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There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the…

Analysis of PDEs · Mathematics 2025-11-10 Xuenan Li , Robert V. Kohn

Origami structures, particularly Miura-ori patterns, offer unique capabilities for surface approximation and deployable designs. In this study, a constrained mapping optimization algorithm is designed for designing surface-aligned Miura-ori…

Computational Geometry · Computer Science 2026-04-23 Ka Ho Lai , Hei Tung Tsang , Gary P. T. Choi , Lok Ming Lui

The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…

Optimization and Control · Mathematics 2014-03-10 Andrej Cherkaev

Nonlinear metasurfaces offer a new paradigm to realize optical nonlinear devices with new and unparalleled behavior compared to nonlinear crystals, due to the interplay between photonic resonances and materials properties. The complicated…

This paper deals with themes such as approximate counting/evaluation of the total number of flat-foldings for random origami diagrams, evaluation of the values averaged over various instances, obtaining forcing sets for general origami…

Statistical Mechanics · Physics 2024-09-06 Chihiro Nakajima

The structural complexity of metamaterials is limitless, although in practice, most designs comprise periodic architectures which lead to materials with spatially homogeneous features. More advanced tasks, arising in e.g. soft robotics,…

Soft Condensed Matter · Physics 2016-08-03 Corentin Coulais , Eial Teomy , Koen de Reus , Yair Shokef , Martin van Hecke

Inverse methods of statistical mechanics have facilitated the discovery of pair potentials that stabilize a wide variety of targeted lattices at zero temperature. However, such methods are complicated by the need to compare, within the…

Statistical Mechanics · Physics 2016-09-19 Beth A. Lindquist , Ryan B. Jadrich , Thomas M. Truskett

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…

Optimization and Control · Mathematics 2016-04-12 William W. Hager , Hongchao Zhang

Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction…

We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…

Applied Physics · Physics 2019-10-17 Trevor Brown , Chaitanya Narendra , Yousef Vahabzadeh , Christophe Caloz , Puyan Mojabi

Existing Civil Engineering structures have limited capability to adapt their configurations for new functions, non-stationary environments, or future reuse. Although origami principles provide capabilities of dense packaging and…

Applied Physics · Physics 2024-03-19 Yi Zhu , Evgueni T. Filipov

Aperiodic metamaterials represent a class of structural systems that are composed of different building blocks (cells), instead of a self-repeating chain of the same unit cells. Optimizing aperiodic cellular structural systems thus presents…

Computational Engineering, Finance, and Science · Computer Science 2020-07-31 Amir Behjat , Manaswin Oddiraju , Mohammad Ali Attarzadeh , Mostafa Nouh , Souma Chowdhury

In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general convex penalty term. When the data is given exactly, we give a…

Numerical Analysis · Mathematics 2016-01-13 Yuling Jiao , Qinian Jin , Xiliang Lu , Weijie Wang

Electromagnetic absorbers combining ultrathin profiles with robust absorptivity across wide incidence angles are essential for applications such as stealth technology, wireless communications, and quantum computing. Traditional designs,…

Optics · Physics 2025-04-22 Eunbi Jang , Junghee Cho , Chanik Kang , Haejun Chung

Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but…

Soft Condensed Matter · Physics 2018-10-18 Corentin Coulais , Alberico Sabbadini , Fré Vink , Martin van Hecke

Fully harnessing the vast design space enabled by metamaterials to control electromagnetic (EM) fields remains an open problem for researchers. Inverse-design techniques have shown to best exploit the degrees of freedom available in design,…

Optics · Physics 2025-11-27 Jorge Ruiz-Garcia , Anthony Grbic

Designing a robot or structure that can fold itself into a target shape is a process that involves challenges originated from multiple sources. For example, the designer of rigid self-folding robots must consider foldability from geometric…

Robotics · Computer Science 2020-11-23 Yue Hao , Weilin Guan , Edwin A Peraza Hernandez , Jyh-Ming Lien

We propose an optimisation method for the inverse structural design of self-assembly of anisotropic patchy particles. The anisotropic interaction can be expressed by the spherical harmonics of the surface pattern on a patchy particle, and…

Soft Condensed Matter · Physics 2025-02-21 Uyen Tu Lieu , Natsuhiko Yoshinaga

A fundamental challenge in the design of photonic devices, and electromagnetic structures more generally, is the optimization of their overall architecture to achieve a desired response. To this end, topology or shape optimizers based on…

Object manipulation is a fundamental challenge in robotics, where systems must balance trade-offs among manipulation capabilities, system complexity, and throughput. Distributed manipulator systems (DMS) use the coordinated motion of…

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