Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

Study of packing lines for stone fruits and citrus using two instrumented spheres in some cooperatives in the region of Murcia (Spain).

Two instrumented spheres IS 100 were used to evaluate the quality of post-harvest operations. Results obtained from measurements made with both IS (8.8 cm 0 and 6.2 cm 0) show significant differences. Both IS measure the same values of the same variables for soft materials, but not for hard surfaces. Four packing lines belonging to different cooperatives of the region of Murcia (two for stone fruits and two for citrus) were tested. IS values obtained in transfers belonging to the tested lines lay well above 50 g's in most of them Much higher impact intensities are registered in citrus lines than in stone fruit packing lines. To study the incidence of a certain packing line on different products an interaction fruit-packing line test was perf01med. In all cases, more than 50% of fruits belonging to the post-handling sample showed some kind of damage. Bruises evolve after 48 hours storage at room temperature.

Conchoid surfaces of spheres

The conchoid of a surface F with respect to given xed point O is roughly speaking the surface obtained by increasing the radius function with respect to O by a constant. This paper studies conchoid surfaces of spheres and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in R3 and R4. Moreover we point to remarkable geometric properties of these surfaces and their construction.

Interaction between like-charged colloidal spheres in electrolyte solutions

How colloidal particles interact with each other is one of the key issues that determines our ability to interpret experimental results for phase transitions in colloidal dispersions and our ability to apply colloid science to various industrial processes. The long-accepted theories for answering this question have been challenged by results from recent experiments. Herein we show from Monte-Carlo simulations that there is a short-range attractive force between identical macroions in electrolyte solutions containing divalent counterions. Complementing some recent and related results by others, we present strong evidence of attraction between a pair of spherical macroions in the presence of added salt ions for the conditions where the interacting macroion pair is not affected by any other macroions that may be in the solution. This attractive force follows from the internal-energy contribution of counterion mediation. Contrary to conventional expectations, for charged macroions in an electrolyte solution, the entropic force is repulsive at most solution conditions because of localization of small ions in the vicinity of macroions. Both Derjaguin–Landau–Verwey–Overbeek theory and Sogami–Ise theory fail to describe the attractive interactions found in our simulations; the former predicts only repulsive interaction and the latter predicts a long-range attraction that is too weak and occurs at macroion separations that are too large. Our simulations provide fundamental “data” toward an improved theory for the potential of mean force as required for optimum design of new materials including those containing nanoparticles.

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs’ free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p_(co) = 11.5727(10)k_(B)T/σ^(3)] and the interfacial free energy [γ_({100}) = 0.636(11)k_(B)T/σ^(2)].

Phase diagram of a polydisperse soft-spheres model for liquids and colloids

The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.

Scattering coefficients for the backscattering of electromagnetic waves from perfectly conducting spheres; research information series.

Mode of access: Internet.

L' Usage des globes celeste et terrestre, et des spheres suivant les differens systemes du monde. Precede d'un traite de Cosmographie ... Troisiéme edition revûe, corrigée & augmentée par le sieur Bion ingenieur pour les instrumens de mathematique, sur le Quay de l'Horloge du Palais, au Soleil d'or, ou l'on trouve des Spheres & des Globes des toutes facons.

Mode of access: Internet.