Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Interaction of miltefosine with intercellular membranes of stratum corneum and biomimetic lipid vesicles

Miltefosine (MT) is an alkylphospholipid approved for breast cancer metastasis and visceral leishmaniasis treatments, although the respective action mechanisms at the molecular level remain poorly understood. In this work, the interaction of miltefosine with the lipid component of stratum corneum (SC), the uppermost skin layer, was studied by electron paramagnetic resonance (EPR) spectroscopy of several fatty acid spin-labels. In addition, the effect of miltefosine on (i) spherical lipid vesicles of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC) and (ii) lipids extracted from SC was also investigated, by EPR and time-resolved polarized fluorescence methods. In SC of neonatal Wistar rats, 4% (w/w) miltefosine give rise to a large increase of the fluidity of the intercellular membranes, in the temperature range from 6 to about 50 degrees C. This effect becomes negligible at temperatures higher that ca. 60 degrees C. In large unilamelar vesicles of DPPC no significant changes could be observed with a miltefosine concentration 25% molar, in close analogy with the behavior of biomimetic vesicles prepared with bovine brain ceramide, behenic acid and cholesterol. In these last samples, a 25 mol% molar concentration of miltefosine produced only a modest decrease in the bilayer fluidity. Although miltefosine is not a feasible skin permeation enhancer due to its toxicity, the information provided in this work could be of utility in the development of a MT topical treatment of cutaneous leishmaniasis. Published by Elsevier B.V.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.