The Fast Multipole Method and Point Dipole Moment Polarizable Force Fields

We present an implementation of the fast multipole method for computing coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected $O(N)$ scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation in molecular dynamics at the nanosecond scale by performing simulations of a protein complex embedded in a coarse-grained solvent using a standard integrator and a multiple time step integrator. Our tests show the applicability of FMM combined with state-of-the-art chemical models in molecular dynamical systems.Comment: 11 pages, 8 figures, accepted by J. Chem. Phy

A New Estimate of the Hubble Time with Improved Modeling of Gravitational Lenses

This paper examines free-form modeling of gravitational lenses using Bayesian ensembles of pixelated mass maps. The priors and algorithms from previous work are clarified and significant technical improvements are made. Lens reconstruction and Hubble Time recovery are tested using mock data from simple analytic models and recent galaxy-formation simulations. Finally, using published data, the Hubble Time is inferred through the simultaneous reconstruction of eleven time-delay lenses. The result is H_0^{-1}=13.7^{+1.8}_{-1.0} Gyr.Comment: 24 pages, 9 figures. Accepted to Ap

Alpha- and beta-adrenergic mediation of changes in metabolism and Na/K exchange in rat brown fat

Double- and triple-barreled ion-sensitive microelectrodes were used to measure changes in extracellular K+ and Na+ concentrations ([K+]o, [Na+]o) in brown fat. Redox states of different respiratory enzymes were measured simultaneously in order to correlate ion movements with metabolic activity. Trains of stimuli applied to the efferent nerves evoked two distinct increases in [K+]o. A first, small, rapid increase occurred within 10 s and accompanied a first, rapid membrane depolarization. A second, slow increase of [K+]o occurred several minutes after stimulation and accompanied a second, slow depolarization. A few seconds after stimulation onset, while the membrane was repolarizing and shifts in redox states indicated increases in lipolysis and respiration, [K+]o decreased. The [K+]o decrease was accompanied by an increase in [Na+]o, and could be partly blocked by ouabain. Phentolamine, an alpha-antagonist that blocks the first depolarization, also blocked the first, rapid [K+]o increase and part of the subsequent decrease. Propranolol, a beta-antagonist, had little effect on the first depolarization and the first increase in [K+]o, but blocked part of the subsequent [K+]o decrease and the second, slow [K+]o increase. The changes in [K+]o were almost completely abolished in the presence of both antagonists. It is concluded that brown adipocytes take up K+ and simultaneously lose Na+ in response to the interaction of noradrenaline with alpha- and beta-receptors, and this indicates a very early stimulation of the Na+ pump

Optical Polarization of 13^{13}C Nuclei in Diamond through Nitrogen-Vacancy Centers

We determine the polarization of the bulk $^{13}$C nuclear spin system in diamond produced by interaction with optically oriented nitrogen-vacancy (NV-) defect centers. $^{13}$C nuclei are polarized into the higher energy Zeeman state with a bulk-average polarization up to 5.2%, although local polarization may be higher. The kinetics of polarization are temperature independent, and occur within 5 minutes. Fluctuations in the dipolar field of the NV- center spin bath are identified as the mechanism by which nuclear spin transitions are induced near defect centers. Polarization is then transported to the bulk material via spin diffusion, which accounts for the observed kinetics of polarization. These results indicate control over the nuclear spin bath, a methodology to study dynamics of an NV- center ensemble, and application to sensitivity-enhanced NMR.Comment: 4 pages, 2 figure

Gravitational lens recovery with glass: measuring the mass profile and shape of a lens

We use a new non-parametric gravitational modelling tool - glass - to determine what quality of data (strong lensing, stellar kinematics, and/or stellar masses) are required to measure the circularly averaged mass profile of a lens and its shape. glass uses an underconstrained adaptive grid of mass pixels to model the lens, searching through thousands of models to marginalize over model uncertainties. Our key findings are as follows: (i) for pure lens data, multiple sources with wide redshift separation give the strongest constraints as this breaks the well-known mass-sheet or steepness degeneracy; (ii) a single quad with time delays also performs well, giving a good recovery of both the mass profile and its shape; (iii) stellar masses - for lenses where the stars dominate the central potential - can also break the steepness degeneracy, giving a recovery for doubles almost as good as having a quad with time-delay data, or multiple source redshifts; (iv) stellar kinematics provide a robust measure of the mass at the half-light radius of the stars r1/2 that can also break the steepness degeneracy if the Einstein radius rE ≠ r1/2; and (v) if rE∼r1/2, then stellar kinematic data can be used to probe the stellar velocity anisotropy β - an interesting quantity in its own right. Where information on the mass distribution from lensing and/or other probes becomes redundant, this opens up the possibility of using strong lensing to constrain cosmological model

