We study the minimum energy configuration of a uniform distribution of negative charge subject to Coulomb repulsive self-interaction and attractive interaction with a fixed positively charged domain. After having established existence and uniqueness of a minimizing configuration, we prove charge neutrality and the complete screening of the Coulomb potential exerted by the positive charge, and w...

where Ω is an open bounded set of R and W and V are two non-negative continuous functions vanishing at α, β and α, β, respectively. In the previous functional, we fix a = 2 − p and u is a scalar density function, Tu denotes its trace on ∂Ω, d(x, ∂Ω) stands for the distance function to the boundary ∂Ω. We show that the singular limit of the energies Fε leads to a coupled problem of bulk and surf...

1. Liquid–Liquid Phase Transitions Consider a fluid confined into a container Ω ⊂ R . Assume that the total mass of the fluid is m, so that admissible density distributions u : Ω→ R satisfy the constraint ∫ Ω u(x) dx = m. The total energy is given by the functional u 7→ ∫ Ω W (u(x)) dx, where W : R→ [0,∞) is the energy per unit volume. Assume that W supports two phases a < b, that is, W is a do...

Plastic 60Co buildup caps have been widely used to protect ionization chambers when calibrating high-energy x-ray and electron beams in water, and have been used consistently by the Radiological Physics Center. Recent calibration protocols base their calculations on a theory that assumes that no protective cap is used during calibration in phantom. The change in ionization within the chamber du...

稲葉 次郎,西 村義一,市 川竜資:放 射線医学総合研究所 環境衛生研究部 千葉市 穴川4-9-1,〒260 Co-60 metabolism/Seaweed cobalt/Rat The objective of this study is to compare whole-body retention in the rat of radiocobalt incorporated into a marine green alga with that of 60Co in inorganic form. Ulva pertusa was incubated in aerated seawater containing 60Co under fluorescent lamp for 7 days. The radio active seaweed was homogenated and...

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called particles) remains O(1). Using the languag...

We study, by means of Γ-convergence, the asymptotic behaviour of a variational problem modeling a dislocation ensemble moving on a slip plane through a discrete array of obstacles. The variational problem is a two dimensional phase transition type energy given by a non local term and a non linear potential which penalizes non integer values. In this paper we consider a regime corresponding to a...