Related papers: Addendum to: Capillary floating and the billiard b…
The effective capillary interaction potentials for small colloidal particles trapped at the surface of liquid droplets are calculated analytically. Pair potentials between capillary monopoles and dipoles, corresponding to particles floating…
In this paper we present a sufficient condition for the existence of a solution for an equilibrium problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we propose a framework for the convergence…
The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height…
This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…
Consider two $k$-gons $P$ and $Q$. We say that the billiard flows in $P$ and $Q$ are homotopically equivalent if the set of conjugacy classes in the fundamental group of $P$ which contain a periodic billiard orbit agrees with the analogous…
We present a weighted version of the Caffarelli-Kohn-Nirenberg inequality in the framework of variable exponents. The combination of this inequality with a variant of the fountain theorem, yields the existence of infinitely many solutions…
A review on the fluctuation relation, fluctuation theorem and related topics.
We investigate a duality relation between floating and illumination bodies. The definitions of these two bodies suggest that the polar of the floating body should be similar to the illumination body of the polar. We consider this question…
A new concept of an equilibrium in games is introduced that solves an open question posed by A. Neyman.
Thermally excited capillary waves at fluid interfaces in binary liquid mixtures exhibit simultaneously both density and composition fluctuations. Based on a density functional theory for inhomogeneous binary liquid mixtures we derive an…
A rigid object moving in a viscous fluid and in close proximity with an elastic wall experiences self-generated elastohydrodynamic interactions. This has been the subject of an intense research activity, with a recent and growing attention…
An important challenge in active matter lies in harnessing useful global work from entities that produce work locally, e.g., via self-propulsion. We investigate here the active matter version of a classical capillary rise effect, by…
We revisit the issue of the correct Lagrangian description of a perfect fluid (pressure versus minus energy density) in relation with modified gravity theories in which galactic luminous matter couples nonminimally to the Ricci scalar.…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
In this article we study the one-dimensional dynamics of elastic collisions of particles with positive and negative mass. We show that such systems are equivalent to billiards induced by an inner product of possibly indefinite signature, we…
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of…
In this paper we study existence and regularity of solutions to the capillarity problem for compressible liquids in a tube. We introduce an appropriate space of functions of bounded variation, in which the energy functional recently…
Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density different from 1/2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine, which…
We study immiscible two-phase flow of a compressible and an incompressible fluid inside a capillary tube of varying radius under steady-state conditions. The incompressible fluid is Newtonian and the compressible fluid is an inviscid ideal…
In the recent papers~[18],~[5], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained…