784 research outputs found
Periodically driven Taylor-Couette turbulence
We study periodically driven Taylor-Couette turbulence, i.e. the flow
confined between two concentric, independently rotating cylinders. Here, the
inner cylinder is driven sinusoidally while the outer cylinder is kept at rest
(time-averaged Reynolds number is ). Using particle image
velocimetry (PIV), we measure the velocity over a wide range of modulation
periods, corresponding to a change in Womersley number in the range . To understand how the flow responds to a given modulation, we
calculate the phase delay and amplitude response of the azimuthal velocity.
In agreement with earlier theoretical and numerical work, we find that for
large modulation periods the system follows the given modulation of the
driving, i.e. the system behaves quasi-stationary. For smaller modulation
periods, the flow cannot follow the modulation, and the flow velocity responds
with a phase delay and a smaller amplitude response to the given modulation. If
we compare our results with numerical and theoretical results for the laminar
case, we find that the scalings of the phase delay and the amplitude response
are similar. However, the local response in the bulk of the flow is independent
of the distance to the modulated boundary. Apparently, the turbulent mixing is
strong enough to prevent the flow from having radius-dependent responses to the
given modulation.Comment: 12 pages, 6 figure
Generalized Lenard Chains, Separation of Variables and Superintegrability
We show that the notion of generalized Lenard chains naturally allows
formulation of the theory of multi-separable and superintegrable systems in the
context of bi-Hamiltonian geometry. We prove that the existence of generalized
Lenard chains generated by a Hamiltonian function defined on a four-dimensional
\omega N manifold guarantees the separation of variables. As an application, we
construct such chains for the H\'enon-Heiles systems and for the classical
Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler
potential are found.Comment: 14 pages Revte
Alternative linear structures for classical and quantum systems
The possibility of deforming the (associative or Lie) product to obtain
alternative descriptions for a given classical or quantum system has been
considered in many papers. Here we discuss the possibility of obtaining some
novel alternative descriptions by changing the linear structure instead. In
particular we show how it is possible to construct alternative linear
structures on the tangent bundle TQ of some classical configuration space Q
that can be considered as "adapted" to the given dynamical system. This fact
opens the possibility to use the Weyl scheme to quantize the system in
different non equivalent ways, "evading", so to speak, the von Neumann
uniqueness theorem.Comment: 32 pages, two figures, to be published in IJMP
Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
The problem of the invariant classification of the orthogonal coordinate webs
defined in Euclidean space is solved within the framework of Felix Klein's
Erlangen Program. The results are applied to the problem of integrability of
the Calogero-Moser model
The Stabilized Poincare-Heisenberg algebra: a Clifford algebra viewpoint
The stabilized Poincare-Heisenberg algebra (SPHA) is the Lie algebra of
quantum relativistic kinematics generated by fifteen generators. It is obtained
from imposing stability conditions after attempting to combine the Lie algebras
of quantum mechanics and relativity which by themselves are stable, however not
when combined. In this paper we show how the sixteen dimensional Clifford
algebra CL(1,3) can be used to generate the SPHA. The Clifford algebra path to
the SPHA avoids the traditional stability considerations, relying instead on
the fact that CL(1,3) is a semi-simple algebra and therefore stable. It is
therefore conceptually easier and more straightforward to work with a Clifford
algebra. The Clifford algebra path suggests the next evolutionary step toward a
theory of physics at the interface of GR and QM might be to depart from working
in space-time and instead to work in space-time-momentum.Comment: 14 page
Regularity of Kobayashi metric
We review some recent results on existence and regularity of Monge-Amp\`ere
exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit
at least one such exhaustion of sufficiently high regularity. A main
consequence of our results is the fact that the Kobayashi pseudo-metric k on an
appropriare open subset of each of the above domains is actually a smooth
Finsler metric. The class of domains to which our result apply is very large.
It includes for instance all smoothly bounded strongly pseudoconvex complete
circular domains and all their sufficiently small deformations.Comment: 14 pages, 8 figures - The previously announced main result had a gap.
In this new version the corrected statement is given. To appear on the volume
"Geometric Complex Analysis - Proceedings of KSCV 12 Symposium
Кон'юнктурний аналіз розвитку ринку рекреаційних послуг АР Крим
Метою дослідження є кон’юнктурний аналіз розвитку ринку рекреаційних послуг АР Крим та порівняльна оцінка функціонування конкурентоспроможних рекреаційних районів
Equivalence problem for the orthogonal webs on the sphere
We solve the equivalence problem for the orthogonally separable webs on the
three-sphere under the action of the isometry group. This continues a classical
project initiated by Olevsky in which he solved the corresponding canonical
forms problem. The solution to the equivalence problem together with the
results by Olevsky forms a complete solution to the problem of orthogonal
separation of variables to the Hamilton-Jacobi equation defined on the
three-sphere via orthogonal separation of variables. It is based on invariant
properties of the characteristic Killing two-tensors in addition to properties
of the corresponding algebraic curvature tensor and the associated Ricci
tensor. The result is illustrated by a non-trivial application to a natural
Hamiltonian defined on the three-sphere.Comment: 32 page
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