88,364 research outputs found
Geometry, thermodynamics, and finite-size corrections in the critical Potts model
We establish an intriguing connection between geometry and thermodynamics in
the critical q-state Potts model on two-dimensional lattices, using the q-state
bond-correlated percolation model (QBCPM) representation. We find that the
number of clusters of the QBCPM has an energy-like singularity for q different
from 1, which is reached and supported by exact results, numerical simulation,
and scaling arguments. We also establish that the finite-size correction to the
number of bonds, has no constant term and explains the divergence of related
quantities as q --> 4, the multicritical point. Similar analyses are applicable
to a variety of other systems.Comment: 12 pages, 6 figure
Grouping of coefficients for the calculation of inter-molecular similarity and dissimilarity using 2D fragment bit-strings
This paper compares 22 different similarity coefficients when they are used for searching databases of 2D fragment bit-strings. Experiments with the National Cancer Institute's AIDS and IDAlert databases show that the coefficients fall into several well-marked clusters, in which the members of a cluster will produce comparable rankings of a set of molecules. These clusters provide a basis for selecting combinations of coefficients for use in data fusion experiments. The results of these experiments provide a simple way of increasing the effectiveness of fragment-based similarity searching systems
Grouping of coefficients for the calculation of inter-molecular similarity and dissimilarity using 2D fragment bit-strings
This paper compares 22 different similarity coefficients when they are used for searching databases of 2D fragment bit-strings. Experiments with the National Cancer Institute's AIDS and IDAlert databases show that the coefficients fall into several well-marked clusters, in which the members of a cluster will produce comparable rankings of a set of molecules. These clusters provide a basis for selecting combinations of coefficients for use in data fusion experiments. The results of these experiments provide a simple way of increasing the effectiveness of fragment-based similarity searching systems
Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters
Percolation models with multiple percolating clusters have attracted much
attention in recent years. Here we use Monte Carlo simulations to study bond
percolation on planar random lattices, duals of random
lattices, and square lattices with free and periodic boundary conditions, in
vertical and horizontal directions, respectively, and with various aspect ratio
. We calculate the probability for the appearance of
percolating clusters, the percolating probabilities, , the average
fraction of lattice bonds (sites) in the percolating clusters,
(), and the probability distribution function for the fraction
of lattice bonds (sites), in percolating clusters of subgraphs with
percolating clusters, (). Using a small number of
nonuniversal metric factors, we find that , ,
(), and () for random lattices, duals
of random lattices, and square lattices have the same universal finite-size
scaling functions. We also find that nonuniversal metric factors are
independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure
Gluon GPDs and Exclusive Photoproduction of a Quarkonium in Forward Region
Forward photoproduction of can be used to extract Generalized Parton
Distributions(GPD's) of gluons. We analyze the process at twist-3 level and
study relevant classifications of twist-3 gluon GPD's. At leading power or
twist-2 level the produced is transversely polarized. We find that at
twist-3 the produced is longitudinally polarized. Our study shows that
in high energy limit the twist-3 amplitude is only suppressed by the inverse
power of the heavy quark mass relatively to the twist-2 amplitude. This
indicates that the power correction to the cross-section of unpolarized
can have a sizeable effect. We have also derived the amplitude of the
production of at twist-3, but the result contains end-point
singularities. The production of other quarkonia has been briefly discussed.Comment: Discussions of results are adde
Nonequilibrium Dynamics of Charged Particles in an Electromagnetic Field: Causal and Stable Dynamics from 1/c Expansion of QED
We derive from a microscopic Hamiltonian a set of stochastic equations of
motion for a system of spinless charged particles in an electromagnetic (EM)
field based on a consistent application of a dimensionful 1/c expansion of
quantum electrodynamics (QED). All relativistic corrections up to order 1/c^3
are captured by the dynamics, which includes electrostatic interactions
(Coulomb), magnetostatic backreaction (Biot-Savart), dissipative backreaction
(Abraham-Lorentz) and quantum field fluctuations at zero and finite
temperatures. With self-consistent backreaction of the EM field included we
show that this approach yields causal and runaway-free equations of motion,
provides new insights into charged particle backreaction, and naturally leads
to equations consistent with the (classical) Darwin Hamiltonian and has quantum
operator ordering consistent with the Breit Hamiltonian. To order 1/c^3 the
approach leads to a nonstandard mass renormalization which is associated with
magnetostatic self-interactions, and no cutoff is required to prevent runaways.
Our new results also show that the pathologies of the standard Abraham-Lorentz
equations can be seen as a consequence of applying an inconsistent (i.e.
incomplete, mixed-order) expansion in 1/c, if, from the start, the analysis is
viewed as generating a low-energy effective theory rather than an exact
solution. Finally, we show that the 1/c expansion within a Hamiltonian
framework yields well-behaved noise and dissipation, in addition to the
multiple-particle interactions.Comment: 17 pages, 2 figure
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