201 research outputs found
How does the Smaller Alignment Index (SALI) distinguish order from chaos?
The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from
ordered motion, has been demonstrated recently in several
publications.\cite{Sk01,GRACM} Basically it is observed that in chaotic regions
the SALI goes to zero very rapidly, while it fluctuates around a nonzero value
in ordered regions. In this paper, we make a first step forward explaining
these results by studying in detail the evolution of small deviations from
regular orbits lying on the invariant tori of an {\bf integrable} 2D
Hamiltonian system. We show that, in general, any two initial deviation vectors
will eventually fall on the ``tangent space'' of the torus, pointing in
different directions due to the different dynamics of the 2 integrals of
motion, which means that the SALI (or the smaller angle between these vectors)
will oscillate away from zero for all time.Comment: To appear in Progress of Theoretical Physics Supplemen
Th17 Response and Inflammatory Autoimmune Diseases
The proinflammatory activity of T helper 17 (Th17) cells can be beneficial to the host during infection. However, uncontrolled or inappropriate Th17 activation has been linked to several autoimmune and autoinflammatory pathologies. Indeed, preclinical and clinical data show that Th17 cells are associated with several autoimmune diseases such as arthritis, multiple sclerosis, psoriasis, and lupus. Furthermore, targeting the interleukin-17 (IL-17) pathway has attenuated disease severity in preclinical models of autoimmune diseases. Interestingly, a recent report brings to light a potential role for Th17 cells in the autoinflammatory disorder adult-onset Still's disease (AOSD). Whether Th17 cells are the cause or are directly involved in AOSD remains to be shown. In this paper, we discuss the biology of Th17 cells, their role in autoimmune disease development, and in AOSD in particular, as well as the growing interest of the pharmaceutical industry in their use as therapeutic targets
Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model
We study the distinction and quantification of chaotic and regular motion in
a time-dependent Hamiltonian barred galaxy model. Recently, a strong
correlation was found between the strength of the bar and the presence of
chaotic motion in this system, as models with relatively strong bars were shown
to exhibit stronger chaotic behavior compared to those having a weaker bar
component. Here, we attempt to further explore this connection by studying the
interplay between chaotic and regular behavior of star orbits when the
parameters of the model evolve in time. This happens for example when one
introduces linear time dependence in the mass parameters of the model to mimic,
in some general sense, the effect of self-consistent interactions of the actual
N-body problem. We thus observe, in this simple time-dependent model also, that
the increase of the bar's mass leads to an increase of the system's chaoticity.
We propose a new way of using the Generalized Alignment Index (GALI) method as
a reliable criterion to estimate the relative fraction of chaotic vs. regular
orbits in such time-dependent potentials, which proves to be much more
efficient than the computation of Lyapunov exponents. In particular, GALI is
able to capture subtle changes in the nature of an orbit (or ensemble of
orbits) even for relatively small time intervals, which makes it ideal for
detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A:
Math. Theo
Application of new dynamical spectra of orbits in Hamiltonian systems
In the present article, we investigate the properties of motion in
Hamiltonian systems of two and three degrees of freedom, using the distribution
of the values of two new dynamical parameters. The distribution functions of
the new parameters, define the S(g) and the S(w) dynamical spectra. The first
spectrum definition, that is the S(g) spectrum, will be applied in a
Hamiltonian system of two degrees of freedom (2D), while the S(w) dynamical
spectrum will be deployed in a Hamiltonian system of three degrees of freedom
(3D). Both Hamiltonian systems, describe a very interesting dynamical system
which displays a large variety of resonant orbits, different chaotic components
and also several sticky regions. We test and prove the efficiency and the
reliability of these new dynamical spectra, in detecting tiny ordered domains
embedded in the chaotic sea, corresponding to complicated resonant orbits of
higher multiplicity. The results of our extensive numerical calculations,
suggest that both dynamical spectra are fast and reliable discriminants between
different types of orbits in Hamiltonian systems, while requiring very short
computation time in order to provide solid and conclusive evidence regarding
the nature of an orbit. Furthermore, we establish numerical criteria in order
to quantify the results obtained from our new dynamical spectra. A comparison
to other previously used dynamical indicators, reveals the leading role of the
new spectra.Comment: Published in Nonlinear Dynamics (NODY) journal. arXiv admin note:
text overlap with arXiv:1009.1993 by other author
Application of the MEGNO technique to the dynamics of Jovian irregular satellites
We apply the MEGNO (Mean Exponential Growth of Nearby Orbits) technique to
the dynamics of Jovian irregular satellites. We demonstrate the efficiency of
applying the MEGNO indicator to generate a mapping of relevant phase-space
regions occupied by observed jovian irregular satellites. The construction of
MEGNO maps of the Jovian phase-space region within its Hill-sphere is addressed
and the obtained results are compared with previous studies regarding the
dynamical stability of irregular satellites. Since this is the first time the
MEGNO technique is applied to study the dynamics of irregular satellites we
provide a review of the MEGNO theory. We consider the elliptic restricted
three-body problem in which Jupiter is orbited by a massless test satellite
subject to solar gravitational perturbations. The equations of motion of the
system are integrated numerically and the MEGNO indicator computed from the
systems variational equations. An unprecedented large set of initial conditions
are studied to generate the MEGNO maps. The chaotic nature of initial
conditions are demonstrated by studying a quasi-periodic orbit and a chaotic
orbit. As a result we establish the existence of several high-order mean-motion
resonances detected for retrograde orbits along with other interesting
dynamical features. The computed MEGNO maps allows to qualitatively
differentiate between chaotic and quasi-periodic regions of the irregular
satellite phase-space given only a relatively short integration time. By
comparing with previous published results we can establish a correlation
between chaotic regions and corresponding regions of orbital instability.Comment: 15 pages, 13 figures, 2 tables, submitted to MNRA
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