604 research outputs found
Andreev tunneling into a one-dimensional Josephson junction array
In this letter we consider Andreev tunneling between a normal metal and a one
dimensional Josephson junction array with finite-range Coulomb energy. The
characteristics strongly deviate from the classical linear Andreev
current. We show that the non linear conductance possesses interesting scaling
behavior when the chain undergoes a T=0 superconductor-insulator transition of
Kosterlitz-Thouless-Berezinskii type. When the chain has quasi-long range
order, the low lying excitation are gapless and the curves are power-law
(the linear relation is recovered when charging energy can be disregarded).
When the chain is in the insulating phase the Andreev current is blocked at a
threshold which is proportional to the inverse correlation length in the chain
(much lower than the Coulomb gap) and which vanishes at the transition point.Comment: 8 pages LATEX, 3 figures available upon reques
Singularities of Nonlinear Elliptic Systems
Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities
as well as Hausdorff contents/dimensions, this paper estimates the singular
sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a
class of quadratic functionals inducing harmonic maps.Comment: 18 pages Communications in Partial Differential Equation
Entropy-based measure of structural order in water
We analyze the nature of the structural order established in liquid TIP4P
water in the framework provided by the multi-particle correlation expansion of
the statistical entropy. Different regimes are mapped onto the phase diagram of
the model upon resolving the pair entropy into its translational and
orientational components. These parameters are used to quantify the relative
amounts of positional and angular order in a given thermodynamic state, thus
allowing a structurally unbiased definition of low-density and high-density
water. As a result, the structurally anomalous region within which both types
of order are simultaneously disrupted by an increase of pressure at constant
temperature is clearly identified through extensive molecular-dynamics
simulations.Comment: 5 pages, 2 figures, to appear in Phys. Rev. E (Rapid Communication
Semi-classical Green kernel asymptotics for the Dirac operator
We consider a semi-classical Dirac operator in arbitrary spatial dimensions
with a smooth potential whose partial derivatives of any order are bounded by
suitable constants. We prove that the distribution kernel of the inverse
operator evaluated at two distinct points fulfilling a certain hypothesis can
be represented as the product of an exponentially decaying factor involving an
associated Agmon distance and some amplitude admitting a complete asymptotic
expansion in powers of the semi-classical parameter. Moreover, we find an
explicit formula for the leading term in that expansion.Comment: 46 page
A note on boundedness of operators in Grand Grand Morrey spaces
In this note we introduce grand grand Morrey spaces, in the spirit of the
grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is
applicable to a variety of operators to reduce their boundedness in grand grand
Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of
this application, we obtain the boundedness of the Hardy-Littlewood maximal
operator and Calder\'on-Zygmund operators in the framework of grand grand
Morrey spaces.Comment: 8 page
Geometric approach to nonvariational singular elliptic equations
In this work we develop a systematic geometric approach to study fully
nonlinear elliptic equations with singular absorption terms as well as their
related free boundary problems. The magnitude of the singularity is measured by
a negative parameter , for , which reflects on
lack of smoothness for an existing solution along the singular interface
between its positive and zero phases. We establish existence as well sharp
regularity properties of solutions. We further prove that minimal solutions are
non-degenerate and obtain fine geometric-measure properties of the free
boundary . In particular we show sharp
Hausdorff estimates which imply local finiteness of the perimeter of the region
and a.e. weak differentiability property of
.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos
Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis
201
Functional Liftings of Vectorial Variational Problems with Laplacian Regularization
We propose a functional lifting-based convex relaxation of variational
problems with Laplacian-based second-order regularization. The approach rests
on ideas from the calibration method as well as from sublabel-accurate
continuous multilabeling approaches, and makes these approaches amenable for
variational problems with vectorial data and higher-order regularization, as is
common in image processing applications. We motivate the approach in the
function space setting and prove that, in the special case of absolute
Laplacian regularization, it encompasses the discretization-first
sublabel-accurate continuous multilabeling approach as a special case. We
present a mathematical connection between the lifted and original functional
and discuss possible interpretations of minimizers in the lifted function
space. Finally, we exemplarily apply the proposed approach to 2D image
registration problems.Comment: 12 pages, 3 figures; accepted at the conference "Scale Space and
Variational Methods" in Hofgeismar, Germany 201
The mixed problem for the Laplacian in Lipschitz domains
We consider the mixed boundary value problem or Zaremba's problem for the
Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on
part of the boundary and Neumann data on the remainder of the boundary. We
assume that the boundary between the sets where we specify Dirichlet and
Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p
and the Dirichlet data is in the Sobolev space of functions having one
derivative in L^p for some p near 1. Under these conditions, there is a unique
solution to the mixed problem with the non-tangential maximal function of the
gradient of the solution in L^p of the boundary. We also obtain results with
data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since
the paper appeared long ago, this submission includes the complete paper,
followed by a short section that gives the correction to one step in the
proo
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