Creation and characterization of vortex clusters in atomic Bose-Einstein condensates

We show that a moving obstacle, in the form of an elongated paddle, can create vortices that are dispersed, or induce clusters of like-signed vortices in 2D Bose-Einstein condensates. We propose new statistical measures of clustering based on Ripley's K-function which are suitable to the small size and small number of vortices in atomic condensates, which lack the huge number of length scales excited in larger classical and quantum turbulent fluid systems. The evolution and decay of clustering is analyzed using these measures. Experimentally it should prove possible to create such an obstacle by a laser beam and a moving optical mask. The theoretical techniques we present are accessible to experimentalists and extend the current methods available to induce 2D quantum turbulence in Bose-Einstein condensates.Comment: 9 pages, 9 figure

Dynamic quantum clustering: a method for visual exploration of structures in data

A given set of data-points in some feature space may be associated with a Schrodinger equation whose potential is determined by the data. This is known to lead to good clustering solutions. Here we extend this approach into a full-fledged dynamical scheme using a time-dependent Schrodinger equation. Moreover, we approximate this Hamiltonian formalism by a truncated calculation within a set of Gaussian wave functions (coherent states) centered around the original points. This allows for analytic evaluation of the time evolution of all such states, opening up the possibility of exploration of relationships among data-points through observation of varying dynamical-distances among points and convergence of points into clusters. This formalism may be further supplemented by preprocessing, such as dimensional reduction through singular value decomposition or feature filtering.Comment: 15 pages, 9 figure

Spatially embedded random networks

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples

Non-equilibrium dynamics of stochastic point processes with refractoriness

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze non-stationary renewal processes.Comment: 8 pages, 4 figure

Frequency Dependent Rheology of Vesicular Rhyolite

Frequency dependent rheology of magmas may result from the presence of inclusions (bubbles, crystals) in the melt and/or from viscoelastic behavior of the melt itself. With the addition of deformable inclusions to a melt possessing viscoelastic properties one might expect changes in the relaxation spectrum of the shear stresses of the material (e.g., broadening of the relaxation spectrum) resulting from the viscously deformable geometry of the second phase. We have begun to investigate the effect of bubbles on the frequency dependent rheology of rhyolite melt. The present study deals with the rheology of bubble-free and vesicular rhyolite melts containing spherical voids of 10 and 30 vol %. We used a sinusoidal torsion deformation device. Vesicular rhyolite melts were generated by the melting (at 1 bar) of an Armenian obsidian (Dry Fountain, Erevan, Armenia) and Little Glass Mountain obsidian (California). The real and imaginary parts of shear viscosity and shear modulus have been determined in a frequency range of 0.005–10 Hz and temperature range of 600°–900°C. The relaxed shear viscosities of samples obtained at low frequencies and high temperatures compare well with data previously obtained by parallel plate viscometry. The relaxed shear viscosity of vesicular rhyolites decreases progressively with increasing bubble content. The relaxation spectrum for rhyolite melt without bubbles has an asymmetric form and fits an extended exponent relaxation. The presence of deformable bubbles results in an imaginary component of the shear modulus that becomes more symmetrical and extends into the low-frequency/high-temperature range. The internal friction Q −1 is unaffected in the high-frequency/low-temperature range by the presence of bubbles and depends on the bubble content in the high-temperature/low-frequency range. The present work, in combination with the previous study of Stein and Spera (1992), illustrates that magma viscosity can either increase or decrease with bubble content, depending upon the rate of style of strain during magmatic flow

The Geography of Scientific Productivity: Scaling in U.S. Computer Science

Here we extract the geographical addresses of authors in the Citeseer database of computer science papers. We show that the productivity of research centres in the United States follows a power-law regime, apart from the most productive centres for which we do not have enough data to reach definite conclusions. To investigate the spatial distribution of computer science research centres in the United States, we compute the two-point correlation function of the spatial point process and show that the observed power-laws do not disappear even when we change the physical representation from geographical space to cartogram space. Our work suggests that the effect of physical location poses a challenge to ongoing efforts to develop realistic models of scientific productivity. We propose that the introduction of a fine scale geography may lead to more sophisticated indicators of scientific output.Comment: 6 pages, 3 figures; minor change

Anaerobic digestion of whole-crop winter wheat silage for renewable energy production

With biogas production expanding across Europe in response to renewable energy incentives, a wider variety of crops need to be considered as feedstock. Maize, the most commonly used crop at present, is not ideal in cooler, wetter regions, where higher energy yields per hectare might be achieved with other cereals. Winter wheat is a possible candidate because, under these conditions, it has a good biomass yield, can be ensiled, and can be used as a whole crop material. The results showed that, when harvested at the medium milk stage, the specific methane yield was 0.32 m3 CH4 kg–1 volatile solids added, equal to 73% of the measured calorific value. Using crop yield values for the north of England, a net energy yield of 146–155 GJ ha–1 year–1 could be achieved after taking into account both direct and indirect energy consumption in cultivation, processing through anaerobic digestion, and spreading digestate back to the land. The process showed some limitations, however: the relatively low density of the substrate made it difficult to mix the digester, and there was a buildup of soluble chemical oxygen demand, which represented a loss in methane potential and may also have led to biofoaming. The high nitrogen content of the wheat initially caused problems, but these could be overcome by acclimatization. A combination of these factors is likely to limit the loading that can be applied to the digester when using winter wheat as a substrat

Enhanced statistical stability in coherent interferometric imaging

http://iopscience.iop.org/0266-5611/International audienc

Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data

We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we demonstrate the potential that MCMC techniques may hold for the computation of posterior distributions of parameters of the binary system that created the gravity radiation signal. We describe the use of the Gibbs sampler method, and present examples whereby signals are detected and analyzed from within noisy data.Comment: 21 pages, 10 figure

Extracting galactic binary signals from the first round of Mock LISA Data Challenges

We report on the performance of an end-to-end Bayesian analysis pipeline for detecting and characterizing galactic binary signals in simulated LISA data. Our principal analysis tool is the Blocked-Annealed Metropolis Hasting (BAM) algorithm, which has been optimized to search for tens of thousands of overlapping signals across the LISA band. The BAM algorithm employs Bayesian model selection to determine the number of resolvable sources, and provides posterior distribution functions for all the model parameters. The BAM algorithm performed almost flawlessly on all the Round 1 Mock LISA Data Challenge data sets, including those with many highly overlapping sources. The only misses were later traced to a coding error that affected high frequency sources. In addition to the BAM algorithm we also successfully tested a Genetic Algorithm (GA), but only on data sets with isolated signals as the GA has yet to be optimized to handle large numbers of overlapping signals.Comment: 13 pages, 4 figures, submitted to Proceedings of GWDAW-11 (Berlin, Dec. '06