47,045 research outputs found
Honeycomb lattice polygons and walks as a test of series analysis techniques
We have calculated long series expansions for self-avoiding walks and
polygons on the honeycomb lattice, including series for metric properties such
as mean-squared radius of gyration as well as series for moments of the
area-distribution for polygons. Analysis of the series yields accurate
estimates for the connective constant, critical exponents and amplitudes of
honeycomb self-avoiding walks and polygons. The results from the numerical
analysis agree to a high degree of accuracy with theoretical predictions for
these quantities.Comment: 16 pages, 9 figures, jpconf style files. Presented at the conference
"Counting Complexity: An international workshop on statistical mechanics and
combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda
Loci Controlling Resistance to High Plains Virus and Wheat Streak Mosaic Virus in a B73 Ă— Mo17 Population of Maize
High Plains disease has the potential to cause significant yield loss in susceptible corn (Zea mays L.) and wheat (Triticum aestivum L.) genotypes, especially in the central and western USA. The primary causal agent, High Plains virus (HPV), is vectored by wheat curl mite (WCM; Aceria tossicheila Keifer), which is also the vector of wheat streak mosaic virus (WSMV). In general, the two diseases occur together as a mixed infection in the field. The objective of this research was to characterize the inheritance of HPV and WSMV resistance using B73 (resistant to HPV and WSMV) Ă— Mo17 (moderately susceptible to HPV and WSMV) recombinant inbred lines. A population of 129 recombinant inbred lines scored for 167 molecular markers was used to evaluate resistance to WSMV and to a mixed infection of WSMV and HPV. Loci conferring resistance to systemic movement of WSMV in plants mapped to chromosomes 3, 6, and 10, consistent with the map position of wsm2, wsm1, and wsm3, respectively. Major genes for resistance to systemic spread of HPV in doubly infected plants mapped to chromosomes 3 and 6, coincident or tightly linked with the WSMV resistance loci. Analysis of doubly infected plants revealed that chromosome 6 had a major effect on HPV resistance, consistent with our previous analysis of B73 Ă— W64A and B73 Ă— Wf9 populations. Quantitative trait loci (QTL) affecting resistance to localized symptom development mapped to chromosomes 4 (umc66), 5 (bnl5.40), and 6 (umc85), and accounted for 24% of the phenotypic variation. Localized symptoms may reflect the amount of mite feeding or the extent of virus spread at the point of infection. Identification of cosegregating markers may facilitate selection for HPV and WSMV resistance in corn breeding programs
Self-avoiding walks and polygons on the triangular lattice
We use new algorithms, based on the finite lattice method of series
expansion, to extend the enumeration of self-avoiding walks and polygons on the
triangular lattice to length 40 and 60, respectively. For self-avoiding walks
to length 40 we also calculate series for the metric properties of mean-square
end-to-end distance, mean-square radius of gyration and the mean-square
distance of a monomer from the end points. For self-avoiding polygons to length
58 we calculate series for the mean-square radius of gyration and the first 10
moments of the area. Analysis of the series yields accurate estimates for the
connective constant of triangular self-avoiding walks, ,
and confirms to a high degree of accuracy several theoretical predictions for
universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure
Scarring in a driven system with wave chaos
We consider acoustic wave propagation in a model of a deep ocean acoustic
waveguide with a periodic range-dependence. Formally, the wave field is
described by the Schrodinger equation with a time-dependent Hamiltonian. Using
methods borrowed from the quantum chaos theory it is shown that in the driven
system under consideration there exists a "scarring" effect similar to that
observed in autonomous quantum systems.Comment: 5 pages, 7 figure
Model independence in two dimensions and polarized cold dipolar molecules
We calculate the energy and wave functions of two particles confined to two
spatial dimensions interacting via arbitrary anisotropic potentials with
negative or zero net volume. The general rigorous analytic expressions are
given in the weak coupling limit where universality or model independence are
approached. The monopole part of anisotropic potentials is crucial in the
universal limit. We illustrate the universality with a system of two
arbitrarily polarized cold dipolar molecules in a bilayer. We discuss the
transition to universality as function of polarization and binding energy, and
compare analytic and numerical results obtained by the stochastic variational
method. The universal limit is essentially reached for experimentally
accessible strengths.Comment: 4.1 pages, 3 figures, published versio
Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach
We show how the scattering-into-cones and flux-across-surfaces theorems in
Quantum Mechanics have very intuitive pathwise probabilistic versions based on
some results by Carlen about large time behaviour of paths of Nelson
diffusions. The quantum mechanical results can be then recovered by taking
expectations in our pathwise statements.Comment: To appear in Journal of Mathematical Physic
Structure of exotic three-body systems
The classification of large halos formed by two identical particles and a
core is systematically addressed according to interparticle distances. The
root-mean-square distances between the constituents are described by universal
scaling functions obtained from a renormalized zero-range model. Applications
for halo nuclei, Li and Be, and for atomic He are briefly
discussed. The generalization to four-body systems is proposed.Comment: Contribution to the International workshop "Critical Stability of
Few-Body Quantum Systems". To be published in "Few-Body Systems
Statistics of lattice animals (polyominoes) and polygons
We have developed an improved algorithm that allows us to enumerate the
number of site animals (polyominoes) on the square lattice up to size 46.
Analysis of the resulting series yields an improved estimate, , for the growth constant of lattice animals and confirms to a very
high degree of certainty that the generating function has a logarithmic
divergence. We prove the bound We also calculate the radius
of gyration of both lattice animals and polygons enumerated by area. The
analysis of the radius of gyration series yields the estimate , for both animals and polygons enumerated by area. The mean
perimeter of polygons of area is also calculated. A number of new amplitude
estimates are given.Comment: 10 pages, 2 eps figure
Enumeration of self-avoiding walks on the square lattice
We describe a new algorithm for the enumeration of self-avoiding walks on the
square lattice. Using up to 128 processors on a HP Alpha server cluster we have
enumerated the number of self-avoiding walks on the square lattice to length
71. Series for the metric properties of mean-square end-to-end distance,
mean-square radius of gyration and mean-square distance of monomers from the
end points have been derived to length 59. Analysis of the resulting series
yields accurate estimates of the critical exponents and
confirming predictions of their exact values. Likewise we obtain accurate
amplitude estimates yielding precise values for certain universal amplitude
combinations. Finally we report on an analysis giving compelling evidence that
the leading non-analytic correction-to-scaling exponent .Comment: 24 pages, 6 figure
Mode-locking in ac-driven vortex lattices with random pinning
We find mode-locking steps in simulated current-voltage characteristics of
ac-driven vortex lattices with {\it random} pinning. For low frequencies there
is mode-locking above a finite ac force amplitude, while for large frequencies
there is mode-locking for any small ac force. This is correlated with the
nature of temporal order in the different regimes in the absence of ac drive.
The mode-locked state is a frozen solid pinned in the moving reference of
frame, and the depinning from the step shows plastic flow and hysteresis.Comment: 4 pages, 4 figure
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