260,383 research outputs found
On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited
In the framework of the planar and circular restricted three-body problem, we
consider an asteroid that orbits the Sun in quasi-satellite motion with a
planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital
resonance with the planet, characterized by a non zero eccentricity and a
resonant angle that librates around zero. Likewise, in the rotating frame with
the planet it describes the same trajectory as the one of a retrograde
satellite even though the planet acts as a perturbator. In the last few years,
the discoveries of asteroids in this type of motion made the term
"quasi-satellite" more and more present in the literature. However, some
authors rather use the term "retrograde satellite" when referring to this kind
of motion in the studies of the restricted problem in the rotating frame. In
this paper we intend to clarify the terminology to use, in order to bridge the
gap between the perturbative co-orbital point of view and the more general
approach in the rotating frame. Through a numerical exploration of the
co-orbital phase space, we describe the quasi-satellite domain and highlight
that it is not reachable by low eccentricities by averaging process. We will
show that the quasi-satellite domain is effectively included in the domain of
the retrograde satellites and neatly defined in terms of frequencies.
Eventually, we highlight a remarkable high eccentric quasi-satellite orbit
corresponding to a frozen ellipse in the heliocentric frame. We extend this
result to the eccentric case (planet on an eccentric motion) and show that two
families of frozen ellipses originate from this remarkable orbit.Comment: 30 pages, 13 figures, 1 tabl
Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
We address two aspects of the dynamics of the forced Duffing oscillator which
are relevant to the technology of micromechanical devices and, at the same
time, have intrinsic significance to the field of nonlinear oscillating
systems. First, we study the stability of periodic motion when the phase shift
between the external force and the oscillation is controlled -contrary to the
standard case, where the control parameter is the frequency of the force.
Phase-shift control is the operational configuration under which self-sustained
oscillators -and, in particular, micromechanical oscillators- provide a
frequency reference useful for time keeping. We show that, contrary to the
standard forced Duffing oscillator, under phase-shift control oscillations are
stable over the whole resonance curve. Second, we analyze a model for the
internal resonance between the main Duffing oscillation mode and a
higher-harmonic mode of a vibrating solid bar clamped at its two ends. We focus
on the stabilization of the oscillation frequency when the resonance takes
place, and present preliminary experimental results that illustrate the
phenomenon. This synchronization process has been proposed to counteract the
undesirable frequency-amplitude interdependence in nonlinear time-keeping
micromechanical devices
Systematic and multifactor risk models revisited
Systematic and multifactor risk models are revisited via methods which were
already successfully developed in signal processing and in automatic control.
The results, which bypass the usual criticisms on those risk modeling, are
illustrated by several successful computer experiments.Comment: First Paris Financial Management Conference, Paris : France (2013
Further Results on Lyapunov Functions for Slowly Time-Varying Systems
We provide general methods for explicitly constructing strict Lyapunov
functions for fully nonlinear slowly time-varying systems. Our results apply to
cases where the given dynamics and corresponding frozen dynamics are not
necessarily exponentially stable. This complements our previous Lyapunov
function constructions for rapidly time-varying dynamics. We also explicitly
construct input-to-state stable Lyapunov functions for slowly time-varying
control systems. We illustrate our findings by constructing explicit Lyapunov
functions for a pendulum model, an example from identification theory, and a
perturbed friction model.Comment: Accepted for publication in Mathematics of Control, Signals, and
Systems (MCSS) on November 20, 200
Growth modes of Fe(110) revisited: a contribution of self-assembly to magnetic materials
We have revisited the epitaxial growth modes of Fe on W(110) and Mo(110), and
propose an overview or our contribution to the field. We show that the
Stranski-Krastanov growth mode, recognized for a long time in these systems, is
in fact characterized by a bimodal distribution of islands for growth
temperature in the range 250-700°C. We observe firstly compact islands
whose shape is determined by Wulff-Kaischev's theorem, secondly thin and flat
islands that display a preferred height, ie independant from nominal thickness
and deposition procedure (1.4nm for Mo, and 5.5nm for W on the average). We
used this effect to fabricate self-organized arrays of nanometers-thick stripes
by step decoration. Self-assembled nano-ties are also obtained for nucleation
of the flat islands on Mo at fairly high temperature, ie 800°C. Finally,
using interfacial layers and solid solutions we separate two effects on the
preferred height, first that of the interfacial energy, second that of the
continuously-varying lattice parameter of the growth surface.Comment: 49 pages. Invited topical review for J. Phys.: Condens. Matte
Frequency-Domain Analysis of Linear Time-Periodic Systems
In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature
Dynamics of shape fluctuations of quasi-spherical vesicles revisited
In this paper, the dynamics of spontaneous shape fluctuations of a single,
giant quasi-spherical vesicle formed of a single lipid species is revisited
theoretically. A coherent physical theory for the dynamics is developed based
on a number of fundamental principles and considerations and a systematic
formulation of the theory is also established. From the systematic theoretical
formulation, an analytical description of the dynamics of shape fluctuations of
quasi-spherical vesicles is derived. In particular, in developing the theory we
have made a new interpretation of some of the phenomenological constants in a
canonical continuum description of fluid lipid-bilayer membranes and shown the
consequences of this new interpretation in terms of the characteristics of the
dynamics of vesicle shape fluctuations. Moreover, we have used the systematic
formulation of our theory as a framework against which we have discussed the
previously existing theories and their discrepancies. Finally, we have made a
systematic prediction about the system-dependent characteristics of the
relaxation dynamics of shape fluctuations of quasi-spherical vesicles with a
view of experimental studies of the phenomenon and also discussed, based on our
theory, a recently published experimental work on the topic.Comment: 18 pages, 4 figure
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