201 research outputs found
Damage-driven fracture with low-order potentials: asymptotic behavior, existence and applications
We study the -convergence of damage to fracture energy functionals in
the presence of low-order nonlinear potentials that allows us to model physical
phenomena such as fluid-driven fracturing, plastic slip, and the satisfaction
of kinematical constraints such as crack non-interpenetration. Existence
results are also addressedComment: 41 pages, 4 Figure
A Compactness Theorem for functions on Poisson point clouds
In this work we show a compactness Theorem for discrete functions on Poisson
point clouds. We consider sequences with equibounded non-local -Dirichlet
energy: the novelty consists in the intermediate-interaction regime at which
the non-local energy is computed
A note on the stability of the Cheeger constant of -gons
The regular -gon provides the minimal Cheeger constant in the class of all
-gons with fixed volume. This result is due to a work of Bucur and Fragal\`a
in 2014. In this note, we address the stability of their result in terms of the
distance between sets. Furthermore, we provide a stability inequality in
terms of the Hausdorff distance between the boundaries of sets in the class of
polygons having uniformly bounded diameter. Finally, we show that our results
are sharp, both in the exponent of decay and in the notion of distance between
sets.Comment: 5 pages, 2 figure
On the Gamma Convergence of Functionals Defined Over Pairs of Measures and Energy-Measures
A novel general framework for the study of -convergence of
functionals defined over pairs of measures and energy-measures is introduced.
This theory allows us to identify the -limit of these kind of
functionals by knowing the -limit of the underlining energies. In
particular, the interaction between the functionals and the underlining
energies results, in the case these latter converge to a non continuous energy,
in an additional effect in the relaxation process. This study was motivated by
a question in the context of epitaxial growth evolution with adatoms.
Interesting cases of application of the general theory are also presented
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