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Related papers: Spectral optimization of inhomogeneous plates

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In this paper, we provide an analytical study of the transmission eigenvalue problem in the context of biharmonic scattering with a penetrable obstacle. We will assume that the underlying physical model is given by an infinite elastic…

Analysis of PDEs · Mathematics 2025-10-10 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…

Analysis of PDEs · Mathematics 2018-07-17 Virginia Agostiniani , Alessandro Lucantonio , Danka Lučić

We prove the existence of optimal metrics for a wide class of combinations of Laplace eigenvalues on closed orientable surfaces of any genus. The optimal metrics are explicitely related to Laplace minimal eigenmaps, defined as branched…

Differential Geometry · Mathematics 2024-10-18 Romain Petrides

Optimal multi-layer device design requires consideration of fabrication uncertainties associated with inter-layer alignment and conformal layering. We present layer-restricted topology optimization (TO), a novel technique which mitigates…

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

Analysis of PDEs · Mathematics 2016-04-13 Fabian Christowiak , Carolin Kreisbeck

A method of measuring the thickness of steel plates using through transmission of an acoustic pulse is demonstrated. This study has been done on a stainless steel plate with regions of thickness 10:0 mm, 9:8 mm, and 9:6 mm, using broadband…

Instrumentation and Detectors · Physics 2012-10-02 Grunde Waag , Lars Hoff , Petter Norli

We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplace--Beltrami operator eigenvalues over a given number of partitions of a surface. We consider…

Analysis of PDEs · Mathematics 2015-03-25 Charles M. Elliott , Thomas Ranner

Radiative heat transfer between uniform plates is bounded by the narrow range and limited contribution of surface waves. Using a combination of analytical calculations and numerical gradient-based optimization, we show that such a…

Mesoscale and Nanoscale Physics · Physics 2017-07-07 Weiliang Jin , Riccardo Messina , Alejandro W. Rodriguez

We present a methodology to perform inverse analysis on reconfigurable topological insulators for flexural waves in plate-like structures. First the unit cell topology of a phononic plate is designed, which offers two-fold degeneracy in the…

Mesoscale and Nanoscale Physics · Physics 2021-10-27 Chuong Nguyen , S. S. Nanthakumar , Xiaoying Zhuang , Ludovic Chamoin , Yabin Jin , Timon Rabczuk

Numerical simulations shed light on control of shear elastic wave propagation in plates structured with inertial resonators. The structural element is composed of a heavy core connected to the main freestanding plate through tiny ligaments.…

Materials Science · Physics 2015-07-21 Younes Achaoui , André Diatta , Sébastien Guenneau

We give results on optimal constants of isoperimetric inequalities involving Steklov eigenvalues on surfaces with boundary. We both consider this question on Riemannian surfaces with a same given topology or more specifically belonging to…

Differential Geometry · Mathematics 2025-08-15 Romain Petrides

We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal…

Soft Condensed Matter · Physics 2009-11-10 P. Melby , F. Vega Reyes , A. Prevost , R. Robertson , P. Kumar , D. A. Egolf , J. S. Urbach

In the framework of linearized elasticity, we study thin elastic composite plates with thickness $\delta$. The plates contain small, rigid rectangular plates distributed periodically along $\varepsilon$. Between two neighboring rigid plates…

Analysis of PDEs · Mathematics 2025-12-02 Amartya Chakrabortty , Georges Griso , Julia Orlik

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…

Statistics Theory · Mathematics 2007-06-13 Arthur Berg , Dimitris Politis

We use small-amplitude inviscid theory to study the swimming performance of a flexible flapping plate with time-varying flexibility. The stiffness of the plate oscillates at twice the frequency of the kinematics in order to maintain a…

Fluid Dynamics · Physics 2023-04-12 David Yudin , Daniel Floryan , Tyler Van Buren

We address extremum problems for spectral quantities associated with operators of the form $\Delta^2-\tau\Delta$ with Dirichlet boundary conditions, for non-negative values of $\tau$. The focus is on two shape optimisation problems:…

Analysis of PDEs · Mathematics 2025-07-10 Pedro Freitas , Roméo Leylekian

We develop new tools to compute the index of symmetry in the context of homogeneous fibrations. As a consequence of our results, we determine the index of symmetry of every homogeneous space diffeomorphic to a compact rank-one symmetric…

Differential Geometry · Mathematics 2026-05-28 Ángel Cidre-Díaz , Carlos E. Olmos , Alberto Rodríguez-Vázquez

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…

Optimization and Control · Mathematics 2019-07-16 Marc Dambrine , Helmut Harbrecht

We find a new type of boundary layers that occur at the top and bottom surfaces of an inhomogeneous plate. The boundary layers of this type never occur in homogeneous plates or plates made of layers of homogeneous materials. The thickness…

Mathematical Physics · Physics 2021-08-17 A. G. Kolpakov , S. I. Rakin

In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. A mathematical treatment of the elec- trostatic polarizability is formulated in…

Optics · Physics 2018-11-14 Dimitrios C. Tzarouchis , Ari Sihvola