Phasefield theory for fractional diffusion-reaction equations and applications

This paper is concerned with diffusion-reaction equations where the classical diffusion term, such as the Laplacian operator, is replaced with a singular integral term, such as the fractional Laplacian operator. As far as the reaction term is concerned, we consider bistable non-linearities. After properly rescaling (in time and space) these integro-differential evolution equations, we show that the limits of their solutions as the scaling parameter goes to zero exhibit interfaces moving by anisotropic mean curvature. The singularity and the unbounded support of the potential at stake are both the novelty and the challenging difficulty of this work.Comment: 41 page

Chromospheric explosions

Three issues relative to chromospheric explosions were debated. (1) Resolved: The blue-shifted components of x-ray spectral lines are signatures of chromospheric evaporation. It was concluded that the plasma rising with the corona is indeed the primary source of thermal plasma observed in the corona during flares. (2) Resolved: The excess line broading of UV and X-ray lines is accounted for by a convective velocity distribution in evaporation. It is concluded that the hypothesis that convective evaporation produces the observed X-ray line widths in flares is no more than a hypothesis. It is not supported by any self-consistent physical theory. (3) Resolved: Most chromospheric heating is driven by electron beams. Although it is possible to cast doubt on many lines of evidence for electron beams in the chromosphere, a balanced view that debaters on both sides of the question might agree to is that electron beams probably heat the low corona and upper chromosphere, but their direct impact on evaporating the chromosphere is energetically unimportant when compared to conduction. This represents a major departure from the thick-target flare models that were popular before the Workshop

Power sums and Homfly skein theory

The Murphy operators in the Hecke algebra H_n of type A are explicit commuting elements, whose symmetric functions are central in H_n. In [Skein theory and the Murphy operators, J. Knot Theory Ramif. 11 (2002), 475-492] I defined geometrically a homomorphism from the Homfly skein C of the annulus to the centre of each algebra H_n, and found an element P_m in C, independent of n, whose image, up to an explicit linear combination with the identity of H_n, is the m-th power sum of the Murphy operators. The aim of this paper is to give simple geometric representatives for the elements P_m, and to discuss their role in a similar construction for central elements of an extended family of algebras H_{n,p}.Comment: Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper15.abs.htm

Do you want to bet? The prevalence of problem gambling amongst athletes in the UK

This presentation was given as part of the 2011 London Workshop on Problem Gambling: Theory and (Best) Practice by Dr Daniel Rhind from the Sports Sciences subject area at Brunel University. The workshop was organised by Professor Fernand Gobet and Dr Marvin Schiller and hosted by Brunel University on the 13th September 2011

Manifestly supersymmetric M-theory

In this paper, the low-energy effective dynamics of M-theory, eleven-dimensional supergravity, is taken off-shell in a manifestly supersymmetric formulation. We show that a previously proposed relaxation of the superspace torsion constraints does indeed accommodate a current supermultiplet which lifts the equations of motion corresponding to the ordinary second order derivative supergravity lagrangian. Whether the auxiliary fields obtained this way can be used to construct an off-shell lagrangian is not yet known. We comment on the relation and application of this completely general formalism to higher-derivative (R^4) corrections. Some details of the calculation are saved for a later publication.Comment: 13 pages, plain tex. v2: minor changes, one ref. adde

Sedimentation stacking diagrams of binary mixtures of thick and thin hard rods

We use Onsager theory and the local density approximation to study sedimentation-diffusion equilibrium density profiles of binary mixtures of thick and thin hard rods. We construct stacking diagrams for three diameter ratios, and find that even a simple spindle-shaped phase diagram with only isotropic-nematic demixing can lead to counter-intuitive stacking sequences such as an isotropic phase sandwiched between two nematic phases. For the most complex phase diagram considered here, we find sixteen distinct stacking sequences, including several with five sedimented layers. By adding sedimentation paths to composition-pressure and density-density phase diagrams and calculating density and composition profiles, we show that conclusions about bulk phase diagrams of binary mixtures on the basis of sedimentation-diffusion equilibria should be drawn warily.Comment: 9 pages, 8 figures, extended discussion in section 4, added references, minor changes to figures (results unchanged

Educational Administration: Theory and Practice

Educational Administration: Theory & Practice: Vol 25, Issue

Multiaccess Channels with State Known to One Encoder: Another Case of Degraded Message Sets

We consider a two-user state-dependent multiaccess channel in which only one of the encoders is informed, non-causally, of the channel states. Two independent messages are transmitted: a common message transmitted by both the informed and uninformed encoders, and an individual message transmitted by only the uninformed encoder. We derive inner and outer bounds on the capacity region of this model in the discrete memoryless case as well as the Gaussian case. Further, we show that the bounds for the Gaussian case are tight in some special cases.Comment: 5 pages, Proc. of IEEE International Symposium on Information theory, ISIT 2009, Seoul, Kore