198 research outputs found
The Schr\"odinger operator on an infinite wedge with a tangent magnetic field
We study a model Schr\"odinger operator with constant magnetic field on an
infinite wedge with Neumann boundary condition. The magnetic field is assumed
to be tangent to a face. We compare the bottom of the spectrum to the model
spectral quantities coming from the regular case. We are particularly motivated
by the influence of the magnetic field and the opening angle of the wedge on
the spectrum of the model operator and we exhibit cases where the bottom of the
spectrum is smaller than in the regular case. Numerical computations enlighten
the theoretical approach
Quantum graphs with singular two-particle interactions
We construct quantum models of two particles on a compact metric graph with
singular two-particle interactions. The Hamiltonians are self-adjoint
realisations of Laplacians acting on functions defined on pairs of edges in
such a way that the interaction is provided by boundary conditions. In order to
find such Hamiltonians closed and semi-bounded quadratic forms are constructed,
from which the associated self-adjoint operators are extracted. We provide a
general characterisation of such operators and, furthermore, produce certain
classes of examples. We then consider identical particles and project to the
bosonic and fermionic subspaces. Finally, we show that the operators possess
purely discrete spectra and that the eigenvalues are distributed following an
appropriate Weyl asymptotic law
Spectral Duality for Planar Billiards
For a bounded open domain with connected complement in
and piecewise smooth boundary, we consider the Dirichlet Laplacian
on and the S-matrix on the complement . We
show that the on-shell S-matrices have eigenvalues converging to 1
as exactly when has an eigenvalue at energy
. This includes multiplicities, and proves a weak form of
``transparency'' at . We also show that stronger forms of transparency,
such as having an eigenvalue 1 are not expected to hold in
general.Comment: 33 pages, Postscript, A
On the third critical field in Ginzburg-Landau theory
Using recent results by the authors on the spectral asymptotics of the
Neumann Laplacian with magnetic field, we give precise estimates on the
critical field, , describing the appearance of superconductivity in
superconductors of type II. Furthermore, we prove that the local and global
definitions of this field coincide. Near only a small part, near the
boundary points where the curvature is maximal, of the sample carries
superconductivity. We give precise estimates on the size of this zone and decay
estimates in both the normal (to the boundary) and parallel variables
Approximation of the critical buckling factor for composite panels
This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented
A limit model for thermoelectric equations
We analyze the asymptotic behavior corresponding to the arbitrary high
conductivity of the heat in the thermoelectric devices. This work deals with a
steady-state multidimensional thermistor problem, considering the Joule effect
and both spatial and temperature dependent transport coefficients under some
real boundary conditions in accordance with the Seebeck-Peltier-Thomson
cross-effects. Our first purpose is that the existence of a weak solution holds
true under minimal assumptions on the data, as in particular nonsmooth domains.
Two existence results are studied under different assumptions on the electrical
conductivity. Their proofs are based on a fixed point argument, compactness
methods, and existence and regularity theory for elliptic scalar equations. The
second purpose is to show the existence of a limit model illustrating the
asymptotic situation.Comment: 20 page
Piecewise Tensor Product Wavelet Bases by Extensions and Approximation Rates
Following [Studia Math., 76(2) (1983), pp. 1-58 and 95-136] by Z. Ciesielski and T. Figiel and [SIAM J. Math. Anal., 31 (1999), pp. 184-230] by W. Dahmen and R. Schneider, by the application of extension operators we construct a basis for a range of Sobolev spaces on a domain from corresponding bases on subdomains that form a non-overlapping decomposition. As subdomains, we take hypercubes, or smooth parametric images of those, and equip them with tensor product wavelet bases. We prove approximation rates from the resulting piecewise tensor product basis that are independent of the spatial dimension of . For two- and three-dimensional polytopes we show that the solution of Poisson type problems satisfies the required regularity condition. The dimension independent rates will be realized numerically in linear complexity by the application of the adaptive wavelet-Galerkin scheme
Longtime behavior of nonlocal Cahn-Hilliard equations
Here we consider the nonlocal Cahn-Hilliard equation with constant mobility
in a bounded domain. We prove that the associated dynamical system has an
exponential attractor, provided that the potential is regular. In order to do
that a crucial step is showing the eventual boundedness of the order parameter
uniformly with respect to the initial datum. This is obtained through an
Alikakos-Moser type argument. We establish a similar result for the viscous
nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In
this case the validity of the so-called separation property is crucial. We also
discuss the convergence of a solution to a single stationary state. The
separation property in the nonviscous case is known to hold when the mobility
degenerates at the pure phases in a proper way and the potential is of
logarithmic type. Thus, the existence of an exponential attractor can be proven
in this case as well
āIām only a dog!ā : the Rwandan genocide, dehumanisation and the graphic novel
Graphic novels written in response to the 1994 Rwandan genocide do not confine their depictions of traumatic violence to humans, but extend their coverage to show how the genocide impacted on animals and the environment. Through analysis of the presentation of people and their relationships with other species across a range of graphic narratives, this article shows how animal imagery was used to justify inhumane actions during the genocide, and argues that representations of animals remain central to the recuperation processes in a post-genocide context too. Whilst novels and films that respond to the genocide have been the focus of scholarly work (Dauge-Roth, 2010), the graphic novel has yet to receive substantial critical attention. This article therefore unlocks the archive of French-, Dutch- and English-language graphic narratives written in response to the genocide by providing the first in-depth, comparative analysis of their animal representations. It draws on recent methodological approaches derived from philosophy (Derrida, [2008] trans. 2009), postcolonial ecocriticism (Huggan and Tiffin, 2010) and postcolonial trauma theory (Craps, 2012) in order show how human-centred strategies for recovery, and associated symbolic orders that forcefully position the animal outside of human law, continue to engender unequal and potentially violent relationships between humans, and humans and other species. In this way, graphic narratives that gesture towards more equitable relationships between humans, animals and the environment can be seen to support the processes of recovery and reconciliation in post-genocide Rwanda
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