Related papers: Delaunay-like compact equilibria in the liquid dro…
We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value…
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…
The classical problem of spherical homologous gravitational collapse with a polytropic equation of state for pressure is examined in Lagrangian fluid coordinate, where the position of each initial fluid element {\eta} = r(0) is followed in…
A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show theoretically…
The exact solution for a small falling drop is a classical result by Hadamard and Rybczynski. But experiments show that small drops fall slower than predicted, giving closer agreement with Stokes' result for a falling hard sphere.…
Modeling of a dense spray regime using an Euler-Lagrange approach is challenging because of local high volume loading. A cluster of droplets, that are assumed subgrid, can lead to locally low void fractions for the fluid phase. Under these…
We study the equilibrium solutions of a sessile drop on top of a horizontal substrate when it is partially covered by another inmiscible liquid, so that part of the drop is in contact with a third fluid (typically, air). The shapes of the…
The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant $\beta<2$, in contact with a dielectric wall of dielectric constant…
The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the…
This paper analyzes the configurations of shapes that shows a spacelike liquid drop in Minkowski space deposited over a spacelike plane $\Pi$. We assume the presence of a uniform gravity field directed toward $\Pi$ and that the volume of…
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the 2-body Hamilton equations, performs a canonical transformation to the orbital elements, and obtains…
We consider the problem of finding on a given Euclidean domain $\Omega$ of dimension $n \geq 3$ a complete conformally flat metric whose Schouten curvature $A$ satisfies some equation of the form $f(\lambda(-A)) = 1$. This generalizes a…
Out of self-consistent semi-classical calculations performed within the so-called Extended Thomas-Fermi approach for 212 nuclei at all even angular momentum values I ranging between 0 and 80 \hbar and using the Skyrme SkM* effective force,…
We consider the liquid drop model for nuclei interacting with a neutralizing homogeneous background of electrons. The regime we are interested in is when the fraction between the electronic and the nuclear charge density is small. We show…
We investigate the structure of crystalline particle arrays on constant mean curvature (CMC) surfaces of revolution. Such curved crystals have been realized physically by creating charge-stabilized colloidal arrays on liquid capillary…
The coefficients of different combinations of terms of the liquid drop model have been determined by a least square fitting procedure to the experimental atomic masses. The nuclear masses can also be reproduced using a Coulomb radius taking…
We consider constant mean curvature 1 surfaces in $\mathbb{R}^3$ arising via the DPW method from a holomorphic perturbation of the standard Delaunay potential on the punctured disk. Kilian, Rossman and Schmitt have proven that such a…
We consider the parametric elliptic PDE $-{\rm div} (a(y)\nabla u)=f$ on a spatial domain $\Omega$, with $a(y)$ a scalar piecewise constant diffusion coefficient taking any positive values $y=(y_1, \dots, y_d)\in ]0,\infty[^d$ on fixed…
This paper is concerned with the rigorous analysis of a recently proposed model of Zheng et. al. for describing nematic liquid crystals within the dense regime, with the orientation distribution function as the variable. A key feature of…
We are concerned with a system governing the evolution of the pressureless compressible Euler equations with Riesz interaction and damping in $\mathbb{R}^{d}$ ($d\geq1$), where the interaction force is given by…