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

Preparing oxidizer coated metal fuel particles

A solid propellant composition of improved efficiency is described which includes an oxidizer containing ammonium perchlorate, and a powered metal fuel, preferably aluminum or beryllium, in the form of a composite. The metal fuel is contained in the crystalline lattice framework of the oxidizer, as well as within the oxidizer particles, and is disposed in the interstices between the oxidizer particles of the composition. The propellant composition is produced by a process comprising the crystallization of ammonium perchlorate in water, in the presence of finely divided aluminum or beryllium. A suitable binder is incorporated in the propellant composition to bind the individual particles of metal with the particles of oxidizer containing occluded metal

Entrainment characteristics of unsteady subsonic jets

The effectiveness of jet unsteadiness in enhancing flow entrainment was assessed. It was conducted that entrainment depends on the type and amount of jet unsteadiness. Apparently, the mere introduction of jet unsteadiness by small sinusoidal flow angle variations is insufficient to enhance entrainment but, it should be noted that the results were obtained at measuring stations which are all many nozzle widths downstream of the jet nozzle. Thus, no fully conclusive statement can be made at this time about the entrainment close to the nozzle. The high entrainment of the fluidically oscillated jet was caused by the high-frequency content of this square wave type of oscillation but more detailed measurements are clearly needed, in particular for the fluidically oscillated and the pulsed jets. Practical ejector application requires the proper trade-off between entrainment and primary nozzle thrust efficiency

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.

Preliminary Test of Prescribed Burning for Control of Maple Leaf Cutter (Lepidoptera: Incurvariidae)

Leaf litter burning in the spring resulted in 87.5% mortality of maple leaf cutter pupae, Paraclemensia acerifoliella (Fitch). No apparent damage was observed on sugar maple or beech trees within the burn area

Determination of thermodynamic properties of AeroZINE-50, phase 1

Literature survey of, and test procedure for determination of thermodynamic properties of AeroZINE-5

Percolation Crossing Formulas and Conformal Field Theory

Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the horizontal crossing probability $\Pi_h(r)$, Watts' formula for the horizontal-vertical crossing probability $\Pi_{hv}(r)$, and Cardy's formula for the expected number of clusters crossing horizontally $\mathcal{N}_h(r)$. The main step in our approach implies the identification of the derivative of one primary operator with another. We present operator identities that support this idea and suggest the presence of additional symmetry in $c=0$ conformal field theories.Comment: 12 pages, 5 figures. Numerics improved; minor correction