1,720,972 research outputs found
Symmetry of minimizers of a Gaussian isoperimetric problem
Full text linkWe study an isoperimetric problem described by a functional that consists of the standard Gaussian perimeter and the norm of the barycenter. The second term is in competition with the perimeter, balancing the mass with respect to the origin, and because of that the solution is not always the half-space. We characterize all the minimizers of this functional, when the volume is close to one, by proving that the minimizer is either the half-space or the symmetric strip, depending on the strength of the barycenter term. As a corollary, we obtain that the symmetric strip is the solution of the Gaussian isoperimetric problem among symmetric sets when the volume is close to one. As another corollary we obtain the optimal constant in the quantitative Gaussian isoperimetric inequality
Toughening by crack deflection in the homogenisation of brittle composites with soft inclusions
Full text linkWe present a simple example of a toughening mechanism in the homogenization of composites with soft inclusions, produced by a crack deflection at microscopic level. We show that the mechanism is connected to the irreversibility of the crack process; because of that it cannot be detected through the standard homogenization tool of the Gamma -convergence
Robustness of the Gaussian concentration inequality and the Brunn-Minkowski inequality
Full text linkWe provide a sharp quantitative version of the Gaussian concentration inequality:
for every , the difference between the measure of the -enlargement of a given set
and the -enlargement of a half-space controls the square of the measure of the symmetric
difference between the set and a suitable half-space.
We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set.
This is equivalent to the stability of the Brunn-Minkowski
inequality for the Minkowski sum between a convex set and a generic one
Frank energy for nematic elastomers
Full text linkWe discuss the well-posedness of a new nonlinear model for nematic elastomers. The main novelty in our work is that the Frank energy penalizes spatial variations of the nematic director in the deformed, rather than in the reference configuration, as it is natural in the case of large deformations
A bridging mechanism in the homogenization of brittle composites with soft inclusions
Full text linkWe provide a homogenization result for the energy-functional associated with a purely brittle composite whose microstructure is characterized by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale to obtain, in the limit as tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack
Stability of the Steiner symmetrization of convex sets
No full textThe isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets
Homogenization of the Neumann problem in perforated domains: an alternative approach
Full text linkThe main result of this paper is a compactness theorem for families of functions in the space SBV (Special functions of Bounded Variation)
defined on periodically perforated domains P. Our analysis avoids the use of any extension procedure in SBV , weakens
the hypotheses on P to the minimal one
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity
Full text linkWe define a class of deformations in W^{1,p}(Ω,R^n), p>n−1, with positive Jacobian that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality between the distributional determinant and the pointwise determinant of the gradient. Maps in this class are shown to satisfy a property of weak monotonicity, and, as a consequence, they enjoy an extra degree of regularity. We also prove that these deformations are locally invertible; moreover, the neighbourhood of invertibility is stable along a weak convergent sequence in W^{1,p}, and the sequence of local inverses converges to the local inverse. We use those features to show weak lower semicontinuity of functionals defined in the deformed configuration and functionals involving composition of maps. We apply those results to prove existence of minimizers in some models for nematic elastomers and magnetoelasticity
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