4,479 research outputs found
On the Anisotropic Nature of MRI-Driven Turbulence in Astrophysical Disks
The magnetorotational instability is thought to play an important role in
enabling accretion in sufficiently ionized astrophysical disks. The rate at
which MRI-driven turbulence transports angular momentum is related to both the
strength of the amplitudes of the fluctuations on various scales and the degree
of anisotropy of the underlying turbulence. This has motivated several studies
of the distribution of turbulent power in spectral space. In this paper, we
investigate the anisotropic nature of MRI-driven turbulence using a
pseudo-spectral code and introduce novel ways to robustly characterize the
underlying turbulence. We show that the general flow properties vary in a
quasi-periodic way on timescales comparable to 10 inverse angular frequencies
motivating the temporal analysis of its anisotropy. We introduce a 3D tensor
invariant analysis to quantify and classify the evolution of the anisotropic
turbulent flow. This analysis shows a continuous high level of anisotropy, with
brief sporadic transitions towards two- and three-component isotropic turbulent
flow. This temporal-dependent anisotropy renders standard shell-average,
especially when used simultaneously with long temporal averages, inadequate for
characterizing MRI-driven turbulence. We propose an alternative way to extract
spectral information from the turbulent magnetized flow, whose anisotropic
character depends strongly on time. This consists of stacking 1D Fourier
spectra along three orthogonal directions that exhibit maximum anisotropy in
Fourier space. The resulting averaged spectra show that the power along each of
the three independent directions differs by several orders of magnitude over
most scales, except the largest ones. Our results suggest that a
first-principles theory to describe fully developed MRI-driven turbulence will
likely have to consider the anisotropic nature of the flow at a fundamental
level.Comment: 13 pages, 13 figures, submitted to Ap
Anisotropic particles near surfaces: Self-propulsion and friction
We theoretically study the phenomenon of self-propulsion through Casimir
forces in thermal non-equilibrium. Using fluctuational electrodynamics, we
derive a formula for the self-propulsion force for an arbitrary small object in
two scenarios, i) for the object being isolated, and ii) for the object being
close to a planar surface. In the latter case, the self-propulsion force (i.e.,
the force parallel to the surface) increases with decreasing distance, i.e., it
couples to the near-field. We numerically calculate the lateral force acting on
a hot spheroid near a surface and show that it can be as large as the
gravitational force, thus being potentially measurable in fly-by experiments.
We close by linking our results to well-known relations of linear response
theory in fluctuational electrodynamics: Looking at the friction of the
anisotropic object for constant velocity, we identify a correction term that is
additional to the typically used approach.Comment: 13 pages, 8 figures (v2: References updated
Formation and Evolution of Singularities in Anisotropic Geometric Continua
Evolutionary PDEs for geometric order parameters that admit propagating
singular solutions are introduced and discussed. These singular solutions arise
as a result of the competition between nonlinear and nonlocal processes in
various familiar vector spaces. Several examples are given. The motivating
example is the directed self assembly of a large number of particles for
technological purposes such as nano-science processes, in which the particle
interactions are anisotropic. This application leads to the derivation and
analysis of gradient flow equations on Lie algebras. The Riemann structure of
these gradient flow equations is also discussed.Comment: 38 pages, 4 figures. Physica D, submitte
Euler-Poincar\'e equations for -Strands
The -strand equations for a map into a Lie
group are associated to a -invariant Lagrangian. The Lie group manifold
is also the configuration space for the Lagrangian. The -strand itself is
the map , where and are the
independent variables of the -strand equations. The Euler-Poincar\'e
reduction of the variational principle leads to a formulation where the
dependent variables of the -strand equations take values in the
corresponding Lie algebra and its co-algebra,
with respect to the pairing provided by the variational derivatives of the
Lagrangian.
We review examples of different -strand constructions, including matrix
Lie groups and diffeomorphism group. In some cases the -strand equations are
completely integrable 1+1 Hamiltonian systems that admit soliton solutions.Comment: To appear in Conference Proceedings for Physics and Mathematics of
Nonlinear Phenomena, 22 - 29 June 2013, Gallipoli (Italy)
http://pmnp2013.dmf.unisalento.it/talks.shtml, 9 pages, no figure
A meshless, integration-free, and boundary-only RBF technique
Based on the radial basis function (RBF), non-singular general solution and
dual reciprocity method (DRM), this paper presents an inherently meshless,
integration-free, boundary-only RBF collocation techniques for numerical
solution of various partial differential equation systems. The basic ideas
behind this methodology are very mathematically simple. In this study, the RBFs
are employed to approximate the inhomogeneous terms via the DRM, while
non-singular general solution leads to a boundary-only RBF formulation for
homogenous solution. The present scheme is named as the boundary knot method
(BKM) to differentiate it from the other numerical techniques. In particular,
due to the use of nonsingular general solutions rather than singular
fundamental solutions, the BKM is different from the method of fundamental
solution in that the former does no require the artificial boundary and results
in the symmetric system equations under certain conditions. The efficiency and
utility of this new technique are validated through a number of typical
numerical examples. Completeness concern of the BKM due to the only use of
non-singular part of complete fundamental solution is also discussed
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