arXiv subjects

M. Wilkinson

Publications and source records attributed to M. Wilkinson.

At least 19 recordsLinked to original sources

arXiv2020

Breaking Beta: A comparison of mass modelling methods for spherical systems

We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, using either line-of-sight velocity data only, or adding proper motion data. All methods perform well on isotropic and tangentially anisotropic mock data, recovering the density and velocity anisotropy within their 95% confidence intervals over the radial range 0.25 < R/Rhalf < 4, where Rhalf is the half light radius. However, radially-anisotropic mocks are more challenging. For line-of-sight data alone, only methods that use information about the shape of the velocity distribution function are able to break the degeneracy between the density profile and the velocity anisotropy to obtain an unbiased estimate of both. This shape information can be obtained through directly fitting a global phase space distribution function, by using higher order 'Virial Shape Parameters', or by assuming a Gaussian velocity distribution function locally, but projecting it self-consistently along the line of sight. Including proper motion data yields further improvements, and in this case, all methods give a good recovery of both the radial density and velocity anisotropy profiles.

astro-ph.GA↗

arXiv2019

A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using an example.

cond-mat.stat-mech↗

arXiv2019

Transferability of Operational Status Classification Models Among Different Wind Turbine Typesq

A detailed understanding of wind turbine performance status classification can improve operations and maintenance in the wind energy industry. Due to different engineering properties of wind turbines, the standard supervised learning models used for classification do not generalize across data sets obtained from different wind sites. We propose two methods to deal with the transferability of the trained models: first, data normalization in the form of power curve alignment, and second, a robust method based on convolutional neural networks and feature-space extension. We demonstrate the success of our methods on real-world data sets with industrial applications.

stat.ML↗

arXiv2018

Gaia Radial Velocity Spectrometer

This paper presents the specification, design, and development of the Radial Velocity Spectrometer (RVS) on the European Space Agency's Gaia mission. Starting with the rationale for the full six dimensions of phase space in the dynamical modelling of the Galaxy, the scientific goals and derived top-level instrument requirements are discussed, leading to a brief description of the initial concepts for the instrument. The main part of the paper is a description of the flight RVS, considering the optical design, the focal plane, the detection and acquisition chain, and the as-built performance drivers and critical technical areas. After presenting the pre-launch performance predictions, the paper concludes with the post-launch developments and mitigation strategies, together with a summary of the in-flight performance at the end of commissioning.

astro-ph.IM↗

arXiv2015

Prospects for Indirect Dark Matter Searches with the Cherenkov Telescope Array (CTA)

The Cherenkov Telescope Array (CTA) will have a unique chance of discovery for a large range of masses in Weakly Interacting Massive Particles models of dark matter. The principal target for dark matter searches with CTA is the centre of the Galactic Halo. The best strategy is to perform CTA observations within a few degrees of the Galactic Centre, with the Galactic Centre itself and the most intense diffuse emission regions removed from the analysis. Assuming a cuspy dark matter density profile for the Milky Way, 500 hours of observations in this region provide sensitivities to and below the thermal cross-section of dark matter annihilations, for masses between a few hundred GeV and a few tens of TeV; therefore CTA will have a significant chance of discovery in some models. Since the dark matter density in the Milky Way is far from certain in the inner kpc region, other targets are also proposed for observation, like ultra-faint dwarf galaxies such as Segue 1 with 100 hours per year proposed. Beyond these two observational targets, further alternatives, such as Galactic dark clumps, will be considered closer to the actual date of CTA operations. Sensitivity predictions for dark matter searches are given on the various targets taking into account the latest instrument response functions expected for CTA together with a discussion on the systematic uncertainties from the backgrounds.

astro-ph.HE↗

arXiv2012

A model for alignment between microscopic rods and vorticity

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the product of the strain relaxation time $τ_{\rm s}$ and the angular velocity $ω$ about the vorticity axis. We find that when $ωτ_{\rm s}\gg 1$, the rods are predominantly either perpendicular or parallel to the vorticity.

physics.flu-dyn↗

arXiv2012

Anisotropic covering of fractal sets

We consider the optimal covering of fractal sets in a two-dimensional space using ellipses which become increasingly anisotropic as their size is reduced. If the semi-minor axis is εand the semi-major axis is δ, we set δ=ε^α, where 0<α<1 is an exponent characterising the anisotropy of the covers. For point set fractals, in most cases we find that the number of points N which can be covered by an ellipse centred on any given point has expectation value < N > ~ ε^β, where βis a generalised dimension. We investigate the function β(α) numerically for various sets, showing that it may be different for sets which have the same fractal dimension.

nlin.PS↗

arXiv2011

Accurate Stellar Kinematics at Faint Magnitudes: application to the Bootes~I dwarf spheroidal galaxy

We develop, implement and characterise an enhanced data reduction approach which delivers precise, accurate, radial velocities from moderate resolution spectroscopy with the fibre-fed VLT/FLAMES+GIRAFFE facility. This facility, with appropriate care, delivers radial velocities adequate to resolve the intrinsic velocity dispersions of the very faint dSph dwarf galaxies. Importantly, repeated measurements let us reliably calibrate our individual velocity errors ($0.2 \leq δ_V\leq 5$ km s$^{-1}$) and directly detect stars with variable radial velocities. We show, by application to the Bootes-1 dwarf spheroidal, that the intrinsic velocity dispersion of this system is significantly below 6.5\,km/s reported by previous studies. Our data favor a two-population model of Bootes-1, consisting of a majority `cold' stellar component, with velocity dispersion $2.4^{+0.9}_{-0.5}$\,km/s, and a minority `hot' stellar component, with velocity dispersion $\sim 9$\,km/s, although we can not completely rule out a single component distribution with velocity dispersion $4.6^{0.8}_{-0.6}$\,km/s. We speculate this complex velocity distribution actually reflects the distribution of velocity anisotropy in Bootes-1, which is a measure of its formation processes.