Weak Microlensing

A nearby star having a near-transit of a galaxy will cause a time-dependent weak lensing of the galaxy. Because the effect is small, we refer to this as weak microlensing. This could provide a useful method to weigh low-mass stars and brown dwarfs. We examine the feasibility of measuring masses in this way and we find that a star causes measurable weak microlensing in a galaxy even at 10 Einstein radii away. Of order one magnitude I < 25 galaxy comes close enough to one or other of the ~100 nearest stars per year.Comment: Accepted for publication in MNRAS (4 pages, 5 figures, 1 table

Light versus dark in strong-lens galaxies: Dark matter haloes that are rounder than their stars

We measure the projected density profile, shape and alignment of the stellar and dark matter mass distribution in 11 strong-lens galaxies. We find that the projected dark matter density profile - under the assumption of a Chabrier stellar initial mass function - shows significant variation from galaxy to galaxy. Those with an outermost image beyond $\sim 10$ kpc are very well fit by a projected NFW profile; those with images within 10 kpc appear to be more concentrated than NFW, as expected if their dark haloes contract due to baryonic cooling. We find that over several half-light radii, the dark matter haloes of these lenses are rounder than their stellar mass distributions. While the haloes are never more elliptical than $e_{dm} = 0.2$, their stars can extend to $e_* > 0.2$. Galaxies with high dark matter ellipticity and weak external shear show strong alignment between light and dark; those with strong shear ($\gamma \gtrsim 0.1$) can be highly misaligned. This is reassuring since isolated misaligned galaxies are expected to be unstable. Our results provide a new constraint on galaxy formation models. For a given cosmology, these must explain the origin of both very round dark matter haloes and misaligned strong-lens systems.Comment: 16 pages, 7 figures, 4 tables. Accepted for publication by MNRA

A Sampling Strategy for High-Dimensional Spaces Applied to Free-Form Gravitational Lensing

We present a novel proposal strategy for the Metropolis-Hastings algorithm designed to efficiently sample general convex polytopes in 100 or more dimensions. This improves upon previous sampling strategies used for free-form reconstruction of gravitational lenses, but is general enough to be applied to other fields. We have written a parallel implementation within the lens modeling framework GLASS. Testing shows that we are able to produce uniform uncorrelated random samples which are necessary for exploring the degeneracies inherent in lens reconstruction.Comment: 10 pages, 9 figures. Accepted for publication in MNRA

Algorithms for bounding Folkman numbers

For an undirected, simple graph G, we write G -\u3e (a_1,...,a_k)^v (G -\u3e (a_1,...,a_k)^e) if for every vertex (edge) k-coloring, a monochromatic K_(a_i) is forced in some color i in {1,...,k}. The vertex (edge) Folkman number is defined as F_v(a_1,...,a_k;p) = min{|V(G)| : G -\u3e (a_1,...,a_k;p)^v, K_p not in G} F_e(a_1,...,a_k;p) = min{|V(G)| : G -\u3e (a_1,...,a_k;p)^e, K_p not in G} for p \u3e max{a_1,...,a_k}. Folkman showed in 1970 that these numbers always exist for valid values of p. This thesis concerns the computation of a new result in Folkman number theory, namely that F_v(2,2,3;4)=14. Previously, the bounds stood at 10 \u3c= F_v(2,2,3;4) \u3c= 14, proven by Nenov in 2000. To achieve this new result, specialized algorithms were executed on the computers of the Computer Science network in a distributed processing effort. We discuss the mathematics and algorithms used in the computation. We also discuss ongoing research into the computation of the value of F_e(3,3;4). The current bounds stand at 16 \u3c= F_e(3,3;4) \u3c= 3e10^9. This number was once the subject of an Erd s prize---claimed by Spencer in 1988