16,241 research outputs found
Global Behavior of the Douglas-Rachford Method for a Nonconvex Feasibility Problem
In recent times the Douglas-Rachford algorithm has been observed empirically
to solve a variety of nonconvex feasibility problems including those of a
combinatorial nature. For many of these problems current theory is not
sufficient to explain this observed success and is mainly concerned with
questions of local convergence. In this paper we analyze global behavior of the
method for finding a point in the intersection of a half-space and a
potentially non-convex set which is assumed to satisfy a well-quasi-ordering
property or a property weaker than compactness. In particular, the special case
in which the second set is finite is covered by our framework and provides a
prototypical setting for combinatorial optimization problems
A feasibility approach for constructing combinatorial designs of circulant type
In this work, we propose an optimization approach for constructing various
classes of circulant combinatorial designs that can be defined in terms of
autocorrelations. The problem is formulated as a so-called feasibility problem
having three sets, to which the Douglas-Rachford projection algorithm is
applied. The approach is illustrated on three different classes of circulant
combinatorial designs: circulant weighing matrices, D-optimal matrices, and
Hadamard matrices with two circulant cores. Furthermore, we explicitly
construct two new circulant weighing matrices, a and a
, whose existence was previously marked as unresolved in the most
recent version of Strassler's table
Axion Dark Matter and Cosmological Parameters
We observe that photon cooling after big bang nucleosynthesis (BBN) but
before recombination can remove the conflict between the observed and
theoretically predicted value of the primordial abundance of Li. Such
cooling is ordinarily difficult to achieve. However, the recent realization
that dark matter axions form a Bose-Einstein condensate (BEC) provides a
possible mechanism, because the much colder axions may reach thermal contact
with the photons. This proposal predicts a high effective number of neutrinos
as measured by the cosmic microwave anisotropy spectrum.Comment: 4 pages, one figure. Version to appear in Phys. Rev. Lett.,
incorporating useful comments by the referees and emphasizing that photon
cooling by axion BEC is a possibility, not a certaint
Coronal heating in multiple magnetic threads
Context. Heating the solar corona to several million degrees requires the
conversion of magnetic energy into thermal energy. In this paper, we
investigate whether an unstable magnetic thread within a coronal loop can
destabilise a neighbouring magnetic thread. Aims. By running a series of
simulations, we aim to understand under what conditions the destabilisation of
a single magnetic thread can also trigger a release of energy in a nearby
thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate
the temporal evolution of coronal magnetic fields during a kink instability and
the subsequent relaxation process. We assume that a coronal magnetic loop
consists of non-potential magnetic threads that are initially in an equilibrium
state. Results. The non-linear kink instability in one magnetic thread forms a
helical current sheet and initiates magnetic reconnection. The current sheet
fragments, and magnetic energy is released throughout that thread. We find
that, under certain conditions, this event can destabilise a nearby thread,
which is a necessary requirement for starting an avalanche of energy release in
magnetic threads. Conclusions. It is possible to initiate an energy release in
a nearby, non-potential magnetic thread, because the energy released from one
unstable magnetic thread can trigger energy release in nearby threads, provided
that the nearby structures are close to marginal stability
An EMTP system level model of the PMAD DC test bed
A power management and distribution direct current (PMAD DC) test bed was set up at the NASA Lewis Research Center to investigate Space Station Freedom Electric Power Systems issues. Efficiency of test bed operation significantly improves with a computer simulation model of the test bed as an adjunct tool of investigation. Such a model is developed using the Electromagnetic Transients Program (EMTP) and is available to the test bed developers and experimenters. The computer model is assembled on a modular basis. Device models of different types can be incorporated into the system model with only a few lines of code. A library of the various model types is created for this purpose. Simulation results and corresponding test bed results are presented to demonstrate model validity
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