Related papers: The heat equation shrinks Ising droplets to points
Let $\DD$ be a simply connected, smooth enough domain of $\bbR^2$. For $L>0$ consider the continuous time, zero-temperature heat bath dynamics for the nearest-neighbor Ising model on $\mathbb Z^2$ with initial condition such that…
We consider the continuous time, zero-temperature heat-bath dynamics for the nearest-neighbor Ising model on $Z^2$ with positive magnetic field. For a system of size $L\in N$, we start with initial condition $\sigma$ such that $\sigma_x=-1$…
We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the…
We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the…
This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such…
It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<T_c has an essential branch cut singularity at the origin H=0. The phenomenological droplet theory predicts that near the cut…
We prove that on compact Alexandrov spaces with curvature bounded below the gradient flow of the Dirichlet energy in the $L^2$-space produces the same evolution as the gradient flow of the relative entropy in the $L^2$-Wasserstein space.…
We investigate theoretically the stability of thermo-capillary convection within a droplet when heated by a point source from below. To model the droplet, we use a mathematical model based on lubrication theory. We formulate a base-state…
A density functional for the lattice gas (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. Similar to previous simulation studies, the sequence of droplets…
We investigate the laws of coarsening of a two-dimensional system of Ising spins evolving under single-spin-flip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from…
We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs-Thomson formula for the deviation of the pressure and the…
We examine the evolution of an Ising ferromagnet endowed with zero-temperature single spin-flip dynamics. A large droplet of one phase in the sea of the opposite phase eventually disappears. An interesting behavior occurs in the…
Let $M$ be a Riemannian manifold and $\Omega$ a compact domain of $M$ with smooth boundary. We study the solution of the heat equation on $\Omega$ having constant unit initial conditions and Dirichlet boundary conditions. The purpose of…
Recently Biskup et al. [Europhys. Lett. 60 (2002) 21] studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess $\delta N$ of particles above the ambient gas density. They identify a dimensionless…
We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup…
An isolated Leidenfrost droplet levitating over its own vapor above a superheated flat substrate is considered theoretically, the superheating for water being up to several hundred degrees above the boiling temperature. The focus is on the…
We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existence of smooth flow, starting from a regular droplet and…
We follow the dynamic evolution of a cluster of Ising spins pointing up surrounded by other spins pointing down, on a lattice. The cluster represents a liquid drop. Under a microscopic point of view, the short range ferromagnetic coupling…
We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig…
We propose a simple, self-consistent kinetic model for the evolution of a mixture of droplets and vapor expanding adiabatically in vacuum after rapid, almost isochoric heating. We study the evolution of the two-phase fluid at intermediate…