Source integrals of asymptotic multipole moments

We derive source integrals for multipole moments that describe the behaviour of static and axially symmetric spacetimes close to spatial infinity. We assume isolated non-singular sources but will not restrict the matter content otherwise. Some future applications of these source integrals of the asymptotic multipole moments are outlined as well.Comment: 9 pages, 1 figure, contribution to the proceedings of the conference "Relativity and Gravitation - 100 Years after Einstein in Prague", June 25-29, 2012, Pragu

Simulations over South Asia using the Weather Research and Forecasting model with Chemistry (WRF-Chem): set-up and meteorological evaluation

The configuration and evaluation of the meteorology is presented for simulations over the South Asian region using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem). Temperature, water vapor, dew point temperature, zonal and meridional wind components, precipitation and tropopause pressure are evaluated against radiosonde and satellite-borne (AIRS and TRMM) observations along with NCEP/NCAR reanalysis fields for the year 2008. Chemical fields, with focus on tropospheric ozone, are evaluated in a companion paper. The spatial and temporal variability in meteorological variables is well simulated by the model with temperature, dew point temperature and precipitation showing higher values during summer/monsoon and lower during winter. The index of agreement for all the parameters is estimated to be greater than 0.6 indicating that WRF-Chem is capable of simulating the variations around the observed mean. The mean bias (MB) and root mean square error (RMSE) in modeled temperature, water vapor and wind components show an increasing tendency with altitude. MB and RMSE values are within ±2 K and 1–4 K for temperature, 30% and 20–65% for water vapor and 1.6 m s<sup>−1</sup> and 5.1 m s<sup>−1</sup> for wind components. The spatio-temporal variability of precipitation is also reproduced reasonably well by the model but the model overestimates precipitation in summer and underestimates precipitation during other seasons. Such a behavior of modeled precipitation is in agreement with previous studies on South Asian monsoon. The comparison with radiosonde observations indicates a relatively better model performance for inland sites as compared to coastal and island sites. The MB and RMSE in tropopause pressure are estimated to be less than 25 hPa. Sensitivity simulations show that biases in meteorological simulations can introduce errors of ±(10–25%) in simulations of tropospheric ozone, CO and NO<sub>x</sub>. Nevertheless, a comparison of statistical metrics with benchmarks indicates that the model simulated meteorology is of sufficient quality for use in chemistry simulations

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

General approach for studying first-order phase transitions at low temperatures

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable, an enhanced tempering method, the parallel tempering -- accurate for small and intermediate system sizes with rather low computational cost -- is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phases density at the coexistence.Comment: 5 page

Hexagons become second if symmetry is broken

Pattern formation on the free surface of a magnetic fluid subjected to a magnetic field is investigated experimentally. By tilting the magnetic field the symmetry can be broken in a controllable manner. When increasing the amplitude of the tilted field, the flat surface gives way to liquid ridges. A further increase results in a hysteretic transition to a pattern of stretched hexagons. The instabilities are detected by means of a linear array of magnetic hall sensors and compared with theoretical predictions.Comment: accepted for publication by Physical Review E/Rapid Communicatio

Colligative properties of solutions: I. Fixed concentrations

Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing point depression. The limit of infinitesimal concentrations is described in a subsequent paper.Comment: 28 pages, 1 fig; see also math-ph/0407035 (both to appear in JSP

Adaptive self-organization in a realistic neural network model

Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to criticality. This is further supported by the observation of power-law distributions, which are a hallmark of phase transitions. An important open question is how neural networks could remain close to a critical point while undergoing a continual change in the course of development, adaptation, learning, and more. An influential contribution was made by Bornholdt and Rohlf, introducing a generic mechanism of robust self-organized criticality in adaptive networks. Here, we address the question whether this mechanism is relevant for real neural networks. We show in a realistic model that spike-time-dependent synaptic plasticity can self-organize neural networks robustly toward criticality. Our model reproduces several empirical observations and makes testable predictions on the distribution of synaptic strength, relating them to the critical state of the network. These results suggest that the interplay between dynamics and topology may be essential for neural information processing.Comment: 6 pages, 4 figure