## Journals

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DCDS-B

For the linearized setting of the dynamics of complex bodies we construct
variational integrators and prove their convergence by making use of BV
estimates on the rate fields. We allow for peculiar substructural inertia
and internal dissipation, all accounted for by a d'Alembert-Lagrange-type
principle.

CPAA

We study a $1$-capacitary type problem in $R^2$:
given a set $E$, we minimize the perimeter (in the sense of De Giorgi)
among all the sets containing $E$ (modulo $H^1$) and
satisfying an indecomposability constraint
(according to the definition by [1].
By suitably choosing the representant of the relevant set $E$,
we show that a convexification process characterizes the minimizers.

As a consequence of our result we determine the $1$-capacity of (a suitable representant of) sets with finite perimeter in the plane.

As a consequence of our result we determine the $1$-capacity of (a suitable representant of) sets with finite perimeter in the plane.

DCDS-B

We investigate the asymptotics of obstacle problems for non-local energies in a
vector-valued setting. Motivations arise, in particular, in phase field models
for ferroelectric materials and variational theories for dislocations.

DCDS-B

Human efforts of describing the mechanisms of physical world are a
continuous source of mathematical problems. Models are, in fact,
representations of classes of phenomena inspired and corroborated by
observations intended here as interpretative cataloguing of events.
Mathematics is a language having both qualitative and quantitative nature --
the only one with both features -- so it is natural to use it in
constructing representations with predictive characteristics of the events
in the phenomenological world. In any other human language, in fact, when we
refer to quantification, we use concepts coming from mathematics -- the
standard use of numbers in counting, for example, the words in this paragraph
is a quantitative feature based on a mathematical concept (the one of
numbers indeed) that is added to any type of evaluation of the
literary/philosophical quality of the phrases themselves. Models appear then
as mathematical structures with constituents constrained by the need of
having a clear physical meaning. The mathematical questions appearing in
models of the physical world have twofold nature: On one side we have
technical hitches related, for example, to existence and regularity of
solutions to variational minimality requirements and/or to balance equations
under boundary and/or initial contitions. On the other side there are
foundational problems generated by the quest of the most appropriate form of
models. The target is in fact the physical world: appropriateness is then,
for a model, the ability to describe the essential structures underlying some
classes of phenomena, and their interconnections in non-trivial way,
remaining at the same time rather flexible to allow one the possibility of
hopefully describing unexpected features that the experimental programs
could put in evidence. A model, then, has to be considered not as a manner
of justifying the development of a more or less difficult exercise in
mathematics, rather it is an occasion of exploring by the tools of a
language both qualitative and quantitative, as mathematics is, the intricate
and elegant aspects of the physical world. Distinguishing between different
possible models of the same class of phenomena is a volatile matter decided
by sensibility and culture (the order is not accidental) of the researcher
overburden with the judgement.

For more information please click the "Full Text" above.

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