(1) ut = −(uuxxx)x − (uux)x. This is the one dimensional version of ut = −∇ · (f(u)∇∆u)−∇ · (g(u)∇u), with f(u) = un and g(u) = un. Such equations have been used to model the dynamics of a thin film of viscous liquid spreading on a flat solid surface. The air/liquid interface is at height z = u(x, y, t) ≥ 0 and the liquid/solid interface is at z = 0. The one dimensional equation (1) applies if ...

In this paper, we propose a cooperative energy-efficient localization framework (CELF) for power saving in vehicular long-thin networks (VLTNs) with fleet cyclists using smart phones along a common cycling route. As cyclists upload their position data and download global fleet information, all power-consuming GPS receivers have to be turned on for obtaining their current locations. To minimize ...

The development of the boundary layer along a long thin cylinder aligned with the flow is considered. Numerical solutions are presented and compared with previous asymptotic results. Very near the leading edge the flow is given by the Blasius solution for a flat plate. However, there is soon a significant deviation from Blasius flow, with a thinner boundary layer and higher wall shear stress. L...

We study a binary mixture of long thin rodlike particles using an idealised model in which the rods have restricted orientations and the two types of rod differ only in length. Assuming a hard core potential the virial coefficients up to fourth order are calculated exactly. The free energy is minimized with respect to the orientational distribution functions to give the phase (isotropic or nema...

1 Introduction

We present an experimental and theoretical study of the optical excitation of long-range surface polaritons supported by thin layers of amorphous silicon (a-Si). The large imaginary part of the dielectric constant of a-Si at visible and ultraviolet (UV) frequencies allows the excitation of surface polariton modes similar to long-range surface plasmon polaritons on metals. Propagation of these m...

A long thin good conducting stripline embedded in a dielectric and centered between two large conducting plates, i.e. the stripline environment, is considered. The stripline is modeled as infinitely long, infinitely thin, and perfectly conducting by first considering a stripline of finite length, thickness, and conductivity in a dielectric layer. Starting from Maxwell’s equations and assuming t...

Hocherman and Rosenau conjectured that long-wave unstable Cahn-Hilliard-type interface models develop finite-time singularities when the nonlinearity in the destabilizing term grows faster at large amplitudes than the nonlinearity in the stabilizing term (Phys. D 67, 1993, pp. 113–125). We consider this conjecture for a class of equations, often used to model thin films in a lubrication context...