1,486 research outputs found
Average phase factor in the PNJL model
The average phase factor of the QCD determinant is evaluated at finite quark
chemical potential ({\mu}_q) with the two-flavor version of the Polyakov-loop
extended Nambu-Jona-Lasinio (PNJL) model with the scalar-type eight-quark
interaction. For {\mu}_q larger than half the pion mass at vacuum m_{\pi}, the
average phase factor is finite only when the Polyakov loop is larger than 0.5,
indicating that lattice QCD is feasible only in the deconfinement phase. A
critical endpoint (CEP) lies in the region of the zero average phase factor.
The scalar-type eight-quark interaction makes it shorter a relative distance of
the CEP to the boundary of the region. For {\mu}_q < m_{\pi}/2, the PNJL model
with dynamical mesonic fluctuations can reproduce lattice QCD data below the
critical temperature.Comment: 8 pages, 6 figure
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 at the point of
contact and vanishes at . 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 so that corresponds to the GBC
and analyze the behavior of . 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 such that , 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 . And we
obtain a critical value 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
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