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Related papers: Anisotropic liquid drop models

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An example of capillary phenomena commonly seen and often studied is a droplet of water hanging in air from a horizontal surface. A thin capillary surface interface between the liquid and gas develops tangential surface tension, which…

Fluid Dynamics · Physics 2019-04-09 Dale G. Karr

Electrified liquids are well known to be prone to a variety of interfacial instabilities that result in the onset of apparent interfacial singularities and liquid fragmentation. In the case of electrically conducting liquids, one of the…

Analysis of PDEs · Mathematics 2016-07-19 Cyrill B. Muratov , Matteo Novaga

We obtain existence of minimizers for the $p$-capacity functional defined with respect to a centrally symmetric anisotropy for $1 < p<\infty$, including the case of a crystalline norm in $\mathbb R^N$. The result is obtained by a…

Analysis of PDEs · Mathematics 2023-05-08 Esther Cabezas-Rivas , Salvador Moll , Marcos Solera

We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the…

Mathematical Physics · Physics 2012-05-01 Rustum Choksi , Marco Morandotti , Marco Veneroni

We study the equilibrium shape of a liquid drop resting on top of a liquid surface, i.e., a floating lens. We consider the surface tension forces in non--wetting situations (negative spreading factor), as well as the effects of gravity. We…

Fluid Dynamics · Physics 2020-07-29 P. D. Ravazzoli , A. G. González , J. A. Diez , H. A. Stone

We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We characterize the semicontinuous envelope of the energy in terms of a…

Analysis of PDEs · Mathematics 2022-08-02 Cyrill B. Muratov , Matteo Novaga , Berardo Ruffini

We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the Ericksen's energy for liquid crystals, the Cahn-Hilliard…

Numerical Analysis · Mathematics 2017-09-13 Amanda E. Diegel , Shawn W. Walker

We analyze an elastic surface energy which was recently introduced by G. Napoli and L.Vergori to model thin films of nematic liquid crystals. We show how a novel approach that takes into account also the extrinsic properties of the surfaces…

Mathematical Physics · Physics 2016-06-22 Antonio Segatti , Michael Snarski , Marco Veneroni

In this short note we review results on equilibrium shapes of minimizers to the sessile drop problem. More precisely, we study the Winterbottom problem and prove that the Winterbottom shape is indeed optimal. The arguments presented here…

Analysis of PDEs · Mathematics 2024-12-04 Leonard Kreutz , Bernd Schmidt

Surface-tension-dominant droplet evaporation is ubiquitous and of importance to many applications. We present an improved Coupled Level Set and Volume of Fluid (i-CLSVoF) framework without explicit interface reconstruction for modelling…

Fluid Dynamics · Physics 2022-07-15 Huihuang Xia , Marc Kamlah

We prove two anisotropic type weighted geometric inequalities that hold for star-shaped and $F$-mean convex hypersurfaces in $\mathbb{R}^{n+1}$. These inequalities involve the anisotropic $p$-momentum, the anisotropic perimeter and the…

Differential Geometry · Mathematics 2023-12-29 Rong Zhou , Tailong Zhou

We prove a theorem for the growth of the energy of bounded, globally minimizing solutions to a class of semilinear elliptic systems of the form $\Delta u=\nabla W(u)$, $x\in \mathbb{R}^n$, $n\geq 2$, with $W:\mathbb{R}^m\to \mathbb{R}$,…

Analysis of PDEs · Mathematics 2014-04-09 Christos Sourdis

The relaxation dynamics of a model fluid of platelike colloidal particles is investigated by means of a phenomenological dynamic density functional theory. The model fluid approximates the particles within the Zwanzig model of restricted…

Soft Condensed Matter · Physics 2011-09-14 Markus Bier , Rene van Roij

Given an elliptic integrand of class $ \mathscr{C}^{3} $, we prove that finite unions of disjoint open Wulff shapes with equal radii are the only volume-constrained critical points of the anisotropic surface energy among all sets with…

Analysis of PDEs · Mathematics 2020-10-28 Antonio De Rosa , Sławomir Kolasiński , Mario Santilli

This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. Introducing the model that describes two immiscible fluids…

Analysis of PDEs · Mathematics 2024-09-12 Cyrill B. Muratov , Matteo Novaga , Philip Zaleski

In this paper we study surfaces in R^3 that arise as limit shapes in a class of random surface models arising from dimer models. The limit shapes are minimizers of a surface tension functional, that is, they minimize, for fixed boundary…

Mathematical Physics · Physics 2007-05-23 Richard Kenyon , Andrei Okounkov

We discuss a variational model, given by a weighted sum of perimeter, bending and Riesz interaction energies, that could be considered as a toy model for charged elastic drops. The different contributions have competing preferences for…

Analysis of PDEs · Mathematics 2025-10-15 Michael Goldman , Matteo Novaga , Matthias Röger

The vaporization of a freely moving drop in a uniform, high-temperature gas stream is investigated through direct numerical simulation. The incompressible Navier-Stokes equations with surface tension and phase change are solved in…

Fluid Dynamics · Physics 2023-10-03 Bradley Boyd , Sid Becker , Yue Ling

New liquid drop model with the isospin-square dependence of the volume and surface energy terms is applied to reproduce experimentally known masses of nuclei with number of protons and neutrons larger or equal to twenty. The ground-state…

Nuclear Theory · Physics 2025-04-24 Krzysztof Pomorski , Zhigang Xiao

We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive…

Analysis of PDEs · Mathematics 2022-09-07 Riccardo Durastanti , Lorenzo Giacomelli