3,233 research outputs found
Stationary point approach to the phase transition of the classical XY chain with power-law interactions
The stationary points of the Hamiltonian H of the classical XY chain with
power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the
distance) are analyzed. For a class of "spinwave-type" stationary points, the
asymptotic behavior of the Hessian determinant of H is computed analytically in
the limit of large system size. The computation is based on the Toeplitz
property of the Hessian and makes use of a Szeg\"o-type theorem. The results
serve to illustrate a recently discovered relation between phase transitions
and the properties of stationary points of classical many-body Hamiltonian
functions. In agreement with this relation, the exact phase transition energy
of the model can be read off from the behavior of the Hessian determinant for
exponents {\alpha} between zero and one. For {\alpha} between one and two, the
phase transition is not manifest in the behavior of the determinant, and it
might be necessary to consider larger classes of stationary points.Comment: 9 pages, 6 figure
Targeted Recovery as an Effective Strategy against Epidemic Spreading
We propose a targeted intervention protocol where recovery is restricted to
individuals that have the least number of infected neighbours. Our recovery
strategy is highly efficient on any kind of network, since epidemic outbreaks
are minimal when compared to the baseline scenario of spontaneous recovery. In
the case of spatially embedded networks, we find that an epidemic stays
strongly spatially confined with a characteristic length scale undergoing a
random walk. We demonstrate numerically and analytically that this dynamics
leads to an epidemic spot with a flat surface structure and a radius that grows
linearly with the spreading rate.Comment: 6 pages, 5 figure
Embedding into bipartite graphs
The conjecture of Bollob\'as and Koml\'os, recently proved by B\"ottcher,
Schacht, and Taraz [Math. Ann. 343(1), 175--205, 2009], implies that for any
, every balanced bipartite graph on vertices with bounded degree
and sublinear bandwidth appears as a subgraph of any -vertex graph with
minimum degree , provided that is sufficiently large. We show
that this threshold can be cut in half to an essentially best-possible minimum
degree of when we have the additional structural
information of the host graph being balanced bipartite. This complements
results of Zhao [to appear in SIAM J. Discrete Math.], as well as Hladk\'y and
Schacht [to appear in SIAM J. Discrete Math.], who determined a corresponding
minimum degree threshold for -factors, with and fixed.
Moreover, it implies that the set of Hamilton cycles of is a generating
system for its cycle space.Comment: 16 pages, 2 figure
Interpretation of increased energetic particle flux measurements by SEPT aboard the STEREO spacecraft and contamination
Context. Interplanetary (IP) shocks are known to be accelerators of energetic
charged particles observed in-situ in the heliosphere. However, the
acceleration of near-relativistic electrons by shocks in the interplanetary
medium is often questioned. On 9 August 2011 a Corotating Interaction Region
(CIR) passed STEREO B (STB) that resulted in a flux increase in the electron
and ion channels of the Solar Electron and Proton Telescope (SEPT). Because
electron measurements in the few keV to several 100 keV range rely on the
so-called magnet foil technique, which is utilized by SEPT, ions can contribute
to the electron channels. Aims. We aim to investigate whether the flux increase
in the electron channels of SEPT during the CIR event on 9 August 2011 is
caused by ion contamination only. Methods. We compute the SEPT response
functions for protons and helium utilizing an updated GEANT4 model of SEPT. The
CIR energetic particle ion spectra for protons and helium are assumed to follow
a Band function in energy per nucleon with a constant helium to proton ratio.
Results. Our analysis leads to a helium to proton ratio of 16.9% and a proton
flux following a Band function with the parameters /
(cm2 s sr MeV/nuc.), keV/nuc. and spectral indices of and which are in good agreement with measurements by
the Suprathermal Ion Telescope (SIT) aboard STB. Conclusions. Since our results
explain the SEPT measurements, we conclude that no significant amount of
electrons were accelerated between keV and keV by the CIR
Metastable precursors during the oxidation of the Ru(0001) surface
Using density-functional theory, we predict that the oxidation of the
Ru(0001) surface proceeds via the accumulation of sub-surface oxygen in
two-dimensional islands between the first and second substrate layer. This
leads locally to a decoupling of an O-Ru-O trilayer from the underlying metal.
Continued oxidation results in the formation and stacking of more of these
trilayers, which unfold into the RuO_2(110) rutile structure once a critical
film thickness is exceeded. Along this oxidation pathway, we identify various
metastable configurations. These are found to be rather close in energy,
indicating a likely lively dynamics between them at elevated temperatures,
which will affect the surface chemical and mechanical properties of the
material.Comment: 11 pages including 9 figures. Submitted to Phys. Rev. B. Related
publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm
The spectrum of large powers of the Laplacian in bounded domains
We present exact results for the spectrum of the Nth power of the Laplacian
in a bounded domain. We begin with the one dimensional case and show that the
whole spectrum can be obtained in the limit of large N. We also show that it is
a useful numerical approach valid for any N. Finally, we discuss implications
of this work and present its possible extensions for non integer N and for 3D
Laplacian problems.Comment: 13 pages, 2 figure
Computational Simulations of the Lateral-Photovoltage-Scanning-Method
The major task for the Lateral-Photovoltage-Scanning-Method is to detect doping striations and the shape of the solid-liquid-interface of an indirect semiconductor crystal. This method is sensitive to the gradient of the charge carrier density. Attempting to simulate the signal generation of the LPS-Method, we are using a three dimensional Finite Volume approach for solving the van Roosbroeck equations with COMSOL Multiphysics in a silicon sample. We show that the simulated LPS-voltage is directly proportional to the gradient of a given doping distribution, which is also the case for the measured LPS-voltage
Photon-induced oxidation of graphene/Ir(111) by SO<sub>2</sub> adsorption
We prepare a single layer of graphene oxide by adsorption and subsequent photo-dissociation of SO2 on graphene/Ir(111). Epoxidic oxygen is formed as the main result of this process on graphene, as judged from the appearance of characteristic spectroscopic features in the C 1s and O 1s core level lines. The different stages of decomposition of SO2 into its photo-fragments are examined during the oxidation process. NEXAFS at the carbon K edge reveals a strong disturbance of the graphene backbone after oxidation and upon SO adsorption. The oxide phase is stable up to room temperature, and is fully reversible upon annealing at elevated temperatures. A band gap opening of 330 ± 60 meV between the valence and conduction bands is observed in the graphene oxide phase
Self-adaptation of Mutation Rates in Non-elitist Populations
The runtime of evolutionary algorithms (EAs) depends critically on their
parameter settings, which are often problem-specific. Automated schemes for
parameter tuning have been developed to alleviate the high costs of manual
parameter tuning. Experimental results indicate that self-adaptation, where
parameter settings are encoded in the genomes of individuals, can be effective
in continuous optimisation. However, results in discrete optimisation have been
less conclusive. Furthermore, a rigorous runtime analysis that explains how
self-adaptation can lead to asymptotic speedups has been missing. This paper
provides the first such analysis for discrete, population-based EAs. We apply
level-based analysis to show how a self-adaptive EA is capable of fine-tuning
its mutation rate, leading to exponential speedups over EAs using fixed
mutation rates.Comment: To appear in the Proceedings of the 14th International Conference on
Parallel Problem Solving from Nature (PPSN
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