Zobrazeno 1 - 10
of 1 556
pro vyhledávání: '"49Q10"'
Autor:
Bogosel, Beniamin
The sensitivity of the areas of Reuleaux polygons and disk polygons is computed with respect to vertex perturbations. Computations are completed for both constrained and Lagrangian formulations and they imply that the only critical Reuleaux polygons
Externí odkaz:
http://arxiv.org/abs/2412.13808
Autor:
Deng, Zhipeng
We present a general solution to Bellman's lost-in-a-forest problem. The forest boundary is known and may take any shape. The starting point and the orientation are unspecified. We convert the problem into translation and rotation of the forest bound
Externí odkaz:
http://arxiv.org/abs/2412.10686
Autor:
Baur, Matthias
We present numerical minimizers for the first seven eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field in a wide range of field strengths. Adapting an approach by Antunes and Freitas, we use gradient descent for the minimiza
Externí odkaz:
http://arxiv.org/abs/2412.06533
In this article, we address the problem of determining a domain in $\mathbb{R}^N$ that minimizes the first eigenvalue of the Lam\'e system under a volume constraint. We begin by establishing the existence of such an optimal domain within the class of
Externí odkaz:
http://arxiv.org/abs/2412.06437
Autor:
Baek, Jineon
We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area $2.2195\cdots$.
Comment: 119 pages, 21 figures
Comment: 119 pages, 21 figures
Externí odkaz:
http://arxiv.org/abs/2411.19826
Autor:
Perugini, Matteo
Let $n\geq 1$, and let $\Omega\subset \mathbb{R}^n$ be an open and connected set with finite Lebesgue measure. Among functions of bounded variation in $\Omega$ we introduce the class of \emph{minimally singular} functions. Inspired by the original th
Externí odkaz:
http://arxiv.org/abs/2411.17633
The aim of this work is to analyse a shape optimization problem in a mechanical friction context. Precisely we perform a shape sensitivity analysis of a Tresca friction problem, that is, a boundary value problem involving the usual linear elasticity
Externí odkaz:
http://arxiv.org/abs/2411.10158
For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex geometries, the me
Externí odkaz:
http://arxiv.org/abs/2412.00006
Autor:
de Cordemoy, Aymeric Jacob
This paper investigates a shape optimization problem involving the Signorini unilateral conditions in a linear elastic model, without any penalization procedure. The shape sensitivity analysis is performed using tools from convex and variational anal
Externí odkaz:
http://arxiv.org/abs/2410.12315
This paper investigates, without any regularization or penalization procedure, a shape optimization problem involving a simplified friction phenomena modeled by a scalar Tresca friction law. Precisely, using tools from convex and variational analysis
Externí odkaz:
http://arxiv.org/abs/2410.11750