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Université de Fribourg

Oil-continuous microemulsions mixed with an amphiphilic graft copolymer or with the parent homopolymer. Polymer–droplet interactions as revealed by phase behavior and light scattering

Holmberg, Anna ; Piculell, Lennart ; Schurtenberger, Peter ; Olsson, Ulf

In: Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2004, vol. 250, p. 325-336

Polymer–droplet interactions have been studied in AOT/water/isooctane oil-continuous microemulsions mixed with an amphiphilic graft copolymer, or with the parent homopolymer (AOT = sodium bis(2-ethylhexyl) sulfosuccinate). The graft copolymer has an oil-soluble poly(dodecyl methacrylate) backbone and water-soluble poly(ethylene glycol) side chains. Pseudo-ternary polymer/droplet/isooctane phase...

Université de Fribourg

Suites infinies de surfaces de Riemann parfaites

Casamayou-Boucau, Alexandre

In: Bulletin des Sciences Mathématiques, 2004, vol. 128, p. 739-748

In this article we give two new infinite sequences of perfect non-extremal Riemann surfaces of genus bigger than six. The first sequence consists of weakly eutactic perfect surfaces; the second one of semi-eutactic perfect surfaces.

Université de Fribourg

Heat flow into spheres for a class of energies

Hungerbühler, Norbert

In: Progress in Non-Linear Differential Equations and their Applications, 2004, vol. 59, p. 45-64

Let M and N be compact smooth Riemannian manifolds without boundaries. Then, for a map u : M→N, we consider a class of energies which includes the popular Dirichlet energy and the more general p-energy. Geometric or physical questions motivate to investigate the critical points of such an energy or the corresponding heat flow problem. In the case of the Dirichlet energy, the heat flow problem...

Université de Fribourg

Results on a Navier-Stokes system with applications to electrorheological fluid flow

Dreyfuss, Pierre ; Hungerbühler, Norbert

In: International Journal of Pure and Applied Mathematics, 2004, vol. 14, p. 241-267

We study a Navier-Stokes system which is motivated by models for electrorheological fluids. Its principal features are the weak monotonicity assumptions we impose on the viscosity tensor. Moreover we allow the viscosity to depend on the velocity in order to cover some of the models in electrorheological theory. We establish existence of a weak solution of the corresponding Navier-Stokes system.

Université de Fribourg

Navier-Stokes systems with quasimonotone viscosity tensor.

Dreyfuss, Pierre ; Hungerbühler, Norbert

In: International Journal of Differential Equations and Applications: in press

We (Dreyfuss P., Hungerbühler, N., 2004, Int. J. of Pure and Appl.Math. 14(2): 241–271) investigated a class of Navier-Stokes systems which is motivated by models for electrorheological fluids. We obtained an existence result for a weak solution under mild monotonicity assumptions for the viscosity tensor. In this article, we continue the analysis of such systems, but with various notions of...

Université de Fribourg

Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data

Augsburger, Fabien ; Hungerbühler, Norbert

In: Electronic Journal of Differential Equations, 2004, vol. 144, p. 1-18

We study the quasilinear elliptic system −div σ(x, u,Du) = v(x) + f(x, u) + div g(x, u) on a bounded domain of Rⁿ with homogeneous Dirichlet boundary conditions. This system corresponds to a diffusion problem with a source v in a moving and dissolving substance, where the motion is described by g and the dissolution by f. We prove existence of a weak solution of this system under classical...

Université de Fribourg

Phylogenetic constraints and adaptation explain food-web structure

Cattin, Marie-France ; Bersier, Louis-Félix ; Banašek-Richter, Carolin ; Baltensperger, Richard ; Gabriel, Jean-Pierre

In: Nature, 2004, vol. 427, p. 835-839

Food webs are descriptions of who eats whom in an ecosystem. Although extremely complex and variable, their structure possesses basic regularities. A fascinating question is to find a simple model capturing the underlying processes behind these repeatable patterns. Until now, two models have been devised for the description of trophic interactions within a natural community. Both are essentially...

Université de Fribourg

Mathematical analysis of competition between sensory ganglion cells for neurotrophic factor in the skin

Kohli, R. ; Gabriel, Jean-Pierre ; Clarke, P.G.H.

In: Mathematical Biosciences, 2004, vol. 191, p. 207

A model is presented of competition between sensory axons for trophic molecules (e.g. a neurotrophin such as NGF), produced in a region of skin small enough to permit their free diffusion throughout it; e.g., a touch dome, or a vibrissal follicle hair sinus. The variables specified are the number of high affinity trophic factor receptors per axon terminal and the concentration of trophic factor...

Université de Fribourg

Angular Gaussian and Cauchy estimation

Auderset, Claude ; Mazza, Christian ; Ruh, Ernst A.

In: Journal of Multivariate Analysis, 2005, vol. 93, p. 180-197

This paper proposes a unified treatment of maximum likelihood estimates of angular Gaussian and multivariate Cauchy distributions in both the real and the complex case. The complex case is relevant in shape analysis. We describe in full generality the set of maxima of the corresponding log-likelihood functions with respect to an arbitrary probability measure. Our tools are the convexity of...

Université de Fribourg

Optimized point shifts and poles in the linear rational pseudospectral method for boundary value problems

Berrut, Jean-Paul ; Mittelmann, Hans D.

In: Journal of Computational Physics, 2005, vol. 204, p. 292-301

Due to their rapid – often exponential – convergence as the number N of interpolation/collocation points is increased, polynomial pseudospectral methods are very efficient in solving smooth boundary value problems. However, when the solution displays boundary layers and/or interior fronts, this fast convergence will merely occur with very large N. To address this difficulty, we present a...