2,024 research outputs found
Genus of numerical semigroups generated by three elements
In this paper we study numerical semigroups generated by three elements. We
give a characterization of pseudo-symmetric numerical semigroups. Also, we will
give a simple algorithm to get all the pseudo-symmetric numerical semigroups
with give Frobenius number.Comment: 7 page
Nonequilibrium Green's Function Approach to Phonon Transport in Defective Carbon Nanotubes
We have developed a new theoretical formalism for phonon transport in
nanostructures using the nonequilibrium phonon Green's function technique and
have applied it to thermal conduction in defective carbon nanotubes. The
universal quantization of low-temperature thermal conductance in carbon
nanotubes can be observed even in the presence of local structural defects such
as vacancies and Stone-Wales defects, since the long wavelength acoustic
phonons are not scattered by local defects. At room temperature, however,
thermal conductance is critically affected by defect scattering since incident
phonons are scattered by localized phonons around the defects. We find a
remarkable change from quantum to classical features for the thermal transport
through defective CNTs with increasing temperature.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let
Energy landscape analysis of neuroimaging data
Computational neuroscience models have been used for understanding neural
dynamics in the brain and how they may be altered when physiological or other
conditions change. We review and develop a data-driven approach to neuroimaging
data called the energy landscape analysis. The methods are rooted in
statistical physics theory, in particular the Ising model, also known as the
(pairwise) maximum entropy model and Boltzmann machine. The methods have been
applied to fitting electrophysiological data in neuroscience for a decade, but
their use in neuroimaging data is still in its infancy. We first review the
methods and discuss some algorithms and technical aspects. Then, we apply the
methods to functional magnetic resonance imaging data recorded from healthy
individuals to inspect the relationship between the accuracy of fitting, the
size of the brain system to be analyzed, and the data length.Comment: 22 pages, 4 figures, 1 tabl
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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