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The morphological paths towards equilibrium droplets during the late stages of the dewetting process of a liquid film from a liquid substrate is investigated experimentally and theoretically. As liquids, short chained polystyrene (PS) and…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
The thermodynamic properties of disks moving in a channel sufficiently narrow that they can collide only with their nearest neighbors can be solved exactly by determining the eigenvalues and eigenfunctions of an integral equation. Using it…
We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C.…
We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the…
We prove an asymptotic crystallization result in two dimensions for a class of nonlocal particle systems. To be precise, we consider the best approximation with respect to the 2-Wasserstein metric of a given absolutely continuous…
In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a…
We generalize the shape optimization problem for the existence of stable equilibrium configurations of nematic and cholesteric liquid crystal drops surrounded by an isotropic solution to include a broader family of admissible domains with…
The dewetting dynamics of an ultrathin film is studied in the presence of evaporation - or reaction - of adatoms on the substrate. KMC simulations are in good agreement with an analytical model with diffusion, rim facetting, and substrate…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
In this paper we use a formal discrete-to-continuum procedure to derive a continuum variational model for two chains of atoms with slightly incommensurate lattices. The chains represent a cross-section of a three-dimensional system…
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive…
A fluid in a pore can form diverse heterogeneous structures. We combine a capillary description with the cubic-plus-association equation of state to study the thermodynamic stability of droplets, bubbles and films of water at 358 K in a…
We investigate the large time behavior of compactly supported solutions for a one-dimensional thin-film equation with linear mobility in the regime of partial wetting. We show the stability of steady state solutions. The proof uses the…
A PDE-based model combining surface electromigration and wetting is developed for the analysis of morphological stability of ultrathin solid films. Adatom mobility is assumed anisotropic, and two directions of the electric field (parallel…
The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…
We derive scaling laws for the spin decoherence of neutral atoms trapped near conducting and superconducting plane surfaces. A new result for thin films sheds light on the measurement of Y.J. Lin, I. Teper, C. Chin, and V. Vuleti\'{c}…
We study a many-body system of interacting fermionic atoms of two species that are in thermodynamic equilibrium with their condensed heteronuclear bound states (molecules). In order to describe such an equilibrium state, we use a…
Thermodynamic theory is developed for the ferroelectric phase transition of an ultrathin film in equilibrium with a chemical environment that supplies ionic species to compensate its surface. Equations of state and free energy expressions…
We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed to have jump discontinuities on some (unknown) set. The free…