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The solidification of metallic droplets into powder particles involves a complex interplay between heat diffusion, surface tension, and geometric constraints. In confined, curved systems -- such as those encountered in atomisation,…
An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The…
In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…
The present contribution deals with the thermomechanical modeling of the strain-induced crystallization in unfilled polymers. This phenomenon significantly influences mechanical and thermal properties of polymers and has to be taken into…
The migration characteristics of a suspended deformable droplet in a parallel plate microchannel is studied, both analytically and numerically, under the combined influence of a constant temperature gradient in the transverse direction and…
The water-repellence properties of superhydrophobic surfaces make them promising for many applications. However, in some extreme environments, such as high humidities and low temperatures, condensation on the surface is inevitable, which…
We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension - also known as the Stefan problem with Gibbs-Thomson correction.
According to the Kosterlitz-Thouless-Theory two-dimensional solid films melt by the unbinding of dislocation pairs. A model including quenched random impurities was already studied by Nelson [Phys. Rev. B 27 (1983) 2902], who predicted a…
In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…
We perform extensive simulations of $10^4$ Lennard-Jones particles to study the effect of particle size dispersity on the thermodynamic stability of two-dimensional solids. We find a novel phase diagram in the dispersity-density parameter…
We investigate the effects of the reversal of the gravitational field onto a sedimented and partially crystallised suspension of nearly-hard sphere colloids. We analyse the structural changes that take place during the melting of the…
Melting in two-dimensional systems has remained controversial as theory, simulations, and experiments show contrasting results. One issue that obscures this discussion is whether or not theoretical predictions on strictly 2D systems…
We study the temperature dependence of the electrical resistivity of interacting two-dimensional metallic systems. We perform a numerical simulation of the nonequilibrium state based on semiclassical Boltzmann transport theory. Through our…
Natural convection is ubiquitous throughout the physical sciences and engineering, yet many of its important properties remain elusive. To study convection in a novel context, we derive and solve a quasilinear form of the Rayleigh-B\'enard…
A general theory for the melting of two dimensional solids explaining the universal and non-universal properties is an open problem up to date. Although the celebrated KTHNY theory have been able to predict the critical properties of the…
The evolution of two grains, which lie on a substrate and are in contact with each other, can be roughly described by a model in which the exterior surfaces of the grains evolve by surface diffusion and the grain boundary, namely the…
Active liquid crystals or active gels are soft materials which can be physically realised e.g. by preparing a solution of cytoskeletal filaments interacting with molecular motors. We study the hydrodynamics of an active liquid crystal in a…
Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The…
We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…
We revisit the problem of computing the boundary density profile of a droplet of two-dimensional one-component plasma (2D OCP) with logarithmic interaction between particles in a confining harmonic potential. At a sufficiently low…