3,042 research outputs found
A model for the quasi-static growth of brittle fractures based on local minimization
We study a variant of the variational model for the quasi-static growth of
brittle fractures proposed by Francfort and Marigo. The main feature of our
model is that, in the discrete-time formulation, in each step we do not
consider absolute minimizers of the energy, but, in a sense, we look for local
minimizers which are sufficiently close to the approximate solution obtained in
the previous step. This is done by introducing in the variational problem an
additional term which penalizes the -distance between the approximate
solutions at two consecutive times. We study the continuous-time version of
this model, obtained by passing to the limit as the time step tends to zero,
and show that it satisfies (for almost every time) some minimality conditions
which are slightly different from those considered in Francfort and Marigo and
in our previous paper, but are still enough to prove (under suitable regularity
assumptions on the crack path) that the classical Griffith's criterion holds at
the crack tips. We prove also that, if no initial crack is present and if the
data of the problem are sufficiently smooth, no crack will develop in this
model, provided the penalization term is large enough.Comment: 20 page
On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation
In the framework of toroidal Pseudodifferential operators on the flat torus
we begin by proving the closure under
composition for the class of Weyl operators with
simbols . Subsequently, we
consider when where and we exhibit the toroidal version of the
equation for the Wigner transform of the solution of the Schr\"odinger
equation. Moreover, we prove the convergence (in a weak sense) of the Wigner
transform of the solution of the Schr\"odinger equation to the solution of the
Liouville equation on written in the measure sense.
These results are applied to the study of some WKB type wave functions in the
Sobolev space with phase functions in the class
of Lipschitz continuous weak KAM solutions (of positive and negative type) of
the Hamilton-Jacobi equation for with , and to the study of the
backward and forward time propagation of the related Wigner measures supported
on the graph of
Damage as Gamma-limit of microfractures in anti-plane linearized elasticity
A homogenization result is given for a material having brittle inclusions arranged in a periodic structure.
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According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence.
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In particular, damage is obtained as limit of periodically distributed
microfractures
Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients
In this paper we give an affirmative answer to an open question mentioned in
[Le Bris and Lions, Comm. Partial Differential Equations 33 (2008),
1272--1317], that is, we prove the well-posedness of the Fokker-Planck type
equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie
Variational approximation of a second order free discontinuity problem in computer vision
We consider a functional, proposed by Blake and Zisserman for computer vision
problems, which depends on free discontinuities, free gradient discontinuities, and second order
derivatives. We show how this functional can be approximated by elliptic functionals defined on
Sobolev spaces. The approximation takes place in a variational sense, the De Giorgi Γ-convergence,
and extends to this second order model an approximation of the Mumford–Shah functional obtained
by Ambrosio and Tortorelli. For the purpose of illustration an algorithm based on the Γ-convergent
approximation is applied to the problem of computing depth from stereo images and some numerical
examples are presented
On the isoperimetric problem in the Heisenberg group \u210dn
It has been recently conjectured that, in the context of the Heisenberg groupHn endowed with its Carnot\u2013Carath\ue9odory metric and Haar measure, the isoperimetricsets (i.e., minimizers of the H-perimeter among sets of constant Haar measure) couldcoincide with the solutions to a \u201crestricted\u201d isoperimetric problem within the class ofsets having finite perimeter, smooth boundary, and cylindrical symmetry. In this paper,we derive new properties of these restricted isoperimetric sets, which we call Heisenbergbubbles. In particular, we show that their boundary has constant mean H-curvature and, quitesurprisingly, that it is foliated by the family of minimal geodesics connecting two specialpoints. In view of a possible strategy for proving that Heisenberg bubbles are actuallyisoperimetric among the whole class of measurable subsets of Hn, we turn our attentionto the relationship between volume, perimeter, and -enlargements. In particular, we provea Brunn\u2013Minkowski inequality with topological exponent as well as the fact that the Hperimeterof a bounded, open set F 82 Hn of class C2 can be computed via a generalizedMinkowski content, defined by means of any bounded set whose horizontal projection is the2n-dimensional unit disc. Some consequences of these properties are discussed
Early suppression of lymphoproliferative response in dogs with natural infection by Leishmania infantum.
Dogs are the domestic reservoirs of zoonotic visceral leishmaniasis caused by Leishmania
infantum. Early detection of canine infections evolving to clinically patent disease may be
important to leishmaniasis control. In this study we firstly investigated the peripheral blood
mononuclear cell (PBMC) response to leishmanial antigens and to polyclonal activators
concanavalin A, phytohemagglutinin and pokeweed mitogen, of mixed-breed dogs with natural
L. infantum infection, either in presymptomatic or in patent disease condition, compared to healthy
animals. Leishmania antigens did not induce a clear proliferative response in any of the animals
examined. Furthermore, mitogen-induced lymphocyte proliferation was found strongly reduced not
only in symptomatic, but also in presymptomatic dogs suggesting that the cell-mediated immunity
is suppressed in progressive canine leishmaniasis. To test this finding, naive Beagle dogs were
exposed to natural L. infantum infection in a highly endemic area of southern Italy. Two to 10
months after exposure all dogs were found to be infected by Leishmania, and on month 2 of
exposure they all showed a significant reduction in PBMC activation by mitogens. Our results
indicate that suppression of the lymphoproliferative response is a common occurrence in dogs
already at the beginning of an established leishmanial infection. # 1999 Elsevier Science B.V. All
rights reserved
BV functions and sets of finite perimeters in sub-Riemannian manifolds
We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets whose characteristic function is BV, in sub-Riemannian manifolds. Under an assumption on the nilpotent approximation, we prove a blowup theorem, generalizing the one obtained for step-2 Carnot groups
A decomposition theorem for BV functions
The Jordan decomposition states that a function f: R \u2192 R is of bounded variation if and only if it can be written as the dierence of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A counterexample is given which prevents further extensions
Monge's transport problem in the Heisenberg group
We prove the existence of solutions to Monge transport problem between two
compactly supported Borel probability measures in the Heisenberg group equipped
with its Carnot-Caratheodory distance assuming that the initial measure is
absolutely continuous with respect to the Haar measure of the group
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