3,055 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
Telling time with an intrinsically noisy clock
Intracellular transmission of information via chemical and transcriptional
networks is thwarted by a physical limitation: the finite copy number of the
constituent chemical species introduces unavoidable intrinsic noise. Here we
provide a method for solving for the complete probabilistic description of
intrinsically noisy oscillatory driving. We derive and numerically verify a
number of simple scaling laws. Unlike in the case of measuring a static
quantity, response to an oscillatory driving can exhibit a resonant frequency
which maximizes information transmission. Further, we show that the optimal
regulatory design is dependent on the biophysical constraints (i.e., the
allowed copy number and response time). The resulting phase diagram illustrates
under what conditions threshold regulation outperforms linear regulation.Comment: 10 pages, 5 figure
Preface "Nonlinear processes in oceanic and atmospheric flows"
Nonlinear phenomena are essential ingredients in many oceanic and atmospheric
processes, and successful understanding of them benefits from multidisciplinary
collaboration between oceanographers, meteorologists, physicists and
mathematicians. The present Special Issue on ``Nonlinear Processes in Oceanic
and Atmospheric Flows'' contains selected contributions from attendants to the
workshop which, in the above spirit, was held in Castro Urdiales, Spain, in
July 2008. Here we summarize the Special Issue contributions, which include
papers on the characterization of ocean transport in the Lagrangian and in the
Eulerian frameworks, generation and variability of jets and waves, interactions
of fluid flow with plankton dynamics or heavy drops, scaling in meteorological
fields, and statistical properties of El Ni\~no Southern Oscillation.Comment: This is the introductory article to a Special Issue on "Nonlinear
Processes in Oceanic and Atmospheric Flows'', published in the journal
Nonlinear Processes in Geophysics, where the different contributions are
summarized. The Special Issue itself is freely available from
http://www.nonlin-processes-geophys.net/special_issue103.htm
Extreme Supernova Models for the Superluminous Transient ASASSN-15lh
The recent discovery of the unprecedentedly superluminous transient
ASASSN-15lh (or SN 2015L) with its UV-bright secondary peak challenges all the
power-input models that have been proposed for superluminous supernovae. Here
we examine some of the few viable interpretations of ASASSN-15lh in the context
of a stellar explosion, involving combinations of one or more power inputs. We
model the lightcurve of ASASSN-15lh with a hybrid model that includes
contributions from magnetar spin-down energy and hydrogen-poor circumstellar
interaction. We also investigate models of pure circumstellar interaction with
a massive hydrogen-deficient shell and discuss the lack of interaction features
in the observed spectra. We find that, as a supernova ASASSN-15lh can be best
modeled by the energetic core-collapse of a ~40 Msun star interacting with a
hydrogen-poor shell of ~20 Msun. The circumstellar shell and progenitor mass
are consistent with a rapidly rotating pulsational pair-instability supernova
progenitor as required for strong interaction following the final supernova
explosion. Additional energy injection by a magnetar with initial period of 1-2
ms and magnetic field of 0.1-1 x 10^14 G may supply the excess luminosity
required to overcome the deficit in single-component models, but this requires
more fine-tuning and extreme parameters for the magnetar, as well as the
assumption of efficient conversion of magnetar energy into radiation. We thus
favor a single-input model where the reverse shock formed in a strong SN
ejecta-CSM interaction following a very powerful core-collapse SN explosion can
supply the luminosity needed to reproduce the late-time UV-bright plateau.Comment: 8 pages, 3 figure
Axial-Force Reduction by Interference Between Jet and Neighboring Afterbody
Experimental results are presented for an exploratory investigation of the effectiveness of interference between jet and afterbody in reducing the axial force on an afterbody with a neighboring jet. In addition to the interference axial force., measurements are presented of the interference normal force and the center of pressure of the interference normal force. The free-stream Mach number was 2.94, the jet-exit Mach number was 2.71, and the Reynolds number was 0.25 x 10, based on body diameter. The variables investigated include static-pressure ratio of the jet (up to 9), nacelle position relative to afterbody, angle of attack (-5 deg to 10 deg), and afterbody shape. Two families of afterbody shapes were tested. One family consisted of tangent-ogive bodies of revolution with varying length and base areas. The other family was formed by taking a planar slice off a circular cylinder with varying angle between the plane and cylinder. The trends with these variables are shown for conditions near maximum jet-afterbody interference. The interference axial forces are large and favorable. For several configurations the total afterbody axial force is reduced to zero by the interference
Self-organized Beating and Swimming of Internally Driven Filaments
We study a simple two-dimensional model for motion of an elastic filament
subject to internally generated stresses and show that wave-like propagating
shapes which can propel the filament can be induced by a self-organized
mechanism via a dynamic instability. The resulting patterns of motion do not
depend on the microscopic mechanism of the instability but only of the filament
rigidity and hydrodynamic friction. Our results suggest that simplified
systems, consisting only of molecular motors and filaments could be able to
show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe
Control of Integrable Hamiltonian Systems and Degenerate Bifurcations
We discuss control of low-dimensional systems which, when uncontrolled, are
integrable in the Hamiltonian sense. The controller targets an exact solution
of the system in a region where the uncontrolled dynamics has invariant tori.
