Related papers: Convergence analysis of an explicit splitting meth…
Active Flux (AF) is a modified Finite Volume method that evolves additional Degrees of Freedom (DoF) located on the cell interfaces to compute high-order approximations to the numerical fluxes through the respective interface. We present an…
Operator splitting methods solve composite optimization problems by breaking them into smaller sub-problems that can be solved sequentially or in parallel. In this paper, we propose a unified framework for certifying both linear and…
In this letter, cutting-edge 3D Particle-In-Cell simulations are used to demonstrate that so-called relativistic plasma mirrors irradiated by PetaWatt (PW) lasers and naturally curved by laser radiation pressure can be used to tightly focus…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasmas. Taking into account Coulomb collisions…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
A new scheme for numerical integration of the 1D2V relativistic Vlasov-Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the…
The alternating direction method of multipliers (ADMM) is a popular method for solving convex separable minimization problems with linear equality constraints. The generalization of the two-block ADMM to the three-block ADMM is not trivial…
Recent developments in high peak-power table-top laser systems reaching highly relativistic light intensities have led to significant advances in laser-driven particle acceleration schemes (mainly the laser wakefield acceleration, LWFA)…
Operator splitting methods have been successfully used in computational sciences, statistics, learning and vision areas to reduce complex problems into a series of simpler subproblems. However, prevalent splitting schemes are mostly…
We present a novel method for aligning a laser ionized plasma source to a pair of ultra-relativistic electron beams that comprise a plasma wakefield accelerator (PWFA). We achieve alignment by analyzing the plasma afterglow light observed…
The nonlinear optical dynamics of nano-materials comprised of plasmons interacting with quantum emitters is investigated by a self-consistent model based on the coupled Maxwell-Liouville-von Neumann equations. It is shown that ultra-short…
To expand on recent work, we introduce collisional terms in the analysis of the warm ion-electron, two-fluid equations for a homogeneous plasma at rest. Consequently, the plasma is now described by six variables: the magnetisation, the…
When an electromagnetic wave is obliquely incident on an inhomogeneous high density plasma, it will be absorbed resonantly as long as it is polarized in the plane of incidence and has an electric field component along the plasma electron…
We demonstrate a tandem lens optical setup, comprising two diffractive optics, that focuses a high-power ultrafast laser with a shaped on-axis intensity profile, producing a meter-long Bessel focus. The intended use of the optical setup is…
Understanding magnetized laser-plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. In the long-pulse regime, interactions are dominated by…
In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's…
We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the "ideal-gas" limit for…
In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
The generation of ultra-strong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum…