3,419 research outputs found
A discontinuous finite element approximation of quasi-static growth of brittle fractures
We propose a discontinuous finite element approximation for a model of
quasi-static growth of brittle fractures in linearly elastic bodies formulated
by Francfort and Marigo, and based on the classical Griffith's criterion. We
restrict our analysis to the case of anti-planar shear and we consider
discontinuous displacements which are piecewise affine with respect to a
regular triangulation.Comment: 34 pages, 4 figure
Bouncing Universes in Scalar-Tensor Gravity Models admitting Negative Potentials
We consider the possibility to produce a bouncing universe in the framework
of scalar-tensor gravity models in which the scalar field potential may be
negative, and even unbounded from below. We find a set of viable solutions with
nonzero measure in the space of initial conditions passing a bounce, even in
the presence of a radiation component, and approaching a constant gravitational
coupling afterwards. Hence we have a model with a minimal modification of
gravity in order to produce a bounce in the early universe with gravity tending
dynamically to general relativity (GR) after the bounce.Comment: 12 pages, Improved presentation with 4 figures, Results and
conclusions unchange
Switching quantum reference frames in the N-body problem and the absence of global relational perspectives
Given the importance of quantum reference systems to both quantum and
gravitational physics, it is pertinent to develop a systematic method for
switching between the descriptions of physics relative to different choices of
quantum reference systems, which is valid in both fields. Here, we continue
with such a unifying approach, begun in arxiv:1809.00556, whose key ingredients
is a gravity-inspired symmetry principle, which enforces physics to be
relational and leads, thanks to gauge related redundancies, to a
perspective-neutral structure which contains all frame choices at once and via
which frame perspectives can be consistently switched. Formulated in the
language of constrained systems, the perspective-neutral structure turns out to
be the constraint surface classically and the gauge invariant Hilbert space in
the Dirac quantized theory. By contrast, a perspective relative to a specific
frame corresponds to a gauge choice and the associated reduced phase and
Hilbert space. Quantum reference frame switches thereby amount to a symmetry
transformation. In the quantum theory, they require a transformation that takes
one from the Dirac to a reduced quantum theory and we show that it amounts to a
trivialization of the constraints and a subsequent projection onto the
classical gauge fixing conditions. We illustrate this method in the relational
-body problem with rotational and translational symmetry. This model is
particularly interesting because it features the Gribov problem so that
globally valid gauge fixing conditions are impossible which, in turn, implies
also that globally valid relational frame perspectives are absent in both the
classical and quantum theory. These challenges notwithstanding, we exhibit how
one can systematically construct the quantum reference frame transformations
for the three-body problem.Comment: 22 pages, plus appendice
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