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Outstanding advances in solid-state laser technology, employing the optical parametric chirped-pulse-amplification (OPCPA) technique, have led physicists to focus laser pulses to highly-relativistic intensities which led to novel schemes…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
Electromigration, a significant lifetime reliability concern in highperformance integrated circuits, is projected to grow even more important in future heterogeneously integrated systems that will service higher current loads. Today, EM…
A major challenge in the molecular simulation of electric double layer capacitors (EDLCs) is the choice of an appropriate model for the electrode. Typically, in such simulations the electrode surface is modeled using a uniform fixed charge…
The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet \& Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vlasov equation with a strong external magnetic field. In this…
Recently proposed modifications of the standard particle-in-cell (PIC) method resolve long-standing limitations such as exact preservation of physically conserved quantities and unbiased ensemble down-sampling. Such advances pave the way…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
This paper studies the design and dynamic modelling of a novel thermal energy storage (TES) system combined with a refrigeration system based on phase change materials (PCM). Cold-energy production supported by TES systems is a very…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…
A simulation package employing a Particle in Cell (PIC) method is developed to study the high current beam transport and the dynamics of plasmas. This package includes subroutines those are suited for various planned projects at University…
Electrochemical metallization (ECM) memristors have potential applications in future neuromorphic computing hardware. The set, reset, and variable-resistance features of these devices originate in the formation and breakup of metal…
Integrals of the Liouville $1$-form, known as the first Poincar\'e integral invariant, provide a computable figure of merit for monitoring the conservation of symplecticity in the numerical integration of Hamiltonian systems. These…
Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modelling of atomistic electrode charges when studying the electrode-electrolyte interface at the nanoscale. Here we extend the theoretical framework of…
Particle-in-cell methods couple mesh-based methods for the solution of continuum mechanics problems, with the ability to advect and evolve particles. They have a long history and many applications in scientific computing. However, they have…
This work is devoted to design and study efficient and accurate numerical schemes to approximate a chemo-attraction model with consumption effects, which is a nonlinear parabolic system for two variables; the cell density and the…
Ab initio modeling of electrochemical systems is becoming a key tool for understanding and predicting electrochemical behavior. Development and careful benchmarking of computational electrochemical methods are essential to ensure their…
Proton exchange membrane (PEM) electrolyzers are pivotal for sustainable hydrogen production, yet their long-term performance is hindered by membrane degradation, which poses reliability and safety challenges. Therefore, accurate modeling…
The particle-in-cell (PIC) method is a well-established and widely used kinetic plasma modelling approach that provides a hybrid Lagrangian-Eulerian approach to solve the plasma kinetic equation. Despite its power in capturing details of…
With the great development of parallel computing techniques, the particle-particle (PP) model has been successfully applied in a number of plasma applications. Comparing to particle-mesh (PM) models, for example the widely used…