3,562 research outputs found
A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem
A computational procedure that allows the detection of a new type of
high-dimensional chaotic saddle in Hamiltonian systems with three degrees of
freedom is presented. The chaotic saddle is associated with a so-called
normally hyperbolic invariant manifold (NHIM). The procedure allows to compute
appropriate homoclinic orbits to the NHIM from which we can infer the existence
a chaotic saddle. NHIMs control the phase space transport across an equilibrium
point of saddle-centre-...-centre stability type, which is a fundamental
mechanism for chemical reactions, capture and escape, scattering, and, more
generally, ``transformation'' in many different areas of physics. Consequently,
the presented methods and results are of broad interest. The procedure is
illustrated for the spatial Hill's problem which is a well known model in
celestial mechanics and which gained much interest e.g. in the study of the
formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys
Natural clustering: the modularity approach
We show that modularity, a quantity introduced in the study of networked
systems, can be generalized and used in the clustering problem as an indicator
for the quality of the solution. The introduction of this measure arises very
naturally in the case of clustering algorithms that are rooted in Statistical
Mechanics and use the analogy with a physical system.Comment: 11 pages, 5 figure enlarged versio
Multiple Transition States and Roaming in Ion-Molecule Reactions: a Phase Space Perspective
We provide a dynamical interpretation of the recently identified `roaming'
mechanism for molecular dissociation reactions in terms of geometrical
structures in phase space. These are NHIMs (Normally Hyperbolic Invariant
Manifolds) and their stable/unstable manifolds that define transition states
for ion-molecule association or dissociation reactions. The associated dividing
surfaces rigorously define a roaming region of phase space, in which both
reactive and nonreactive trajectories can be trapped for arbitrarily long
times.Comment: 20 pages, 6 figure
Dynamical epidemic suppression using stochastic prediction and control
We consider the effects of noise on a model of epidemic outbreaks, where the
outbreaks appear. randomly. Using a constructive transition approach that
predicts large outbreaks, prior to their occurrence, we derive an adaptive
control. scheme that prevents large outbreaks from occurring. The theory
inapplicable to a wide range of stochastic processes with underlying
deterministic structure.Comment: 14 pages, 6 figure
Isomerization dynamics of a buckled nanobeam
We analyze the dynamics of a model of a nanobeam under compression. The model
is a two mode truncation of the Euler-Bernoulli beam equation subject to
compressive stress. We consider parameter regimes where the first mode is
unstable and the second mode can be either stable or unstable, and the
remaining modes (neglected) are always stable. Material parameters used
correspond to silicon. The two mode model Hamiltonian is the sum of a
(diagonal) kinetic energy term and a potential energy term. The form of the
potential energy function suggests an analogy with isomerisation reactions in
chemistry. We therefore study the dynamics of the buckled beam using the
conceptual framework established for the theory of isomerisation reactions.
When the second mode is stable the potential energy surface has an index one
saddle and when the second mode is unstable the potential energy surface has an
index two saddle and two index one saddles. Symmetry of the system allows us to
construct a phase space dividing surface between the two "isomers" (buckled
states). The energy range is sufficiently wide that we can treat the effects of
the index one and index two saddles in a unified fashion. We have computed
reactive fluxes, mean gap times and reactant phase space volumes for three
stress values at several different energies. In all cases the phase space
volume swept out by isomerizing trajectories is considerably less than the
reactant density of states, proving that the dynamics is highly nonergodic. The
associated gap time distributions consist of one or more `pulses' of
trajectories. Computation of the reactive flux correlation function shows no
sign of a plateau region; rather, the flux exhibits oscillatory decay,
indicating that, for the 2-mode model in the physical regime considered, a rate
constant for isomerization does not exist.Comment: 42 pages, 6 figure
Discrete Dynamical Systems Embedded in Cantor Sets
While the notion of chaos is well established for dynamical systems on
manifolds, it is not so for dynamical systems over discrete spaces with
variables, as binary neural networks and cellular automata. The main difficulty
is the choice of a suitable topology to study the limit . By
embedding the discrete phase space into a Cantor set we provided a natural
setting to define topological entropy and Lyapunov exponents through the
concept of error-profile. We made explicit calculations both numerical and
analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running
top to bottom in figures, to appear in J. Math. Phy
Recent Developments: The Uniform Arbitration Act
This Article is an overview of recent court decisions that interpret state versions of the Uniform Arbitration Act ( U.A.A. ).\u27 Arbitration statutes patterned after the U.A.A. have been adopted by thirty-four states and the District of Columbia. The goal of this project is to promote uniformity in the interpretation of the U.A.A. by articulating the underlying policies and rationales of recent court decisions interpreting the U.A.A
Recent Developments: The Uniform Arbitration Act
This Article is an overview of recent court decisions that interpret state versions of the Uniform Arbitration Act ( U.A.A. ).\u27 Arbitration statutes patterned after the U.A.A. have been adopted by thirty-four states and the District of Columbia. The goal of this project is to promote uniformity in the interpretation of the U.A.A. by articulating the underlying policies and rationales of recent court decisions interpreting the U.A.A
The role of body rotation in bacterial flagellar bundling
In bacterial chemotaxis, E. coli cells drift up chemical gradients by a
series of runs and tumbles. Runs are periods of directed swimming, and tumbles
are abrupt changes in swimming direction. Near the beginning of each run, the
rotating helical flagellar filaments which propel the cell form a bundle. Using
resistive-force theory, we show that the counter-rotation of the cell body
necessary for torque balance is sufficient to wrap the filaments into a bundle,
even in the absence of the swirling flows produced by each individual filament
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