma-ray propagation, we show the…