7,404 research outputs found
Hyperbolic Covariant Coherent Structures in two dimensional flows
A new method to describe hyperbolic patterns in two dimensional flows is
proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which
have the properties to be covariant with the dynamics, and thus being mapped by
the tangent linear operator into another CLVs basis, they are norm independent,
invariant under time reversal and can be not orthonormal. CLVs can thus give a
more detailed information on the expansion and contraction directions of the
flow than the Lyapunov Vector bases, that are instead always orthogonal. We
suggest a definition of Hyperbolic Covariant Coherent Structures (HCCSs), that
can be defined on the scalar field representing the angle between the CLVs.
HCCSs can be defined for every time instant and could be useful to understand
the long term behaviour of particle tracers.
We consider three examples: a simple autonomous Hamiltonian system, as well
as the non-autonomous "double gyre" and Bickley jet, to see how well the angle
is able to describe particular patterns and barriers. We compare the results
from the HCCSs with other coherent patterns defined on finite time by the
Finite Time Lyapunov Exponents (FTLEs), to see how the behaviour of these
structures change asymptotically
Detection of Total Rotations on 2D-Vector Fields with Geometric Correlation
Correlation is a common technique for the detection of shifts. Its
generalization to the multidimensional geometric correlation in Clifford
algebras additionally contains information with respect to rotational
misalignment. It has been proven a useful tool for the registration of vector
fields that differ by an outer rotation. In this paper we proof that applying
the geometric correlation iteratively has the potential to detect the total
rotational misalignment for linear two-dimensional vector fields. We further
analyze its effect on general analytic vector fields and show how the rotation
can be calculated from their power series expansions
Basins of Attraction for Chimera States
Chimera states---curious symmetry-broken states in systems of identical
coupled oscillators---typically occur only for certain initial conditions. Here
we analyze their basins of attraction in a simple system comprised of two
populations. Using perturbative analysis and numerical simulation we evaluate
asymptotic states and associated destination maps, and demonstrate that basins
form a complex twisting structure in phase space. Understanding the basins'
precise nature may help in the development of control methods to switch between
chimera patterns, with possible technological and neural system applications.Comment: Please see Ancillary files for the 4 supplementary videos including
description (PDF
The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current
This article reviews several recently developed Lagrangian tools and shows
how their combined use succeeds in obtaining a detailed description of purely
advective transport events in general aperiodic flows. In particular, because
of the climate impact of ocean transport processes, we illustrate a 2D
application on altimeter data sets over the area of the Kuroshio Current,
although the proposed techniques are general and applicable to arbitrary time
dependent aperiodic flows. The first challenge for describing transport in
aperiodical time dependent flows is obtaining a representation of the phase
portrait where the most relevant dynamical features may be identified. This
representation is accomplished by using global Lagrangian descriptors that when
applied for instance to the altimeter data sets retrieve over the ocean surface
a phase portrait where the geometry of interconnected dynamical systems is
visible. The phase portrait picture is essential because it evinces which
transport routes are acting on the whole flow. Once these routes are roughly
recognised it is possible to complete a detailed description by the direct
computation of the finite time stable and unstable manifolds of special
hyperbolic trajectories that act as organising centres of the flow.Comment: 40 pages, 24 figure
Spin-1 gravitational waves. Theoretical and experimental aspects
Exact solutions of Einstein field equations invariant for a non-Abelian
2-dimensional Lie algebra of Killing fields are described. Physical properties
of these gravitational fields are studied, their wave character is checked by
making use of covariant criteria and the observable effects of such waves are
outlined. The possibility of detection of these waves with modern detectors,
spherical resonant antennas in particular, is sketched
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