6,198 research outputs found
The Compositional Structure of the Asteroid Belt
The past decade has brought major improvements in large-scale asteroid
discovery and characterization with over half a million known asteroids and
over 100,000 with some measurement of physical characterization. This explosion
of data has allowed us to create a new global picture of the Main Asteroid
Belt. Put in context with meteorite measurements and dynamical models, a new
and more complete picture of Solar System evolution has emerged. The question
has changed from "What was the original compositional gradient of the Asteroid
Belt?" to "What was the original compositional gradient of small bodies across
the entire Solar System?" No longer is the leading theory that two belts of
planetesimals are primordial, but instead those belts were formed and sculpted
through evolutionary processes after Solar System formation. This article
reviews the advancements on the fronts of asteroid compositional
characterization, meteorite measurements, and dynamical theories in the context
of the heliocentric distribution of asteroid compositions seen in the Main Belt
today. This chapter also reviews the major outstanding questions relating to
asteroid compositions and distributions and summarizes the progress and current
state of understanding of these questions to form the big picture of the
formation and evolution of asteroids in the Main Belt. Finally, we briefly
review the relevance of asteroids and their compositions in their greater
context within our Solar System and beyond.Comment: Accepted chapter in Asteroids IV in the Space Science Series to be
published Fall 201
Negative and Nonlinear Response in an Exactly Solved Dynamical Model of Particle Transport
We consider a simple model of particle transport on the line defined by a
dynamical map F satisfying F(x+1) = 1 + F(x) for all x in R and F(x) = ax + b
for |x| < 0.5. Its two parameters a (`slope') and b (`bias') are respectively
symmetric and antisymmetric under reflection x -> R(x) = -x. Restricting
ourselves to the chaotic regime |a| > 1 and therein mainly to the part a>1 we
study not only the `diffusion coefficient' D(a,b), but also the `current'
J(a,b). An important tool for such a study are the exact expressions for J and
D as obtained recently by one of the authors. These expressions allow for a
quite efficient numerical implementation, which is important, because the
functions encountered typically have a fractal character. The main results are
presented in several plots of these functions J(a,b) and D(a,b) and in an
over-all `chart' displaying, in the parameter plane, all possibly relevant
information on the system including, e.g., the dynamical phase diagram as well
as invariants such as the values of topological invariants (kneading numbers)
which, according to the formulas, determine the singularity structure of J and
D. Our most significant findings are: 1) `Nonlinear Response': The parameter
dependence of these transport properties is, throughout the `ergodic' part of
the parameter plane (i.e. outside the infinitely many Arnol'd tongues)
fractally nonlinear. 2) `Negative Response': Inside certain regions with an
apparently fractal boundary the current J and the bias b have opposite signs.Comment: corrected typos and minor reformulations; 28 pages (revtex) with 7
figures (postscript); accepted for publication in JS
Feature-based time-series analysis
This work presents an introduction to feature-based time-series analysis. The
time series as a data type is first described, along with an overview of the
interdisciplinary time-series analysis literature. I then summarize the range
of feature-based representations for time series that have been developed to
aid interpretable insights into time-series structure. Particular emphasis is
given to emerging research that facilitates wide comparison of feature-based
representations that allow us to understand the properties of a time-series
dataset that make it suited to a particular feature-based representation or
analysis algorithm. The future of time-series analysis is likely to embrace
approaches that exploit machine learning methods to partially automate human
learning to aid understanding of the complex dynamical patterns in the time
series we measure from the world.Comment: 28 pages, 9 figure
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