Capillary wave dynamics on supported viscoelastic films: Single and double layers

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu {\em et al.}, Phys. Rev. E {\bf 74}, 010602 (R) (2006)].Comment: 14 pages, 9 figure

Solving equations in class 2 nilpotent groups

We construct an algorithm to decide if in a class $2$ nilpotent group an equation $\omega = 1$ that contains a variable $X$ such that the exponent sum of $X$ within $\omega$ is non-zero admits a solution. Besides the existence of such an $X$ in $\omega$, there are no restrictions on any other variables. We do this by associating the equation to a system of integer equations and congruences equivalent to it, and give an algorithm to solve this system. We also construct an algorithm to decide if any equation in a group that is virtually the Heisenberg group admits a solution.Comment: 21 pages Fixed error in main theore

Rheology and nonlinear mechanics of transiently cross linked semiflexible networks: Bundling, ripping, healing, and mechnomemory

Transiently cross linked networks of semiflexible filaments make up the principal structural component of the cell — the cytoskeleton. This intracellular network, along with molecular motors, forms the basis for cellular control of morphology and force generation. In this talk, I report on investigations of the effect of transiently bound cross linkers on the structure and mechanics of semiflexible networks. Specifically, I address the role of Casimir or fluctuation-induced interactions between cross linkers in the formation of filament bundles. I report on the linear viscoelasticity of transiently cross-linked networks of bundles. Finally, I discuss the nonlinear mechanical response of such networks, where applied stress induces a persistent structural rearrangement of the network that can dramatically alter its nonlinear response to stresses subsequently applied

Quadratic Diophantine equations, the Heisenberg group and formal languages

We express the solutions to quadratic equations with two variables in the ring of integers using EDT0L languages. We use this to show that EDT0L languages can be used to describe the solutions to one-variable equations in the Heisenberg group. This is done by reducing the question of solving a one-variable equation in the Heisenberg group to solving an equation in the ring of integers, exploiting the strong link between the ring of integers and nilpotent groups.Comment: 33 page