Counterion Penetration and Effective Electrostatic Interactions in Solutions of Polyelectrolyte Stars and Microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modelling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.Comment: 15 pages, 5 figure

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Solvent structure contributions to the small-angle scattering from colloidal dispersions

By postulating an approximate analytic form for the force between two colloidal particles arising from the structure of the intervening solvent, the solvent structure contributions to the small angle scattering from colloidal dispersions are analysed within a perturbation theory based on the random phase approximation. The force between two colloidal particles due to the solvent structure is seen to make in general a small but non-negligible contribution to both the osmotic compressibility and the small wavevector form of the static structure factor of the dispersion.Supposant une forme analytique approximative pour la force entre deux particules colloïdales, on analyse, dans le cadre d'une théorie de perturbation fondée sur l'approximation de phase aléatoire, l'influence de la structure du solvant sur la diffusion centrale de dispersions colloïdales. On observe que la contribution à la force entre deux particules colloïdales due A la structure du solvant exerce en général une influence minime mais non négligeable sur la compressibilité osmotique et sur la forme du facteur de structure statique de la dispersion aux petits vecteurs d'ondes

The structure of deformable particles in applied external fields

The structure of two dimensional deformable particles of low interfacial tension is studied theoretically. Closed loops in the plane are used to model droplets of one liquid in a second with surface active molecules residing at the liquid-liquid interface. The mechanical properties of the surfactant layer are represented by a bending energy contribution due to Helfrich, where the relevant parameters are rigidity and local curvature, and a surface tension. Thermal shape fluctuations and the deformational response to external fields, such as those due to confining walls or neighbouring particles, are studied by a method of functional integration in conjunction with a Monte Carlo sampling technique. Our results include particle shape distribution functions for different geometrical constraints and interfacial conditions which are relevant to bilayer lipid vesicles, microemulsion particles and emulsion droplets.On présente une étude théorique de la structure de particules déformables de basse tension interfaciale. Il s'agit de gouttelettes à deux dimensions, délimitées par une couche interfaciale formée de molécules tensioactives ; elles sont représentées par des boucles fermées dans un plan et on étudie les déformations de ces boucles. Les propriétés mécaniques du film superficiel sont décrites sur l'énergie libre de flexion d'Helfrich les paramètres pertinents étant la rigidité et la courbure locale, ainsi que la tension superficielle. On étudie les fluctuations spontanées et la réponse déformationnelle à des champs extérieurs qui peuvent être des murs contraignants ou des particules voisines ; la méthode est une intégration fonctionnelle liée à une technique d'échantillonnage du type Monte Carlo. On obtient la distribution des formes des particules pour différentes contraintes géométriques et différentes conditions interfaciales ; les résultats s'appliquent aux vésicules de lipides, aux microémulsions et aux gouttelettes des émulsions

Shouldered hard sphere model for charged colloidal dispersions

The experimentally determined structure factor for an aqueous dispersion of charged polystyrene spheres is analyzed in terms of a system of particles interacting through a shouldered hard sphere potential. The fit of the model system to the experimental data is sufficiently good that the fluid represents a suitable reference system for perturbation studies of the small-angle scattering

A progressive scheme for stereo matching

Brute-force dense matching is usually not satisfactory because the same search range is used for the entire image, yielding potentially many false matches. In this paper, we propose a progressive scheme for stereo matching which uses two fundamental concepts: the disparity gradient limit principle and the least commitment strategy. The first states that the disparity should vary smoothly almost everywhere, and the disparity gradient should not exceed a certain limit. The second states that we should first select only the most reliable matches and therefore postpone unreliable decisions until enough confidence is accumulated. Our technique starts with a few reliable point matches obtained automatically via feature correspondence or through user input. New matches are progressively added during an iterative matching process. At each stage, the current reliable matches constrain the search range for their neighbors according to the disparity gradient limit, thereby reducing potential matching ambiguities of those neighbors. Only unambiguous matches are selected and added to the set of reliable matches in accordance with the least commitment strategy. In addition, a correlation match measure that allows rotation of the match template is used to provide a more robust estimate. The entire process is cast within a Bayesian inference framework. Experimental results illustrate the robustness of our proposed dense stereo matching approach