1,433 research outputs found
An exactly solvable model for driven dissipative systems
We introduce a solvable stochastic model inspired by granular gases for
driven dissipative systems. We characterize far from equilibrium steady states
of such systems through the non-Boltzmann energy distribution and compare
different measures of effective temperatures. As an example we demonstrate that
fluctuation-dissipation relations hold, however with an effective temperature
differing from the effective temperature defined from the average energy.Comment: Some further clarifications. No changes in results or conclusion
Lagrangian Based Methods for Coherent Structure Detection
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. (C) 2015 AIP Publishing LLC.ONR N000141210665Center for Nonlinear Dynamic
Functional thinking in cost estimation through the tools and concepts of axiomatic design
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (leaf 27).There has been an increasing demand for cost estimation tools which aid in the reduction of system cost or the active consideration of cost as a design constraint. The existing tools are currently incapable of anticipating the unseen or latent effects of design changes made in an effort to cut cost. This paper presents an example of how the tools and concepts of axiomatic design theory can be integrated with the parametric cost estimation process, and then presents a series of arguments for why tools such as these which examine the functional architecture of a system are useful for optimizing cost at the preliminary design level.by Lael Ulam Odhner.S.B
An algebraic formulation of the graph reconstruction conjecture
The graph reconstruction conjecture asserts that every finite simple graph on
at least three vertices can be reconstructed up to isomorphism from its deck -
the collection of its vertex-deleted subgraphs. Kocay's Lemma is an important
tool in graph reconstruction. Roughly speaking, given the deck of a graph
and any finite sequence of graphs, it gives a linear constraint that every
reconstruction of must satisfy.
Let be the number of distinct (mutually non-isomorphic) graphs on
vertices, and let be the number of distinct decks that can be
constructed from these graphs. Then the difference measures
how many graphs cannot be reconstructed from their decks. In particular, the
graph reconstruction conjecture is true for -vertex graphs if and only if
.
We give a framework based on Kocay's lemma to study this discrepancy. We
prove that if is a matrix of covering numbers of graphs by sequences of
graphs, then . In particular, all
-vertex graphs are reconstructible if one such matrix has rank . To
complement this result, we prove that it is possible to choose a family of
sequences of graphs such that the corresponding matrix of covering numbers
satisfies .Comment: 12 pages, 2 figure
Hierarchy of Chaotic Maps with an Invariant Measure
We give hierarchy of one-parameter family F(a,x) of maps of the interval
[0,1] with an invariant measure. Using the measure, we calculate
Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of
these maps analytically, where the results thus obtained have been approved
with numerical simulation. In contrary to the usual one-parameter family of
maps such as logistic and tent maps, these maps do not possess period doubling
or period-n-tupling cascade bifurcation to chaos, but they have single fixed
point attractor at certain parameter values, where they bifurcate directly to
chaos without having period-n-tupling scenario exactly at these values of
parameter whose Lyapunov characteristic exponent begins to be positive.Comment: 18 pages (Latex), 7 figure
Transport in time-dependent dynamical systems: Finite-time coherent sets
We study the transport properties of nonautonomous chaotic dynamical systems
over a finite time duration. We are particularly interested in those regions
that remain coherent and relatively non-dispersive over finite periods of time,
despite the chaotic nature of the system. We develop a novel probabilistic
methodology based upon transfer operators that automatically detects maximally
coherent sets. The approach is very simple to implement, requiring only
singular vector computations of a matrix of transitions induced by the
dynamics. We illustrate our new methodology on an idealized stratospheric flow
and in two and three dimensional analyses of European Centre for Medium Range
Weather Forecasting (ECMWF) reanalysis data
Geometry of pseudocharacters
If G is a group, a pseudocharacter f: G-->R is a function which is "almost" a
homomorphism. If G admits a nontrivial pseudocharacter f, we define the space
of ends of G relative to f and show that if the space of ends is complicated
enough, then G contains a nonabelian free group. We also construct a
quasi-action by G on a tree whose space of ends contains the space of ends of G
relative to f. This construction gives rise to examples of "exotic"
quasi-actions on trees.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper26.abs.htm
Method of constructing exactly solvable chaos
We present a new systematic method of constructing rational mappings as
ergordic transformations with nonuniform invariant measures on the unit
interval [0,1]. As a result, we obtain a two-parameter family of rational
mappings that have a special property in that their invariant measures can be
explicitly written in terms of algebraic functions of parameters and a
dynamical variable. Furthermore, it is shown here that this family is the most
generalized class of rational mappings possessing the property of exactly
solvable chaos on the unit interval, including the Ulam=Neumann map y=4x(1-x).
Based on the present method, we can produce a series of rational mappings
resembling the asymmetric shape of the experimentally obtained first return
maps of the Beloussof-Zhabotinski chemical reaction, and we can match some
rational functions with other experimentally obtained first return maps in a
systematic manner.Comment: 12 pages, 2 figures, REVTEX. Title was changed. Generalized Chebyshev
maps including the precise form of two-parameter generalized cubic maps were
added. Accepted for publication in Phys. Rev. E(1997
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