New sum rule identities and duality relation for the Potts nn-point correlation function

It is shown that certain sum rule identities exist which relate correlation functions for $n$ Potts spins on the boundary of a planar lattice for $n\geq 4$. Explicit expressions of the identities are obtained for $n=4,5$. It is also shown that the identities provide the missing link needed for a complete determination of the duality relation for the $n$-point correlation function. The $n=4$ duality relation is obtained explicitly. More generally we deduce the number of correlation identities for any $n$ as well as an inversion relation and a conjecture on the general form of the duality relation.Comment: 11 pages in RevTeX, 4 PS figures, submitted to PR

Duality relation for frustrated spin models

We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with some of its plaquettes frustrated has a dual which is an Ising model with an external field $i\pi/2$ applied to the dual sites centered at frustrated plaquettes. In the case that all plaquettes are frustrated, this leads to the known result that the dual model has a uniform field $i\pi/2$ whose partition function can be evaluated in the thermodynamic limit for regular lattices. The analysis is extended to a Potts spin glass with analogous results obtained.Comment: Several relevant references are added. Comments on their relation to this work are also adde

Effects of channel cross-sectional geometry on long wave generation and propagation

Joint theoretical and experimental studies are carried out to investigate the effects of channel cross-sectional geometry on long wave generation and propagation in uniform shallow water channels. The existing channel Boussinesq and channel KdV equations are extended in the present study to include the effects of channel sidewall slope at the waterline in the first-order section-mean equations. Our theoretical results show that both the channel cross-sectional geometry below the unperturbed water surface (characterized by a shape factor kappa) and the channel sidewall slope at the waterline (represented by a slope factor gamma) affect the wavelength (lambda) and time period (Ts) of waves generated under resonant external forcing. A quantitative relationship between lambda, Ts, kappa, and gamma is given by our theory which predicts that, under the condition of equal mean water depth and equal mean wave amplitude, lambda and Ts increase with increasing kappa and gamma. To verify the theoretical results, experiments are conducted in two channels of different geometries, namely a rectangular channel with kappa[equivalent]1, gamma=0 and a trapezoidal channel with kappa=1.27, gamma=0.16, to measure the wavelength of free traveling solitary waves and the time period of wave generation by a towed vertical hydrofoil moving with critical speed. The experimental results are found to be in broad agreement with the theoretical predictions

Gradient design of metal hollow sphere (MHS) foams with density gradients

This is the post-print version of the final paper published in Composites Part B: Engineering. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.Metal hollow sphere (MHS) structures with a density gradient have attracted increasing attention in the effort to pursue improved energy absorption properties. In this paper, dynamic crushing of MHS structures of different gradients are discussed, with the gradients being received by stacks of hollow spheres of the same external diameter but different wall thicknesses in the crushing direction. Based on the dynamic performance of MHS structures with uniform density, a crude semi-empirical model is developed for the design of MHS structures in terms of gradient selections for energy absorption and protection against impact. Following this, dynamic responses of density graded MHS foams are comparatively analyzed using explicit finite element simulation and the proposed formula. Results show that the simple semi-empirical model can predict the response of density gradient MHS foams and is ready-to-use in the gradient design of MHS structures.The National Science Foundation of China and the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Lifetime Difference and Endpoint effect in the Inclusive Bottom Hadron Decays

The lifetime differences of bottom hadrons are known to be properly explained within the framework of heavy quark effective field theory(HQEFT) of QCD via the inverse expansion of the dressed heavy quark mass. In general, the spectrum around the endpoint region is not well behaved due to the invalidity of $1/m_Q$ expansion near the endpoint. The curve fitting method is adopted to treat the endpoint behavior. It turns out that the endpoint effects are truly small and the explanation on the lifetime differences in the HQEFT of QCD is then well justified. The inclusion of the endpoint effects makes the prediction on the lifetime differences and the extraction on the CKM matrix element $|V_{cb}|$ more reliable.Comment: 11 pages, Revtex, 10 figures, 6 tables, published versio