arXiv subjects

Mark Wilkinson

Publications and source records attributed to Mark Wilkinson.

28 records · Page 2Linked to original sources

arXiv2016

On the Convergence of Soft Potential Dynamics to Hard Sphere Dynamics

We address a question raised in the work of Gallagher, Saint-Raymond and Texier (From Newton to Boltzmann: Hard Spheres and Short-range Potentials, Zürich Lectures in Advanced Mathematics, EMS, 2013) that concerns the convergence of soft-potential dynamics to hard sphere dynamics. In the case of two particles, we establish that hard sphere dynamics is the limit of soft sphere dynamics in the weak-star topology of BV. We view our result as establishing a topological method by which to construct weak solutions to the ODE of hard sphere motion.

math-ph↗

arXiv2015

Non-existence of Physical Classical Solutions to Euler's Equations of Rigid Body Dynamics

We prove that one cannot construct, for arbitrary initial data, global-in-time physical classical solutions to Euler's equations of continuum rigid body mechanics when the constituent rigid bodies are not perfect spheres. By 'physical' solutions, we mean those that conserve the total linear momentum, angular momentum and kinetic energy of any given initial datum. The reason for absence of classical solutions is due to the non-existence of velocity scattering maps which resolve a collision between two non-spherical rigid bodies in such a way that (i) they do not interpenetrate, and (ii) total linear momentum, angular momentum and kinetic energy of the bodies are conserved through collision. In particular, this implies that when solving Euler's equations, it is necessary to deal with rigid body trajectories which experience infinitely-many collisions in a finite time interval.

math-ph↗

arXiv2015

On Collision Invariants for Linear Scattering

In this article, we extend the result of Boltzmann on characterisation of collision invariants from the case of hard disks to a class of two-dimensional compact, strictly-convex particles.

math-ph↗

arXiv2013

Dynamic Statistical Scaling in the Landau-de Gennes Theory of Nematic Liquid Crystals

We investigate the asymptotic behaviour of a correlation function associated with a nematic liquid crystal system undergoing an isotropic-nematic phase transition following an instantaneous change of temperature. Within the setting of Landau-de Gennes theory, we confirm a hypothesis in the condensed matter physics literature on the average self-similar behaviour of the correlation function in the asymptotic regime at time infinity. In the final sections, we comment on other possible scaling behaviour of the correlation function.

math.AP↗

arXiv2013

AGN outflows trigger starbursts in gas-rich galaxies

Recent well resolved numerical simulations of AGN feedback have shown that its effects on the host galaxy may be not only negative but also positive. In the late gas poor phase, AGN feedback blows the gas away and terminates star formation. However, in the gas-rich phase(s), AGN outflows trigger star formation by over-compressing cold dense gas and thus provide positive feedback on their hosts. In this paper we study this AGN-triggered starburst effect. We show that star formation rate in the burst increases until the star formation feedback counteracts locally the AGN outflow compression. Globally, this predicts a strong nearly linear statistical correlation between the AGN and starburst bolometric luminosities in disc galaxies, L_* \propto L_{AGN}^{5/6}. The correlation is statistical only because AGN activity may fluctuate on short time scales (as short as tens of years), and because AGN may turn off but its effects on the host may continue to last until the AGN-driven outflow leaves the host, which may be up to 10 times longer than the duration of the AGN activity. The coefficient in front of this relation depends on the clumpiness and morphology of the cold gas in the galaxy. A "maximum starburst" takes place in am azimuthally uniform gas disc, for which we derive an upper limit of L_* \sim 50 times larger than L_{AGN} for typical quasars. For more clumpy and/or compact cold gas distributions, the starburst luminosity decreases. We also suggest that similar AGN-triggerred starbursts are possible in hosts of all geometries, including during galaxy mergers, provided the AGN is activated. Finally, we note that due to the short duration of the AGN activity phase the accelerating influence of AGN on starbursts may be much more common than observations of simultaneous AGN and starbursts would suggest.

astro-ph.GA↗

arXiv2012

Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential

We study the existence, regularity and so-called `strict physicality' of weak solutions of a coupled Navier-Stokes Q-tensor system which is proposed as a model for the incompressible flow of nematic liquid crystal materials. An important contribution to the dynamics comes from a singular potential introduced by John Ball and Apala Majumdar (Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory, Mol. Cryst. Liq. Cryst., Vol. 525: pp. 1-11, 2010) which replaces the commonly employed Landau-de Gennes bulk potential. This is built into our model to ensure that a natural physical constraint on the eigenvalues of the Q-tensor order parameter is respected by the dynamics of the system.

