Related papers: Droplet condensation and isoperimetric towers
We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features…
We unravel the existence and nonequilibrium response of one-dimensional harmonically trapped droplet configurations in the presence of a central potential barrier or well. For fixed negative chemical potentials, it is shown that droplets…
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article…
We discuss variational problems on two-dimensional domains with energy densities of linear growth and with radially symmetric data. The smoothness of generalized minimizers is established under rather weak ellipticity assumptions. Further…
The condensational growth of spherical water microdroplets is studied in a laboratory setup and with a mathematical model. In the experiment, droplet clusters are kept in a freely levitated state within an upward-oriented flow of water…
We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
Inspired by a planar partitioning problem involving multiple improper chambers, this article investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint…
We present a theoretical study for the intermediate stages of the growth of membranes and vesicles in supersaturated solutions of amphiphilic molecules. The problem presents important differences with the growth of droplets in the classical…
The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.
The growth by condensation of small water droplets in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are…
We consider the isoperimetric problem for clusters in the plane with a double density, that is, perimeter and volume depend on two weights. In this paper we consider the isotropic case, in the parallel paper "On the Steiner property for…
We present a theory that explains the experimentally observed crystallisation of a dilute dysprosium condensate into a lattice of droplets. The key ingredient of our theory is a conservative three-body interaction which stabilises the…
We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a…
We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and…
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the…
We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…
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 consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a…