116 research outputs found
A viscoelastic traction layer model of mucociliary flow
A new mathematical model of the transport of mucus and periciliary liquid (PCL) in the airways by cilia is presented. Mucus is represented by a linearly viscoelastic fluid, the mat of cilia is modelled as an âactive porous medium.â The propulsive effect of the cilia is modelled by a time-dependent force acting in a shear-thinned âtraction layerâ between the mucus and the PCL. The effects of surface and interface tension are modelled by constraining the mucus free surface and mucusâPCL interface to be flat. It is assumed that the epithelium is impermeable to fluid. Using Fourier series, the system is converted into ODEs and solved numerically. We calculate values for mean mucus speed close to those observed by Matsui et~al. [{J. Clin. Invest.}, 102(6):1125â1131, 1998], (~40 ÎŒmsâ1). We obtain more detail regarding the dynamics of the flow and the nonlinear relationships between physical parameters in healthy and diseased states than in previously published models. Pressure gradients in the PCL caused by interface and surface tension are vital to ensuring efficient transport of mucus, and the role of the mucusâPCL interface appears to be to support such pressure gradients, ensuring efficient transport. Mean transport of PCL is found to be very small, consistent with previous analyses, providing insight into theories regarding the normal tonicity of PCL
On a model mechanism for the spatial patterning of teeth primordia in the Alligator
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986, 1987, 1990) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction-diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw ofA. mississippiensis. The results for the precise spatio-temporal sequence compare well with detailed developmental experiments
Locating Overlap Information in Quantum Systems
When discussing the black hole information problem the term ``information
flow'' is frequently used in a rather loose fashion. In this article I attempt
to make this notion more concrete. I consider a Hilbert space which is
constructed as a tensor product of two subspaces (representing for example
inside and outside the black hole). I discuss how the system has the capacity
to contain information which is in NEITHER of the subspaces. I attempt to
quantify the amount of information located in each of the two subspaces, and
elsewhere, and analyze the extent to which unitary evolution can correspond to
``information flow''. I define the notion of ``overlap information'' which
appears to be well suited to the problem.Comment: 25 pages plain LaTeX, no figures. Imperial/TP/93-94/2
Torsion cycles as non-local magnetic sources in non-orientable spaces
Non-orientable spaces can appear to carry net magnetic charge, even in the
absence of magnetic sources. It is shown that this effect can be understood as
a physical manifestation of the existence of torsion cycles of codimension one
in the homology of space.Comment: 17 pages, 4 figure
Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach
We present a theory where the statistical mechanics for dilute ideal gases
can be derived from random matrix approach. We show the connection of this
approach with Srednicki approach which connects Berry conjecture with
statistical mechanics. We further establish a link between Berry conjecture and
random matrix theory, thus providing a unified edifice for quantum chaos,
random matrix theory, and statistical mechanics. In the course of arguing for
these connections, we observe sum rules associated with the outstanding
counting problem in the theory of braid groups. We are able to show that the
presented approach leads to the second law of thermodynamics.Comment: 23 pages, TeX typ
Global Topology and Local Violation of Discrete Symmetries
Cosmological models that are locally consistent with general relativity and
the standard model in which an object transported around the universe undergoes
P, C and CP transformations, are constructed. This leads to generalization of
the gauge fields that describe electro-weak and strong interactions by
enlarging the gauge groups to include anti-unitary transformations. Gedanken
experiments show that if all interactions obey Einstein causality then P, C and
CP cannot be violated in these models. But another model, which would violate
charge superselection rule even for an isolated system, is allowed. It is
suggested that the fundamental physical laws must have these discrete
symmetries which are broken spontaneously, or they must be non causal.Comment: 12 pages, 1 figure, latex, Revtex. Charge conjugation which is
physically implemented in a cosmology with the appropriate topology is
described in more detail. Some minor errors are corrected. Shortened to meet
the page limit of Physical Review Letters to which this paper was submitte
Statistical properties of random density matrices
Statistical properties of ensembles of random density matrices are
investigated. We compute traces and von Neumann entropies averaged over
ensembles of random density matrices distributed according to the Bures
measure. The eigenvalues of the random density matrices are analyzed: we derive
the eigenvalue distribution for the Bures ensemble which is shown to be broader
then the quarter--circle distribution characteristic of the Hilbert--Schmidt
ensemble. For measures induced by partial tracing over the environment we
compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints
correcte
Monopole operators in three-dimensional N=4 SYM and mirror symmetry
We study non-abelian monopole operators in the infrared limit of
three-dimensional SU(N_c) and N=4 SU(2) gauge theories. Using large N_f
expansion and operator-state isomorphism of the resulting superconformal field
theories, we construct monopole operators which are (anti-)chiral primaries and
compute their charges under the global symmetries. Predictions of
three-dimensional mirror symmetry for the quantum numbers of these monopole
operators are verified.Comment: 23 pages, LaTex; v2: section 3.4 modified, section 3.5 extended,
references adde
Localization of Events in Space-Time
The present paper deals with the quantum coordinates of an event in
space-time, individuated by a quantum object. It is known that these
observables cannot be described by self-adjoint operators or by the
corresponding spectral projection-valued measure. We describe them by means of
a positive-operator-valued (POV) measure in the Minkowski space-time,
satisfying a suitable covariance condition with respect to the Poincare' group.
This POV measure determines the probability that a measurement of the
coordinates of the event gives results belonging to a given set in space-time.
We show that this measure must vanish on the vacuum and the one-particle
states, which cannot define any event. We give a general expression for the
Poincare' covariant POV measures. We define the baricentric events, which lie
on the world-line of the centre-of-mass, and we find a simple expression for
the average values of their coordinates. Finally, we discuss the conditions
which permit the determination of the coordinates with an arbitrary accuracy.Comment: 31 pages, latex, no figure
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