Related papers: An integral transform technique for kinetic system…
High-order semi-Lagrangian methods for kinetic equations have been under rapid development in the past few decades. In this work, we propose a semi-Lagrangian adaptive rank (SLAR) integrator in the finite difference framework for linear…
We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
Let the group G of m-th roots of unity act on the complex line by multiplication, inducing an action on the algebra, Diff, of polynomial differential operators on the line. Following Crawley-Boevey and Holland, we introduce a multiparameter…
The gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work…
The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we investigate the performance of the macro-element HDG method…
The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…
We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…
We introduce a new discrete-ordinate scheme for solving the general relativistic Boltzmann transport equation in the context of core-collapse supernovae. Our algorithm avoids the need to spell out the complicated advection terms in energy…
Quadrature-based moment-closure methods are a class of approximations that replace high-dimensional kinetic descriptions with lower-dimensional fluid models. In this work we investigate some of the properties of a sub-class of these methods…
We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The…
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 describe the implementation of 1d1v and 1d2v Vlasov and Fokker-Planck kinetic solvers with adaptive mesh refinement in phase space (AMPS) and coupling these kinetic solvers to Poisson equation solver for electric field. We demonstrate…
The first nonlinear gyrokinetic simulations obtained using a moment approach based on the Hermite-Laguerre decomposition of the distribution function are presented, implementing advanced models for the collision operator. Turbulence in a…
A new implicit BGK collision model using a semi-Lagrangian approach is proposed in this paper. Unlike existing models, in which the implicit BGK collision is resolved either by a temporal extrapolation or by a variable transformation, the…
We introduce a no-reaction-plane (no-RP) method for extracting directed (\(v_1\)) and elliptic (\(v_2\)) flows in heavy-ion collisions, which eliminates the need for event-plane reconstruction. %by scanning over fixed test angles and using…
We investigate the equivalence theorem for integrable systems using two formulations of the Alday-Arutyunov-Frolov model. We show that the S-matrix is invariant under the field transformation which reduces the non-linear Dirac brackets of…
We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…
Convex Integration is a theory developed in the '70s by M. Gromov. This theory allows to solve families of differential problems satisfying some convex assumptions. From a subsolution, the theory iteratively builds a solution by applying a…
The G-matrix equation is most straightforwardly formulated in the resonating-group method if the quark-exchange kernel is directly used as the driving term for the infinite sum of all the ladder diagrams. The inherent energy-dependence…