5,402 research outputs found
Fuchsian differential equation for the perimeter generating function of three-choice polygons
Using a simple transfer matrix approach we have derived very long series
expansions for the perimeter generating function of three-choice polygons. We
find that all the terms in the generating function can be reproduced from a
linear Fuchsian differential equation of order 8. We perform an analysis of the
properties of the differential equation.Comment: 13 pages, 2 figures, talk presented in honour of X. Viennot at
Seminaire Lotharengien, Lucelle, France, April 3-6 2005. Paper amended and
sligtly expanded after refereein
Role of conformational entropy in force-induced bio-polymer unfolding
A statistical mechanical description of flexible and semi-flexible polymer
chains in a poor solvent is developed in the constant force and constant
distance ensembles. We predict the existence of many intermediate states at low
temperatures stabilized by the force. A unified response to pulling and
compressing forces has been obtained in the constant distance ensemble. We show
the signature of a cross-over length which increases linearly with the chain
length. Below this cross-over length, the critical force of unfolding decreases
with temperature, while above, it increases with temperature. For stiff chains,
we report for the first time "saw-tooth" like behavior in the force-extension
curves which has been seen earlier in the case of protein unfolding.Comment: 4 pages, 5 figures, ReVTeX4 style. Accepted in Phys. Rev. Let
Compressed self-avoiding walks, bridges and polygons
We study various self-avoiding walks (SAWs) which are constrained to lie in
the upper half-plane and are subjected to a compressive force. This force is
applied to the vertex or vertices of the walk located at the maximum distance
above the boundary of the half-space. In the case of bridges, this is the
unique end-point. In the case of SAWs or self-avoiding polygons, this
corresponds to all vertices of maximal height. We first use the conjectured
relation with the Schramm-Loewner evolution to predict the form of the
partition function including the values of the exponents, and then we use
series analysis to test these predictions.Comment: 29 pages, 6 figure
Small Rocket Measurements / Validation in Support of SABER
Small rocket measurements in the Mesosphere and lower Thermosphere / Ionosphere will serve to validate and improve measurements being made by the TIMED satellite\u27s SABER instrument. This validation can be made more cost effective and versatile by developing a smaller, lighter, and less expensive radiometer module. Recent developments in technology have allowed us to proceed in developing this smaller, more lightweight radiometric instrument We are currently working on a miniature 2-channel radiometer that will interface with a Viper DART sounding rocket payload, Along with its support circuitry and housing, we estimate the 2-channel radiometer to weigh less than 1 1/2 lbs and be less than 8 inches long with a 2 1/8 diameter, In this report we will discuss the development of this instrument, termed MINRAD, and our current standing
Correction-to-scaling exponents for two-dimensional self-avoiding walks
We study the correction-to-scaling exponents for the two-dimensional
self-avoiding walk, using a combination of series-extrapolation and Monte Carlo
methods. We enumerate all self-avoiding walks up to 59 steps on the square
lattice, and up to 40 steps on the triangular lattice, measuring the
mean-square end-to-end distance, the mean-square radius of gyration and the
mean-square distance of a monomer from the endpoints. The complete endpoint
distribution is also calculated for self-avoiding walks up to 32 steps (square)
and up to 22 steps (triangular). We also generate self-avoiding walks on the
square lattice by Monte Carlo, using the pivot algorithm, obtaining the
mean-square radii to ~0.01% accuracy up to N = 4000. We give compelling
evidence that the first non-analytic correction term for two-dimensional
self-avoiding walks is Delta_1 = 3/2. We compute several moments of the
endpoint distribution function, finding good agreement with the field-theoretic
predictions. Finally, we study a particular invariant ratio that can be shown,
by conformal-field-theory arguments, to vanish asymptotically, and we find the
cancellation of the leading analytic correction.Comment: LaTeX 2.09, 56 pages. Version 2 adds a renormalization-group
discussion near the end of Section 2.2, and makes many small improvements in
the exposition. To be published in the Journal of Statistical Physic
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