math.AP↗

arXiv2011

Weakening dark-matter cusps by clumpy baryonic infall

We consider the infall of a massive clump into a dark-matter halo as a simple and extreme model for the effect of baryonic physics (neglected in gravity-only simulations of large-scale structure formation) on the dark-matter. We find that such an infalling clump is extremely efficient in altering the structure of the halo and reducing its central density: a clump of 1% the mass of the halo can remove about twice its own mass from the inner halo and transform a cusp into a core or weaker cusp. If the clump is subsequently removed, mimicking a galactic wind, the central halo density is further reduced and the mass removed from the inner halo doubled. Lighter clumps are even more efficient: the ratio of removed mass to clump mass increases slightly towards smaller clump masses. This process is the more efficient the more radially anisotropic the initial dark-matter velocities. While such a clumpy infall may be somewhat unrealistic, it demonstrates that the baryons need to transfer only a small fraction of their initial energy to the dark matter via dynamical friction to explain the discrepancy between predicted dark-matter density profiles and those inferred from observations of dark-matter dominated galaxies.

astro-ph.CO↗

arXiv2010

SPARQL Assist Language-Neutral Query Composer

SPARQL query composition is difficult for the lay-person or even the experienced bioinformatician in cases where the data model is unfamiliar. Established best-practices and internationalization concerns dictate that semantic web ontologies should use terms with opaque identifiers, further complicating the task. We present SPARQL Assist: a web application that addresses these issues by providing context-sensitive type-ahead completion to existing web forms. Ontological terms are suggested using their labels and descriptions, leveraging existing XML support for internationalization and language-neutrality.

cs.IR↗

arXiv2008

What is a galaxy? How Cold is Cold Dark Matter? Recent progress in Near Field Cosmology

There has been a vast recent improvement in photometric and kinematic data for star clusters, Ultra Compact dwarfs, galactic nuclei, and local dSph galaxies, with Subaru contributing substantially to the photometric studies in particular. These data show that there is a bimodal distribution in half-light radii, with stable star clusters always being smaller than 35pc, while stable galaxies are always larger than 120pc. We extend the previously known observational relationships and interpret them in terms of a more fundamental pair of intrinsic properties of dark matter itself: dark matter forms cored mass distributions, with a core scale length of greater than about 100pc, and always has a maximum central mass density with a narrow range. The dark matter in dSph galaxies appears to be clustered such that there is a mean volume mass density within the stellar distribution which has the very low value of about 0.1$M_{\odot}$ pc$^{-3}$. None of the dSphs displays kinematics which require the presence of an inner cusp, while in two dSphs there is evidence that the density profile is shallow (cored) in the inner regions. The maximum central dark matter density derived is model dependent, but is likely to have a mean value (averaged over a volume of radius 10pc) of about 0.1$M_{\odot}$ pc$^{-3}$, which is 5GeV/c$^2$cm$^{-3}$). Galaxies are embedded in dark matter halos with these properties; smaller systems containing dark matter are not observed.

astro-ph↗

arXiv1997

Lens Models with Density Cusps

Lens models appropriate for representing cusped galaxies and clusters are developed. The analogue of the odd number theorem for cusped density distributions is given. Density cusps are classified into strong, isothermal or weak, according to their lensing properties. Strong cusps cause multiple imaging for any source position, whereas isothermal and weak cusps give rise to only one image for distant sources. Isothermal cusps always possess a pseudo-caustic. When the source crosses the pseudo-caustic, the number of images changes by unity.Two families of cusped galaxy and cluster models are examined in detail. The double power-law family has an inner cusp, followed by a transition region and an outer envelope. One member of this family -- the isothermal double power-law model -- possesses an exceedingly scarce property, namely, the lens equation is exactly solvable for any source position. This means that the magnifications, the time delay and the lensing cross-sections are all readily available. The model has a three dimensional density that is cusped like $r^{-2}$ at small radii and falls off like $r^{-4}$ asymptotically. Thus, it provides a very useful representation of the lensing properties of a galaxy or cluster of finite total mass with a flat rotation curve. The second set of models studied is the single power-law family. These are single density cusps of infinite extent. The properties of the critical curves and caustics and the behaviour of the lenses in the presence of external shear are all discussed in some detail.

astro-ph↗