Both dissipative and conservative controllers are considered. We show that the
shear flow structure of the undriven system causes a Takens-Bogdanov
birfurcation to occur when control is applied. This implies extreme noise
sensitivity. We then consider an example of these results using the driven
nonlinear Schrodinger equation.Comment: 25 pages, 11 figures, resubmitted to Physical Review E March 2004
(originally submitted June 2003), added content and reference
Reduction of a metapopulation genetic model to an effective one island model
We explore a model of metapopulation genetics which is based on a more
ecologically motivated approach than is frequently used in population genetics.
The size of the population is regulated by competition between individuals,
rather than by artificially imposing a fixed population size. The increased
complexity of the model is managed by employing techniques often used in the
physical sciences, namely exploiting time-scale separation to eliminate fast
variables and then constructing an effective model from the slow modes.
Remarkably, an initial model with 2 variables, where
is the number of islands in the metapopulation, can be reduced to a model with
a single variable. We analyze this effective model and show that the
predictions for the probability of fixation of the alleles and the mean time to
fixation agree well with those found from numerical simulations of the original
model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure
The role of dredge-up in double white dwarf mergers
We present the results of an investigation of the dredge-up and mixing during
the merger of two white dwarfs with different chemical compositions by
conducting hydrodynamic simulations of binary mergers for three representative
mass ratios. In all the simulations, the total mass of the two white dwarfs is
. Mergers involving a CO and a He white dwarf have
been suggested as a possible formation channel for R Coronae Borealis type
stars, and we are interested in testing if such mergers lead to conditions and
outcomes in agreement with observations. Even if the conditions during the
merger and subsequent nucleosynthesis favor the production of , the merger must avoid dredging up large amounts of , or
else it will be difficult to produce sufficient to explain
the oxygen ratio observed to be of order unity. We performed a total of 9
simulations using two different grid-based hydrodynamics codes using fixed and
adaptive meshes, and one smooth particle hydrodynamics (SPH) code. We find that
in most of the simulations, of is
indeed dredged up during the merger. However, in SPH simulations where the
accretor is a hybrid He/CO white dwarf with a layer of
helium on top, we find that no is being dredged up, while in
the simulation of has been
brought up, making a WD binary consisting of a hybrid CO/He WD and a companion
He WD an excellent candidate for the progenitor of RCB stars.Comment: Accepted for publication in Ap
Resonance Zones and Lobe Volumes for Volume-Preserving Maps
We study exact, volume-preserving diffeomorphisms that have heteroclinic
connections between a pair of normally hyperbolic invariant manifolds. We
develop a general theory of lobes, showing that the lobe volume is given by an
integral of a generating form over the primary intersection, a subset of the
heteroclinic orbits. Our definition reproduces the classical action formula in
the planar, twist map case. For perturbations from a heteroclinic connection,
the lobe volume is shown to reduce, to lowest order, to a suitable integral of
a Melnikov function.Comment: ams laTeX, 8 figure
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