Rattleback dynamics and its reversal time of rotation.

A rattleback is a rigid, semielliptic toy which exhibits unintuitive behavior; when it is spun in one direction, it soon begins pitching and stops spinning, then it starts to spin in the opposite direction, but in the other direction, it seems to spin just steadily. This puzzling behavior results from the slight misalignment between the principal axes for the inertia and those for the curvature; the misalignment couples the spinning with the pitching and the rolling oscillations. It has been shown that under the no-slip condition and without dissipation the spin can reverse in both directions, and Garcia and Hubbard obtained the formula for the time required for the spin reversal t_{r} [Proc. R. Soc. Lond. A 418, 165 (1988)1364-502110.1098/rspa.1988.0078]. In this work, we reformulate the rattleback dynamics in a physically transparent way and reduce it to a three-variable dynamics for spinning, pitching, and rolling. We obtain an expression of the Garcia-Hubbard formula for t_{r} by a simple product of four factors: (1) the misalignment angle, (2) the difference in the inverses of inertia moment for the two oscillations, (3) that in the radii for the two principal curvatures, and (4) the squared frequency of the oscillation. We perform extensive numerical simulations to examine validity and limitation of the formula, and find that (1) the Garcia-Hubbard formula is good for both spinning directions in the small spin and small oscillation regime, but (2) in the fast spin regime especially for the steady direction, the rattleback may not reverse and shows a rich variety of dynamics including steady spinning, spin wobbling, and chaotic behavior reminiscent of chaos in a dissipative system.

The relationship between Bell's palsy and morphometric aspects of the facial nerve.

Epidemiological data of Bell's palsy (BP) have been reported. For example, the annual incidence of BP is 15-30 per 100,000 persons, with equal numbers of men and women affected, and there is no predilection for either side of the face. However, details of the relationship between BP and morphometric aspects of the facial nerve have not been available in textbooks. We performed a morphometric analysis of human facial nerve fibers and estimated the total number of myelinated axons (TN) and average transverse area of myelinated axons (ATA). The facial nerve showed a significant decrease of TN with increasing age (r = -0.77; p < 0.01), but showed no significant changes of ATA with age (r = -0.01; p = 0.96). We supposed that the TN decrease with age was a factor in the delayed recovery from BP seen in the elderly. Moreover, the TN and ATA showed no significant differences between female and male specimens (p < 0.05), or between the right and left side specimens (p < 0.05). Our present results seem to explain the absence of significant sex and affected side differences in BP.

Similarities and differences between intraductal papillary tumors of the bile duct with and without macroscopically visible mucin secretion.

Intraductal papillary neoplasms of the bile duct (IPNB) have been recently proposed as the biliary counterpart of intraductal papillary mucinous neoplasms of the pancreas (IPMN-P). However, in contrast to IPMN-P, IPNB include a considerable number of the tumors without macroscopically visible mucin secretion. Here we report the similarities and differences between IPNB with and without macroscopically visible mucin secretion (IPNB-M and IPNB-NM). Surgically resected 27 consecutive cases with IPNB were divided into IPNB-M (n=10) and IPNB-NM (n=17), and their clinicopathologic features were examined. Clinically, both tumors were similar. Pathologically, the most frequent histopathologic types were pancreatobiliary in IPNB-NM and intestinal in IPNB-M. Various degrees of cytoarchitectural atypia within the same tumor were exhibited in 8 IPNB-M, but only 3 in IPNB-NM. Although the tumor size was similar, 9 IPNB-NM were invasive carcinoma, whereas all but 1 IPNB-M with carcinoma were in situ or minimally invasive. Immunohistochemically, positive MUC2 expression was significantly more frequent in IPNB-M than in IPNB-NM, whereas MUC1 tended to be more frequently expressed in IPNB-NM compared with IPNB-M. Among IPNB-NM with positive MUC1 expression, 3 had negative MUC2 and MUC5AC expressions. These tumors showed a tubulopapillary growth with uniform degree of cytoarchitectural atypia. All IPNB-M were negative for p53, and the frequency of positive p53 protein in IPNB-NM was at the middle level of that in IPNB-M and nonpapillary cholangiocarcinoma. In conclusion, IPNB-M showed striking similarities to IPMN-P, but IPNB-NM contained heterogeneous disease groups.

Loewner driving functions for off-critical percolation clusters.

We numerically study the Loewner driving function Ut of a site percolation cluster boundary on the triangular lattice for ppc.

Anatomical study of meandering and functions of human intralaryngeal artery.

In recent years, partial laryngectomy and partial reconstruction are increasingly intended for conservation of functions of phonation and swallowing. In partial reconstruction, it is important to comprehend morphological characteristics of the blood vessels distributed in the larynx, but there have been only few reports discussing detailed information about them. Previous reports on laryngeal blood vessels have shown that branches of some arteries show remarkable "meandering". In the present study, we devised a method for objectively determining the morphological nature, "meandering" and assessed functions of the arteries. Intralaryngeal arteries were excised from the larynx of cadavers prepared for practice in anatomy, and images of the "meandering" artery were analyzed with NIH Image. The extent of "meandering" was expressed mainly as the ratio of the total length of the blood vessel to the distance between the starting point and the end point of meandering. The results showed that there was a significant difference in the extent of meandering between superior posterior and medial posterior branches of superior laryngeal artery. These arteries, which were distributed in the arytenoid region, were found to be of primary importance in partial laryngectomy and partial reconstruction of the larynx.