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Related papers: Determining the volume fraction in 2-phase composi…

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Bounds are obtained on the volume fraction in a two-dimensional body containing two elastically isotropic materials with known bulk and shear moduli. These bounds use information about the average stress and strain fields, energy,…

Analysis of PDEs · Mathematics 2015-05-30 Graeme Walter Milton , Loc Hoang Nguyen

Universal bounds on the electrical and elastic response of two-phase (and multiphase) ellipsoidal or parallelopipedic bodies have been obtained by Nemat-Nasser and Hori. Here we show how their bounds can be improved and extended to bodies…

Materials Science · Physics 2015-05-28 Graeme W. Milton

We study the size estimate problem for the two-phase shallow shell equations in this paper. Our aim is to derive bounds on the volume fraction of each phase assuming that the material properties of the two phases are given. The approach in…

Analysis of PDEs · Mathematics 2012-04-24 Hyeonbae Kang , Graeme W. Milton , Jenn-Nan Wang

In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…

Analysis of PDEs · Mathematics 2022-06-22 Sergio Conti , Robert Kohn , Oleksandr Misiats

We develop a theoretical framework for time-modulated acoustic metasurfaces comprising a line array of modulated cavities, and show that bound acoustic surface waves can undergo temporal diffraction from bound states localised at an…

Applied Physics · Physics 2025-12-22 E. Paul , G. J. Chaplain , J. Li , T. A. Starkey , S. A. R. Horsley

Lower bounds are obtained on the maximum field strength in one or both phases in a body containing two-phases. These bounds only incorporate boundary data that can be obtained from measurements at the surface of the body, and thus may be…

An incident wave at a temporal interface, created by an abrupt change in system parameters, generates time-refracted and time-reflected waves. We find topological characteristics associated with the temporal interface that separates…

Optics · Physics 2025-04-25 Huisheng Xu , Zhaohui Dong , Luqi Yuan , Liang Jin

The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by…

Analysis of PDEs · Mathematics 2010-04-05 Pierluigi Colli , Philippe Laurençot

To derive bounds on the strain and stress response of a two-component composite material with viscoelastic phases, we revisit the so-called analytic method (Bergman 1978), which allows one to approximate the complex effective tensor,…

Mathematical Physics · Physics 2016-02-11 Ornella Mattei , Graeme W. Milton

We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…

Dynamical Systems · Mathematics 2022-12-29 Yuyang Gao , Anatoly Neishtadt , Alexey Okunev

We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…

Analysis of PDEs · Mathematics 2015-06-09 Andrew E. Thaler , Graeme W. Milton

We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus. Our formula depends on an appropriate measurement of the displacement…

Analysis of PDEs · Mathematics 2015-06-09 Andrew E. Thaler , Graeme W. Milton

The well-posedness of a phase-field approximation to the Willmore flow with area and volume constraints is established when the functional approximating the area has no critical point satisfying the two constraints. The existence proof…

Analysis of PDEs · Mathematics 2012-12-27 Pierluigi Colli , Philippe Laurencot

We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an…

Optimization and Control · Mathematics 2019-06-19 Dong Wang , Andrej Cherkaev , Braxton Osting

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

Numerical Analysis · Mathematics 2026-05-12 T. Catoe , V. J. Ervin

We discuss a unified framework of dealing with electrically charged, anyonic vortices in 2+1 dimensional spacetimes and extended, anyonic string-like vortices in one higher dimension. We elaborate on two ways of charging these topological…

High Energy Physics - Theory · Physics 2018-12-21 Alexander Gußmann , Debajyoti Sarkar , Nico Wintergerst

By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2pi/L on a lattice with spatial volume L^3. We use Chiral Perturbation Theory to study finite-volume…

High Energy Physics - Lattice · Physics 2009-10-09 C. T. Sachrajda , G. Villadoro

Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems…

Soft Condensed Matter · Physics 2021-04-28 Nicholay S. Tonchev

Phase-field models have proven indispensable for deciphering the microstructure complexities inherent in multicomponent systems. The confluence of varying phase molar volumes presents unique challenges. Understanding the impact of molar…

Materials Science · Physics 2025-03-25 Chengyin Wu , Yanzhou Ji

The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…

Numerical Analysis · Mathematics 2022-02-04 Jörg Nick , Balázs Kovács , Christian Lubich
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