247 research outputs found
Self Similar Spherical Collapse Revisited: a Comparison between Gas and Dark Matter Dynamics
We reconsider the collapse of cosmic structures in an Einstein-de Sitter
Universe, using the self similar initial conditions of Fillmore & Goldreich
(1984). We first derive a new approximation to describe the dark matter
dynamics in spherical geometry, that we refer to the "fluid approach". This
method enables us to recover the self-similarity solutions of Fillmore &
Goldreich for dark matter. We derive also new self-similarity solutions for the
gas. We thus compare directly gas and dark matter dynamics, focusing on the
differences due to their different dimensionalities in velocity space. This
work may have interesting consequences for gas and dark matter distributions in
large galaxy clusters, allowing to explain why the total mass profile is always
steeper than the X-ray gas profile. We discuss also the shape of the dark
matter density profile found in N-body simulations in terms of a change of
dimensionality in the dark matter velocity space. The stable clustering
hypothesis has been finally considered in the light of this analytical
approach.Comment: 14 pages, 2 figures, accepted for publication in The Astrophysical
Journa
Infinite ergodic theory and Non-extensive entropies
We bring into account a series of result in the infinite ergodic theory that
we believe that they are relevant to the theory of non-extensive entropie
A Two-Temperature Model of the Intracluster Medium
We investigate evolution of the intracluster medium (ICM), considering the
relaxation process between the ions and electrons. According to the standard
scenario of structure formation, ICM is heated by the shock in the accretion
flow to the gravitational potential well of the dark halo. The shock primarily
heats the ions because the kinetic energy of an ion entering the shock is
larger than that of an electron by the ratio of masses. Then the electrons and
ions exchange the energy through coulomb collisions and reach the equilibrium.
From simple order estimation we find that the region where the electron
temperature is considerably lower than the ion temperature spreads out on a Mpc
scale. We then calculate the ion and electron temperature profiles by combining
the adiabatic model of two-temperature plasma by Fox & Loeb (1997) with
spherically symmetric N-body and hydrodynamic simulations based on three
different cosmological models. It is found that the electron temperature is
about a half of the mean temperature at radii 1 Mpc. This could lead to
an about 50 % underestimation in the total mass contained within 1 Mpc
when the electron temperature profiles are used. The polytropic indices of the
electron temperature profiles are whereas those of mean
temperature for Mpc. This result is consistent both
with the X-ray observations on electron temperature profiles and with some
theoretical and numerical predictions about mean temperature profiles.Comment: 20 pages with 6 figures. Accepted for publication in Ap
Analysing Lyapunov spectra of chaotic dynamical systems
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of
a variety of fully chaotic dynamical systems can be understood in terms of a
statistical analysis. Using random matrix theory we derive numerical and in
particular analytical results which provide insights into the overall behaviour
of the Lyapunov exponents particularly for strange attractors. The
corresponding distributions for the unstable periodic orbits are investigated
for comparison.Comment: 4 pages, 4 figure
Reduction and Realization in Toda and Volterra
We construct a new symplectic, bi-hamiltonian realization of the KM-system by
reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is
constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper
we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page
An Overview of the 13:8 Mean Motion Resonance between Venus and Earth
It is known since the seminal study of Laskar (1989) that the inner planetary
system is chaotic with respect to its orbits and even escapes are not
impossible, although in time scales of billions of years. The aim of this
investigation is to locate the orbits of Venus and Earth in phase space,
respectively to see how close their orbits are to chaotic motion which would
lead to unstable orbits for the inner planets on much shorter time scales.
Therefore we did numerical experiments in different dynamical models with
different initial conditions -- on one hand the couple Venus-Earth was set
close to different mean motion resonances (MMR), and on the other hand Venus'
orbital eccentricity (or inclination) was set to values as large as e = 0.36 (i
= 40deg). The couple Venus-Earth is almost exactly in the 13:8 mean motion
resonance. The stronger acting 8:5 MMR inside, and the 5:3 MMR outside the 13:8
resonance are within a small shift in the Earth's semimajor axis (only 1.5
percent). Especially Mercury is strongly affected by relatively small changes
in eccentricity and/or inclination of Venus in these resonances. Even escapes
for the innermost planet are possible which may happen quite rapidly.Comment: 14 pages, 11 figures, submitted to CMD
Mean Field Theory of Spherical Gravitating Systems
Important gaps remain in our understanding of the thermodynamics and
statistical physics of self-gravitating systems. Using mean field theory, here
we investigate the equilibrium properties of several spherically symmetric
model systems confined in a finite domain consisting of either point masses, or
rotating mass shells of different dimension. We establish a direct connection
between the spherically symmetric equilibrium states of a self-gravitating
point mass system and a shell model of dimension 3. We construct the
equilibrium density functions by maximizing the entropy subject to the usual
constraints of normalization and energy, but we also take into account the
constraint on the sum of the squares of the individual angular momenta, which
is also an integral of motion for these symmetric systems. Two new statistical
ensembles are introduced which incorporate the additional constraint. They are
used to investigate the possible occurrence of a phase transition as the
defining parameters for each ensemble are altered
Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians
The quartic H\'enon-Heiles Hamiltonian passes the Painlev\'e test for
only four sets of values of the constants. Only one of these, identical to the
traveling wave reduction of the Manakov system, has been explicitly integrated
(Wojciechowski, 1985), while the three others are not yet integrated in the
generic case . We integrate them by building
a birational transformation to two fourth order first degree equations in the
classification (Cosgrove, 2000) of such polynomial equations which possess the
Painlev\'e property. This transformation involves the stationary reduction of
various partial differential equations (PDEs). The result is the same as for
the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases,
a general solution which is meromorphic and hyperelliptic with genus two. As a
consequence, no additional autonomous term can be added to either the cubic or
the quartic Hamiltonians without destroying the Painlev\'e integrability
(completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200
Baxterization, dynamical systems, and the symmetries of integrability
We resolve the `baxterization' problem with the help of the automorphism
group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations.
This infinite group of symmetries is realized as a non-linear (birational)
Coxeter group acting on matrices, and exists as such, {\em beyond the narrow
context of strict integrability}. It yields among other things an unexpected
elliptic parametrization of the non-integrable sixteen-vertex model. It
provides us with a class of discrete dynamical systems, and we address some
related problems, such as characterizing the complexity of iterations.Comment: 25 pages, Latex file (epsf style). WARNING: Postscript figures are
BIG (600kB compressed, 4.3MB uncompressed). If necessary request hardcopy to
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