Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

Damage assessment of concrete gravity dams using vibration characteristics

Vibration-based Structural Health Monitoring (VBSHM) has emerged as a feasible technique in long-term monitoring, structural performance evaluation and damage assessment of civil structures. As an important as-pect of the complete VBSHM system, over the last three decades, many vibration-based damage detection methods have been developed for buildings and bridges. However, the application of these techniques to con-crete gravity (CG) dams has been limited. In the present study, damage indices based on changes in modal flexibility and modal strain energy are suitably enhanced to be applicable for plane-strain structures. They are then used to investigate the feasibility of detecting and locating damage in a finite element CG dam model without noise effects. Results show that the enhanced damage indices can be promising for locating damage in the upstream part of CG dams by using only the first lateral mode of vibration. In addition, it is necessary to monitor both horizontal and vertical mode shape components and use these for structural damage diagnoses in CG dams

Low-Cost, Accessible Fabrication Methods for Microfluidics Research in Low-Resource Settings

Microfluidics are expected to revolutionize the healthcare industry especially in developing countries since it would bring portable, easy-to-use, self-contained diagnostic devices to places with limited access to healthcare. To date, however, microfluidics has not yet been able to live up to these expectations. One non-negligible factor can be attributed to inaccessible prototyping methods for researchers in low-resource settings who are unable to afford expensive equipment and/or obtain critical reagents and, therefore, unable to engage and contribute to microfluidics research. In this paper, we present methods to create microfluidic devices that reduce initial costs from hundreds of thousands of dollars to about $6000 by using readily accessible consumables and inexpensive equipment. By including the scientific community most embedded and aware of the requirements of healthcare in developing countries, microfluidics will be able to increase its reach in the research community and be better informed to provide relevant solutions to global healthcare challenges

A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres

We construct an invariant J_M of integral homology spheres M with values in a completion \hat{Z[q]} of the polynomial ring Z[q] such that the evaluation at each root of unity \zeta gives the the SU(2) Witten-Reshetikhin-Turaev invariant \tau_\zeta(M) of M at \zeta. Thus J_M unifies all the SU(2) Witten-Reshetikhin-Turaev invariants of M. As a consequence, \tau_\zeta(M) is an algebraic integer. Moreover, it follows that \tau_\zeta(M) as a function on \zeta behaves like an ``analytic function'' defined on the set of roots of unity. That is, the \tau_\zeta(M) for all roots of unity are determined by a "Taylor expansion" at any root of unity, and also by the values at infinitely many roots of unity of prime power orders. In particular, \tau_\zeta(M) for all roots of unity are determined by the Ohtsuki series, which can be regarded as the Taylor expansion at q=1.Comment: 66 pages, 8 figure

Seasonal variation of phytoplankton in My Thanh River, Mekong delta, Vietnam

A study on the seasonal variation of phytoplankton composition was conducted at the upper, middle, and lower parts of the My Thanh River, which supplies an important source of water for aquaculture. Qualitative and quantitative samples of phytoplankton were collected monthly at both high and low tide. The results showed that a total of 171 phytoplankton (algae) species were recorded, belonging to 59 genera and 5 phyla. Diatoms were the most abundant group with the highest species number, followed by green algae. The other phyla possessed a lower number of species. The species composition was more diverse in the rainy season and at high tide at most of the sampling sites. The mean density of algae varied from 30,900-43,521 ind.L^-1^. The density of diatoms was higher in the middle and lower parts. At the same time, euglenoids displayed the highest density in the upper part, showing a difference in the dominant algae group under the influence of salinity. Salinity was found to be significantly positively correlated (p<0.01) with diatoms, whereas it was negatively correlated (p<0.05) with blue-green algae and euglenoids. The algae composition was quite diverse, with the H' index ranging from 2.0-3.3, showing the water quality was slightly to moderately polluted

Cataloging the radio-sky with unsupervised machine learning: a new approach for the SKA era

We develop a new analysis approach towards identifying related radio components and their corresponding infrared host galaxy based on unsupervised machine learning methods. By exploiting PINK, a self-organising map algorithm, we are able to associate radio and infrared sources without the a priori requirement of training labels. We present an example of this method using $894,415$ images from the FIRST and WISE surveys centred towards positions described by the FIRST catalogue. We produce a set of catalogues that complement FIRST and describe 802,646 objects, including their radio components and their corresponding AllWISE infrared host galaxy. Using these data products we (i) demonstrate the ability to identify objects with rare and unique radio morphologies (e.g. 'X'-shaped galaxies, hybrid FR-I/FR-II morphologies), (ii) can identify the potentially resolved radio components that are associated with a single infrared host and (iii) introduce a "curliness" statistic to search for bent and disturbed radio morphologies, and (iv) extract a set of 17 giant radio galaxies between 700-1100 kpc. As we require no training labels, our method can be applied to any radio-continuum survey, provided a sufficiently representative SOM can be trained