Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

In situ observations of domain wall motion in Mn–Zn and Ni–Zn ferrites by Lorentz microscopy and electron holography

Domain wall motion in Mn–Zn and Ni–Zn ferrites with applied magnetic fields is investigated by in situ observations with Lorentz microscopy and electron holography. It is found that both Mn–Zn and Ni–Zn ferrites have a mean grain size of approximately 10 μm and several pores with sizes ranging from 0.2 to 1.1 μm. In situ observations by Lorentz microscopy with an applied magnetic field reveals that in Mn–Zn ferrite, the domain walls move easily across the grain boundary, while in Ni–Zn ferrite, the domain walls move along the grain boundary but are pinned at the grain boundary and pores. From in situ observations of Ni–Zn ferrite by electron holography, it is clarified that domain wall pinning at the grain boundary retards a sensitive increase in magnetic flux parallel to the applied field direction, which is considered to result in high hysteresis loss.     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

Route stability in vehicle routing decisions: a bi-objective approach using metaheuristics

In this paper, we argue that vehicle routing solutions are often tactical decisions, that should not be changed too often or too much. For marketing or other reasons, vehicle routing solutions should be stable, i.e. a new solution (when e.g. new customers require service) should be as similar as possible to a solution already in use. Simultaneously however, this new solution should still have a good quality in the traditional sense (e.g. small total travel cost). In this paper, we develop a way to measure the difference between two vehicle routing solutions. We use this distance measure to create a metaheuristic approach that will find solutions that are “close” (in the solution space) to a given baseline solution and at the same time have a high quality in the sense that their total distance traveled is small. By using this approach, the dispatcher is offered a choice of Pareto-optimal solutions, allowing him to make a trade-off between changing his existing solution and allowing a longer travel distance. Some experiments are performed to show the effectiveness of the approach.     

Magnetic properties of the Cr(0 0 1) surface studied by spin-polarized scanning tunneling spectroscopy

The magnetic properties of the Cr(0 0 1) surface have been studied by spin-polarized scanning tunneling spectroscopy (SP-STS). Spatially resolved mapping of the spectroscopic dI/dU signal at an energy close to the spin-polarized Cr(0 0 1) surface state allows the confirmation of the topological antiferromagnetic order of the Cr(0 0 1) surface. It is shown that the presence of screw dislocations leads to the formation of domain walls which exhibit a width of 120–170 nm. A long-period modulation of the SP-STS signal was not observed indicating that the bulk spin-density wave is modified at the surface due to symmetry breaking.     

Algebraic Dirichlet-to-Neumann mapping for linear elasticity problems with extreme contrasts in the coefficients

The convergence of iterative based domain decomposition methods is linked with the absorbing boundary conditions defined on the interface between the sub-domains. For linear elasticity problems, the optimal absorbing boundary conditions are associated with non-local Dirichlet-to-Neumann maps. Most of the methods to approximate these non-local maps are based on a continuous analysis. In this paper, an original algebraic technique based on the computation of local Dirichlet-to-Neumann maps is investigated. Numerical experiments are presented for linear elasticity problems with extreme contrasts in the coefficients.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

Balancing domain decomposition for problems with large jumps in coefficients

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size . Computational experiments for two- and three-dimensional problems confirm the theory.