Related papers: Moving boundary approximation for curved streamer …
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local…
We consider pressure-driven flows of electrolyte solutions in small channels or capillaries in which tracer particles are used to probe velocity profiles. Under the assumption that the double layer is thin compared to the channel…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters…
Explicit predictions for Scanning Tunneling Microscopy (STM) on interacting one-dimensional electron systems are made using the Luttinger liquid formalism. The STM current changes with distance from an impurity or boundary in a…
Streamer discharges are the primary mode of electric breakdown of air in lightning and high voltage technology. Streamer channels branch many times, which determines the developing tree-like discharge structure. Understanding these branched…
Positive and negative streamers are studied in ambient air at 1 bar; they emerge from a needle electrode placed 40 mm above a planar electrode. The amplitudes of the applied voltage pulses range from 5 to 96 kV; most pulses have rise times…
Positive streamer discharges have been studied and modelled extensively in air. Here we study positive streamers in CO$_2$ with and without oxygen admixtures; they are relevant for current high voltage technology as well as for discharges…
The conformal structure on minimal surfaces plays a key role in studying the properties of minimal surfaces. Here we extend the results of uniformization of surfaces with boundary to get the (weak) uniformization results for triple junction…
Serrations are commonly employed to mitigate the turbulent boundary layer trailing-edge noise. However, significant discrepancies persist between model predictions and experimental observations. In this paper, we show that this results from…
We investigate spatial and temporal cross-correlations between streamwise and normal velocity components in three shear flows: a low-dimensional model for vortex-streak interactions, direct numerical simulations for a nearly homogeneous…
Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields,…
The flow within an oscillatory boundary layer, which approximates the flow generated by propagating sea waves of small amplitude close to the bottom, is simulated numerically by integrating Navier-Stokes and continuity equations. The bottom…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located…
The minimal surfaces meeting in triples with equal angles along a common boundary naturally arise from soap films and other physical phenomenon. They are also the natural extension of the usual minimal surface. In this paper, we consider…
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods. This paper establishes the stability and a priori error…
Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness for a large class of subordinate killed Brownian motions in bounded C1,1 domains, C1,1 domains with…
Streamers are ionization fronts that occur in gases at atmospheric and sub-atmospheric pressures. Numerical studies of streamers are important for practical applications but are challenging due to the multiscale nature of this discharge…
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…