Related papers: A Note on Wetting Transition for Gradient Fields
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We analyse the evolution of scalar and gauge fields during a second order phase transition using a Langevin equation approach. We show that topological defects formed during the phase transition are stable to thermal fluctuations. Our…
We study the crossover between the mean-field and critical behavior of the two-dimensional Bose gas throughout the fluctuation region of the Berezinskii--Kosterlitz--Thouless phase transition point. We argue that this crossover is described…
The derivation of a quasi-geostrophic (QG) system from the rotating shallow water equations on a midlatitude beta-plane coupled with moisture is presented. Condensation is prescribed to occur whenever the moisture at a point exceeds a…
For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the…
We study the laws of the two-dimensional vector-valued Dirichlet Gaussian free field and its massive lattice counterpart, conditioned to avoid a ball at every site of a subdomain. We prove that, under this conditioning, the norm of the…
The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single…
Guided motion of emulsions is studied via combined experimental and theoretical investigations. The focus of the work is on basic issues related to driving forces generated via a step-wise (abrupt) change in wetting properties of the…
We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…
We investigate critical wetting transitions for fluids adsorbed in wedge-like geometries where the substrate height varies as a power-law, $z(x,y) \sim |x| ^\gamma$, in one direction. As $\gamma$ is increased from 0 to 1, the substrate…
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian…
Liquid drops on textured surfaces show different dynamical behaviors depending on their wetting states. They are extremely mobile when they are supported by composite solid-liquid-air interfaces (Cassie-Baxter state) and immobile when they…
We consider a random field $\varphi:\{1,...,N\}\to\mathbb{R}$ as a model for a linear chain attracted to the defect line $\varphi=0$, that is, the x-axis. The free law of the field is specified by the density…
We provide a description of phase transitions at finite temperature in strongly coupled field theories using holography. For this purpose, we introduce a general class of gravity duals to superconducting theories that exhibit various types…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
We study the zero-temperature phase transitions of two-dimensional superconducting arrays with both the self- and the junction capacitances in the presence of external magnetic fields. We consider two kinds of excitations from the Mott…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
We provide a complete description of the low temperature wetting transition for the two dimensional Solid-On-Solid model. More precisely we study the integer-valued field $(\phi(x))_{x\in \mathbb Z^2}$, associated associated to the energy…
We study the interfacial phenomenology of a fluid in contact with a microstructured substrate within the mean-field approximation. The sculpted substrate is a one-dimensional array of infinitely long grooves of sinusoidal section of…