相关论文: Non-spherical equilibrium shapes in the liquid dro…

In this paper we study the bifurcation of branches of non-symmetric solutions from the symmetric branch of solutions to the Euler-Lagrange equations satisfied by optimal functions in functional inequalities of Caffarelli-Kohn-Nirenberg…

We construct steady non-spherical bubbles and drops, which are traveling wave solutions to the axisymmetric two-phase Euler equations with surface tension, whose inner phase is a bounded connected domain. The solutions have a uniform…

The impact of liquid drops on solid surfaces is ubiquitous in nature, and of practical importance in many industrial processes. A drop hitting a flat surface retains a circular symmetry throughout the impact process. Here we show that a…

In statistical physics, it is well established that the liquid-gas (LG) phase transition with divergent critical fluctuations belongs to the Ising universality class. Whether non-equilibrium effects can alter this universal behavior remains…

This note presents two nontrivial, rotational equilibrium solutions to the spatial uniform gas pressure (isobaric) approximate model of Prosperetti in the inviscid case. Building on Gavrilov's work [GAFA 2019], we first establish the…

Liquids in systems with spherically symmetric interactions are not thermodynamically stable when the range of the attraction is reduced sufficiently. However, these metastable liquids have lifetimes long enough that they are readily…

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…

See http://youtu.be/Mf4IE8gWcJs for a YouTube video showing part of the results in this paper. We consider helicoidal immersions in the Euclidean space whose axis of symmetry is the z-axis that are solutions of the equation 2 H=\Lambda_0-a…

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…

The shape of a weightless spinning liquid droplet is governed by the balance between the surface tension and centrifugal forces. The axisymmetric shape for slow rotation becomes unstable to a non-axisymmetric distortion above a critical…

We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field.…

We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is…

Much attention has been devoted to water's metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship…

Breakup of a liquid jet into a chain of droplets is common in nature and industry. Previous researchers developed profound mathematic and fluid dynamic models to address this breakup phenomenon starting from tiny perturbations. However, the…

We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…

The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…

We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…

We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…

Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from…

Non-Fermi liquids in $d>2$ remain poorly understood, particularly when relevant perturbations destabilize them. In one spatial dimension, chirally stabilized fixed points provide a rare class of analytically tractable non-Fermi-liquid…