Motion of the Tippe Top : Gyroscopic Balance Condition and Stability

We reexamine a very classical problem, the spinning behavior of the tippe top on a horizontal table. The analysis is made for an eccentric sphere version of the tippe top, assuming a modified Coulomb law for the sliding friction, which is a continuous function of the slip velocity $\vec v_P$ at the point of contact and vanishes at $\vec v_P=0$. We study the relevance of the gyroscopic balance condition (GBC), which was discovered to hold for a rapidly spinning hard-boiled egg by Moffatt and Shimomura, to the inversion phenomenon of the tippe top. We introduce a variable $\xi$ so that $\xi=0$ corresponds to the GBC and analyze the behavior of $\xi$. Contrary to the case of the spinning egg, the GBC for the tippe top is not fulfilled initially. But we find from simulation that for those tippe tops which will turn over, the GBC will soon be satisfied approximately. It is shown that the GBC and the geometry lead to the classification of tippe tops into three groups: The tippe tops of Group I never flip over however large a spin they are given. Those of Group II show a complete inversion and the tippe tops of Group III tend to turn over up to a certain inclination angle $\theta_f$ such that $\theta_f<\pi$, when they are spun sufficiently rapidly. There exist three steady states for the spinning motion of the tippe top. Giving a new criterion for stability, we examine the stability of these states in terms of the initial spin velocity $n_0$. And we obtain a critical value $n_c$ of the initial spin which is required for the tippe top of Group II to flip over up to the completely inverted position.Comment: 52 pages, 11 figures, to be published in SIAM Journal on Applied Dynamical Syste

Analysis and Application of Decaying Turbulence with Initial Fractal Geometry

In this paper, we address high‐Schmidt‐number (Sc) scalar turbulent mixing that results from grid‐generated turbulence using the initial fractal geometry of the velocity profile. More specifically, as was proposed in our recent study, we adopt an initial flow field generated by a fractal grid and apply it to a water channel experiment based on a high‐Sc‐number scalar‐mixing layer in order to create grid‐generated turbulence, and thus solve our current research problem. The high‐Sc‐number scalar and velocity fields of the grid‐generated turbulence are then measured using planar laser‐induced fluorescence (PLIF) and particle image velocimetry (PIV), respectively. By means of fractal analysis, this study specifically addresses the turbulent mixing phenomena in which the fractal dimension of the mixing interface of an observed high‐Sc‐number scalar field is calculated. Additionally, we discuss the efficiency of using fractal grids as devices for enhancing high‐Sc‐number scalar turbulent mixing by observing turbulent intensities and dissipation by PIV

Effects of rehabilitation program for an anatomical abnormality

Introduction : Spina bifida occulta (SBO) is a common malformation of lamina of the spine, most commonly occurring in the sacrum or lower lumbar spine. Athletes with anatomical abnormalities such as SBO may be vulnerable to discoordination of muscles and/or skeletal structures. Case Report : We present a case of a 15-year-old male adolescent who presented with persistent low back pain (LBP) associated with SBO at T11-L1 that had been overlooked for several years. He participated in karate as a top-level competitor at the nationallevel, but the LBP interfered with his play. Dynamic X-ray films showed limited range of motion (ROM) in his lower lumbar spine (L3-S1). Instead, the thoracolumbar junction compensated for the lack of ROM in the lumbar spine, enabling trunk flexion and extension. To restore normal coordination, he was treated with a 2-week rehabilitation program including flexibility and core conditioning for the trunk to improve coordination of spinal movement. Two weeks later, his LBP resolved. Conclusion : These results suggest that evaluation of the coordination of the muscles and skeletal structures has an important role in the treatment of cases with an anatomical abnormality such as SBO

Renormalization group approach to multiple-arc random matrix models

We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large-N renormalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is identified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The latter signifies a novel universality of large-N correlators other than the usual single arc type. This phase structure is consistent with the universality classification of two-level correlators for multiple-arc models by Ambjorn and Akemann. We also establish the stability of the gaussian fixed point in the multi-coupling model.Comment: 11 pages, 1 figure, LaTeX + a4.sty, epsf.st

Reaction pathway analysis for dislocation nucleation from a Ni surface step

Abstract Threshold strain required for a thermally activated dislocation nucleation from a Ni surface step has been measured using an atomistic-based reaction pathway analysis. We show that the saddle-point configuration and the stress-dependent activation energy are strongly influenced by the presence of a surface step. Our results provide insight into the previous experimental findings concerning the mechanism on a coherency loss at the Ni/Cu(001) interface. We conclude that the coherency strain caused by a lattice mismatch between Ni and Cu does not yield a sufficient driving force for the dislocation nucleation