Related papers: The onset of tree-like patterns in negative stream…

The high order fluid model developed in the preceding paper is employed here to study the propagation of negative planar streamer fronts in pure nitrogen. The model consists of the balance equations for electron density, average electron…

Plasma models, consisting of advection-diffusion Partial Differential Equations coupled with chemical reactions, are widely adopted to describe corona, streamers and dielectric barrier discharges. However, the complex geometry of the…

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer…

In this paper we use a hydrodynamic minimal streamer model to study negative corona discharge. By reformulating the model in terms of a quantity called shielding factor, we deduce laws for the evolution in time of both the radius and the…

A numerical simulation of evolution of an identical interacting streamers array in semiconductors has been performed using the diffusion-drift approximation and taking into account the impact and tunnel ionization. It has been assumed that…

We introduce in this paper new and very effective numerical methods based on neural networks for the approximation of the mean curvature flow of either oriented or non-orientable surfaces. To learn the correct interface evolution law, our…

Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…

The propagation mechanisms of plasma streamers have been observed and investigated in a surface dielectric barrier discharge (SDBD) using 2D particle in cell simulations. The investigations are carried out under a simulated air mixture,…

We present results from a systematic numerical study of structural properties of an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid with an initial energy spectrum that develops a cascade of kinetic…

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…

Consider a population of infinitesimally small frogs on the real line. Initially the frogs on the positive half-line are dormant while those on the negative half-line are awake and move according to the heat flow. At the interface, the…

We study the pairwise interactions of drops in an applied uniform DC electric field within the framework of the leaky dielectric model. We develop three-dimensional numerical simulations using the boundary integral method and an analytical…

We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show…

Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters.…

The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the…

Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…

We show that the ion beam induced incompressible amorphous solid flow in terms of advection transport mechanism leads to the erosion and deposition of atoms at the amorphous/crystalline (a/c) interface resulting in the formation of pattern…

Particle models for streamer ionization fronts contain correct electron energy distributions, runaway effects and single electron statistics. Conventional fluid models are computationally much more efficient for large particle numbers, but…

A phase field model of a crack front propagating in a three dimensional brittle material is used to study the fractographic patterns induced by the branching instability. The numerical results of this model give rise to crack surfaces that…

Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate…