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...

Let M‾ be a compact smoothly stratified pseudomanifold with boundary, satisfying the Witt assumption. In this paper we introduce de Rham signature and Hodge of M‾, prove their equality. Next, building also on recent work Albin Gell-Redman, extend Atiyah-Patodi-Singer index theory established in our previous under hypothesis that has stratification depth 1 to general case, establishing particula...

Introduction Relative dose computation is a necessary step in radiation treatment planning. Therefore, finding an approach that is both fast and accurate seems to be necessary. The purpose of this work was to investigate the feasibility of natural cubic spline to reconstruct dose maps for linear accelerator radiation treatment fields in comparison with those of the simulation. Materials and Met...

Let Γ be a discrete finitely generated group. Let M̂ → T be a Γ-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary Z. We assume that Γ → M̂ → M̂/Γ is a Galois covering of a compact manifold with boundary. Let (D(θ))θ∈T be a Γ-equivariant family of Dirac-type operators. Under the assumption that the boundary family is L-invertible , we define an inde...

We establish a quantitative isoperimetric inequality in higher codimension. In particular, we prove that for any closed (n − 1)-dimensional manifold Γ in Rn+k the following inequality D(Γ) ≥ Cd(Γ) holds true. Here, D(Γ) stands for the isoperimetric gap of Γ, i.e. the deviation in measure of Γ from being a round sphere and d(Γ) denotes a natural generalization of the Fraenkel asymmetry index of ...

A heat exchanger using nanofluid needs to operate at optimum mass concentration level to get the maximum heat transfer performance. A numerical analysis is performed on the heat transfer and pressure drop of water-based γ-Al2O3 nanofluid gasketed-plate heat exchanger to specify its optimum conditions. Cold water will be heated by γ-Al2O3/water nanofluid. The results showed that optimal volume c...

Let T be a k-regular tree (k ≥ 3) and A = Aut(T ) its automorphism group. We analyze a generic finitely generated subgroup Γ of A. We show that Γ is free and establish a trichotomy on the closure Γ of Γ in A. It turns out that Γ is either discrete, compact or has index at most 2 in A.

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...