Comparative Monte Carlo Efficiency by Monte Carlo Analysis

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs properly in order to sample this eigenfunction faithfully. We present a simple procedure to solve this sign problem and then test our Monte Carlo methods by computing the $\lambda_2$ of various Markov chain transition matrices. We first computed ${\lambda_2}$ for several one and two dimensional Ising models, which have a discrete phase space, and compared the relative efficiencies of the Metropolis and heat-bath algorithms as a function of temperature and applied magnetic field. Next, we computed $\lambda_2$ for a model of an interacting gas trapped by a harmonic potential, which has a mutidimensional continuous phase space, and studied the efficiency of the Metropolis algorithm as a function of temperature and the maximum allowable step size $\Delta$. Based on the $\lambda_2$ criterion, we found for the Ising models that small lattices appear to give an adequate picture of comparative efficiency and that the heat-bath algorithm is more efficient than the Metropolis algorithm only at low temperatures where both algorithms are inefficient. For the harmonic trap problem, we found that the traditional rule-of-thumb of adjusting $\Delta$ so the Metropolis acceptance rate is around 50% range is often sub-optimal. In general, as a function of temperature or $\Delta$, $\lambda_2$ for this model displayed trends defining optimal efficiency that the acceptance ratio does not. The cases studied also suggested that Monte Carlo simulations for a continuum model are likely more efficient than those for a discretized version of the model.Comment: 23 pages, 8 figure

Probing 5f-state configurations in URu2Si2 with U L3-edge resonant x-ray emission spectroscopy

Resonant x-ray emission spectroscopy (RXES) was employed at the U L3 absorption edge and the La1 emission line to explore the 5f occupancy, nf, and the degree of 5f orbital delocalization in the hidden order compound URu2Si2. By comparing to suitable reference materials such as UF4, UCd11, and alpha-U, we conclude that the 5f orbital in URu2Si2 is at least partially delocalized with nf = 2.87 +/- 0.08, and does not change with temperature down to 10 K within the estimated error. These results place further constraints on theoretical explanations of the hidden order, especially those requiring a localized f2 ground state.Comment: 11 pages,7 figure

Food-conditioned odour rejection in the late stages of the meal, mediating learnt control of meal volume by aftereffects of food consumption

In a two-bottle choice test, rats drank more of the fluid having a novel odour than that having an odour which had previously been presented in the later part of meals on concentrated maltodextrin solution. Rats are normally more averse to a novel odour than to a familiar odour; therefore, the conditioned reaction to the odour acquired in these circumstances is likely to be an ingestive aversion, rather than merely a lack of preference. Furthermore, this learnt odour rejection was seen only in the second half of the meal, indicating that it is dependent on an ingestion-induced state of repletion. Together then, these observations are evidence that the volume of meals rich in carbohydrate can be controlled by learnt rejection of particular food flavours in the presence of visceral cues specific to repletion (previously dubbed "conditioned satiety"), the only known mechanism by which aftereffects of ingested energy could reduce meal volume

Hypergraph Acyclicity and Propositional Model Counting

We show that the propositional model counting problem #SAT for CNF- formulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore, we present a polynomial time algorithm that computes a disjoint branches decomposition of a given hypergraph if it exists and rejects otherwise. Finally, we show that some slight extensions of the class of hypergraphs with disjoint branches decompositions lead to intractable #SAT, leaving open how to generalize the counting result of this paper

Self-Adaptive Quadrature and Numerical Path Integration

In the present paper we explore the use of generalized Gaussian quadrature methods in the context of equilibrium path integral applications. Using moment techniques, we devise a compact, self-adaptive approach for use in conjunction with selected classes of interaction potentials. We demonstrate that, when applicable, the resulting approach reduces appreciably the number of potential energy evaluations required in equilibrium path integral simulations

Alfven-Wave Studies On Pretext

Fusion Research Cente

Quantifying structural damage from self-irradiation in a plutonium superconductor

The 18.5 K superconductor PuCoGa5 has many unusual properties, including those due to damage induced by self-irradiation. The superconducting transition temperature decreases sharply with time, suggesting a radiation-induced Frenkel defect concentration much larger than predicted by current radiation damage theories. Extended x-ray absorption fine-structure measurements demonstrate that while the local crystal structure in fresh material is well ordered, aged material is disordered much more strongly than expected from simple defects, consistent with strong disorder throughout the damage cascade region. These data highlight the potential impact of local lattice distortions relative to defects on the properties of irradiated materials and underscore the need for more atomic-resolution structural comparisons between radiation damage experiments and theory.Comment: 7 pages, 5 figures, to be published in PR

Horizon energy and angular momentum from a Hamiltonian perspective

Classical black holes and event horizons are highly non-local objects, defined in terms of the causal past of future null infinity. Alternative, (quasi)local definitions are often used in mathematical, quantum, and numerical relativity. These include apparent, trapping, isolated, and dynamical horizons, all of which are closely associated to two-surfaces of zero outward null expansion. In this paper we show that three-surfaces which can be foliated with such two-surfaces are suitable boundaries in both a quasilocal action and a phase space formulation of general relativity. The resulting formalism provides expressions for the quasilocal energy and angular momentum associated with the horizon. The values of the energy and angular momentum are in agreement with those derived from the isolated and dynamical horizon frameworks.Comment: 39 pages, 3 figures, Final Version : content essentially unchanged but many small improvements made in response to referees, a few references adde

Studies on the Occurrence and Elemental Composition of Bacteria in Freshwater Plankton

The occurrence and cation content of bacteria in a eutrophic freshwater lake (Rostherne Mere, Cheshire, UK) were investigated over a one year sampling period in relation to cation changes in the lake surface water and phytoplankton. Scanning electron microscope examination of trawl-net and filtered samples demonstrated bacterial association with Anabaena, Aphanizomenon and diatoms. Direct counts of associated and unassociated bacteria showed that increases in bacterial population relate to population decline of major algal constituents. Spectrophotometric determination of selected cation levels in the lake water demonstrated wide fluctuations throughout the sampling period, with elevated levels of transition metals before and at the end of Summer stratification. Zn and Pb also showed increased levels in relation to episodic events. Mass fractions of spectrophotometrically-determined selected cations (Fe, Cu, Zn and Pb) in phytoplankton also varied considerably during the sampling period, with major increases apparently following peaks in water level. X-ray microanalysis of whole, unassociated bacterial eel ls demonstrated high levels of soluble and bound cations, including K, Ca, Fe, Cu, Ni, Zn and Pb. Changes in the cation levels of bacteria did not follow a similar pattern to the general phytoplankton - probably due to differences in uptake or adsorption or to cycling of bacterial cells in the water column