11,169 research outputs found
A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith)
We consider a family of integro-differential equations depending upon a
parameter as well as a symmetric integral kernel . When and
is the peakon kernel (i.e. up to rescaling) the
dispersionless Camassa-Holm equation results, while the Degasperis-Procesi
equation is obtained from the peakon kernel with . Although these two
cases are integrable, generically the corresponding integro-PDE is
non-integrable. However,for the family restricts to the pulson family of
Fringer & Holm, which is Hamiltonian and numerically displays elastic
scattering of pulses. On the other hand, for arbitrary it is still possible
to construct a nonlocal Hamiltonian structure provided that is the peakon
kernel or one of its degenerations: we present a proof of this fact using an
associated functional equation for the skew-symmetric antiderivative of .
The nonlocal bracket reduces to a non-canonical Poisson bracket for the peakon
dynamical system, for any value of .Comment: Contribution to volume of Journal of Nonlinear Mathematical Physics
in honour of Francesco Caloger
The mod 2 cohomology of fixed point sets of anti-symplectic involutions
Let be a compact, connected symplectic manifold with a Hamiltonian action
of a compact -dimensional torus . Suppose that is an
anti-symplectic involution compatible with the -action. The real locus of
is , the fixed point set of . Duistermaat uses Morse theory to
give a description of the ordinary cohomology of in terms of the cohomology
of . There is a residual \G=(\Zt)^n action on , and we can use
Duistermaat's result, as well as some general facts about equivariant
cohomology, to prove an equivariant analogue to Duistermaat's theorem. In some
cases, we can also extend theorems of Goresky-Kottwitz-MacPherson and
Goldin-Holm to the real locus.Comment: 21 pages, 1 figur
High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model
We report measurements of the critical exponents of the classical
three-dimensional Heisenberg model on simple cubic lattices of size with
= 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long
single-cluster Monte Carlo simulations near the phase transition. We compute
high precision estimates of the critical coupling , Binder's parameter
\nu,\beta / \nu, \eta\alpha / \nu$,
using extensively histogram reweighting and optimization techniques that allow
us to keep control over the statistical errors. Measurements of the
autocorrelation time show the expected reduction of critical slowing down at
the phase transition as compared to local update algorithms. This allows
simulations on significantly larger lattices than in previous studies and
consequently a better control over systematic errors in finite-size scaling
analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript
file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first
version arrived incomplete due to mailer problems
The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems
We present a new variational principle for the gyrokinetic system, similar to
the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in
the Eulerian frame and based on constrained variations of the phase space fluid
velocity and particle distribution function. Using a Legendre transform, we
explicitly derive the field theoretic Hamiltonian structure of the system. This
is carried out with a modified Dirac theory of constraints, which is used to
construct meaningful brackets from those obtained directly from
Euler-Poincar\'{e} theory. Possible applications of these formulations include
continuum geometric integration techniques, large-eddy simulation models and
Casimir type stability methods.
[1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur
Aggregation kinetics of stiff polyelectrolytes in the presence of multivalent salt
Using molecular dynamics simulations, the kinetics of bundle formation for
stiff polyelectrolytes such as actin is studied in the solution of multivalent
salt. The dominant kinetic mode of aggregation is found to be the case of one
end of one rod meeting others at right angle due to electrostatic interactions.
The kinetic pathway to bundle formation involves a hierarchical structure of
small clusters forming initially and then feeding into larger clusters, which
is reminiscent of the flocculation dynamics of colloids. For the first few
cluster sizes, the Smoluchowski formula for the time evolution of the cluster
size gives a reasonable account for the results of our simulation without a
single fitting parameter. The description using Smoluchowski formula provides
evidence for the aggregation time scale to be controlled by diffusion, with no
appreciable energy barrier to overcome.Comment: 6 pages, 5 figures, Phys. Rev. E (Accepted
Effects of Surface-Active Agents on the Susceptibility of Swiss Mice to Candida Albicans
EFFECTS OF SURFACE-ACTIVE AGENTS ON THE SUSCEPTIBILITY OF SWISS MICE TO CANDIDA ALBICANS
Harvey W. Holm, Master of Science
The thesis here abstracted was written under the direction of Dr. Richard M. Marwln and approved by Dr. Robert G. Fischer and Dr. Jerald L. Connelly as members of the examlng committee of which Or. Marwln was Chairman.
White Swiss mice are generally resistant to Candida albicans injected 1ntraper1tonea11y. An effort was made to determine 1f surfactants when combined with Candida albicans would decrease the LD50 of this organism. The surfactants tested were Plurafac B26, Polyethylene Glycol 1*00 Mono Laurate, Mulsor 22k, and Pluronlc L62. Peritoneal leukocyte and differential counts, tissue sections, and blood cultures were done to determine the action of surfactants.
The following conclusions were made: (a) Plurafac B26, Polyethylene Glycol 1*00 Mono Laurate, Pluronlc L62, and Mulsor 221* increase mouse susceptibility to Candida albicans, (b) The degree of susceptibility enhancement varies among the surfactants tested. (c) Plurafac B26 Initially destroys leukocytes in the peritoneal cavity. (d) Massive Invasion of the pancreas may be the cause of death of animals given a Candida albicans - surfactant combination 1ntra- perttoneal1y.
The results suggest that surfactants may be a diagnostic tool of value 1n enhancing mouse susceptibility to Candida albicans
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