1,071 research outputs found
Symmetry breaking perturbations and strange attractors
The asymmetrically forced, damped Duffing oscillator is introduced as a
prototype model for analyzing the homoclinic tangle of symmetric dissipative
systems with \textit{symmetry breaking} disturbances. Even a slight fixed
asymmetry in the perturbation may cause a substantial change in the asymptotic
behavior of the system, e.g. transitions from two sided to one sided strange
attractors as the other parameters are varied. Moreover, slight asymmetries may
cause substantial asymmetries in the relative size of the basins of attraction
of the unforced nearly symmetric attracting regions. These changes seems to be
associated with homoclinic bifurcations. Numerical evidence indicates that
\textit{strange attractors} appear near curves corresponding to specific
secondary homoclinic bifurcations. These curves are found using analytical
perturbational tools
Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
We investigate the dynamics of chaotic trajectories in simple yet physically
important Hamiltonian systems with non-hierarchical borders between regular and
chaotic regions with positive measures. We show that the stickiness to the
border of the regular regions in systems with such a sharply divided phase
space occurs through one-parameter families of marginally unstable periodic
orbits and is characterized by an exponent \gamma= 2 for the asymptotic
power-law decay of the distribution of recurrence times. Generic perturbations
lead to systems with hierarchical phase space, where the stickiness is
apparently enhanced due to the presence of infinitely many regular islands and
Cantori. In this case, we show that the distribution of recurrence times can be
composed of a sum of exponentials or a sum of power-laws, depending on the
relative contribution of the primary and secondary structures of the hierarchy.
Numerical verification of our main results are provided for area-preserving
maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution
figures is available at http://www.pks.mpg.de/~edugal
NASA space station automation: AI-based technology review
Research and Development projects in automation for the Space Station are discussed. Artificial Intelligence (AI) based automation technologies are planned to enhance crew safety through reduced need for EVA, increase crew productivity through the reduction of routine operations, increase space station autonomy, and augment space station capability through the use of teleoperation and robotics. AI technology will also be developed for the servicing of satellites at the Space Station, system monitoring and diagnosis, space manufacturing, and the assembly of large space structures
NASA space station automation: AI-based technology review. Executive summary
Research and Development projects in automation technology for the Space Station are described. Artificial Intelligence (AI) based technologies are planned to enhance crew safety through reduced need for EVA, increase crew productivity through the reduction of routine operations, increase space station autonomy, and augment space station capability through the use of teleoperation and robotics
Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape
Lobe dynamics and escape from a potential well are general frameworks
introduced to study phase space transport in chaotic dynamical systems. While
the former approach studies how regions of phase space are transported by
reducing the flow to a two-dimensional map, the latter approach studies the
phase space structures that lead to critical events by crossing periodic orbit
around saddles. Both of these frameworks require computation with curves
represented by millions of points-computing intersection points between these
curves and area bounded by the segments of these curves-for quantifying the
transport and escape rate. We present a theory for computing these intersection
points and the area bounded between the segments of these curves based on a
classification of the intersection points using equivalence class. We also
present an alternate theory for curves with nontransverse intersections and a
method to increase the density of points on the curves for locating the
intersection points accurately.The numerical implementation of the theory
presented herein is available as an open source software called Lober. We used
this package to demonstrate the application of the theory to lobe dynamics that
arises in fluid mechanics, and rate of escape from a potential well that arises
in ship dynamics.Comment: 33 pages, 17 figure
Alternative 3' UTRs direct localization of functionally diverse protein isoforms in neuronal compartments
The proper subcellular localization of RNAs and local translational regulation is crucial in highly compartmentalized cells, such as neurons. RNA localization is mediated by specific cis-regulatory elements usually found in mRNA 3'UTRs. Therefore, processes that generate alternative 3'UTRs-alternative splicing and polyadenylation-have the potential to diversify mRNA localization patterns in neurons. Here, we performed mapping of alternative 3'UTRs in neurites and soma isolated from mESC-derived neurons. Our analysis identified 593 genes with differentially localized 3'UTR isoforms. In particular, we have shown that two isoforms of Cdc42 gene with distinct functions in neuronal polarity are differentially localized between neurites and soma of mESC-derived and mouse primary cortical neurons, at both mRNA and protein level. Using reporter assays and 3'UTR swapping experiments, we have identified the role of alternative 3'UTRs and mRNA transport in differential localization of alternative CDC42 protein isoforms. Moreover, we used SILAC to identify isoform-specific Cdc42 3'UTR-bound proteome with potential role in Cdc42 localization and translation. Our analysis points to usage of alternative 3'UTR isoforms as a novel mechanism to provide for differential localization of functionally diverse alternative protein isoforms
A saddle in a corner - a model of collinear triatomic chemical reactions
A geometrical model which captures the main ingredients governing atom-diatom
collinear chemical reactions is proposed. This model is neither near-integrable
nor hyperbolic, yet it is amenable to analysis using a combination of the
recently developed tools for studying systems with steep potentials and the
study of the phase space structure near a center-saddle equilibrium. The
nontrivial dependence of the reaction rates on parameters, initial conditions
and energy is thus qualitatively explained. Conditions under which the phase
space transition state theory assumptions are satisfied and conditions under
which these fail are derived
Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions
In contrast to classical physics, quantum mechanics divides particles into
two classes-bosons and fermions-whose exchange statistics dictate the dynamics
of systems at a fundamental level. In two dimensions quasi-particles known as
'anyons' exhibit fractional exchange statistics intermediate between these two
classes. The ability to simulate and observe behaviour associated to
fundamentally different quantum particles is important for simulating complex
quantum systems. Here we use the symmetry and quantum correlations of entangled
photons subjected to multiple copies of a quantum process to directly simulate
quantum interference of fermions, bosons and a continuum of fractional
behaviour exhibited by anyons. We observe an average similarity of 93.6\pm0.2%
between an ideal model and experimental observation. The approach generalises
to an arbitrary number of particles and is independent of the statistics of the
particles used, indicating application with other quantum systems and large
scale application.Comment: 10 pages, 5 figure
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Preliminary Outline for Book: Engineering for Nuclear Reactor Fuel Reprocessing
This document outlines a book on the subject of reactor fuel reprocessing that is still in the planning stages, representing the authors' thinking as of the arbitrary cut-off date of October 15, 1957. The subject matter that was intended for inclusion was: special considerations in radiochemical processing; chemical processes and operations; mechanical operations; fluid flow; heat transfer operations; solvent extraction; other mass diffusion operations; instrumentation; auxiliary equipment; plant design and operation; and fuel processing economics
Approximating multi-dimensional Hamiltonian flows by billiards
Consider a family of smooth potentials , which, in the limit
, become a singular hard-wall potential of a multi-dimensional
billiard. We define auxiliary billiard domains that asymptote, as
to the original billiard, and provide asymptotic expansion of
the smooth Hamiltonian solution in terms of these billiard approximations. The
asymptotic expansion includes error estimates in the norm and an
iteration scheme for improving this approximation. Applying this theory to
smooth potentials which limit to the multi-dimensional close to ellipsoidal
billiards, we predict when the separatrix splitting persists for various types
of potentials
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