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Discontinuous free form deformations
12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings., 2004Contemporary deformation tools let designers modify the geometry of deformed models. This approach can be restrictive if the designer wants to incorporate holes or gaps into a model while deforming it into a different shape. This work presents a variant of FFD that would let the designer incorporate isoparametric discontinuities into the deformation ...
S. Schein, G. Elber
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REGULAR APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS
Mathematical Models and Methods in Applied Sciences, 2000We consider a class of smooth local nonconvex functionals defined on W2,2(Ω), depending on a small parameter ε and we prove that they converge, as ε tends to 0, to a functional F(u,Ω) with a bulk density depending on the gradient of u and a surface energy concentrated on the jump set of u.
Bouchitté, G., Dubs, C., Seppecher, P.
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Nonlocal Approximation of Nonisotropic Free-Discontinuity Problems
SIAM Journal on Applied Mathematics, 1999A large class of problems in fracture mechanics, image segmentation, liquid cristals theory can be formulated as ``free-discontinuity problems'' in which one looks for the minimum of integral functionals of the form: \[ \int_{\Omega}g(x,\nabla u) dx + \int_{S_u}\varphi(x,[u],\nu_u) d{\mathcal{H}}^{n-1}, \] where \(\Omega\) is an open and bounded set in
CORTESANI G, TOADER, Rodica
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Homogenization of free discontinuity problems
Archive for Rational Mechanics and Analysis, 1996Following Griffith's theory, hyperelastic brittle media subject to fracture can be modeled by the introduction, in addition to the elastic volume energy, of a surface term which accounts for crack initiation. In its simplest formulation, the energy of a deformation \(u\) is of the form \[ E(u, K)=\int_{\Omega\setminus K}f(\nabla u)dx+ \lambda{\mathcal ...
Braides A., Defranceschi A., Vitali E.
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FREE DISCONTINUITY PROBLEMS WITH UNBOUNDED DATA
Mathematical Models and Methods in Applied Sciences, 1994We prove the existence of a minimizing pair for a free discontinuity problem, i.e. a variational problem in which the unknowns are a closed set K and a function suitably smooth outside K. Examples of such problems come from pattern recognition and mathematical physics, when both “volume” energy and “surface” energy are present.
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A discontinuous nonlinear eigenvalue/Free boundary problem
Mathematical Methods in the Applied Sciences, 1982AbstractWe study the problem (H is the Heaviside unit step function) in spherical domains Ω of arbitrary dimension. When g = 0, there are two branches of radial solutions; for small nonzero g there are solutions near the corresponding radial solution. Moreover, the set where μ = 1 is in all cases an analytic hypersurface.
Roger Alexander, P. H. Rabinowitz
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LOWER SEMICONTINUITY RESULTS FOR FREE DISCONTINUITY ENERGIES
Mathematical Models and Methods in Applied Sciences, 2010We establish new lower semicontinuity results for energy functionals containing a very general volume term of polyconvex type and a surface term depending on the spatial variable in a discontinuous way.
AMAR, Micol +2 more
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Minimisers of Free Discontinuity Problems
2000Abstract In this chapter and in the next one we study existence and regularity of solutions of a class of free discontinuity problems whose model is the Mumford-Shah functional introduced in Chapter 4.
Luigi Ambrosio +2 more
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Discontinuous free rotations in uniaxial ferrimagnets
Journal of Magnetism and Magnetic Materials, 1999The magnetic-phase diagram of the free-powder anisotropic Neel ferrimagnet is presented in terms of the reduced sublattice anisotropy fields, x and y. It marks the boundaries of the regions of field-induced first-order transitions involving the collinear and the non-collinear states.
ASTI G., SOLZI, Massimo
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