144 research outputs found
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
Random walks on finite lattice tubes
Exact results are obtained for random walks on finite lattice tubes with a
single source and absorbing lattice sites at the ends. Explicit formulae are
derived for the absorption probabilities at the ends and for the expectations
that a random walk will visit a particular lattice site before being absorbed.
Results are obtained for lattice tubes of arbitrary size and each of the
regular lattice types; square, triangular and honeycomb. The results include an
adjustable parameter to model the effects of strain, such as surface curvature,
on the surface diffusion. Results for the triangular lattice tubes and the
honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag
carbon nano-tubes with open ends.Comment: 22 pages, 4 figure
Closure of two dimensional turbulence: the role of pressure gradients
Inverse energy cascade regime of two dimensional turbulence is investigated
by means of high resolution numerical simulations. Numerical computations of
conditional averages of transverse pressure gradient increments are found to be
compatible with a recently proposed self-consistent Gaussian model. An
analogous low order closure model for the longitudinal pressure gradient is
proposed and its validity is numerically examined. In this case numerical
evidence for the presence of higher order terms in the closure is found. The
fundamental role of conditional statistics between longitudinal and transverse
components is highlighted.Comment: 4 pages, 2 figures, in press on PR
Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces
This paper is the third in a sequel to develop a super-analogue of the
classical Selberg trace formula, the Selberg supertrace formula. It deals with
bordered super Riemann surfaces. The theory of bordered super Riemann surfaces
is outlined, and the corresponding Selberg supertrace formula is developed. The
analytic properties of the Selberg super zeta-functions on bordered super
Riemann surfaces are discussed, and super-determinants of Dirac-Laplace
operators on bordered super Riemann surfaces are calculated in terms of Selberg
super zeta-functions.Comment: 43 pages, amste
Normal fluid eddies in the thermal counterflow past a cylinder
A recent Particle Image Velocimetry (PIV) experiment in He II counterflow
around a cylindrical obstacle showed the existence of apparently stationary
normal fluid ddies both downstream (at the rear) and upstream (in front) of the
cylinder. This rather surprising result does not have an analogue in
experimental observations of classical fluid flows. We suggest that the
explanation for the apparent stability of such eddies can be provided entirely
from the viewpoint of classical fluid dynamics. We also discuss a possible
connection between the emergence of the normal fluid eddies and the
polarization of the vortex tangle in superfluid.Comment: submitte
Supercoherent States, Super K\"ahler Geometry and Geometric Quantization
Generalized coherent states provide a means of connecting square integrable
representations of a semi-simple Lie group with the symplectic geometry of some
of its homogeneous spaces. In the first part of the present work this point of
view is extended to the supersymmetric context, through the study of the
OSp(2/2) coherent states. These are explicitly constructed starting from the
known abstract typical and atypical representations of osp(2/2). Their
underlying geometries turn out to be those of supersymplectic OSp(2/2)
homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of
OSp(2/2) are exhibited via Berezin's symbols. When considered within
Rothstein's general paradigm, these results lead to a natural general
definition of a super K\"ahler supermanifold, the supergeometry of which is
determined in terms of the usual geometry of holomorphic Hermitian vector
bundles over K\"ahler manifolds. In particular, the supergeometry of the above
orbits is interpreted in terms of the geometry of Einstein-Hermitian vector
bundles. In the second part, an extension of the full geometric quantization
procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler
character of the latter, this procedure leads to explicit super unitary
irreducible representations of OSp(2/2) in super Hilbert spaces of
superholomorphic sections of prequantum bundles of the Kostant type. This work
lays the foundations of a program aimed at classifying Lie supergroups'
coadjoint orbits and their associated irreducible representations, ultimately
leading to harmonic superanalysis. For this purpose a set of consistent
conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts
Discrete cilia modelling with singularity distributions
We discuss in detail techniques for modelling flows due to finite and infinite arrays of beating cilia. An efficient technique, based on concepts from previous âsingularity modelsâ is described, that is accurate in both near and far-fields. Cilia are modelled as curved slender ellipsoidal bodies by distributing Stokeslet and potential source dipole singularities along their centrelines, leading to an integral equation that can be solved using a simple and efficient discretisation. The computed velocity on the cilium surface is found to compare favourably with the boundary condition. We then present results for two topics of current interest in biology. 1) We present the first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a âposterior tilt,â and track particle motion in an array of three simulated nodal cilia. We find that, contrary to recent suggestions, there is no continuous layer of negative fluid transport close to the ciliated boundary. The mean leftward particle transport is found to be just over 1 ÎŒm/s, within experimentally measured ranges. We also discuss the accuracy of models that represent the action of cilia by steady rotlet arrays, in particular, confirming the importance of image systems in the boundary in establishing the far-field fluid transport. Future modelling may lead to understanding of the mechanisms by which morphogen gradients or mechanosensing cilia convert a directional flow to asymmetric gene expression. 2) We develop a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid. Our results confirm that shear flow of the mucous layer drives a significant volume of periciliary liquid in the direction of mucus transport even during the recovery stroke of the cilia. Finally, we discuss the advantages and disadvantages of the singularity technique and outline future theoretical and experimental developments required to apply this technique to various other biological problems, particularly in the reproductive system
On membrane diffusion with near-equilibrium reaction
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32779/1/0000152.pd
A 14-year experience with kidney transplantation.
Between November, 1962 and August, 1975, 668 kidney transplants were done in 556 consecutive patients at Denver, Colorado. The Denver experience has been divided into 7 periods of time, according to the conditions of care during each period. The results in related transplantation have changed little during the decade beginning in 1966. The results in unrelated transplantation have not materially changed since 1968. The long-term patient survival after related transplantation has been better than after cadaver transplantation. The results of transplantation in 57 children ages 3 to 18 years have been slightly better than the results of adult transplantation. The outcome of kidney transplantation and the feasibility of improving this therapy with present techniques are limited by our inability to accurately match each patient with the immunologically best donor and by our inability to precisely control the immune system of the recipient. Rejection is still the main reason for graft loss, and sepsis remains the main cause of patient mortality. More specific and less toxic means of achieving graft acceptance are needed before a higher level of patient service can be realized. However, even with the tools now available, thousands of recipients throughout the world have been returned to useful lives
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