Some Aspects of the Exact Foldy-Wouthuysen Transformation for a Dirac Fermion

The Foldy-Wouthuysen transformation (FWT) is used to separate distinct components of relativistic spinor field, e.g. electron and positron. Usually, the FWT is perturbative, but in some cases there is an involution operator and the transformation can be done exactly. We consider some aspects of an exact FWT and show that, even if the theory does not admit an involution operator, one can use the technique of exact FWT to obtain the conventional perturbative result. Several particular cases can be elaborated as examples

Study of the topological Hall effect on simple models

Recently, a chirality-driven contribution to the anomalous Hall effect has been found that is induced by the Berry phase and does not directly involve spin-orbit coupling. In this paper, we will investigate this effect numerically in a two-dimensional electron gas with a simple magnetic texture model. Both the adiabatic and non-adiabatic regimes are studied, including the effect of disorder. By studying the transition between both regimes the discussion about the correct adiabaticity criterium in the diffusive limit is clarified.Comment: 8 pages, 7 figures, revtex

Quasi-Topological Field Theories in Two Dimensions as Soluble Models

We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus $g$, the partition function $Z$ is defined for a triangulation consisting of $n$ triangles of area $\epsilon$. The reason these models are called quasi-topological is that $Z$ depends on $g$, $n$ and $\epsilon$ but not on the details of the triangulation. They are also soluble in the sense that the computation of their partition functions can be reduced to a soluble one dimensional problem. We show that the continuum limit is well defined if the model approaches a topological field theory in the zero area limit, i.e., $\epsilon \to 0$ with finite $n$. We also show that the universality classes of such quasi-topological lattice field theories can be easily classified. Yang-Mills and generalized Yang-Mills theories appear as particular examples of such continuum limits.Comment: 23 pages, 16 figures, uses psbox.te

Optimal placement of excitations and sensors by simulated annealing

The optimal placement of discrete actuators and sensors is posed as a combinatorial optimization problem. Two examples for truss structures were used for illustration; the first dealt with the optimal placement of passive dampers along existing truss members, and the second dealt with the optimal placement of a combination of a set of actuators and a set of sensors. Except for the simplest problems, an exact solution by enumeration involves a very large number of function evaluations, and is therefore computationally intractable. By contrast, the simulated annealing heuristic involves far fewer evaluations and is best suited for the class of problems considered. As an optimization tool, the effectiveness of the algorithm is enhanced by introducing a number of rules that incorporate knowledge about the physical behavior of the problem. Some of the suggested rules are necessarily problem dependent

Electron paramagnetic resonance studies of slowly tumbling vanadyl spin probes in nematic liquid crystals

An analysis of EPR line shapes by the method of Polnaszek, Bruno, and Freed is made for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals. The use of typical vanadyl complexes as spin probes for nematic liquid crystals is shown to simplify the theoretical analysis and the subsequent interpretation. Rotational correlation times tau and orientational ordering parameters S sub Z where slow tumbling effects are expected to be observed in vanadyl EPR spectra are indicated in a plot. Analysis of the inertial effects on the probe reorientation, which are induced by slowly fluctuating torque components of the local solvent structure, yield quantitative values for tau and S sub Z. The weakly ordered probe VOAA is in the slow tumbling region and displays these inertial effects throughout the nematic range of BEPC and Phase V. VOAA exhibits different reorientation behavior near the isotropic-nematic transition temperature than that displayed far below this transition temperature

ESR studies of the slow tumbling of vanadyl spin probes in nematic liquid crystals

ESR line shapes that are appropriate for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals were calculated by the stochastic Liouville method. Because of the symmetry possessed by vanadyl, the analysis and interpretation of these line shapes was simplified considerably. Spectral line shapes agreed well with experimental spectra of VOAcAc in the nematic liquid crystal Phase V and BEPC. Deviations from Brownian rotational diffusion were noted. A slowly fluctuating torque analysis yielded good agreement with the experimental spectra

