Fine structure of distributions and central limit theorem in diffusive billiards

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean square displacement, but changes the limiting shape of the distributions to a non-gaussian one. Using the same methods, we give numerical evidence that a non-chaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.Comment: 16 pages, 19 figures. Accepted for publication in Physical Review E. Some higher quality figures at http://www.maths.warwick.ac.uk/~dsander

Observations of fast anisotropic ion heating, ion cooling, and ion recycling in large-amplitude drift waves

Large-amplitude drift wave fluctuations are observed to cause severe ion temperature oscillations in plasmas of the Caltech Encore tokamak [J. M. McChesney, P. M. Bellan, and R. A. Stern, Phys. Fluids B 3, 3370 (1991)]. Experimental investigations of the complete ion dynamical behavior in these waves are presented. The wave electric field excites stochastic ion orbits in the plane normal (perpendicular to) to B, resulting in rapid perpendicular to heating. Ion-ion collisions impart energy along (parallel to) B, relaxing the perpendicular to-parallel to temperature anisotropy. Hot ions with large orbit radii escape confinement, reaching the chamber wall and cooling the distribution. Cold ions from the plasma edge convect back into the plasma (i.e., recycle), causing further cooling and significantly replenishing the density depleted by orbit losses. The ion-ion collision period tau(ii)similar to Tau(3/2)/n fluctuates strongly with the drift wave phase, due to intense (approximate to 50%) fluctuations in n and Tau. Evidence for particle recycling is given by observations of bimodal ion velocity distributions near the plasma edge, indicating the presence of cold ions (0.4 eV) superposed atop the hot (4-8 eV) plasma background. These appear periodically, synchronous with the drift wave phase at which ion fluid flow from the wall toward the plasma center peaks. Evidence is presented that such a periodic heat/loss/recycle/cool process is expected in plasmas with strong stochastic heating

Real-time phase-selective data acquisition system for measurement of wave phenomena in pulsed plasma discharges

A novel data acquisition system and methodology have been developed for the study of wave phenomena in pulsed plasma discharges. The method effectively reduces experimental uncertainty due to shot-to-shot fluctuations in high repetition rate experiments. Real-time analysis of each wave form allows classification of discharges by wave amplitude, phase, or other features. Measurements can then be constructed from subsets of discharges having similar wave properties. The method clarifies the trade-offs between experimental uncertainty reduction and increased demand for data storage capacity and acquisition time. Finally, this data acquisition system is simple to implement and requires relatively little equipment: only a wave form digitizer and a moderately fast computer

Using permeable membranes to produce hydrogen and oxygen from water

Concept may make it profitable to obtain hydrogen fuel from water. Laboratory tests have demonstrated that method enables decomposition of water several orders of magnitude beyond equilibrium state where only small amounts of free hydrogen are present

A Bulk-Parallel Priority Queue in External Memory with STXXL

We propose the design and an implementation of a bulk-parallel external memory priority queue to take advantage of both shared-memory parallelism and high external memory transfer speeds to parallel disks. To achieve higher performance by decoupling item insertions and extractions, we offer two parallelization interfaces: one using "bulk" sequences, the other by defining "limit" items. In the design, we discuss how to parallelize insertions using multiple heaps, and how to calculate a dynamic prediction sequence to prefetch blocks and apply parallel multiway merge for extraction. Our experimental results show that in the selected benchmarks the priority queue reaches 75% of the full parallel I/O bandwidth of rotational disks and and 65% of SSDs, or the speed of sorting in external memory when bounded by computation.Comment: extended version of SEA'15 conference pape

Partitioning Complex Networks via Size-constrained Clustering

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the size-constrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm's configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis

The Adequacy of Speculation in Agricultural Futures Markets: Too Much of a Good Thing?

The objective of this report is to re-visit the “adequacy of speculation” debate in agricultural futures markets. The Commodity Futures Trading Commission makes available the positions held by index funds and other large traders in their Commitment of Traders reports. The results suggest that after an initial surge from early 2004 through mid-2005, index fund positions have stabilized as a percent of total open interest. Traditional speculative measures do not show any material changes or shifts over the sample period. In most markets, the increase in long speculative positions was equaled or surpassed by an increase in short hedging. So, even after adjusting speculative indices for index fund positions, values are within the historical ranges reported in prior research. One implication is that long-only index funds may be beneficial in markets traditionally dominated by short hedging. Attempts to curb speculation through regulatory means should be weighed carefully against the potential benefits provided by this class of speculators.Commitment’s of Traders, index funds, commodity futures markets, Agricultural Finance, Financial Economics,

A Speculative Bubble in Commodity Futures Prices? Cross-Sectional Evidence

Recent accusations against speculators in general and long-only commodity index funds in particular, include: increasing market volatility, distorting historical price relationships, and fueling a rapid increase and decrease in commodity inflation. Some researchers have argued that these market participants—through their impact on market prices—may inadvertently prevented the efficient distribution of food aid to deserving groups. Certainly, this result—if substantiated— would counter the classical argument that speculators make prices more efficient and thus improve the economic efficiency of the agricultural and food marketing system. Given the very important policy implications, it is crucial to develop a more thorough understanding of long-only index funds and their potential market impact. Here, we review the criticisms (and rebuttals) levied against (and for) commodity index funds in recent U.S. Congressional testimonies. Then, additional empirical evidence is added regarding cross-sectional market returns and the relative levels of long-only index fund participation in 12 commodity futures markets. The results suggest that index fund positions across futures markets have no impact on relative price changes across those markets. The empirical results provide no evidence that long-only index funds impact commodity futures prices.Commitment’s of Traders, index funds, commodity futures markets, Agribusiness, Agricultural Finance, Farm Management, Financial Economics, Research Methods/ Statistical Methods, Risk and Uncertainty,