Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Computational structures for robotic computations

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed

Natural TeV-Scale Left-Right Seesaw for Neutrinos and Experimental Tests

We present a TeV-scale left-right ultraviolet completion of type-I seesaw for neutrino masses based on the $SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ gauge group without parity, which leads to "large" light-heavy neutrino mixing while keeping the neutrino masses small in a natural manner guaranteed by discrete symmetries. We point out specific observable implications of this class of models if the $SU(2)_R$-breaking scale is of order 5 TeV, in searches for lepton flavor violating processes such as $\mu\to e\gamma$, $\mu\to 3 e$ and $\mu-e$ conversion in nuclei, and lepton number violating processes such as neutrinoless double beta decay as well as at the LHC. In particular, if the upper limit on BR$(\mu\to e\gamma)$ improves by one order of magnitude, a large range of the parameters of the model would be ruled out.Comment: 34 pages, 8 figures, 10 tables; some comments and references added; version accepted for publication in Phys. Rev.

Development of a variational SEASAT data analysis technique

Oceans are data-sparse areas in terms of conventional weather observations. The surface pressure field obtained solely by analyzing the conventional weather data is not expected to possess high accuracy. On the other hand, in entering asynoptic data such as satellite-derived temperature soundings into an atmospheric prediction system, an improved surface analysis is crucial for obtaining more accurate weather predictions because the mass distribution of the entire atmosphere will be better represented in the system as a result of the more accurate surface pressure field. In order to obtain improved surface pressure analyses over the oceans, a variational adjustment technique was developed to help blend the densely distributed surface wind data derived from the SEASAT-A radar observations into the sparsely distributed conventional pressure data. A simple marine boundary layer scheme employed in the adjustment technique was discussed. In addition, a few aspects of the current technique were determined by numerical experiments

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure