Lifting classes for the fixed point theory of nn-valued maps

The theory of lifting classes and the Reidemeister number of single-valued maps of a finite polyhedron $X$ is extended to $n$-valued maps by replacing liftings to universal covering spaces by liftings with codomain an orbit configuration space, a structure recently introduced by Xicot\'encatl. The liftings of an $n$-valued map $f$ split into self-maps of the universal covering space of $X$ that we call lift-factors. An equivalence relation is defined on the lift-factors of $f$ and the number of equivalence classes is the Reidemeister number of $f$. The fixed point classes of $f$ are the projections of the fixed point sets of the lift-factors and are the same as those of Schirmer. An equivalence relation is defined on the fundamental group of $X$ such that the number of equivalence classes equals the Reidemeister number. We prove that if $X$ is a manifold of dimension at least three, then algebraically the orbit configuration space approach is the same as one utilizing the universal covering space. The Jiang subgroup is extended to $n$-valued maps as a subgroup of the group of covering transformations of the orbit configuration space and used to find conditions under which the Nielsen number of an $n$-valued map equals its Reidemeister number. If an $n$-valued map splits into $n$ single-valued maps, then its $n$-valued Reidemeister number is the sum of their Reidemeister numbers.Comment: near complete rewrite from previous versio

3-D SPH simulations of colliding winds in eta Carinae

We study colliding winds in the superluminous binary eta Carinae by performing three-dimensional, Smoothed Particle Hydrodynamics (SPH) simulations. For simplicity, we assume both winds to be isothermal. We also assume that wind particles coast without any net external forces. We find that the lower density, faster wind from the secondary carves out a spiral cavity in the higher density, slower wind from the primary. Because of the phase-dependent orbital motion, the cavity is very thin on the periastron side, whereas it occupies a large volume on the apastron side. The model X-ray light curve using the simulated density structure fits very well with the observed light curve for a viewing angle of i=54 degrees and phi=36 degrees, where i is the inclination angle and phi is the azimuth from apastron.Comment: 6 pages, 3 figures, To be published in Proceedings of IAU Symposium 250: Massive Stars as Cosmic Engines, held in Kauai, Hawaii, USA, Dec 2007, edited by F. Bresolin, P.A. Crowther & J. Puls (Cambridge University Press

Phonons in potassium doped graphene: the effects of electron-phonon interactions, dimensionality and ad-atom ordering

Graphene phonons are measured as a function of electron doping via the addition of potassium adatoms. In the low doping regime, the in-plane carbon G-peak hardens and narrows with increasing doping, analogous to the trend seen in graphene doped via the field-effect. At high dopings, beyond those accessible by the field-effect, the G-peak strongly softens and broadens. This is interpreted as a dynamic, non-adiabatic renormalization of the phonon self-energy. At dopings between the light and heavily doped regimes, we find a robust inhomogeneous phase where the potassium coverage is segregated into regions of high and low density. The phonon energies, linewidths and tunability are remarkably similar for 1-4 layer graphene, but significantly different to doped bulk graphite.Comment: Accepted in Phys. Rev. B as a Rapid Communication. 5 pages, 3 figures, revised text with additional dat

Unbiased and Consistent Nested Sampling via Sequential Monte Carlo

We introduce a new class of sequential Monte Carlo methods called Nested Sampling via Sequential Monte Carlo (NS-SMC), which reframes the Nested Sampling method of Skilling (2006) in terms of sequential Monte Carlo techniques. This new framework allows convergence results to be obtained in the setting when Markov chain Monte Carlo (MCMC) is used to produce new samples. An additional benefit is that marginal likelihood estimates are unbiased. In contrast to NS, the analysis of NS-SMC does not require the (unrealistic) assumption that the simulated samples be independent. As the original NS algorithm is a special case of NS-SMC, this provides insights as to why NS seems to produce accurate estimates despite a typical violation of its assumptions. For applications of NS-SMC, we give advice on tuning MCMC kernels in an automated manner via a preliminary pilot run, and present a new method for appropriately choosing the number of MCMC repeats at each iteration. Finally, a numerical study is conducted where the performance of NS-SMC and temperature-annealed SMC is compared on several challenging and realistic problems. MATLAB code for our experiments is made available at https://github.com/LeahPrice/SMC-NS .Comment: 45 pages, some minor typographical errors fixed since last versio

The ATPase cycle of PcrA helicase and its coupling to translocation on DNA.

The superfamily 1 bacterial helicase PcrA has a role in the replication of certain plasmids, acting with the initiator protein (RepD) that binds to and nicks the double-stranded origin of replication. PcrA also translocates single-stranded DNA with discrete steps of one base per ATP hydrolyzed. Individual rate constants have been determined for the DNA helicase PcrA ATPase cycle when bound to either single-stranded DNA or a double-stranded DNA junction that also has RepD bound. The fluorescent ATP analogue 2'(3')-O-(N-methylanthraniloyl)ATP was used throughout all experiments to provide a complete ATPase cycle for a single nucleotide species. Fluorescence intensity and anisotropy stopped-flow measurements were used to determine rate constants for binding and release. Quenched-flow measurements provided the kinetics of the hydrolytic cleavage step. The fluorescent phosphate sensor MDCC-PBP was used to measure phosphate release kinetics. The chemical cleavage step is the rate-limiting step in the cycle and is essentially irreversible and would result in the bound ATP complex being a major component at steady state. This cleavage step is greatly accelerated by bound DNA, producing the high activation of this protein compared to the protein alone. The data suggest the possibility that ADP is released in two steps, which would result in bound ADP also being a major intermediate, with bound ADP.P(i) being a very small component. It therefore seems likely that the major transition in structure occurs during the cleavage step, rather than P(i) release. ATP rebinding could then cause reversal of this structural transition. The kinetic mechanism of the PcrA ATPase cycle is very little changed by potential binding to RepD, supporting the idea that RepD increases the processivity of PcrA by increasing affinity to DNA rather than affecting the enzymatic properties per se

X-ray Modeling of \eta\ Carinae and WR140 from SPH Simulations

The colliding wind binary (CWB) systems \eta\ Carinae and WR140 provide unique laboratories for X-ray astrophysics. Their wind-wind collisions produce hard X-rays that have been monitored extensively by several X-ray telescopes, including RXTE. To interpret these RXTE X-ray light curves, we model the wind-wind collision using 3D smoothed particle hydrodynamics (SPH) simulations. Adiabatic simulations that account for the absorption of X-rays from an assumed point source at the apex of the wind-collision shock cone by the distorted winds can closely match the observed 2-10keV RXTE light curves of both \eta\ Car and WR140. This point-source model can also explain the early recovery of \eta\ Car's X-ray light curve from the 2009.0 minimum by a factor of 2-4 reduction in the mass loss rate of \eta\ Car. Our more recent models relax the point-source approximation and account for the spatially extended emission along the wind-wind interaction shock front. For WR140, the computed X-ray light curve again matches the RXTE observations quite well. But for \eta\ Car, a hot, post-periastron bubble leads to an emission level that does not match the extended X-ray minimum observed by RXTE. Initial results from incorporating radiative cooling and radiatively-driven wind acceleration via a new anti-gravity approach into the SPH code are also discussed.Comment: 5 pages, 3 figures, Proceedings of the 39th Li\'ege Astrophysical Colloquium, held in Li\`ege 12-16 July 2010, edited by G. Rauw, M. De Becker, Y. Naz\'e, J.-M. Vreux, P. William

The Hydrodynamics of M-Theory

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets [hep-th/0205051]. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.Comment: 1+19 pages, references added, section 5 clarified, eq. (72) correcte