Aspects of noncommutative (1+1)-dimensional black holes

We present a comprehensive analysis of the spacetime structure and thermodynamics of $(1+1)-$dimensional black holes in a noncommutative framework. It is shown that a wider variety of solutions are possible than the commutative case considered previously in the literature. As expected, the introduction of a minimal length $\sqrt{\theta}$ cures singularity pathologies that plague the standard two-dimensional general relativistic case, where the latter solution is recovered at large length scales. Depending on the choice of input parameters (black hole mass $M$, cosmological constant $\Lambda$, etc...), black hole solutions with zero, up to six, horizons are possible. The associated thermodynamics allows for the either complete evaporation, or the production of black hole remnants.Comment: 24 pages, 12 figures, some comments added, conclusions not modified, version matching that published on PR

The angular power spectrum of radio emission at 2.3 GHz

We have analysed the Rhodes/HartRAO survey at 2326 MHz and derived the global angular power spectrum of Galactic continuum emission. In order to measure the angular power spectrum of the diffuse component, point sources were removed from the map by median filtering. A least-square fit to the angular power spectrum of the entire survey with a power law spectrum C_l proportional to l^{-alpha}, gives alpha = 2.43 +/- 0.01 for l = 2-100. The angular power spectrum of radio emission appears to steepen at high Galactic latitudes and for observed regions with |b| > 20 deg, the fitted spectral index is alpha = 2.92 +/- 0.07. We have extrapolated this result to 30 GHz (the lowest frequency channel of Planck) and estimate that no significant contribution to the sky temperature fluctuation is likely to come from synchrotron at degree-angular scalesComment: 10 pages, 10 figures, accepted for publication by Astronomy & Astrophysic

Towards Handling Uncertainty in Prognostic Scenarios: Advanced Learning from the Past

Das Forschungsprogramm „Earth System Sciences (ESS)“, ein Programm des Bundesministeriums für Wissenschaft, Forschung und Wirtschaft (BMWFW), durchgeführt von der ÖAW, hat die Erforschung des Systems Erde zum Ziel. Im Rahmen von Ausschreibungen werden wissenschaftliche Forschungsprojekte gefördert, die dem neusten Stand der Wissenschaft entsprechen. Das Programm ESS sieht es als seine Aufgabe, Lücken in der österreichischen Förderungslandschaft zu schließen. Dies bezieht sich etwa auf interdisziplinäre Projekte, Projekte zur Langzeitforschung sowie auf Projekte, die auf derzeit noch gering beforschte Bereiche fokussiert sind und denen wissenschaftlich

Towards Handling Uncertainty in Prognostic Scenarios: Advanced Learning from the Past

In this report we introduce the paradigm of learning from the past which is realized in a controlled prognostic context. It is a data-driven exploratory approach to assessing the limits to credibility of any expectations about the system’s future behavior which are based on a time series of a historical observations of the analyzed system. This horizon of the credible expectations is derived as the length of explainable outreach of the data, that is, the spatio-temporal extent which, in lieu of the knowledge contained in the historical observations, we are justified in believing contains the system’s future observations. Explainable outreach is of practical interest to stakeholders since it allows them to assess the credibility of scenarios produced by models of the analyzed system. It also indicates the scale of measures required to overcome the system’s inertia. In this report we propose a method of learning in a controlled prognostic context which is based on a polynomial regression technique. A polynomial regression model is used to understand the system’s dynamics, revealed by the sample of historical observations, while the explainable outreach is constructed around the extrapolated regression function. The proposed learning method was tested on various sets of synthetic data in order to identify its strengths and weaknesses, and formulate guidelines for its practical application. We also demonstrate how it can be used in context of earth system sciences by using it to derive the explainable outreach of historical anthropogenic CO2 emissions and atmospheric CO2 concentrations. We conclude that the most robust method of building the explainable outreach is based on linear regression. However, the explainable outreach of the analyzed datasets (representing credible expectations based on extrapolation of the linear trend) is rather short

Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement

Colloidal patchy particles with divalent attractive interaction can self-assemble into linear polymer chains. Their equilibrium properties in 2D and 3D are well described by Wertheim's thermodynamic perturbation theory which predicts a well-defined exponentially decaying equilibrium chain length distribution. In experimental realizations, due to gravity, particles sediment to the bottom of the suspension forming a monolayer of particles with a gravitational height smaller than the particle diameter. In accordance with experiments, an anomalously high monomer concentration is observed in simulations which is not well understood. To account for this observation, we interpret the polymerization as taking place in a highly confined quasi-2D plane and extend the Wertheim thermodynamic perturbation theory by defining addition reactions constants as functions of the chain length. We derive the theory, test it on simple square well potentials, and apply it to the experimental case of synthetic colloidal patchy particles immersed in a binary liquid mixture that are described by an accurate effective critical Casimir patchy particle potential. The important interaction parameters entering the theory are explicitly computed using the integral method in combination with Monte Carlo sampling. Without any adjustable parameter, the predictions of the chain length distribution are in excellent agreement with explicit simulations of self-assembling particles. We discuss generality of the approach, and its application range.Comment: The following article has been submitted to The Journal of Chemical Physic

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case

The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to $\exp( - c w_2^{3/2})$, where $w_2$ is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.Comment: 17 pages, 2 figure