Correlation Functions of a Conformal Field Theory in Three Dimensions

We derive explicit forms of the two--point correlation functions of the $O(N)$ non-linear sigma model at the critical point, in the large $N$ limit, on various three dimensional manifolds of constant curvature. The two--point correlation function, $G(x, y)$, is the only $n$-point correlation function which survives in this limit. We analyze the short distance and long distance behaviour of $G(x, y)$. It is shown that $G(x, y)$ decays exponentially with the Riemannian distance on the spaces $R^2 \times S^1,~S^1 \times S^1 \times R, ~S^2 \times R,~H^2 \times R$. The decay on $R^3$ is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behaviour of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight $\delta=-{1 \over 2}$; we illustrate this using the example of the manifold $S^2 \times R$ whose metric is conformally equivalent to that of $R^3-\{0\}$ up to a reparametrization.Comment: 15 pages, Late

Two Dimensional Quantum Chromodynamics on a Cylinder

We study two dimensional Quantum Chromodynamics with massive quarks on a cylinder in a light--cone formalism. We eliminate the non--dynamical degrees of freedom and express the theory in terms of the quark and Wilson loop variables. It is possible to perform this reduction without gauge fixing. The fermionic Fock space can be defined independent of the gauge field in this light--cone formalism.Comment: 8 pages, UR-128

Studies on vibration of some rib-stiffened cantilever plates

The vibrational mode shapes and frequencies of rib-stiffened skew cantilever plates as determined by holographic interferometry are given. The effects of varying the sweep back angle, rib stiffness and aspect ratio are studied along with the influence of varying the boundary conditions at the root chord on the vibrational behavior of the plates. The study is applicable to investigating the vibrational behavior of stiffened plates often used in the design of guided rockets and missiles

Minimax Optimum Estimators for Phase Synchronization in IEEE 1588

The IEEE 1588 protocol has received recent interest as a means of delivering sub-microsecond level clock phase synchronization over packet-switched mobile backhaul networks. Due to the randomness of the end-to-end delays in packet networks, the recovery of clock phase from packet timestamps in IEEE 1588 must be treated as a statistical estimation problem. A number of estimators for this problem have been suggested in the literature, but little is known about the best achievable performance. In this paper, we describe new minimax estimators for this problem, that are optimum in terms of minimizing the maximum mean squared error over all possible values of the unknown parameters. Minimax estimators that utilize information from past timestamps to improve accuracy are also introduced. Simulation results indicate that significant performance gains over conventional estimators can be obtained via such optimum processing techniques. These minimax estimators also provide fundamental limits on the performance of phase offset estimation schemes.Comment: 11 pages, 19 figure

High-temperature hardness of Ga_(1−x)In_xAs

Substantial solid‐solution strengthening of GaAs by In acting as InAs_4 units has recently been predicted for an intermediate‐temperature plateau region. This strengthening could account, in part, for the reduction of dislocation density in GaAs single crystals grown from the melt. Hardness measurements at high temperatures up to 900 °C have been carried out on (100) GaAs, Ga_(0.9975)In_(0.0025)As, and Ga_(0.99)In_(0.01)As wafers, all of which contain small amounts of boron. Results show a significant strengthening effect in In‐doped GaAs. A nominally temperature‐independent flow‐stress region is observed for all three alloys. The In‐doped GaAs shows a higher plateau stress level with increasing In content. The results are consistent with the solid‐solution strengthening model. The magnitude of the solid‐solution hardening is sufficient to explain the reduction in dislocation density with In addition

Disordered free fermions and the Cardy Ostlund fixed line at low temperature

Using functional RG, we reexamine the glass phase of the 2D random-field Sine Gordon model. It is described by a line of fixed points (FP) with a super-roughening amplitude $\bar{(u(0)-u(r))^2} \sim A(T) \ln^2 r$ as temperature $T$ is varied. A speculation is that this line is identical to the one found in disordered free-fermion models via exact results from ``nearly conformal'' field theory. This however predicts $A(T=0)=0$, contradicting numerics. We point out that this result may be related to failure of dimensional reduction, and that a functional RG method incorporating higher harmonics and non-analytic operators predicts a non-zero $A(T=0)$ which compares reasonably with numerics.Comment: 8 pages, 3 figures, only material adde

K-matrices for non-abelian quantum Hall states

Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.Comment: LaTeX, 12 page

Shear-Enhanced Crystallization in Isotactic Polypropylene. 3. Evidence for a Kinetic Pathway to Nucleation

In situ rheo-optical techniques are combined with synchrotron wide-angle X-ray diffraction (WAXD) to investigate the oriented crystallization precursors that develop upon strongly shearing an isothermal melt of polydisperse isotactic polypropylene (iPP). The “short-term shearing” experimental protocol, developed by Janeschitz-Kriegl and co-workers, is used under conditions previously determined to induce oriented crystallite growth. Surprisingly, the time for these precursors to appear decreases with increasing temperature, tracking the melt dynamics of the polymer moleculesa behavior unanticipated by current models. Thus, nucleation proceeds via a “nonclassical” kinetic pathway that effectively eliminates the activation barrier for nucleation. To characterize the importance of chain length distribution for the formation of nucleation precursors, experiments were performed with model bidisperse systems containing a small percentage of high molecular weight iPP blended with lower molecular weight iPP of matched stereoregularity. Oriented crystallization was not observed for the individual components of the blend under the most extreme experimental conditions investigated, but it was readily observed for the bidisperse blend. This suggests that, under intense shear, nucleation of oriented crystallites is governed by the rheologically determined formation of a critical anisotropic configuration of polymer chains in the melt