Related papers: An equilibrium problem on the sphere with two equa…
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…
We study a class of radially symmetric Coulomb gas ensembles at inverse temperature $\beta=2$, for which the droplet consists of a number of concentric annuli, having at least one bounded ``gap'' $G$, i.e., a connected component of the…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
A three dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches -…
We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence to equilibrium) in a class of star-shaped initial data for…
We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem $$-\Delta u=|u|^{2^*-2-\e}u \hbox{in}\Omega, \quad u=0 \hbox{on}\partial \Omega,$$ where $\Omega$ is a smooth bounded domain in…
We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based…
This research paper investigates the impact of non-metricity and matter source on the geometry of charged spheres in the presence of anisotropic matter configuration. We use a specific model of extended symmetric teleparallel theory to…
See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the…
We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion…
Approximate solutions representing the gravitational-electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…
The shape of drop on a flat horizontal plane is obtained by including the first order of correction by the weight. The sphere solution of the weightless drop is used to introduce a new polar coordinate by which the perturbative expression…
We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S^d in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that…
Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…
We consider an extremal problem for subsets of high-dimensional spheres that can be thought of as an extension of the classical isoperimetric problem on the sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere $\mathbb{S}^{m-1}$,…
In this paper we perform a fine blow-up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant on the standard sphere. We derive from this analysis some a…
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…
We study the deformation and breakup of an axisymmetric electrolyte drop which is freely suspended in an infinite dielectric medium and subjected to an imposed electric field. The electric potential in the drop phase is assumed small, so…
The experiment shows that small liquid droplets under the action of gravity and the Archimedes force move in the external viscous liquid practically according to the Stokes drag force equation, and not in accordance with the…