351 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
Variation of the Dependence of the Transient Process Duration on the Initial Conditions in Systems with Discrete Time
Dependence of the transient process duration on the initial conditions is
considered in one- and two-dimensional systems with discrete time, representing
a logistic map and the Eno map, respectively.Comment: 4 pages, 2 figure
Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei
[Abridged] In galactic nuclei with sufficiently short relaxation times,
binary supermassive black holes can evolve beyond their stalling radii via
continued interaction with stars. We study this "collisional" evolutionary
regime using both fully self-consistent N-body integrations and approximate
Fokker-Planck models. The N-body integrations employ particle numbers up to
0.26M and a direct-summation potential solver; close interactions involving the
binary are treated using a new implementation of the Mikkola-Aarseth chain
regularization algorithm. Even at these large values of N, two-body scattering
occurs at high enough rates in the simulations that they can not be simply
scaled to the large-N regime of real galaxies. The Fokker-Planck model is used
to bridge this gap; it includes, for the first time, binary-induced changes in
the stellar density and potential. The Fokker-Planck model is shown to
accurately reproduce the results of the N-body integrations, and is then
extended to the much larger N regime of real galaxies. Analytic expressions are
derived that accurately reproduce the time dependence of the binary semi-major
axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is
shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80
km/s. Formation of a core results from a competition between ejection of stars
by the binary and re-supply of depleted orbits via two-body scattering. Mass
deficits as large as ~4 times the binary mass are produced before coalescence.
After the two black holes coalesce, a Bahcall-Wolf cusp appears around the
single hole in one relaxation time, resulting in a nuclear density profile
consisting of a flat core with an inner, compact cluster, similar to what is
observed at the centers of low-luminosity spheroids.Comment: 21 page
Exact Quantum Solutions of Extraordinary N-body Problems
The wave functions of Boson and Fermion gases are known even when the
particles have harmonic interactions. Here we generalise these results by
solving exactly the N-body Schrodinger equation for potentials V that can be
any function of the sum of the squares of the distances of the particles from
one another in 3 dimensions. For the harmonic case that function is linear in
r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) =
\zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2
M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the
solution is given in terms of the one or two body problem with potential U(r)
in 3 dimensions. The degeneracies of the levels are derived for distinguishable
particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter
involve significant combinatorial analysis which may have application to the
shell model of atomic nuclei. For large N the Fermionic ground state gives the
binding energy of a degenerate white dwarf star treated as a giant atom with an
N-body wave function. The N-body forces involved in these extraordinary N-body
problems are not the usual sums of two body interactions, but nor are forces
between quarks or molecules. Bose-Einstein condensation of particles in 3
dimensions interacting via these strange potentials can be treated by this
method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal
Societ
Balancing Biases and Preserving Privacy on Balanced Faces in the Wild
Demographic biases exist in current models used for facial recognition (FR).
Our Balanced Faces in the Wild (BFW) dataset is a proxy to measure bias across
ethnicity and gender subgroups, allowing one to characterize FR performances
per subgroup. We show that results are non-optimal when a single score
threshold determines whether sample pairs are genuine or imposters.
Furthermore, within subgroups, performance often varies significantly from the
global average. Thus, specific error rates only hold for populations matching
the validation data. We mitigate the imbalanced performances using a novel
domain adaptation learning scheme on the facial features extracted from
state-of-the-art neural networks, boosting the average performance. The
proposed method also preserves identity information while removing demographic
knowledge. The removal of demographic knowledge prevents potential biases from
being injected into decision-making and protects privacy since demographic
information is no longer available. We explore the proposed method and show
that subgroup classifiers can no longer learn from the features projected using
our domain adaptation scheme. For source code and data, see
https://github.com/visionjo/facerec-bias-bfw.Comment: arXiv admin note: text overlap with arXiv:2102.0894
Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics
The sensitivity to initial conditions and relaxation dynamics of
two-dimensional maps are analyzed at the edge of chaos, along the lines of
nonextensive statistical mechanics. We verify the dual nature of the entropic
index for the Henon map, one () related to its sensitivity to
initial conditions properties, and the other, graining-dependent
(), related to its relaxation dynamics towards its stationary
state attractor. We also corroborate a scaling law between these two indexes,
previously found for -logistic maps. Finally we perform a preliminary
analysis of a linearized version of the Henon map (the smoothed Lozi map). We
find that the sensitivity properties of all these -logistic, Henon and Lozi
maps are the same, Comment: Communication at NEXT2003, Second Sardinian International Conference
on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy,
21-28 September 2003. Submitted to Physica A. Elsevier Latex, 8 pages, 6 eps
figure
A Method for Determining the Transient Process Duration in Dynamic Systems in the Regime of Chaotic Oscillations
We describe a method for determining the transient process duration in a
standard two-dimensionaldynamic system with discrete time (Henon map),
occurring in the regime of chaotic oscillationsComment: 4 pages, 2 figure
Analytical solutions of the lattice Boltzmann BGK model
Analytical solutions of the two dimensional triangular and square lattice
Boltzmann BGK models have been obtained for the plain Poiseuille flow and the
plain Couette flow. The analytical solutions are written in terms of the
characteristic velocity of the flow, the single relaxation time and the
lattice spacing. The analytic solutions are the exact representation of these
two flows without any approximation.Comment: 10 pages, no postscript figure provide
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
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