729 research outputs found
Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
As originally formulated, the Generalized Alignment Index (GALI) method of
chaos detection has so far been applied to distinguish quasiperiodic from
chaotic motion in conservative nonlinear dynamical systems. In this paper we
extend its realm of applicability by using it to investigate the local dynamics
of periodic orbits. We show theoretically and verify numerically that for
stable periodic orbits the GALIs tend to zero following particular power laws
for Hamiltonian flows, while they fluctuate around non-zero values for
symplectic maps. By comparison, the GALIs of unstable periodic orbits tend
exponentially to zero, both for flows and maps. We also apply the GALIs for
investigating the dynamics in the neighborhood of periodic orbits, and show
that for chaotic solutions influenced by the homoclinic tangle of unstable
periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during
which their amplitudes change by many orders of magnitude. Finally, we use the
GALI method to elucidate further the connection between the dynamics of
Hamiltonian flows and symplectic maps. In particular, we show that, using for
the computation of GALIs the components of deviation vectors orthogonal to the
direction of motion, the indices of stable periodic orbits behave for flows as
they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of
Bifurcation and Chaos
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Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem
We study chaotic orbits of conservative low--dimensional maps and present
numerical results showing that the probability density functions (pdfs) of the
sum of iterates in the large limit exhibit very interesting
time-evolving statistics. In some cases where the chaotic layers are thin and
the (positive) maximal Lyapunov exponent is small, long--lasting
quasi--stationary states (QSS) are found, whose pdfs appear to converge to
--Gaussians associated with nonextensive statistical mechanics. More
generally, however, as increases, the pdfs describe a sequence of QSS that
pass from a --Gaussian to an exponential shape and ultimately tend to a true
Gaussian, as orbits diffuse to larger chaotic domains and the phase space
dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in
the International Journal of Bifurcation and Chaos, on Jun 21, 201
Weak Chaos and the "Melting Transition" in a Confined Microplasma System
We present results demonstrating the occurrence of changes in the collective
dynamics of a Hamiltonian system which describes a confined microplasma
characterized by long--range Coulomb interactions. In its lower energy regime,
we first detect macroscopically, the transition from a "crystalline--like" to a
"liquid--like" behavior, which we call the "melting transition". We then
proceed to study this transition using a microscopic chaos indicator called the
\emph{Smaller Alignment Index} (SALI), which utilizes two deviation vectors in
the tangent dynamics of the flow and is nearly constant for ordered
(quasi--periodic) orbits, while it decays exponentially to zero for chaotic
orbits as , where
are the two largest Lyapunov exponents. During the
"melting phase", SALI exhibits a peculiar, stair--like decay to zero,
reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of
resonance islands. This alerts us to the importance of the
variations in that regime and helps us
identify the energy range over which "melting" occurs as a multi--stage
diffusion process through weakly chaotic layers in the phase space of the
microplasma. Additional evidence supporting further the above findings is given
by examining the indices, which generalize SALI (=) to the
case of deviation vectors and depend on the complete spectrum of Lyapunov
exponents of the tangent flow about the reference orbit.Comment: 21 pages, 7 figures, submitted at PR
Numerical and experimental evaluation of sonic resonance against ultrasonic pulse velocity and compression tests on concrete core samples
Destructive Testing, like core drilling, remains today the only reliable method to calculate with accuracy concrete’s strength parameters. However, the damage of the constructions is always a limitation. On the contrary, Non-Destructive Tests (NDT) are fast and cost-effective which make them attractive nowadays. Nevertheless, the results of Ultrasonic Pulse Velocity (UPV) test are highly dispersed. Therefore, it is necessary to combine them along with destructive tests. The purpose of this study is to investigate the feasibility to adopt the Sonic Resonance (SR) test to determine the strength parameters of the concrete. UPV and SR were used in conjunction with the Uniaxial Compression Test. Experimental and numerical analysis were conducted. More than 200 concrete cores from existing constructions were tested and more than 70 Finite Element Method (FEM) models were simulated. The results were correlated, and two empirical equations derived. It was observed that the dispersion of the of SR alone is smaller than the UPV, but also the UPV dispersion can be narrowed as long as the Poisson’s ratio is known
Scaling similarities of multiple fracturing of solid materials
It has recently reported that electromagnetic flashes of low-energy <IMG WIDTH='12' HEIGHT='29' ALIGN='MIDDLE' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img1.gif' ALT=''>-rays emitted during multi-fracturing on a neutron star, and electromagnetic pulses emitted in the laboratory by a disordered material subjected to an increasing external load, share distinctive statistical properties with earthquakes, such as power-law energy distributions (Cheng et al., 1996; Kossobokov et al., 2000; Rabinovitch et al., 2001; Sornette and Helmstetter, 2002). The neutron starquakes may release strain energies up to <IMG WIDTH='32' HEIGHT='16' ALIGN='BOTTOM' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img2.gif' ALT=''>erg, while, the fractures in laboratory samples release strain energies approximately a fraction of an erg. An earthquake fault region can build up strain energy up to approximately <IMG WIDTH='32' HEIGHT='16' ALIGN='BOTTOM' BORDER='0' src='http://www.nonlin-processes-geophys.net/11/137/2004/npg-11-137-img3.gif' ALT=''>erg for the strongest earthquakes. Clear sequences of kilohertz-megahertz electromagnetic avalanches have been detected from a few days up to a few hours prior to recent destructive earthquakes in Greece. A question that arises effortlessly is if the pre-seismic electromagnetic fluctuations also share the same statistical properties. Our study justifies a positive answer. Our analysis also reveals 'symptoms' of a transition to the main rupture common with earthquake sequences and acoustic emission pulses observed during laboratory experiments (Maes et al., 1998)
Engineering of composite metallic microfibers towards development of plasmonic devices for sensing applications
The paper discusses the analysis of tapered hybrid composite microfibers based on a metal-core and dielectric-cladding composite material system. Its advantages over the pure metal tips conventionally used, are the inherent enhanced environmental robustness due to inert borosilicate cladding and the capability of multiple excitation of the tapered nanowire through the length of the fiber due to the enabled total internal reflection at the borosilicate/air interface. Simulations through finite element method (FEM) have demonstrated an improved field enhancement at the tapered region of such microfibers. Furthermore, experimental results on tapering in copper based microfibers together with light coupling and propagation studies will be demonstrated revealing the potential for the development of plasmonic devices for sensing applications
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