Brunnian Braids and Lie Algebras

Brunnian braids have interesting relations with homotopy groups of spheres. In this work, we study the graded Lie algebra of the descending central series related to Brunnian subgroup of the pure braid group. A presentation of this Lie algebra is obtained.Comment: 21 page

A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate

In this paper, we introduce a three-dimensional numerical method for computing the wake behind a flat plate advancing perpendicular to the flow. Our numerical method is inspired by the panel method of J. Katz and A. Plotkin [J. Katz and A. Plotkin, Low-speed Aerodynamics, 2001] and the 2D vortex blob method of Krasny [R. Krasny, Lectures in Appl. Math., 28 (1991), pp. 385--402]. The accuracy of the method will be demonstrated by comparing the 3D computation at the center section of a very high aspect ratio plate with the corresponding two-dimensional computation. Furthermore, we compare the numerical results obtained by our 3D numerical method with the corresponding experimental results obtained recently by Ringuette [M. J. Ringuette, Ph.D. Thesis, 2004] in the towing tank. Our numerical results are shown to be in excellent agreement with the experimental results up to the so-called formation time

Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.Comment: 22 pages in Revtex, 6 PS files, submitted to PR

On practical design for joint distributed source and network coding

This paper considers the problem of communicating correlated information from multiple source nodes over a network of noiseless channels to multiple destination nodes, where each destination node wants to recover all sources. The problem involves a joint consideration of distributed compression and network information relaying. Although the optimal rate region has been theoretically characterized, it was not clear how to design practical communication schemes with low complexity. This work provides a partial solution to this problem by proposing a low-complexity scheme for the special case with two sources whose correlation is characterized by a binary symmetric channel. Our scheme is based on a careful combination of linear syndrome-based Slepian-Wolf coding and random linear mixing (network coding). It is in general suboptimal; however, its low complexity and robustness to network dynamics make it suitable for practical implementation

Exact Solution of a Three-Dimensional Dimer System

We consider a three-dimensional lattice model consisting of layers of vertex models coupled with interlayer interactions. For a particular non-trivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. The result is applied to analyze the phase transitions in a realistic three-dimensional dimer system.Comment: 11 pages in REVTex with 2 PS figure

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.

Study of the ionic Peierls-Hubbard model using density matrix renormalization group methods

Density matrix renormalization group methods are used to investigate the quantum phase diagram of a one-dimensional half-filled ionic Hubbard model with bond-charge attraction, which can be mapped from the Su-Schrieffer-Heeger-type electron-phonon coupling at the antiadiabatic limit. A bond order wave (dimerized) phase which separates the band insulator from the Mott insulator always exists as long as electron-phonon coupling is present. This is qualitatively different from that at the adiabatic limit. Our results indicate that electron-electron interaction, ionic potential and quantum phonon fluctuations combine in the formation of the bond-order wave phase