Kinetic energy choice in Hamiltonian/hybrid Monte Carlo

We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are established on integrator stability and geometric convergence, and we show that choices of kinetic energy that result in heavy-tailed momentum distributions can exhibit an undesirable negligible moves property, which we define. A general efficiency-robustness trade off is outlined, and implementations which rely on approximate gradients are also discussed. Two numerical studies illustrate our theoretical findings, showing that the standard choice which results in a Gaussian momentum distribution is not always optimal in terms of either robustness or efficiency.Comment: 15 pages (+7 page supplement, included here as an appendix), 2 figures (+1 in supplement

An electric-field representation of the harmonic XY model

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.Comment: 13 pages, 10 figure

Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.Comment: 11 pages, 6 figure

Phase order in superfluid helium films

Classic experimental data on helium films are transformed to estimate a finite-size phase order parameter that measures the thermal degradation of the condensate fraction in the two-dimensional superfluid. The order parameter is found to evolve thermally with the exponent $\beta = 3 \pi^2/128$, a characteristic, in analogous magnetic systems, of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Universal scaling near the BKT fixed point generates a collapse of experimental data on helium and ferromagnetic films, and implies new experiments and theoretical protocols to explore the phase order. These results give a striking example of experimental finite-size scaling in a critical system that is broadly relevant to two-dimensional Bose fluids.Comment: 6 pages, 2 figure

Functional Connectivity of the Raphe Nuclei: Link to Tobacco Withdrawal in Smokers.

BackgroundAlthough nicotine alters serotonergic neurochemistry, clinical trials of serotonergic medications for smoking cessation have provided mixed results. Understanding the role of serotonergic dysfunction in tobacco use disorder may advance development of novel pharmacotherapies.MethodsFunctional magnetic resonance imaging was used to measure resting-state functional connectivity of the raphe nuclei as an indicator of serotonergic function. Connectivity of the dorsal and median raphe nuclei was compared between 18 young smokers (briefly abstinent, ~40 minutes post-smoking) and 19 young nonsmokers (16-21 years old); connectivity was also examined in a separate sample of overnight-abstinent smokers (18-25 years old), before and after smoking the first cigarette of the day. Relationships between connectivity of the raphe nuclei with psychological withdrawal and craving were tested in smokers.ResultsConnectivity of the median raphe nucleus with the right hippocampal complex was weaker in smokers than in nonsmokers and was negatively correlated with psychological withdrawal in smokers. In overnight-abstinent smokers, smoking increased connectivity of the median raphe nucleus with the right hippocampal complex, and the increase was positively correlated with the decrease in psychological withdrawal.ConclusionsRelief of withdrawal due to smoking is potentially linked to the serotonergic pathway that includes the median raphe nucleus and hippocampal complex. These results suggest that serotonergic medications may be especially beneficial for smokers who endorse strong psychological withdrawal during abstinence from smoking

Minimal-Time Ship Routing

A recently theory of minimal-time ship routing through time-dependent ocean wave height and direction fields is put to a numerical test by using a series of semidaily analyses furnished by the U.S. Navy Fleet Numerical Weather Facility. The interpolations and integrations required are found to be feasible. A resume of the theory is given.http://archive.org/details/minimaltimeshipr00bleiN

Constraining f(R) Gravity as a Scalar Tensor Theory

We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called chameleon effect. However, in both cases, it appears likely that any late-time cosmic acceleration will be observationally indistinguishable from acceleration caused by a cosmological constant. We also explore further observational constraints from, e.g., big bang nucleosynthesis and inflation.Comment: 15 pages, 5 figure

Deformation monitoring of a simply supported railway bridge under varying dynamic loads

This is the author accepted manuscript. The final version is available from IABMAS via the link in this recordStructural health monitoring is a useful tool for evaluating the condition of bridges, with permanent systems installed on bridges which form vital links on the major transport network. The economic cost of the monitoring systems limits their installation on smaller bridges which make up the wider transport network. A short-term monitoring system can be quickly installed and adjusted to suit the requirements of individual bridges. These systems are ideal for rural regions with a high number of single span bridges on isolated road and rail networks. This report will review a single span bridge on a private heritage railway under loading from passing steam engines, including the Flying Scotsman. Acceleration data are used to determine the rotations and deflections of the bridge deck. To verify the data, deflection measurements at mid-span were recorded using a video-based measurement system. The deflection measurements from the accelerometers correlate with the video imagery measurements

Persistent Current of Free Electrons in the Plane

Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function. Instead of piecewise constant persistent current of free electrons on the plane one has a current which varies linearly with the flux and is antisymmetric with regard to all time preserving values of $\alpha$ including $1/2$. Different self-adjoint extensions of the problem and role of the resonance are discussed.Comment: (Comment on "Relation between Persistent Currents and the Scattering Matrix", Phys. Rev. Lett. {\bf 66}, 76 (1991)) plain latex, 4pp., IPNO/TH 94-2