Consider the parabolic free boundary problem ∆u− ∂tu = 0 in {u > 0} , |∇u| = 1 on ∂{u > 0} . For a realistic class of solutions, containing for example all limits of the singular perturbation problem ∆uε − ∂tuε = βε(uε) as ε → 0, we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary ∂{u > 0} can be decomposed into an ...

This paper explores the broad issues of why the meaningful use of ICT to engage in deep learning has not been widespread in K-12 schools. We argue a critical reason is the lack of sustainability in the implementation of ICT-enabled pedagogies in schools, arising from a failure to understand the conditions for systemic innovations. We describe the key issues related to sustainability from litera...

This review collates a wide variety of free boundary problems which are characterized by the uniform proximity of the free boundary to a prescribed surface. Such situations can often be approximated by mixed boundary value problems in which the boundary data switches across a “codimension-two” free boundary, namely, the edge of the region obtained by projecting the free boundary normally onto t...

This paper explores the potentially powerful role e-assessment practices can have on culture change in learning and teaching. This paper demonstrates how new e-assessment practices can ‘push back’ through educational institutions. This is done by applying the work of Gibbs and Simpson (2004/5) to e-assessment practices. To illustrate the practical effects of this evidence-based framework, the a...

Free spans or suspended spans normally occur in subsea pipelines due to the irregularity of seabed and byscouring phenomena around the installed non-buried pipeline. The hydrodynamic around the pipeline canlead to a vibration of the pipeline.This kind of vibration may cause fatigue damage to the pipeline. In orderto study the hydrodynamic around the pipeline, calculating the natural frequency o...

epoxy powder coatings containing zinc aluminum phosphate (zap) and zinc phosphate (zp), which are the 2nd and 1st generation of phosphate-based pigments respectively, were applied to the surface of mild steel sheets. the anticorrosive performances of the coated samples were studied using electrochemical impedance spectroscopy (eis). cathodic disbonding resistance and the adhesion performance of...

this paper studies pull-in behavior of a bio-mass sensor with a cantilevered cnt actuated electrostatically considering rippling deformation. although this phenomenon can change the behavior of cnt remarkably, its effect on the performance of a cnt-based mass sensor is not investigated yet. this investigation is based on modified euler-bernoulli beam theory and rippling effect is entered the eq...

This paper is a continuation of [9], where we analyzed steady-states of the nonlinear parabolic problem ut = ∆u− λf(x) (1+u)2 on a bounded domain Ω of R with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS) device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at −1....