Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes

In modified theories of gravity, the potentials appearing in theSchr\"odinger-like equations that describe perturbations of non-rotating blackholes are also modified. In this paper we ask: can these modifications beconstrained with high-precision gravitational-wave measurements of the blackhole's quasinormal mode frequencies? We expand the modifications in a smallperturbative parameter regulating the deviation from the general-relativisticpotential, and in powers of $M/r$. We compute the quasinormal modes of themodified potential up to quadratic order in the perturbative parameter. Then weuse Markov-chain-Monte-Carlo (MCMC) methods to recover the coefficients in the$M/r$ expansion in an ``optimistic'' scenario where we vary them one at a time,and in a ``pessimistic'' scenario where we vary them all simultaneously. Inboth cases, we find that the bounds on the individual parameters are notrobust. Because quasinormal mode frequencies are related to the behavior of theperturbation potential near the light ring, we propose a different strategy.Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that thevalue of the potential and of its second derivative at the light ring can berobustly constrained. These constraints allow for a more direct comparisonbetween tests based on black hole spectroscopy and observations of black hole`shadows'' by the Event Horizon Telescope and future instruments.<br

The Potential of Restarts for ProbSAT

This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.Comment: Eurocast 201

Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.Comment: 15 pages, 4 figures, Phys. Rev. B., in pres

Intrinsic hole mobility and trapping in a regio-regular poly(thiophene)

The transport properties of high-performance thin-film transistors (TFT) made with a regio-regular poly(thiophene) semiconductor (PQT-12) are reported. The room-temperature field-effect mobility of the devices varied between 0.004 cm2/V s and 0.1 cm2/V s and was controlled through thermal processing of the material, which modified the structural order. The transport properties of TFTs were studied as a function of temperature. The field-effect mobility is thermally activated in all films at T<200 K and the activation energy depends on the charge density in the channel. The experimental data is compared to theoretical models for transport, and we argue that a model based on the existence of a mobility edge and an exponential distribution of traps provides the best interpretation of the data. The differences in room-temperature mobility are attributed to different widths of the shallow localized state distribution at the edge of the valence band due to structural disorder in the film. The free carrier mobility of the mobile states in the ordered regions of the film is the same in all structural modifications and is estimated to be between 1 and 4 cm2/V s.Comment: 20 pages, 8 figure

Electron spin relaxation of the PO3 2- radical in ferroelectric betaine phosphite and in the proton glass betaine phosphate/betaine phosphite

Measurements of the electron spin-lattice relaxation time T1 and the phase memory time TM of the PO3 2- radical in γ-irradiated betaine phosphite and betaine phosphate/betaine phosphite are presented. The temperature dependence of T1 indicates the interaction of the electron spin with two groups of optical branches via Raman processes in both crystals. An additional relaxation path due to the interaction with two-level local tunneling states has been observed in the mixed crystal confirming glassy behaviour. The TM temperature dependence reflects thermally activated local motional effects of the PO3 group in both crystals. © 1994

Scattering of magnetic solitons in two dimensions

Solitons which have the form of a vortex-antivortex pair have recently been found in the Landau-Lifshitz equation which is the standard model for the ferromagnet. We simulate numerically head-on collisions of two vortex-antivortex pairs and observe a right angle scattering pattern. We offer a resolution of this highly nontrivial dynamical behavior by examining the Hamiltonian structure of the model, specifically the linear momentum of the two solitons. We further investigate the dynamics of vortices in a modified nonlinear sigma-model which arises in the description of antiferromagnets. We confirm numerically that a robust feature of the dynamics is the right angle scattering of two vortices which collide head-on. A generalization of our theory is given for this model which offers arguments towards an understanding of the observed dynamical behavior.Comment: 10 pages RevTeX, 9 figure

Zwischen Hang und Aue - Kohlenstoffdynamik im Einzugsgebiet des Otterbach

Die Nutzung und Umgestaltung der Landschaft durch den Menschen führt seit dem Neolithikum dazu, dass Umlagerungsprozesse z.B. von kohlenstoffhaltigen Sedimenten ausgelöst werden. In solchen dynamischen Landschaften ist der organische Kohlenstoff im Boden (SOC) sehr heterogen verteilt und zum Teil unter mächtigen Sedimentauflagen begraben. Ziel der Untersuchung war es herauszufinden, wo genau sich der SOC innerhalb eines Landschaftsausschnitts akkumuliert und wie sich einzelne Geländepositionen voneinander hinsichtlich ihrer Kohlenstoffeigenschaften unterscheiden. Das Untersuchungsgebiet befindet sich in den Ausläufern des Bayerischen Waldes. Innerhalb des Einzugsgebietes des Otterbachs, einem Tributär der Donau, wurden drei verschiedene Geländepositionen beprobt: a) Unterhang, b) Hangfuß und c) Aue. Innerhalb der jeweiligen Geländepositionen wurden mehrere Profile angelegt, um die kleinräumige Heterogenität der Böden abzubilden. Die Profile wurden horizontbezogen bis in eine Tiefe von 150 cm beprobt und auf ihre Lagerungsdichte, Kohlenstoffmenge (TC, IC und OC) und Textur analysiert. Anschließend wurden Kohlenstoffgehalte und -vorräte berechnet. Eine zweistufige physikalische Dichtefraktionierung in Natriumpolywolframatlösung (1.8 g cm-³ und 2.4 g cm-³) wurde angewandt, um die Anteile der verschiedenen Fraktionen der organischen Substanz am Gesamtkohlenstoffgehalt zu ermitteln. Die Analyse der chemischen Zusammensetzung der Fraktionen mit Kernspinresonanzspektroskopie (NMR) sowie ihres Alters mit Radiokohlenstoffdatierung (AMS C-14) ermöglichte eine genaue qualitative Differenzierung der organischen Bodensubstanz und ließ Rückschlüsse auf ihre Stabilität und ihren Abbaugrad zu. Durch die Kombination der Verfahren konnte ein genaues Bild der Verteilung des SOC in einem Landschaftsausschnitt gezeichnet und seine Qualität detailliert beschrieben werden. In den Ergebnissen zeigt sich, dass die mit rund 1000 Jahren relativ jungen Auenböden eine besondere Rolle bei der Speicherung von SOC spielen. Diese weisen signifikant höhere SOC Vorräte auf als die Profile im Akkumulationsbereich des Hangfußes. Auch verteilen sich die Vorräte in den Auenprofilen über die gesamte Profiltiefe. Im Unterhang und im Hangfuß kann eine solche Verteilung nicht nachgewiesen werden, hier ist der Großteil des Kohlenstoffs nur in den obersten 30 cm gespeichert