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

Modified Iterative Extended Hueckel. 2: Application to the interaction of Na(+), Na(+)(aq.), Mg(+)-2(aq.) with adenine and thymine

Modified Iterative Extended Hueckel, which includes explicit effective internuclear and electronic interactions, is applied to the study of the energetics of Na(+),Mg(+), Na(+) (aqueous), and Mg(+2) (aqueous) ions approaching various possible binding sites on adenine and thymine. Results for the adenine + ion and thymine + ion are in good qualitative agreement with ab initio work on analogous systems. Energy differences between competing sites are in excellent agreement. Hydration appears to be a critical factor in determining favorable binding sites. That the adenine Nl and N3 sites cannot displace a water molecule from the hydrated cation indicates that they are not favorable binding sites in aqueous media. Of those sites investigated, 04 was the most favorable binding site on the thymine for the bare Na(+). However, the 02 site was the most favorable binding site for either hydrated cation

A Modified Optical Potential Approach to Low-energy Electron-helium Scattering

Optical potential approach to low energy electron- helium scatterin

Computer aided design and analysis of gear tooth geometry

A simulation method for gear hobbing and shaping of straight and spiral bevel gears is presented. The method is based upon an enveloping theory for gear tooth profile generation. The procedure is applicable in the computer aided design of standard and nonstandard tooth forms. An inverse procedure for finding a conjugate gear tooth profile is presented for arbitrary cutter geometry. The kinematic relations for the tooth surfaces of straight and spiral bevel gears are proposed. The tooth surface equations for these gears are formulated in a manner suitable for their automated numerical development and solution

Synthesis of structural damping, volume I Final report

Hysteresis model for analyzing dynamic behavior of complex structure

Roles of mechanistic target of rapamycin and transforming growth factor-B signaling in the molting gland (Y-organ) of the blackback land crab, Gecarcinus lateralis

Molting in decapod crustaceans is controlled by molt-inhibiting hormone (MIH), an eyestalk neuropeptide that suppresses production of ecdysteroids by a pair of molting glands (Y-organs or YOs). Eyestalk ablation (ESA) activates the YOs, which hypertrophy and increase ecdysteroid secretion. At mid premolt, which occurs 7–14 days post-ESA, the YO transitions to the committed state; hemolymph ecdysteroid titers increase further and the animal reaches ecdysis ~ 3 weeks post-ESA. Two conserved signaling pathways, mechanistic target of rapamycin (mTOR) and transforming growth factor-β (TGF-β), are expressed in the Gecarcinus lateralis YO. Rapamycin, an mTOR antagonist, inhibits YO ecdysteroidogenesis in vitro. In this study, rapamycin lowered hemolymph ecdysteroid titer in ESA G. lateralis in vivo; levels were significantly lower than in control animals at all intervals (1–14 days post-ESA). Injection of SB431542, an activin TGF-β receptor antagonist, lowered hemolymph ecdysteroid titers 7 and 14 days post-ESA, but had no effect on ecdysteroid titers at 1 and 3 days post-ESA. mRNA levels of mTOR signaling genes Gl-mTOR, Gl-Akt, and Gl-S6k were increased by 3 days post-ESA; the increases in Gl-mTOR and Gl-Akt mRNA levels were blocked by SB431542. Gl-elongation factor 2 and Gl-Rheb mRNA levels were not affected by ESA, but SB431542 lowered mRNA levels at Days 3 and 7 post-ESA. The mRNA level of an activin TGF-β peptide, Gl-myostatin-like factor (Mstn), increased 5.5-fold from 0 to 3 days post-ESA, followed by a 50-fold decrease from 3 to 7 days post-ESA. These data suggest that (1) YO activation involves an up regulation of the mTOR signaling pathway; (2) mTOR is required for YO commitment; and (3) a Mstn-like factor mediates the transition of the YO from the activated to the committed state

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