16,531 research outputs found
Rational Approximate Symmetries of KdV Equation
We construct one-parameter deformation of the Dorfman Hamiltonian operator
for the Riemann hierarchy using the quasi-Miura transformation from topological
field theory. In this way, one can get the approximately rational symmetries of
KdV equation and then investigate its bi-Hamiltonian structure.Comment: 14 pages, no figure
A review of Monte Carlo simulations of polymers with PERM
In this review, we describe applications of the pruned-enriched Rosenbluth
method (PERM), a sequential Monte Carlo algorithm with resampling, to various
problems in polymer physics. PERM produces samples according to any given
prescribed weight distribution, by growing configurations step by step with
controlled bias, and correcting "bad" configurations by "population control".
The latter is implemented, in contrast to other population based algorithms
like e.g. genetic algorithms, by depth-first recursion which avoids storing all
members of the population at the same time in computer memory. The problems we
discuss all concern single polymers (with one exception), but under various
conditions: Homopolymers in good solvents and at the point, semi-stiff
polymers, polymers in confining geometries, stretched polymers undergoing a
forced globule-linear transition, star polymers, bottle brushes, lattice
animals as a model for randomly branched polymers, DNA melting, and finally --
as the only system at low temperatures, lattice heteropolymers as simple models
for protein folding. PERM is for some of these problems the method of choice,
but it can also fail. We discuss how to recognize when a result is reliable,
and we discuss also some types of bias that can be crucial in guiding the
growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011
Healing of Tendon Defects Implanted with a Porous Collagen-GAG Matrix: Histological Evaluation
There is currently no method to restore normal function in tendon injuries that result in a gap. The objective of this study was to evaluate the early healing of tendon defects implanted with a porous collagen–glycosaminoglycan (CG) matrix, previously shown to facilitate the regeneration of dermis and peripheral nerve. A novel animal model that isolates the tendon defect site from surrounding tissue during healing was employed. This model used a silicone tube to entubulate the surgically produced tendon gap of 10 mm, allowing for the evaluation of the effects of the analog of extracellular matrix on healing of tendon, absent the influences of the external environment. The results showed that tendon stumps induced synthesis of a tissue cable inside the silicone tube in both the presence and absence of CG matrix. The presence of the CG matrix, however, altered the process of tendon healing. Tubes filled with CG matrix contained a significantly greater volume of tissue at the time periods of evaluation: 3, 6, and 12 weeks. Granulation tissue persisted for a longer period of time in the lesion site of CG-filled defects, and the amount of dense fibrous tissue increased continuously during the period of study in defects filled with CG matrix. In contrast, the amount of dense fibrous tissue decreased after 6 weeks in originally empty tubes. In tubes that did not contain the CG matrix, the new tissue consisted of dense aggregates of crimped fibers with a wavelength and fiber bundle thickness that were significantly shorter than those in normal tendon, and consistent with the type of scar that is the end result of repair of many connective tissues. Although, CG-filled tubes contained dense fibrous tissue by 12 weeks, the tissue had no crimp. The CG matrix may have prolonged the synthesis of granulation tissue and delayed or prevented the formation of scar.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63265/1/ten.1997.3.187.pd
Micellization of Sliding Polymer Surfactants
Following up a recent paper on grafted sliding polymer layers (Macromolecules
2005, 38, 1434-1441), we investigated the influence of the sliding degree of
freedom on the self-assembly of sliding polymeric surfactants that can be
obtained by complexation of polymers with cyclodextrins. In contrast to the
micelles of quenched block copolymer surfactants, the free energy of micelles
of sliding surfactants can have two minima: the first corresponding to small
micelles with symmetric arm lengths, and the second corresponding to large
micelles with asymmetric arm lengths. The relative sizes and concentrations of
small and large micelles in the solution depend on the molecular parameters of
the system. The appearance of small micelles drastically reduces the kinetic
barrier signifying the fast formation of equilibrium micelles.Comment: Submitted to Macromolecule
Fisher Renormalization for Logarithmic Corrections
For continuous phase transitions characterized by power-law divergences,
Fisher renormalization prescribes how to obtain the critical exponents for a
system under constraint from their ideal counterparts. In statistical
mechanics, such ideal behaviour at phase transitions is frequently modified by
multiplicative logarithmic corrections. Here, Fisher renormalization for the
exponents of these logarithms is developed in a general manner. As for the
leading exponents, Fisher renormalization at the logarithmic level is seen to
be involutory and the renormalized exponents obey the same scaling relations as
their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee
problem at their upper critical dimensions, where predictions for logarithmic
corrections are made.Comment: 10 pages, no figures. Version 2 has added reference
Chiral Phase Transition within Effective Models with Constituent Quarks
We investigate the chiral phase transition at nonzero temperature and
baryon-chemical potential within the framework of the linear sigma
model and the Nambu-Jona-Lasinio model. For small bare quark masses we find in
both models a smooth crossover transition for nonzero and and a
first order transition for T=0 and nonzero . We calculate explicitly the
first order phase transition line and spinodal lines in the plane.
As expected they all end in a critical point. We find that, in the linear sigma
model, the sigma mass goes to zero at the critical point. This is in contrast
to the NJL model, where the sigma mass, as defined in the random phase
approximation, does not vanish. We also compute the adiabatic lines in the
plane. Within the models studied here, the critical point does not
serve as a ``focusing'' point in the adiabatic expansion.Comment: 22 pages, 18 figure
Dynamical Stability of Six-dimensional Warped Flux Compactification
We show the dynamical stability of a six-dimensional braneworld solution with
warped flux compactification recently found by the authors. We consider linear
perturbations around this background spacetime, assuming the axisymmetry in the
extra dimensions. The perturbations are expanded by scalar-, vector- and
tensor-type harmonics of the four-dimensional Minkoswki spacetime and we
analyze each type separately. It is found that there is no unstable mode in
each sector and that there are zero modes only in the tensor sector,
corresponding to the four-dimensional gravitons. We also obtain the first few
Kaluza-Klein modes in each sector.Comment: 46 pages, 8 figures. Version to appear in JCA
Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models
A connection between integrability properties and general statistical
properties of the spectra of symmetric transfer matrices of the asymmetric
eight-vertex model is studied using random matrix theory (eigenvalue spacing
distribution and spectral rigidity). For Yang-Baxter integrable cases,
including free-fermion solutions, we have found a Poissonian behavior, whereas
level repulsion close to the Wigner distribution is found for non-integrable
models. For the asymmetric eight-vertex model, however, the level repulsion can
also disappearand the Poisson distribution be recovered on (non Yang--Baxter
integrable) algebraic varieties, the so-called disorder varieties. We also
present an infinite set of algebraic varieties which are stable under the
action of an infinite discrete symmetry group of the parameter space. These
varieties are possible loci for free parafermions. Using our numerical
criterion we have tested the generic calculability of the model on these
algebraic varieties.Comment: 25 pages, 7 PostScript Figure
Nano-displacement measurements using spatially multimode squeezed light
We demonstrate the possibility of surpassing the quantum noise limit for
simultaneous multi-axis spatial displacement measurements that have zero mean
values. The requisite resources for these measurements are squeezed light beams
with exotic transverse mode profiles. We show that, in principle, lossless
combination of these modes can be achieved using the non-degenerate Gouy phase
shift of optical resonators. When the combined squeezed beams are measured with
quadrant detectors, we experimentally demonstrate a simultaneous reduction in
the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below
the quantum noise limit.Comment: 21 pages, 9 figures, submitted to "Special Issue on Fluctuations &
Noise in Photonics & Quantum Optics" of J. Opt.
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