相关论文: Shape Minimization of Dendritic Attenuation
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
We consider a shape optimization problem written in the optimal control form: the governing operator is the $p$-Laplacian in the Euclidean space $\R^d$, the cost is of an integral type, and the control variable is the domain of the state…
In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions…
The main purpose of this article is to establish new uniqueness results for Calder\'on type inverse problems related to damped nonlocal wave equations. To achieve this goal we extend the theory of very weak solutions to our setting, which…
We construct symplectic embeddings of ellipsoids of dimension $2n \ge 6$ into the product of a 4-ball or 4-dimensional cube with Euclidean space. A sequence of these embeddings can be shown to be optimal.
In this paper the smallest or optimal dimensions of a Halbach cylinder of a finite length for a given sample volume and desired flux density are determined using numerical modeling and parameter variation. A sample volume that is centered…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…
Propulsion at microscopic scales is often achieved through propagating traveling waves along hair-like organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of…
We consider shape optimization problems for general integral functionals of the calculus of variations, defined on a domain $\Omega$ that varies over all subdomains of a given bounded domain $D$ of ${\bf R}^d$. We show in a rather…
The problem of finding the optimal tapering of a free (non-supported) javelin is described and solved. For the optimal javelin, the lowest mode of vibration has the highest possible frequency. With this tapering inner damping will lead to…
We consider shape optimization problems with internal inclusion constraints, of the form $$\min\big\{J(\Omega)\ :\ \Dr\subset\Omega\subset\R^d,\ |\Omega|=m\big\},$$ where the set $\Dr$ is fixed, possibly unbounded, and $J$ depends on…
The maximum volume ($\Omega$) of a droplet that can remain attached to a horizontal fiber defines the stability limit of droplet-fiber interactions, phenomena common in nature and critical to diverse engineering applications. Existing…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
We consider polynomials of a few linear forms and show how exploit this type of sparsity for optimization on some particular domains like the Euclidean sphere or a polytope. Moreover, a simple procedure allows to detect this form of…
We study the ridge method for min-max problems, and investigate its convergence without any convexity, differentiability or qualification assumption. The central issue is to determine whether the ''parametric optimality formula'' provides a…
We consider Newton's problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that…
Lower bounds are given for the depths of R/I^t for t at least one when I is the edge ideal of a tree or forest. The bounds are given in terms of the diameter of the tree, or in case of a forest, the largest diameter of a connected component…