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Related papers: Constrained maximization of conformal capacity

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In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

Optimization and Control · Mathematics 2016-06-09 Xiaojing Zhang , Maryam Kamgarpour , Angelos Georghiou , Paul Goulart , John Lygeros

The purpose of this paper is to address a class of hybrid optimal control problems constrained with hyperelasticity and constant global volume. This type of problems can intervene for example in the mechanical aspects of cardiac activity.…

Optimization and Control · Mathematics 2024-09-06 Sébastien Court

Disordered hyperuniform dispersions are exotic amorphous two-phase materials characterized by an anomalous suppression of long-wavelength volume-fraction fluctuations, endowing them with novel physical properties. While such unusual…

Soft Condensed Matter · Physics 2019-03-12 Jaeuk Kim , Salvatore Torquato

This contribution is concerned with the effective viscosity problem, that is, the homogenization of the steady Stokes system with a random array of rigid particles, for which the main difficulty is the treatment of close particles. Standard…

Analysis of PDEs · Mathematics 2022-01-13 Mitia Duerinckx , Antoine Gloria

We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of $\Gamma$-convergence for two singular phenomena. First, for densities constrained near a hyperplane we recover the…

Analysis of PDEs · Mathematics 2021-06-08 Peter Gladbach , Eva Kopfer

For any given natural number $k$, this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by $k$ equal-radius disks in terms of the surface's topology. We show that the bounds given here are…

Geometric Topology · Mathematics 2018-06-11 Jason DeBlois

We consider the setting of two disks in a domain in $\mathbb{R}^2$ which are almost touching and have finite and positive conductivities, giving rise to a divergence form elliptic equation with discontinuous coefficients. We use the maximum…

Analysis of PDEs · Mathematics 2026-01-21 YanYan Li , Ben Weinkove

The study is motivated by the known fact that, in the noncompact case, the main minimum-problem of the theory of interior capacities of condensers in a locally compact space is in general unsolvable, and this occurs even under very natural…

Classical Analysis and ODEs · Mathematics 2009-02-04 Natalia Zorii

We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…

Optimization and Control · Mathematics 2024-04-05 Aida Khajavirad

We prove that among all doubly connected domains of R^n (n>=2) bounded by two spheres of given radii, the Dirichlet heat content at any fixed time achieves its minimum when the spheres are concentric. This is shown to be a special case of a…

Spectral Theory · Mathematics 2021-06-24 Liangpan Li

We study lattice points on hyperbolic circles centred at Heegner points of class number one. Our main result is that, on a density one subset of radii tending to infinity, the angles of such points equidistribute on the unit circle. To…

Number Theory · Mathematics 2022-06-17 Giacomo Cherubini , Alessandro Fazzari

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…

Statistical Mechanics · Physics 2007-05-23 S. Torquato , F. H. Stillinger

We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…

Numerical Analysis · Mathematics 2022-07-04 Harri Hakula , Mohamed M. S. Nasser , Matti Vuorinen

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the…

Dynamical Systems · Mathematics 2022-04-20 Maciej J. Capiński , Natalia Wodka

We introduce the notion of a "crystallographic sphere packing," defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension. We exhibit for the first time an infinite family of…

Metric Geometry · Mathematics 2017-12-04 Alex Kontorovich , Kei Nakamura

We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…

Analysis of PDEs · Mathematics 2019-12-13 Jean-François Babadjian , Vito Crismale

Circumstellar discs are expected to be the nursery of planets. Grain growth within such discs is the first step in the planet formation process in the core-accretion gas-capture scenario. We aim at providing selected criteria on…

Solar and Stellar Astrophysics · Physics 2015-05-20 Juergen Sauter , Sebastian Wolf

Let $X$ be a finite collection of sets (or "clusters"). We consider the problem of counting the number of ways a cluster $A \in X$ can be partitioned into two disjoint clusters $A_1, A_2 \in X$, thus $A = A_1 \uplus A_2$ is the disjoint…

Combinatorics · Mathematics 2017-05-24 Daniel Kane , Terence Tao

Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…

Statistical Mechanics · Physics 2009-11-13 Antonio Trovato , Trinh X. Hoang , Jayanth R. Banavar , Amos Maritan

In \cite{Sz17-2} we proved that to each saturated congruent hyperball packing exists a decomposition of $3$-dimensional hyperbolic space $\mathbb{H}^3$ into truncated tetrahedra. Therefore, in order to get a density upper bound for…

Metric Geometry · Mathematics 2018-12-18 Jenő Szirmai