Related papers: Soap film spanning an elastic link
In this paper we consider a coupled system of pdes modelling the interaction between a two--dimensional incompressible viscous fluid and a one--dimensional elastic beam located on the upper part of the fluid domain boundary. We design a…
We simulate the nonlinear dynamic responses in Kirchhoff rod by including the important effects due to inertia and kinematic coupling of tension and torsion. We begin by reviewing a dynamic rod model of a strand (length of cable or DNA) in…
The mobility of surface electrons localized over helium films underlying solid substrates has been evaluated by solving the Boltzmann equation in the time relaxation approximation and the force balance equation in which an effective…
We show that a smectic in a disordered medium (e.g., aerogel) exhibits anomalous elasticity, with the compression modulus B(k) vanishing and the bend modulus K(k) diverging as k --> 0. In addition, the effective disorder develops long…
We prove well-posedness, partial regularity, and stability of the thin-film equation $h_t + (m(h) h_{zzz})_z = 0$ with general mobility $m(h) = h^n$ and mobility exponent $n\in (1,\tfrac{3}{2})\cup (\tfrac{3}{2},3)$ in the regime of perfect…
The present study aims to investigate the motion of buoyant rings in vertical soap films. Thickness differences and related bi-dimensional densities are considered as the motor leading to bi-dimensional buoyancy. We show how this effect can…
We investigate the question of stability of a solid thin film which experiences external interactions such as van der Waals forces from a contacting surface or forces from an external electric field. Both perfectly elastic and viscoelastic…
We study the stability and bifurcation of relative equilibria of a particle on the Lie group $SO(3)$ whose motion is governed by an $SO(3)\times SO(2)$ invariant metric and an $SO(2)\times SO(2)$ invariant potential. Our method is to reduce…
In this thesis, we consider the thin-film equation with nonlinear surface tension term in one space dimension. Relying on the corresponding energy and entropy estimates, we prove existence of weak solutions as well as nonnegativity results.
"The Life of a Free Soap Film" is a fluid dynamics video for the Gallery of Fluid Motion intended to showcase the novel experimental techniques that we have developed in our laboratory to study the retraction of planar liquid films of…
We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the elastic forces of the liquid crystal, coupled with…
We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field…
In this paper, we prove the existence and a partial regularity of a weak solution to the system governing the interaction between a rigid body and a viscous incompressible Newtonian fluid. The evolution of the system body-fluid is studied…
We analyze existence and qualitative behavior of non-negative weak solutions for fourth order degenerate parabolic equations on graph domains with Kirchhoff's boundary conditions at the inner nodes and Neumann boundary conditions at the…
We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include the membrane and bending energy of the sheet as well as terms due to gravity and surface tension. By studying a suitable…
We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and…
Motivated by observations of snap-through phenomena in buckled elastic strips subject to clamping and lateral end translations, we experimentally explore the multi-stability and bifurcations of thin bands of various widths and compare these…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in…
We prove long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the…
We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our…