astro-ph.GA↗

arXiv2010

Clustering of exponentially separating trajectories

It might be expected that trajectories for a dynamical system which has no negative Lyapunov exponent (implying exponential growth of small separations will not cluster together. However, clustering can occur such that the density $ρ(Δx)$ of trajectories within distance $Δx$ of a reference trajectory has a power-law divergence, so that $ρ(Δx)\sim Δx^{-β}$ when $Δx$ is sufficiently small, for some $0<β<1$. We demonstrate this effect using a random map in one dimension. We find no evidence for this effect in the chaotic logistic map, and argue that the effect is harder to observe in deterministic maps.

nlin.CD↗

arXiv2009

Multiple regimes of diffusion

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases which are considered, some of which have been discussed in earlier work. Here we explore the full space of dimensionless parameters, and introduce an "asymptotic phase diagram" which delineates the limiting regimes.

nlin.CD↗

arXiv2008

Shock fragmentation model for gravitational collapse

A cloud of gas collapsing under gravity will fragment. We present a new theory for this process, in which layers shocked gas fragment due to their gravitational instability. Our model explains why angular momentum does not inhibit the collapse process. The theory predicts that the fragmentation process produces objects which are significantly smaller than most stars, implying that accretion onto the fragments plays an essential role in determining the initial masses of stars. This prediction is also consistent with the hypothesis that planets can be produced by gravitational collapse.

astro-ph↗

arXiv2008

Variable-range Projection Model for Turbulence-driven Collisions

We discuss the probability distribution of relative speed $ΔV$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution $P(ΔV) \sim \exp(-C |ΔV|^{4/3})$ (for some constant $C$). Our conclusions are supported by numerical simulations and the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesised mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.

physics.flu-dyn↗

arXiv2008

Collisions of particles advected in random flows

We consider collisions of particles advected in a fluid. As already pointed out by Smoluchowski [Z. f. physik. Chemie XCII, 129-168, (1917)], macroscopic motion of the fluid can significantly enhance the frequency of collisions between the suspended particles. This effect was invoked by Saffman and Turner [J. Fluid Mech. 1, 16-30, (1956)] to estimate collision rates of small water droplets in turbulent rain clouds, the macroscopic motion being caused by turbulence. Here we show that the Saffman-Turner theory is unsatisfactory because it describes an initial transient only. The reason for this failure is that the local flow in the vicinity of a particle is treated as if it were a steady hyperbolic flow, whereas in reality it must fluctuate. We derive exact expressions for the steady-state collision rate for particles suspended in rapidly fluctuating random flows and compute how this steady state is approached. For incompressible flows, the Saffman-Turner expression is an upper bound.

nlin.CD↗

arXiv2007

Stokes trapping and planet formation

It is believed that planets are formed by aggregation of dust particles suspended in the turbulent gas forming accretion disks around developing stars. We describe a mechanism, termed 'Stokes trapping', by which turbulence limits the growth of aggregates of dust particles, so that their Stokes number (defined as the ratio of the damping time of the particles to the Kolmogorov dissipation timescale) remains close to unity. We discuss possible mechanisms for avoiding this barrier to further growth. None of these is found to be satisfactory and we introduce a new theory which does not involve the growth of small clusters of dust grains.

astro-ph↗

arXiv2007

Stick-Breaking Model for Variable-Range Hopping

We consider the optimal conduction path of the one-dimensional variable-range hopping problem. We describe a hierarchical procedure for constructing the path which is in excellent agreement with numerical results obtained from a percolation approach. The advantage of the hierarchical construction is that it is easier to analyse. We show that the distribution of hopping lengths is well approximated by a model for the repeated breaking of a stick at its weakest point, until the fragments are too strong to be broken.

cond-mat.dis-nn↗

arXiv2007

Precise asymptotics for a variable-range hopping model

For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping model proposed by S. Alexander [Phys. Rev. B 26, 2956 (1982)].

cond-mat.dis-nn↗

arXiv2007

Advective collisions

Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1, 16-30, (1956)]. We show that in complex or random flows the Saffman-Turner theory for the collision rate describes only an initial transient (which we evaluate exactly). We obtain precise expressions for the steady-state collision rate for flows with small Kubo number, including the influence of fractal clustering on the collision rate for compressible flows. For incompressible turbulent flows, where the Kubo number is of order unity, the Saffman-Turner theory is an upper bound.

nlin.CD↗

arXiv2006

Unmixing in Random Flows

We consider particles suspended in a randomly stirred or turbulent fluid. When effects of the inertia of the particles are significant, an initially uniform scatter of particles can cluster together. We analyse this 'unmixing' effect by calculating the Lyapunov exponents for dense particles suspended in such a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time of the random flow (that is, the regime of large Stokes number). In this limit Lyapunov exponents are obtained as a power series in a parameter which is a dimensionless measure of the inertia. We report results for the first seven orders. The perturbation series is divergent, but we obtain accurate results from a Pade-Borel summation. We deduce that particles can cluster onto a fractal set and show that its dimension is in satisfactory agreement with previously reported in simulations of turbulent Navier-Stokes flows. We also investigate the rate of formation of caustics in the particle flow.

nlin.CD↗