1,958 research outputs found
Visualizing the logistic map with a microcontroller
The logistic map is one of the simplest nonlinear dynamical systems that
clearly exhibit the route to chaos. In this paper, we explored the evolution of
the logistic map using an open-source microcontroller connected to an array of
light emitting diodes (LEDs). We divided the one-dimensional interval
into ten equal parts, and associated and LED to each segment. Every time an
iteration took place a corresponding LED turned on indicating the value
returned by the logistic map. By changing some initial conditions of the
system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin
Any-order propagation of the nonlinear Schroedinger equation
We derive an exact propagation scheme for nonlinear Schroedinger equations.
This scheme is entirely analogous to the propagation of linear Schroedinger
equations. We accomplish this by defining a special operator whose algebraic
properties ensure the correct propagation. As applications, we provide a simple
proof of a recent conjecture regarding higher-order integrators for the
Gross-Pitaevskii equation, extend it to multi-component equations, and to a new
class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.
Contractivity of Runge-Kutta methods for convex gradient systems
We consider the application of Runge-Kutta (RK) methods to gradient systems
, where, as in many optimization problems, is
convex and (globally) Lipschitz-continuous with Lipschitz constant
. Solutions of this system behave contractively, i.e. the Euclidean distance
between two solutions and is a nonincreasing function
of . It is then of interest to investigate whether a similar contraction
takes place, at least for suitably small step sizes , for the discrete
solution. Dahlquist and Jeltsch results' imply that (1) there are explicit RK
schemes that behave contractively whenever is below a scheme-dependent
constant and (2) Euler's rule is optimal in this regard. We prove however, by
explicit construction of a convex potential using ideas from robust control
theory, that there exists RK schemes that fail to behave contractively for any
choice of the time-step .Comment: 13 pages, 2 figure
Two-Temperature Intracluster Medium in Merging Clusters of Galaxies
We investigate the evolution of intracluster medium during a cluster merger,
explicitly considering the relaxation process between the ions and electrons by
N-body and hydrodynamical simulations. When two subclusters collide each other,
a bow shock is formed between the centers of two substructures and propagate in
both directions along the collision axis. 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. In the post-shock region the energy is
transported from the ions to electrons via Coulomb coupling. However, since the
energy exchange timescale depends both on the gas density and temperature,
distribution of electron temperature becomes more complex than that of the
plasma mean temperature, especially in the expanding phase. After the collision
of two subclusters, gas outflow occurs not only along the collision axis but
also in its perpendicular direction. The gas which is originally located in the
central part of the subclusters moves both in the parallel and perpendicular
directions. Since the equilibrium timescale of the gas along these directions
is relatively short, temperature difference between ions and electrons is
larger in the directions tilted by the angles of with respect to
the collision axis. The electron temperature could be significantly lower that
the plasma mean temperature by at most. The significance of our
results in the interpretation of X-ray observations is briefly discussed.Comment: 20 pages, 11 figures, Accepted for publication in Ap
Hyperextended Scalar-Tensor Gravity
We study a general Scalar-Tensor Theory with an arbitrary coupling funtion
but also an arbitrary dependence of the ``gravitational
constant'' in the cases in which either one of them, or both, do not
admit an analytical inverse, as in the hyperextended inflationary scenario. We
present the full set of field equations and study their cosmological behavior.
We show that different scalar-tensor theories can be grouped in classes with
the same solution for the scalar field.Comment: latex file, To appear in Physical Review
Spectroscopic ellipsometry of composite thin films with embedded Bi nanocrystals
8 pages, 6 figures, 1 table.-- PACS: 78.66.Jg; 78.66.Nk; 78.20.Ci; 68.55.Ln; 07.60.Fs; 81.05.Ys; 68.55.JkSpectroscopic ellipsometry together with an effective medium model is used to determine simultaneously the effective refractive index, thickness, and metal volume fraction of thin nanocomposite films. The films are formed by Bi nanocrystals embedded in amorphous matrices, either semiconducting (Ge) or dielectric (Al2O3). For the Bi:Ge films (metal in an absorbing host), the values obtained for both the real and imaginary parts of the refractive index vary continuously from that of Ge to that of Bi. The metal contents determined from the ellipsometry analysis are in excellent agreement with those obtained from direct measurements of the composition. For the Bi:Al2O3 films (metal in a nonabsorbing host), the extinction coefficient (k) exhibits a maximum around 360 nm which is related to the metal plasmon resonance frequency of Bi nanocrystals. The metal content determined from the ellipsometry analysis in this case is underestimated, probably due to interaction of the Bi crystals with the Al2O3 host.This work has been partially supported by CICYT
(Spain) under TIC96-0467 project. The authors are grateful
to the GPS (Université de Paris VI et VII, France) for provision
and assistance of Rutherford backscattering facilities.
One of the authors (J.M.B.) greatly acknowledges a FPI
grant from the Spanish Ministry of Education and Culture.Peer reviewe
Scalar-Tensor Cosmological Models
We analyze the qualitative behaviors of scalar-tensor cosmologies with an
arbitrary monotonic function. In particular, we are interested
on scalar-tensor theories distinguishable at early epochs from General
Relativity (GR) but leading to predictions compatible with solar-system
experiments. After extending the method developed by Lorentz-Petzold and
Barrow, we establish the conditions required for convergence towards GR at
. Then, we obtain all the asymptotic analytical solutions
at early times which are possible in the framework of these theories. The
subsequent qualitative evolution, from these asymptotic solutions until their
later convergence towards GR, has been then analyzed by means of numerical
computations. From this analysis, we have been able to establish a
classification of the different qualitative behaviors of scalar-tensor
cosmological models with an arbitrary monotonic function.Comment: uuencoded compressed postscript file containing 41 pages, with 9
figures, accepted for publication in Physical Review
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