461 research outputs found
Necessary conditions for variational regularization schemes
We study variational regularization methods in a general framework, more
precisely those methods that use a discrepancy and a regularization functional.
While several sets of sufficient conditions are known to obtain a
regularization method, we start with an investigation of the converse question:
How could necessary conditions for a variational method to provide a
regularization method look like? To this end, we formalize the notion of a
variational scheme and start with comparison of three different instances of
variational methods. Then we focus on the data space model and investigate the
role and interplay of the topological structure, the convergence notion and the
discrepancy functional. Especially, we deduce necessary conditions for the
discrepancy functional to fulfill usual continuity assumptions. The results are
applied to discrepancy functionals given by Bregman distances and especially to
the Kullback-Leibler divergence.Comment: To appear in Inverse Problem
Two-Stage Rotational Disordering of a Molecular Crystal Surface: C60
We propose a two-stage mechanism for the rotational surface disordering phase
transition of a molecular crystal, as realized in C fullerite. Our
study, based on Monte Carlo simulations, uncovers the existence of a new
intermediate regime, between a low temperature ordered state,
and a high temperature disordered phase. In the intermediate
regime there is partial disorder, strongest for a subset of particularly
frustrated surface molecules. These concepts and calculations provide a
coherent understanding of experimental observations, with possible extension to
other molecular crystal surfaces.Comment: 4 pages, 2 figure
Organic synthesis on Mars by electrochemical reduction of CO2
The sources and nature of organic carbon on Mars have been a subject of intense research. Steele et al. (2012) showed that 10 martian meteorites contain macromolecular carbon phases contained within pyroxene- and olivine-hosted melt inclusions. Here, we show that martian meteorites Tissint, Nakhla, and NWA 1950 have an inventory of organic carbon species associated with fluid-mineral reactions that are remarkably consistent with those detected by the Mars Science Laboratory (MSL) mission. We advance the hypothesis that interactions among spinel-group minerals, sulfides, and a brine enable the electrochemical reduction of aqueous CO2 to organic molecules. Although documented here in martian samples, a similar process likely occurs wherever igneous rocks containing spinel-group minerals and/or sulfides encounter brines
A combined first and second order variational approach for image reconstruction
In this paper we study a variational problem in the space of functions of
bounded Hessian. Our model constitutes a straightforward higher-order extension
of the well known ROF functional (total variation minimisation) to which we add
a non-smooth second order regulariser. It combines convex functions of the
total variation and the total variation of the first derivatives. In what
follows, we prove existence and uniqueness of minimisers of the combined model
and present the numerical solution of the corresponding discretised problem by
employing the split Bregman method. The paper is furnished with applications of
our model to image denoising, deblurring as well as image inpainting. The
obtained numerical results are compared with results obtained from total
generalised variation (TGV), infimal convolution and Euler's elastica, three
other state of the art higher-order models. The numerical discussion confirms
that the proposed higher-order model competes with models of its kind in
avoiding the creation of undesirable artifacts and blocky-like structures in
the reconstructed images -- a known disadvantage of the ROF model -- while
being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure
Important role of alkali atoms in A4C60
We show that hopping via the alkali atoms plays an important role for the t1u
band of A4C60 (A=K, Rb), in strong contrast to A3C60. Thus the t1u band is
broadened by more than 40 % by the presence of the alkali atoms. The difference
between A4C60 and A3C60 is in particular due to the less symmetric location of
the alkali atoms in A4C60.Comment: 5 pages, revtex, 2 figures, submitted to Phys. Rev. B more
information at http://www.mpi-stuttgart.mpg.de/dokumente/andersen/fullerene
Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
We study Newton type methods for inverse problems described by nonlinear
operator equations in Banach spaces where the Newton equations
are regularized variationally using a general
data misfit functional and a convex regularization term. This generalizes the
well-known iteratively regularized Gauss-Newton method (IRGNM). We prove
convergence and convergence rates as the noise level tends to 0 both for an a
priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule.
Our analysis includes previous order optimal convergence rate results for the
IRGNM as special cases. The main focus of this paper is on inverse problems
with Poisson data where the natural data misfit functional is given by the
Kullback-Leibler divergence. Two examples of such problems are discussed in
detail: an inverse obstacle scattering problem with amplitude data of the
far-field pattern and a phase retrieval problem. The performence of the
proposed method for these problems is illustrated in numerical examples
Superconductivity in Fullerides
Experimental studies of superconductivity properties of fullerides are
briefly reviewed. Theoretical calculations of the electron-phonon coupling, in
particular for the intramolecular phonons, are discussed extensively. The
calculations are compared with coupling constants deduced from a number of
different experimental techniques. It is discussed why the A_3 C_60 are not
Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates
of the Coulomb pseudopotential , describing the effect of the Coulomb
repulsion on the superconductivity, as well as possible electronic mechanisms
for the superconductivity are reviewed. The calculation of various properties
within the Migdal-Eliashberg theory and attempts to go beyond this theory are
described.Comment: 33 pages, latex2e, revtex using rmp style, 15 figures, submitted to
Review of Modern Physics, more information at
http://radix2.mpi-stuttgart.mpg.de/fullerene/fullerene.htm
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