Prompt Electromagnetic Transients from Binary Black Hole Mergers

Binary black hole (BBH) mergers provide a prime source for current and future interferometric GW observatories. Massive BBH mergers may often take place in plasma-rich environments, leading to the exciting possibility of a concurrent electromagnetic (EM) signal observable by traditional astronomical facilities. However, many critical questions about the generation of such counterparts remain unanswered. We explore mechanisms that may drive EM counterparts with magnetohydrodynamic simulations treating a range of scenarios involving equal-mass black-hole binaries immersed in an initially homogeneous fluid with uniform, orbitally aligned magnetic fields. We find that the time development of Poynting luminosity, which may drive jet-like emissions, is relatively insensitive to aspects of the initial configuration. In particular, over a significant range of initial values, the central magnetic field strength is effectively regulated by the gas flow to yield a Poynting luminosity of $10^{45}-10^{46} \rho_{-13} M_8^2 \, {\rm erg}\,{\rm s}^{-1}$, with BBH mass scaled to $M_8 \equiv M/(10^8 M_{\odot})$ and ambient density $\rho_{-13} \equiv \rho/(10^{-13} \, {\rm g} \, {\rm cm}^{-3})$. We also calculate the direct plasma synchrotron emissions processed through geodesic ray-tracing. Despite lensing effects and dynamics, we find the observed synchrotron flux varies little leading up to merger.Comment: 22 pages, 21 figures; additional reference + clarifying text added to match published versio

On the definition of velocity in doubly special relativity theories

We discuss the definition of particle velocity in doubly relativity theories. The general formula relating velocity and four-momentum of particle is given.Comment: 7 page

Combined electrophysiological and biosensor approaches to study purinergic regulation of epileptiform activity in cortical tissue

Background: Cortical brain slices offer a readily accessible experimental model of a region of the brain commonly affected by epilepsy. The diversity of recording techniques, seizure-promoting protocols and mutant mouse models provides a rich diversity of avenues of investigation, which is facilitated by the regular arrangement of distinct neuronal populations and afferent fibre pathways, particularly in the hippocampus. New method and results: We have been interested in the regulation of seizure activity in hippocampal and neocortical slices by the purines, adenosine and ATP. Via the use of microelectrode biosensors we have been able to measure the release of these important neuroactive compounds simultaneously with on-going epileptiform activity, even of brief durations. In addition, detailed numerical analysis and computational modelling has produced new insights into the kinetics and spatial distribution of elevations in purine concentration that occur during seizure activity. Comparison and conclusions: Such an approach allows the spatio-temporal characteristics of neurotransmitter/neuromodulator release to be directly correlated with electrophysiological measures of synaptic and seizure activity, and can provide greater insight into the role of purines in epilepsy

Improved parameters of seven Kepler giant companions characterized with SOPHIE and HARPS-N

Radial-velocity observations of Kepler candidates obtained with the SOPHIE and HARPS-N spectrographs have permitted unveiling the nature of the five giant planets Kepler-41b, Kepler-43b, Kepler-44b, Kepler-74b, and Kepler-75b, the massive companion Kepler-39b, and the brown dwarf KOI-205b. These companions were previously characterized with long-cadence (LC) Kepler data. Here we aim at refining the parameters of these transiting systems by i) modelling the published radial velocities (RV) and Kepler short-cadence (SC) data that provide a much better sampling of the transits, ii) performing new spectral analyses of the SOPHIE and ESPaDOnS spectra, and iii) improving stellar rotation periods hence stellar age estimates through gyrochronology, when possible. Posterior distributions of the system parameters were derived with a differential evolution Markov chain Monte Carlo approach. Our main results are as follows: a) Kepler-41b is significantly larger and less dense than previously found because a lower orbital inclination is favoured by SC data. This also affects the determination of the geometric albedo that is lower than previously derived: Ag < 0.135; b) Kepler-44b is moderately smaller and denser than reported in the discovery paper; c) good agreement was achieved with published Kepler-43, Kepler-75, and KOI-205 system parameters, although the host stars Kepler-75 and KOI-205 were found to be slightly richer in metals and hotter, respectively; d) the previously reported non-zero eccentricities of Kepler-39b and Kepler-74b might be spurious. If their orbits were circular, the two companions would be smaller and denser than in the eccentric case. The radius of Kepler-39b is still larger than predicted by theoretical isochrones. Its parent star is hotter and richer in metals than previously determined. [ABRIDGED]Comment: 17 pages, 9 figures, accepted for publication in Astronomy and Astrophysic