Related papers: Asymptotic-preserving gyrokinetic implicit particl…
We study in this paper the accuracy and stability of partially and fully implicit schemes for phase field modeling. Through theoretical and numerical analysis of Allen-Cahn and Cahn-Hillard models, we investigate the potential problems of…
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of…
Building on the framework of Zhang \& Shu \cite{zhangShu_2010a,zhangShu_2010b}, we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
The Energy Conserving semi-implicit method (ECsim), presented by Lapenta in 2017, is a Particle in Cell (PIC) algorithm for the simulation of plasmas. Energy conservation is achieved within a semi-implicit formulation that does not require…
We construct an analytic f(R) gravity model that unifies early-time inflation with late-time cosmic acceleration within a single covariant framework. At high curvature, the model reproduces a Starobinsky-like inflationary plateau, while at…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
Global particle-in-cell (PIC) simulations of pulsar magnetospheres are performed with a volume, surface and pair production-based plasma injection schemes to systematically investigate the transition between electrosphere and force-free…
The simplified delta-f mixed-variable/pull-back electromagnetic simulation algorithm implemented in XGC for core plasma simulations by M. Cole et al. [Phys. Plasmas 28, 034501 (2021)] has been generalized to a total-f electromagnetic…
Imitation learning (IL) and reinforcement learning (RL) each offer distinct advantages for robotics policy learning: IL provides stable learning from demonstrations, and RL promotes generalization through exploration. While existing robot…
Peer methods are a comprehensive class of time integrators offering numerous degrees of freedom in their coefficient matrices that can be used to ensure advantageous properties, e.g. A-stability or super-convergence. In this paper, we show…
In this work, an implicit scheme for particle-in-cell/Fourier electromagnetic simulations is developed and applied to studies of Alfv\'en waves in one dimension and three-dimensional tokamak plasmas. An analytical treatment is introduced to…
Accurate simulations of a condensed system of ions or polar molecules are concerned with proper handlings of the involved electrostatics. For such a Coulomb system at a charged planar interface, the Coulomb interaction averaged over the…
We review common extensions of particle-in-cell (PIC) schemes which account for strong field phenomena in laser-plasma interactions. After describing the physical processes of interest and their numerical implementation, we provide…
Quasi-particles in fractional quantum Hall states are collective excitations that carry fractional charge and anyonic statistics. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies,…
Finite electron gyro-radius influences on the trapping and charge density distribution of electron holes of limited transverse extent are calculated analytically and explored by numerical orbit integration in low to moderate magnetic…
A new adaptive scheme to be used in Particle-In-Cell codes for carrying out gyroaveraging operations with matrices is presented. This new scheme uses an intermediate velocity grid whose resolution is adapted to the local thermal Larmor…
We perform simulations of feedback from supernovae and black holes with smoothed particle hydrodynamics (SPH). Such strong perturbations are inaccurately handled with standard time integration schemes, leading to poor energy conservation, a…
One of the main difficulties in micromagnetics simulation is the norm preserving constraints $\|\mathbf{m}\|=1$ at the continuous or the discrete level. Another difficulty is the stability with the time step constraint. Using standard…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…