Leading-Order Dynamics of Gravity-Driven Flows in?Free-Standing Soap Films

We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier?CStokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.     

Regularity of the solution for a final value problem for the Rayleigh‐Stokes equation

In this paper, we deal with the backward problem of determining initial condition for Rayleigh‐Stokes where the data are given at a fixed time. The problem has many applications in some non‐Newtonian fluids. We give some regularity properties of the solution to backward problem.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

Sequence-based necessary second-order optimality conditions for semilinear elliptic optimal control problems with nonsmooth data

Positivity - The main goal of this note is to formulate sequence-based necessary second-order optimality conditions for a semilinear elliptic optimal control problem, with a pointwise pure state...     

Synthesis of tetraarylthiophenes by regioselective Suzuki cross-coupling reactions of tetrabromothiophene

Tetraarylthiophenes were prepared by regioselective Suzuki cross-coupling reactions of tetrabromothiophene.     

Some mixing properties of time series models

Sufficient conditions are given for linear processes and ARMA processes to have the Gaswirth and Rubin mixing condition. The mixing rates are also determined.     

Bootstrapping the change-point of a hazard rate

This paper concerns the asymptotic validity of the bootstrap method in a non-regular model. Specifically, it is shown that the parametric bootstrap of the change-point parameter in the change-point hazard rate model works.