Modelling of drug diffusion through swellable polymeric systems

A drug diffusion model for the case of diffusion of an initially uniformly distributed drug through a polymeric matrix is presented and solved. Drug diffusion from a single surface is analyzed for the case of countercurrent diffusion of a solvent which is thermodynamically compatible with the polymer. Due to swelling, considerable volume expansion is observed leading to a moving-boundary diffusion problem. Drug concentration profiles within the polymer and drug release rates can be determined. The results are in agreement with experimental data obtained for the system of KCl distributed in hydrophilic hydroxypropyl methyl cellulose matrices, in the form of tablets.     

On logarithmic Sobolev inequalities for higher order fractional derivatives

On ${\mathbb{R}}^n$, we prove the existence of sharp logarithmic Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. Any function f ∈ $H^s({\mathbb{R}}^n)$ satisfies

$\underset{{\mathbb{R}}^n}{\int }|f(x){|}^2\ln (\frac{{|f(x)|}^2}{6f{6}_2^2})\mathrm{d}x+(n+\frac{n}{s}\ln \alpha +\ln \frac{s\mathrm{\Gamma }(\frac{n}{2})}{\mathrm{\Gamma }(\frac{n}{2s})})6f{6}_2^2?\frac{{\alpha }^2}{{\pi }^s}6{(?\mathrm{\Delta })}^{s/2}f{6}_2^2$

with $\alpha >0$ be any number and where the operators ${(?\mathrm{\Delta })}^{s/2}$ in Fourier spaces are defined by $\stackrel{?}{{(?\mathrm{\Delta })}^{s/2}f}(k)\text{:}={(2\pi |k|)}^s\stackrel{?}{f}(k)$. To cite this article: A. Cotsiolis, N.K. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

The string coupling accelerates the expansion of the universed

Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter q ₀ is given by the square of the string coupling, g _s ², up to a negative sign. Hence the expansion of the Universe must accelerate eventually, and the observed value of q ₀ corresponds to g _s ² ∼ 0.6. In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small. First Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

Existence of Solutions and of Multiple Solutions for Nonlinear Nonsmooth Periodic Systems

In this paper we examine nonlinear periodic systems driven by the vectorial p-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the sublinear problem. For the semilinear problem (i.e. p = 2) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the superlinear problem. Our work generalizes some recent results of Tang (PAMS 126(1998)).     

Two nontrivial solutions for quasilinear periodic equations

In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem".

     

Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.     

Interactive resonant scattering by a cluster of air bubbles in water

An exact, analytical solution is developed for the problem of acoustic-wave scattering from a cluster of ideal, gaseous, spherical bubbles in an unbounded, homogeneous, host fluid. This solution takes into account all modes of oscillation of the bubbles as well as all interactions between them; it is applicable to a wide range of bubble sizes and excitation frequencies. In the low frequency regime, the theory of this paper is shown to reduce to the "monopole" approximation, the effect of higher-order modes being non-negligible only for very small bubble-to-bubble separations. A numerical study of interactive backscattering from small clusters, comprising up to three ideal bubbles, is presented. Interactions between the bubbles are shown to produce downward shifts in the resonance frequency of the cluster, when the scattering configuration is symmetric. Furthermore, asymmetries of the scattering configuration are shown to generate sharp resonances at frequencies above the resonance of the symmetric mode. The results of this paper agree with previous theoretical and experimental work.     

Gait recognition using radon transform and linear discriminant analysis.

A new feature extraction process is proposed for gait representation and recognition. The new system is based on the Radon transform of binary silhouettes. For each gait sequence, the transformed silhouettes are used for the computation of a template. The set of all templates is subsequently subjected to linear discriminant analysis and subspace projection. In this manner, each gait sequence is described using a low-dimensional feature vector consisting of selected Radon template coefficients. Given a test feature vector, gait recognition and verification is achieved by appropriately comparing it to feature vectors in a reference gait database. By using the new system on the Gait Challenge database, very considerable improvements in recognition performance are seen in comparison to state-of-the-art methods for gait recognition.     

A numerical investigation of the influence of the aspect ratio in three‐dimensional separated flows

The influence of aspect ratio in three‐dimensional, numerical experiments of separated flows is studied in the case of the backward‐facing step at Reynolds numbers 600, 800, and 950. The computational domain is designed as an actual laboratory experiment. The governing equations are the steady state, isothermal, and incompressible Navier–Stokes equations. The expansion ratio of the computational domain is 1:2. The aspect ratio varies from 1:10 to 1:40. The results of the computations focus on the spanwise variations of the length and the strength of the two eddies along the lower and upper wall. It is concluded that both numerical and laboratory experiments should be designed with an aspect ratio of at least 1:20, if only the accuracy of the position of the detachment and the re‐attachment points matters. If the accuracy of the shear‐stress distributions is also taken into account, then an aspect ratio of at least 1:30 should be chosen. Finally, if the magnitudes of the vortex centers are also considered, then only the aspect ratio of 1:40 qualifies for a realization of two‐dimensional flow conditions in the plane of symmetry. This is contrary to the common practice in the field, at least from the side of laboratory experiments, where an aspect ratio of 1:10 is still considered adequate for this purpose. Copyright © 2011 John Wiley & Sons, Ltd.