2,446 research outputs found
UBM/slit-lamp-photo imaging of pseudoexfoliation deposits in the iridocorneal angle: imaging clues to the genesis of ocular hypertension
This photo essay is aimed at showing slit-lamp photographic views and its ultrasound biomicroscopy (UBM) corollaries of angle deposits in pseudoexfoliation syndrome cases and contributes visual arguments to the hypotheses and explanations of the genesis of ocular hypertension
A characterization of Dirac morphisms
Relating the Dirac operators on the total space and on the base manifold of a
horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps
which pull back (local) harmonic spinor fields onto (local) harmonic spinor
fields.Comment: 18 pages; restricted to the even-dimensional cas
Using force covariance to derive effective stochastic interactions in dissipative particle dynamics
There exist methods for determining effective conservative interactions in
coarse grained particle based mesoscopic simulations. The resulting models can
be used to capture thermal equilibrium behavior, but in the model system we
study do not correctly represent transport properties. In this article we
suggest the use of force covariance to determine the full functional form of
dissipative and stochastic interactions. We show that a combination of the
radial distribution function and a force covariance function can be used to
determine all interactions in dissipative particle dynamics. Furthermore we use
the method to test if the effective interactions in dissipative particle
dynamics (DPD) can be adjusted to produce a force covariance consistent with a
projection of a microscopic Lennard-Jones simulation. The results indicate that
the DPD ansatz may not be consistent with the underlying microscopic dynamics.
We discuss how this result relates to theoretical studies reported in the
literature.Comment: 10 pages, 10 figure
Chebyshev type lattice path weight polynomials by a constant term method
We prove a constant term theorem which is useful for finding weight
polynomials for Ballot/Motzkin paths in a strip with a fixed number of
arbitrary `decorated' weights as well as an arbitrary `background' weight. Our
CT theorem, like Viennot's lattice path theorem from which it is derived
primarily by a change of variable lemma, is expressed in terms of orthogonal
polynomials which in our applications of interest often turn out to be
non-classical. Hence we also present an efficient method for finding explicit
closed form polynomial expressions for these non-classical orthogonal
polynomials. Our method for finding the closed form polynomial expressions
relies on simple combinatorial manipulations of Viennot's diagrammatic
representation for orthogonal polynomials. In the course of the paper we also
provide a new proof of Viennot's original orthogonal polynomial lattice path
theorem. The new proof is of interest because it uses diagonalization of the
transfer matrix, but gets around difficulties that have arisen in past attempts
to use this approach. In particular we show how to sum over a set of implicitly
defined zeros of a given orthogonal polynomial, either by using properties of
residues or by using partial fractions. We conclude by applying the method to
two lattice path problems important in the study of polymer physics as models
of steric stabilization and sensitized flocculation.Comment: 27 pages, 14 figure
A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula
We provide yet another proof of the classical Lagrange-Good multivariable
inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram
Thermodynamic instability and first-order phase transition in an ideal Bose gas
We conduct a rigorous investigation into the thermodynamic instability of
ideal Bose gas confined in a cubic box, without assuming thermodynamic limit
nor continuous approximation. Based on the exact expression of canonical
partition function, we perform numerical computations up to the number of
particles one million. We report that if the number of particles is equal to or
greater than a certain critical value, which turns out to be 7616, the ideal
Bose gas subject to Dirichlet boundary condition reveals a thermodynamic
instability. Accordingly we demonstrate - for the first time - that, a system
consisting of finite number of particles can exhibit a discontinuous phase
transition featuring a genuine mathematical singularity, provided we keep not
volume but pressure constant. The specific number, 7616 can be regarded as a
characteristic number of 'cube' that is the geometric shape of the box.Comment: 1+21 pages; 3 figures (2 color and 1 B/W); Final version to appear in
Physical Review A. Title changed from the previous one, "7616: Critical
number of ideal Bose gas confined in a cubic box
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