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

Approximating multi-dimensional Hamiltonian flows by billiards

Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ 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 $C^{r}$ 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

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