25,906 research outputs found
General solution of an exact correlation function factorization in conformal field theory
We discuss a correlation function factorization, which relates a three-point
function to the square root of three two-point functions. This factorization is
known to hold for certain scaling operators at the two-dimensional percolation
point and in a few other cases. The correlation functions are evaluated in the
upper half-plane (or any conformally equivalent region) with operators at two
arbitrary points on the real axis, and a third arbitrary point on either the
real axis or in the interior. This type of result is of interest because it is
both exact and universal, relates higher-order correlation functions to
lower-order ones, and has a simple interpretation in terms of cluster or loop
probabilities in several statistical models. This motivated us to use the
techniques of conformal field theory to determine the general conditions for
its validity.
Here, we discover a correlation function which factorizes in this way for any
central charge c, generalizing previous results. In particular, the
factorization holds for either FK (Fortuin-Kasteleyn) or spin clusters in the
Q-state Potts models; it also applies to either the dense or dilute phases of
the O(n) loop models. Further, only one other non-trivial set of highest-weight
operators (in an irreducible Verma module) factorizes in this way. In this case
the operators have negative dimension (for c < 1) and do not seem to have a
physical realization.Comment: 7 pages, 1 figure, v2 minor revision
Abraded cadmium-plated cable connectors repaired by conversion coating
Conversion coating procedure repairs scratched and abraded cadmium-plated aluminum cable connectors while they are in assembly
Examining the blueprint : the case of Longburn College in New Zealand Adventist education, 1975-1996 : a research exercise presented in partial fulfilment of the requirements for a B.A honours degree, Massey University Department of History
Study of etchants for corrosion-resistant metals, space shuttle external tank
Acceptable etchant concentrations and application and removal procedures for etching austenitic stainless steel, nickel base alloys, and titanium alloys (annealed) employed on the external tank were formulated. The etchant solutions were to be capable of removing a minimum of 0.4 mils of surface material in less than one hour
Constructive Provability Logic
We present constructive provability logic, an intuitionstic modal logic that
validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting
logical reflection over provability. Two distinct variants of this logic, CPL
and CPL*, are presented in natural deduction and sequent calculus forms which
are then shown to be equivalent. In addition, we discuss the use of
constructive provability logic to justify stratified negation in logic
programming within an intuitionstic and structural proof theory.Comment: Extended version of IMLA 2011 submission of the same titl
Factorization of correlations in two-dimensional percolation on the plane and torus
Recently, Delfino and Viti have examined the factorization of the three-point
density correlation function P_3 at the percolation point in terms of the
two-point density correlation functions P_2. According to conformal invariance,
this factorization is exact on the infinite plane, such that the ratio R(z_1,
z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2,
z_3)]^{1/2} is not only universal but also a constant, independent of the z_i,
and in fact an operator product expansion (OPE) coefficient. Delfino and Viti
analytically calculate its value (1.022013...) for percolation, in agreement
with the numerical value 1.022 found previously in a study of R on the
conformally equivalent cylinder. In this paper we confirm the factorization on
the plane numerically using periodic lattices (tori) of very large size, which
locally approximate a plane. We also investigate the general behavior of R on
the torus, and find a minimum value of R approx. 1.0132 when the three points
are maximally separated. In addition, we present a simplified expression for R
on the plane as a function of the SLE parameter kappa.Comment: Small corrections (final version). In press, J. Phys.
Inversion of polarimetric data from eclipsing binaries
We describe a method for determining the limb polarization and limb darkening
of stars in eclipsing binary systems, by inverting photometric and polarimetric
light curves.
Because of the ill-conditioning of the problem, we use the Backus-Gilbert
method to control the resolution and stability of the recovered solution, and
to make quantitative estimates of the maximum accuracy possible. Using this
method we confirm that the limb polarization can indeed be recovered, and
demonstrate this with simulated data, thus determining the level of
observational accuracy required to achieve a given accuracy of reconstruction.
This allows us to set out an optimal observational strategy, and to critcally
assess the claimed detection of limb polarization in the Algol system.
The use of polarization in stars has been proposed as a diagnostic tool in
microlensing surveys by Simmons et al. (1995), and we discuss the extension of
this work to the case of microlensing of extended sources.Comment: 10pp, 5 figures. To appear in A&
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