3,559 research outputs found
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
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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 with random
scalar potential. Without it, 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 : n is the dimensionality of S, and 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 Rayleigh statistics is attained even
with no absorption; here we extend the study to . 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 (SB) in QCD with
light quark flavours can be described by orthogonal groups as , due to local isomorphisms. Here we discuss the question how specific
this property is. We consider generalised forms of 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 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 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
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