11,989 research outputs found
Exploring the possibility of following the movements of a bird from an artificial earth satellite
The development of a harness to hold the transmitter is discussed along with satellite systems for monitoring the flight paths of the birds, and incorporating biological information into the tracking signal
A Renormalization Group for Hamiltonians: Numerical Results
We describe a renormalization group transformation that is related to the
breakup of golden invariant tori in Hamiltonian systems with two degrees of
freedom. This transformation applies to a large class of Hamiltonians, is
conceptually simple, and allows for accurate numerical computations. In a
numerical implementation, we find a nontrivial fixed point and determine the
corresponding critical index and scaling. Our computed values for various
universal constants are in good agreement with existing data for
area-preserving maps. We also discuss the flow associated with the nontrivial
fixed point.Comment: 11 Pages, 2 Figures. For future updates, check
ftp://ftp.ma.utexas.edu/pub/papers/koch
Comprehensive cosmographic analysis by Markov Chain Method
We study the possibility to extract model independent information about the
dynamics of the universe by using Cosmography. We intend to explore it
systematically, to learn about its limitations and its real possibilities. Here
we are sticking to the series expansion approach on which Cosmography is based.
We apply it to different data sets: Supernovae Type Ia (SNeIa), Hubble
parameter extracted from differential galaxy ages, Gamma Ray Bursts (GRBs) and
the Baryon Acoustic Oscillations (BAO) data. We go beyond past results in the
literature extending the series expansion up to the fourth order in the scale
factor, which implies the analysis of the deceleration, q_{0}, the jerk, j_{0}
and the snap, s_{0}. We use the Markov Chain Monte Carlo Method (MCMC) to
analyze the data statistically. We also try to relate direct results from
Cosmography to dark energy (DE) dynamical models parameterized by the
Chevalier-Polarski-Linder (CPL) model, extracting clues about the matter
content and the dark energy parameters. The main results are: a) even if
relying on a mathematical approximate assumption such as the scale factor
series expansion in terms of time, cosmography can be extremely useful in
assessing dynamical properties of the Universe; b) the deceleration parameter
clearly confirms the present acceleration phase; c) the MCMC method can help
giving narrower constraints in parameter estimation, in particular for higher
order cosmographic parameters (the jerk and the snap), with respect to the
literature; d) both the estimation of the jerk and the DE parameters, reflect
the possibility of a deviation from the LCDM cosmological model.Comment: 24 pages, 7 figure
Renormalization and Quantum Scaling of Frenkel-Kontorova Models
We generalise the classical Transition by Breaking of Analyticity for the
class of Frenkel-Kontorova models studied by Aubry and others to non-zero
Planck's constant and temperature. This analysis is based on the study of a
renormalization operator for the case of irrational mean spacing using
Feynman's functional integral approach. We show how existing classical results
extend to the quantum regime. In particular we extend MacKay's renormalization
approach for the classical statistical mechanics to deduce scaling of low
frequency effects and quantum effects. Our approach extends the phenomenon of
hierarchical melting studied by Vallet, Schilling and Aubry to the quantum
regime.Comment: 14 pages, 1 figure, submitted to J.Stat.Phy
Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems
Incommensurate structures can be described by the Frenkel Kontorova model.
Aubry has shown that, at a critical value K_c of the coupling of the harmonic
chain to an incommensurate periodic potential, the system displays the
analyticity breaking transition between a sliding and pinned state. The ground
state equations coincide with the standard map in non-linear dynamics, with
smooth or chaotic orbits below and above K_c respectively. For the standard
map, Greene and MacKay have calculated the value K_c=.971635. Conversely,
evaluations based on the analyticity breaking of the modulation function have
been performed for high commensurate approximants. Here we show how the
modulation function of the infinite system can be calculated without using
approximants but by Taylor expansions of increasing order. This approach leads
to a value K_c'=.97978, implying the existence of a golden invariant circle up
to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation
provided; Revised version, accepted for publication in Europhysics Letter
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
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