Mathematical modelling of curtain coating

We present a simple mathematical model for the fluid flow in the curtain coating process, exploiting the small aspect ratio, and examine the model in the large-Reynolds-number limit of industrial interest. We show that the fluid is in free fall except for a region close to the substrate, but find that the model can not describe the turning of the curtain onto the substrate. We find that the inclusion of a viscous bending moment close to the substrate allows the curtain to “turn the corner”

Two-channel Kondo model as a generalized one-dimensional inverse square long-range Haldane-Shastry spin model

Majorana fermion representations of the algebra associated with spin, charge, and flavor currents have been used to transform the two-channel Kondo Hamiltonian. Using a path integral formulation, we derive a reduced effective action with long-range impurity spin-spin interactions at different imaginary times. In the semiclassical limit, it is equivalent to a one-dimensional Heisenberg spin chain with two-spin, three-spin, etc. long-range interactions, as a generalization of the inverse-square long-range Haldane-Shastry spin model. In this representation the elementary excitations are "semions", and the non-Fermi-liquid low-energy properties of the two-channel Kondo model are recovered.Comment: 4 pages, no figure, to be published in J. Phys.: Condens. Matter, 200

Mechanical Properties and Biological Responses of Bioactive Glass Ceramics Processed using Indirect SLS

This paper will report on research which aims to generate bone replacement components by processing bioactive glass-ceramic powders using indirect selective laser sintering. The indirect SLS route has been chosen as it offers the ability to tailor the shape of the implant to the implantation site, and two bioactive glass ceramic materials have been processed through this route: apatite-mullite and apatite-wollostanite. The results of bend tests, to investigate mechanical properties, and in vitro and in vivo experiments to investigate biological responses of the materials will be reported, and the suitability of completed components for implant will be assessed.Mechanical Engineerin

Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux

The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $\nu=1.45\pm0.09$ with random scalar potential. Without it, $\nu$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Wave Scattering through Classically Chaotic Cavities in the Presence of Absorption: An Information-Theoretic Model

We propose an information-theoretic model for the transport of waves through a chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint $=\alpha n$: n is the dimensionality of S, and $0\leq \alpha \leq 1, \alpha =0(1)$ meaning complete (no) absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential -Rayleigh statistics- even for n=1. For $n\gg 1$ Rayleigh statistics is attained even with no absorption; here we extend the study to $\alpha <1$. The model is compared with random-matrix-theory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. Thus, in the latter regime, some important physical constraint is missing in the construction of the model.Comment: 4 pages, latex, 3 ps figure

The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles

We analyze statistical properties of the city bus transport in Cuernavaca (Mexico) and show that the bus arrivals display probability distributions conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure

1+1 Dimensional Compactifications of String Theory

We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero the conflict is resolved.Comment: 11 pages, 2 figures v2: added discussion of AdS_2 and comment

On the Isomorphic Description of Chiral Symmetry Breaking by Non-Unitary Lie Groups

It is well-known that chiral symmetry breaking ($\chi$SB) in QCD with $N_{f}=2$ light quark flavours can be described by orthogonal groups as $O(4) \to O(3)$, due to local isomorphisms. Here we discuss the question how specific this property is. We consider generalised forms of $\chi$SB involving an arbitrary number of light flavours of continuum or lattice fermions, in various representations. We search systematically for isomorphic descriptions by non-unitary, compact Lie groups. It turns out that there are a few alternative options in terms of orthogonal groups, while we did not find any description entirely based on symplectic or exceptional Lie groups. If we adapt such an alternative as the symmetry breaking pattern for a generalised Higgs mechanism, we may consider a Higgs particle composed of bound fermions and trace back the mass generation to $\chi$SB. In fact, some of the patterns that we encounter appear in technicolour models. In particular if one observes a Higgs mechanism that can be expressed in terms of orthogonal groups, we specify in which cases it could also represent some kind of $\chi$SB of techniquarks.Comment: 18 pages, to appear in Int. J. Mod. Phys.

VLA Observations of H I in the Helix Nebula (NGC 7293)

We report the detection of 21-cm line emission from H I in the planetary nebula NGC 7293 (the Helix). The observations, made with the Very Large Array, show the presence of a ring of atomic hydrogen that is associated with the outer portion of the ionized nebula. This ring is most probably gas ejected in the AGB phase that has been subsequently photodissociated by radiation from the central star. The H I emission spreads over about 50 km/s in radial velocity. The mass in H I is approximately 0.07 solar masses, about three times larger than the mass in molecular hydrogen and comparable with the mass in ionized hydrogen.Comment: 19 pages, 9 figure

Generalized Riemann sums

The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and elementary, thus available to the "common mathematician in the streets." However one may still see here interesting inter-connection and cohesiveness in mathematics