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The Two-Well Problem For Piecewise-Affine Maps

Publications associées (48)

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Optimal transport of closed differential forms for convex costs

Bernard Dacorogna, Olivier Kneuss

Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...

Elsevier France-Editions Scientifiques Medicales Elsevier2015

Localized Orthogonal Decomposition Techniques For Boundary Value Problems

Patrick Henning

In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For this purpose, we present new boundary correctors which preserve the common ...

Siam Publications2014

Observations on out-of-plane behaviour of URM walls in buildings with RC slabs

Katrin Beyer, Marco Tondelli

In Switzerland many new residential buildings are constructed as unreinforced masonry (URM) structures or as mixed structures where URM walls are coupled with reinforced concrete (RC) walls by RC slabs. At present the boundary conditions of URM walls subje ...

2014

Approximate Matrix Multiplication with Application to Linear Embeddings

Michail Vlachos, Anastasios Kyrillidis

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as the ratio of th ...

Ieee2014

The degenerate two well problem for piecewise affine maps

Bernard Dacorogna

The two well problem consists in finding maps u which satisfy some boundary conditions and whose gradient Du assumes values in the two wells . Here (similarly ) is the well generated by a 2 x 2 matrix A, i.e., is the set of matrices of the form RA, where R ...

Springer Basel Ag2013

Orbital Magnetization as a Local Property

The modern expressions for polarization P and orbital magnetization M are k-space integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the ground-state density matrix, "nearsighted'' in insulators, ind ...

Amer Physical Soc2013

Experimental realization and characterization of unstretched planar one-dimensional diffusion flames

Peter Monkewitz, Etienne Robert

A burner configuration that allows the creation of nearly unstretched one-dimensional diffusion flames has recently been introduced. This paper presents the first detailed characterization of flames produced in such a burner to assess how well they approac ...

Elsevier Science Inc2013

On Generalized Weighted Hilbert Matrices

Olivier Lévêque

We study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, the determinant, and various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic ...

Pacific Journal Mathematics2013

Generalized Flows Satisfying Spatial Boundary Conditions

Boris Buffoni

In a region D in R-2 or R-3, the classical Euler equation for the regular motion of an inviscid and incompressible fluid of constant density is given by partial derivative(t)v + (v . del(x))v = -del(xP), div(x)v = 0, where v(t, x) is the velocity of the pa ...

Birkhäuser-Verlag, Springer2012

Tokamak SOL fluid simulations with self-consistent boundary conditions at the magnetic presheath edge

Paolo Ricci, Joaquim Loizu Cisquella, Sébastien Jolliet, Federico David Halpern, Annamaria Mosetto

Fluid codes simulating the dynamics of magnetized plasmas with field lines terminating on the device vessel require boundary conditions that are consistent with the plasma-wall transition region. When the magnetic field strikes the wall at an oblique angle ...

2012