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

An Optimizing Symbolic Algebra Approach for Generating Fast Multipole Method Operators

We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can generate computer code for any expansion order in multiple languages. The procedure is implemented in the publicly available Python program Mosaic. Optimizations performed at the symbolic level through algebraic manipulations significantly reduce the number of mathematical operations compared with a straightforward implementation of the equations. We find that the optimizer is able to eliminate 20-80% of the floating-point operations and for the expansion orders $p \le 10$ it changes the observed scaling properties. We present our approach using three variants of the operators with the Cartesian basis set for the harmonic potential kernel $1/r$, including the use of totally symmetric and traceless multipole tensors.Comment: Updated to final version submitted to Computer Physics Communications. Accepted on 20 November 201

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

Lessons from a blind study of simulated lenses: image reconstructions do not always reproduce true convergence

In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind tests of lens reconstruction with simulated data are needed for validation. In this paper we present a systematic blind study of a sample of 15 simulated strong gravitational lenses from the EAGLE suite of hydrodynamic simulations. We model these lenses with a free-form technique and evaluate reconstructed mass distributions using criteria based on shape, orientation, and lensed image reconstruction. Especially useful is a lensing analogue of the Roche potential in binary star systems, which we call the $\textit{lensing Roche potential}$. This we introduce in order to factor out the well-known problem of steepness or mass-sheet degeneracy. Einstein radii are on average well recovered with a relative error of ${\sim}5\%$ for quads and ${\sim}25\%$ for doubles; the position angle of ellipticity is on average also reproduced well up to $\pm10^{\circ}$, but the reconstructed mass maps tend to be too round and too shallow. It is also easy to reproduce the lensed images, but optimising on this criterion does not guarantee better reconstruction of the mass distribution.Comment: 20 pages, 12 figures. Published in MNRAS. Agrees with published versio

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

The SATIN project I: Turbulent multi-phase ISM in Milky Way simulations with SNe feedback from stellar clusters

We introduce the star formation and Supernova (SN) feedback model of the SATIN (Simulating AGNs Through ISM with Non-Equilibrium Effects) project to simulate the evolution of the star forming multi-phase interstellar medium (ISM) of entire disk galaxies. This galaxy-wide implementation of a successful ISM feedback model naturally covers an order of magnitude in gas surface density, shear and radial motions. It is implemented in the adaptive mesh refinement code RAMSES at a peak resolution of 9 pc. New stars are represented by star cluster (sink) particles with individual SN delay times for massive stars. With SN feedback, cooling and gravity, the galactic ISM develops a realistic three-phase structure. The star formation rates naturally follow observed scaling relations for the local Milky Way gas surface density. SNe drive additional turbulence in the warm (300 K < $T$ < 10$^4$ K) gas and increase the kinetic energy of the cold gas, cooling out of the warm phase. The majority of the gas leaving the galactic ISM is warm and hot with mass loading factors of $3 \le \eta \le 10$. While the hot gas is leaving the system, the warm and cold gas falls back onto the disc in a galactic fountain flow.Comment: Submitted to MNRA