Journal Article10.1146/ANNUREV-MATSCI-070909-104517
Optimal Design of Heterogeneous Materials
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TL;DR: In this paper, a review of inverse techniques that have been devised to optimize the structure and macroscopic properties of heterogeneous materials such as composite materials, porous media, colloidal dispersions, and polymer blends is presented.
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Abstract: This article reviews recent inverse techniques that we have devised to optimize the structure and macroscopic properties of heterogeneous materials such as composite materials, porous media, colloidal dispersions, and polymer blends. Optimization methods provide a systematic means of designing materials with tailored properties and microstructures for a specific application. This article focuses on two inverse problems that are solved via optimization techniques: (a) the topology optimization procedure used to design heterogeneous materials and (b) stochastic optimization methods employed to reconstruct or construct microstructures.
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Citations
Inferring low-dimensional microstructure representations using convolutional neural networks
TL;DR: In this paper, the authors used activations in a pretrained convolutional neural network to provide a high-dimensional characterization of a set of synthetic microstructural images and then used manifold learning to obtain a low-dimensional embedding of this statistical characterization.
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Inverse Optimization Techniques for Targeted Self-Assembly
TL;DR: This article reviews recent inverse statistical-mechanical methodologies that have devised to optimize interaction potentials in soft matter systems that correspond to stable “target” structures and envision being able to “tailor” potentials that produce varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals.
131
Perspective: Basic understanding of condensed phases of matter via packing models.
TL;DR: This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable, and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions and emphasizes the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps.
Basic Understanding of Condensed Phases of Matter via Packing Models
TL;DR: In this article, a review of the literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions is presented.
113
References
•Book
A Treatise on Electricity and Magnetism
James Clerk Maxwell
- 01 Jan 1873
TL;DR: The most influential nineteenth-century scientist for twentieth-century physics, James Clerk Maxwell (1831-1879) demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field as discussed by the authors.
Strong localization of photons in certain disordered dielectric superlattices
TL;DR: A new mechanism for strong Anderson localization of photons in carefully prepared disordered dielectric superlattices with an everywhere real positive dielectrics constant is described.
10.5K
•Book
Photonic Crystals: Molding the Flow of Light
John D. Joannopoulos,Steven G. Johnson,Joshua N. Winn,Robert D. Meade +3 more
- 03 Jul 1995
TL;DR: In this paper, the authors developed the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory, and investigated the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions.
10.1K
Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.
•Book
Asymptotic analysis for periodic structures
Alain Bensoussan,Alain Bensoussan,Jacques-Louis Lions,George Papanicolaou +3 more
- 01 Jan 1978
TL;DR: In this article, the authors give a systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate.
5.8K
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