Related papers: The Purcell question: why do all viscosities stop …
We consider Navier-Stokes equations for compressible viscous fluids in the one-dimensional case with general viscosity coefficients. We prove the existence of global weak solution when the initial momentum $\rho_0 u_0$ belongs to the set of…
The vacuum condensate due to neutrino and quark mixing behaves as a perfect fluid and, at the present epoch, as a cosmological constant. The very small breaking of the Lorentz invariance constrains today the value of the dark energy.
Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that…
Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related to this problem.
The viscosity of liquids under nanoconfinement remains controversial. Reports range from spontaneous solidification to no change in the viscosity at all. Here, we present thorough measurements with a small-amplitude linear atomic force…
Could it be that the matter from the electrons in high Tc superconductors is of a radically new kind that may be called "many body entangled compressible quantum matter"? Much of this text is intended as an easy to read tutorial, explaining…
Mixtures of quantum fluids, that is gases or liquids, are considered with the emphasis on the conditions characterizing the stability of the mixtures. The mixtures, that can be formed by cold atoms or molecules, are assumed to be quantum…
We point out an interesting connection between fluid dynamics and minimal surface theory: When gluing helicoids into a minimal surface, the limit positions of the helicoids correspond to a "vortex crystal", an equilibrium of point vortices…
When a droplet is gently laid onto the surface of the same liquid, it stays at rest for a moment before coalescence. The coalescence can be delayed and sometimes inhibited by injecting fresh air under the droplet. This can happen when the…
We reveal that realistic fluids generate microscopic-level discontinuity constantly and the discontinuity spreads out with motion of particles rather rapidly and widely. These things cannot be treated by the standard kinetic equations, and…
The stability of floating drops on the liquid surface of the same liquid is considered in terms of viscous drainage theory. We have expressed the minimal thickness of the air film, separating the drop from the liquid surface, and the…
Vorticity plays a prominent role in the dynamics of incompressible viscous flows. In two-dimensional freely decaying turbulence, after a short transient period, evolution is essentially driven by interactions of viscous vortices, the…
Proximity measurements probe whether pairs of particles are close to one another. We consider the impact of post-selected random proximity measurements on a quantum fluid of many distinguishable particles. We show that such measurements…
This work is devoted to the definition and the analysis of the effective viscosity associated with a random suspension of small rigid particles in a steady Stokes fluid. While previous works on the topic have been conveniently assuming that…
The stability of thin liquid coatings is of fundamental interest in every- day life. Homogeneous and non-volatile liquid coatings may dewet either by heterogeneous nucleation, thermal nucleation, or spinodal dewetting. Wetting and dewetting…
Despite the success of modern physics in formulating mathematical theories that can predict the outcome of experiments, we have made remarkably little progress towards answering the most fundamental question of: why is there a universe at…
A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been…
We assert that the solutions to the Cauchy problem of the inviscid vorticity equation remain regular and unique for any smooth initial data of finite energy. However, the primitive formulation of the Euler equations is not well-posed, due…
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…
All liquids (except helium due to quantum effects) crystallize at low temperatures, forming ordered structures. The competition between disorder, which stabilizes the liquid phase, and energy, which favors the ordered crystalline structure,…