Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas. >

Particle-in-Cell Charged Particle Simulations, plus Monte Carlo Collisions with Neutral Atoms, PIC-MCC

. We introduce the notion of generalized mean curvature of a measure. We then focus attention on functionals depending on curvatures, investigating their weak lower semicontinuity. A crucial role in this study is played by the dimension of the tangent spaces to a measure.

Annali della Scuola normale superiore di Pisa, Classe di scienze

In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural changes in the mobility network. We find that long-distance travel was reduced disproportionately strongly. The trimming of long-range network connectivity leads to a more local, clustered network and a moderation of the "small-world" effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by "flattening" the epidemic curve and delaying the spread to geographically distant regions.

https://www.pnas.org/content/pnas/117/52/32883.full.pdf

COVID-19 lockdown induces disease-mitigating structural changes in mobility networks.

Cavitation and Bubble Dynamics: Preface

Sustainable seawater desalination: Current status, environmental implications and future expectations

In this section, we discuss the different multicomponent and multiscale models, which are later applied in simulations. We focus on the coupling of microscopic and macroscopic models, while the microscopic model is related on finer spatial and time scales and the macroscopic model is related to the coarser spatial and time scales. We discuss exemplary engineering problems in the field of electronic application and transport reaction applications in Plasma models. Here, the models and their underlying multiscale and multicomponent methods are discussed. Based on the aligned methods, we see the data flow between the disparate scales and can estimate the accuracy in each micro- and macroscopic model, such that we obtained truly working multiscale and multicomponent approaches.

Models and Applications

In this paper, we present a Picard’s iterative method for the solution of nonlinear multicomponent transport equations. The multicomponent transport equations are important for mixture models of the ionized and neutral particles in plasma simulations. Such mixtures deal with the so-called Stefan–Maxwell approaches for the multicomponent diffusion. The underlying nonlinearities are delicate and it is not necessary to be an analytical function of the dependent variables. The proposed solver method is based on Banach’s contraction fix-point principle that allows to solve such nonlinearities without making any use to Lagrange multipliers and constrained variations. Such an improvement allows to solve delicate nonlinear problems and we test the application to model with multicomponent transport equations.

Picard’s iterative method for nonlinear multicomponent transport equations

In this paper, we present splitting methods that are based on iterative schemes and applied to plasma simulations. The motivation arose of solving the Coulomb collisions, which are modeled by nonlinear stochastic differential equations. We apply Langevin equations to model the characteristics of the collisions and we obtain coupled nonlinear stochastic differential equations, which are delicate to solve. We propose well-known deterministic splitting schemes that can be extended to stochastic splitting schemes, by taking into account the stochastic behavior. The benefit decomposing the different equation parts and solve such parts individual is taken into account in the analysis of the new iterative splitting schemes. Numerical analysis and application to various Coulomb collisions in plasma applications are presented.

Iterative Splitting Methods for Coulomb Collisions in Plasma Simulations

We are motivated to solve differential algebraic equations with new multi-stage and multisplitting methods. The multi-stage strategy of the waveform relaxation (WR) methods are given with outer and inner iterations. While the outer iterations decouple the initial value problem of differential algebraic equations (DAEs) in the form of $A \frac{d y(t)}{dt} + B y(t) = f(t)$ to $M_A \frac{d y^{k+1}(t)}{dt} + M_1 y^{k+1}(t) = N_1 y^k(t) + N_A \frac{d y^{k}(t)} + f(t)$, where $A = M_A - N_A$, $B = M_1 - N_1$. The inner iterations decouple further $M_1 = M_2 - N_2$ and $M_2 = M_3 - N_3$ with additional iterative processes, such that we result to invert simpler matrices and accelerate the solver process. The multisplitting method use additional a decomposition of the outer iterative process with parallel algorithms, based on the partition of unity, such that we could improve the solver method. We discuss the different algorithms and present a first experiment based on a DAE system.

Multi-stage waveform Relaxation and Multisplitting Methods for Differential Algebraic Systems

In this paper, we present a model based on a near-far-field bubble formation We simulate the formation of a gas-bubble in a liquid, eg, water and the transportation of such a gas-bubble in the liquid The modelling approach is based on coupling the near-field model, which is done by the Young-Laplace equation, with the far-field model, which is done with a convection-diffusion equation We decouple the small and large time- and space scales with respect to each adapted model Such a decoupling allows to apply the optimal solvers for each near- or far-field model We discuss the underlying solvers and present the numerical results for the near-far-field bubble formation and transport model

Modelling approach of a near-far-field model for bubble formation and transport

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