The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio of the binary components and the initial distance ratio of the planet relative to the stellar separation distance. Our theoretical results allow us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.Comment: 10 pages, 8 figures, 3 tables; accepted by Astronomy and Astrophysic

Exoplanets Bouncing Between Binary Stars

Exoplanetary systems are found not only among single stars, but also binaries of widely varying parameters. Binaries with separations of 100--1000 au are prevalent in the Solar neighborhood; at these separations planet formation around a binary member may largely proceed as if around a single star. During the early dynamical evolution of a planetary system, planet--planet scattering can eject planets from a star's grasp. In a binary, the motion of a planet ejected from one star has effectively entered a restricted three-body system consisting of itself and the two stars, and the equations of motion of the three body problem will apply as long as the ejected planet remains far from the remaining planets. Depending on its energy, escape from the binary as a whole may be impossible or delayed until the three-body approximation breaks down, and further close interactions with its planetary siblings boost its energy when it passes close to its parent star. Until then this planet may be able to transition from the space around one star to the other, and chaotically `bounce' back and forth. In this paper we directly simulate scattering planetary systems that are around one member of a circular binary, and quantify the frequency of bouncing in scattered planets. We find that a great majority (70 to 85 per cent) of ejected planets will pass at least once through the space of it's host's binary companion, and depending on the binary parameters about 45 to 75 per cent will begin bouncing. The time spent bouncing is roughly log-normally distributed with a peak at about $10^4$ years, with only a small percentage bouncing for more than a Myr. This process may perturb and possibly incite instability among existing planets around the companion star. In rare cases, the presence of multiple planets orbiting both stars may cause post-bouncing capture or planetary swapping.Comment: MNRAS in press. Animations of some orbits can be viewed at http://www.ast.cam.ac.uk/~moeckel/bouncingplanets.htm

The Stability of the Suggested Planet in the nu Octantis System: A Numerical and Statistical Study

We provide a detailed theoretical study aimed at the observational finding about the nu Octantis binary system that indicates the possible existence of a Jupiter-type planet in this system. If a prograde planetary orbit is assumed, it has earlier been argued that the planet, if existing, should be located outside the zone of orbital stability. However, a previous study by Eberle & Cuntz (2010) [ApJ 721, L168] concludes that the planet is most likely stable if assumed to be in a retrograde orbit with respect to the secondary system component. In the present work, we significantly augment this study by taking into account the observationally deduced uncertainty ranges of the orbital parameters for the stellar components and the suggested planet. Furthermore, our study employs additional mathematical methods, which include monitoring the Jacobi constant, the zero velocity function, and the maximum Lyapunov exponent. We again find that the suggested planet is indeed possible if assumed to be in a retrograde orbit, but it is virtually impossible if assumed in a prograde orbit. Its existence is found to be consistent with the deduced system parameters of the binary components and of the suggested planet, including the associated uncertainty bars given by observations.Comment: 11 pages, 10 figures, 3 tables; Monthly Notices of the Royal Astronomical Society (in press

What phonological deficit?

We review a series of experiments aimed at understanding the nature of the phonological deficit in developmental dyslexia. These experiments investigate input and output phonological representations, phonological grammar, foreign speech perception and production, and unconscious speech processing and lexical access. Our results converge on the observation that the phonological representations of people with dyslexia may be intact, and that the phonological deficit surfaces only as a function of certain task requirements, notably short-term memory, conscious awareness, and time constraints. In an attempt to reformulate those task requirements more economically, we propose that individuals with dyslexia have a deficit in access to phonological representations. We discuss the explanatory power of this concept and we speculate that a similar notion might also adequately describe the nature of other associated cognitive deficits when present

Effect of Different Anions Upon the WO3 Morphology and Structure

In this study the effects of various anions (SO42-, ClO4- and PO43-) were investigated on the hydrothermal treatment of WO3 from Na2WO4 and HCl at 180 and 200 degrees C. The products were analyzed by XRD and SEM. With the usage of SO42- the obtained product was hexagonal (h-) WO3 in the form of nanorods at both temperatures. Applying ClO4- resulted in a mixture of WO3 center dot 0.33H(2)O and small amount of m-WO3 at 180 degrees C and pure WO3 center dot 0.33H(2)O at 200 degrees C. The morphology was consisted of cuboid shapes arranged into spherical structures at 180 degrees C and longitudinal ones at 200 degrees C. By the application of PO43- no product formed at either temperature. Using the combination of SO42-, and ClO4- the product was h-WO3 at both 180 and 200 degrees C with rod-like crystals; thus, the effect of ClO4- was overdominated by the SO42- ions. Utilization of PO43- together with SO42-, and/or ClO4- resulted again in no product, meaning that adding PO43- to the reaction mixture completely blocks the hydrothermal formation of solid products by forming water soluble phosphotungstic acids

Replication of CNTNAP2 association with nonword repetition and support for FOXP2 association with timed reading and motor activities in a dyslexia family sample

Two functionally related genes, FOXP2 and CNTNAP2, influence language abilities in families with rare syndromic and common nonsyndromic forms of impaired language, respectively. We investigated whether these genes are associated with component phenotypes of dyslexia and measures of sequential motor ability. Quantitative transmission disequilibrium testing (QTDT) and linear association modeling were used to evaluate associations with measures of phonological memory (nonword repetition, NWR), expressive language (sentence repetition), reading (real word reading efficiency, RWRE; word attack, WATT), and timed sequential motor activities (rapid alternating place of articulation, RAPA; finger succession in the dominant hand, FS-D) in 188 family trios with a child with dyslexia. Consistent with a prior study of language impairment, QTDT in dyslexia showed evidence of CNTNAP2 single nucleotide polymorphism (SNP) association with NWR. For FOXP2, we provide the first evidence for SNP association with component phenotypes of dyslexia, specifically NWR and RWRE but not WATT. In addition, FOXP2 SNP associations with both RAPA and FS-D were observed. Our results confirm the role of CNTNAP2 in NWR in a dyslexia sample and motivate new questions about the effects of FOXP2 in neurodevelopmental disorders

Cognitive Profile of Students Who Enter Higher Education with an Indication of Dyslexia

For languages other than English there is a lack of empirical evidence about the cognitive profile of students entering higher education with a diagnosis of dyslexia. To obtain such evidence, we compared a group of 100 Dutch-speaking students diagnosed with dyslexia with a control group of 100 students without learning disabilities. Our study showed selective deficits in reading and writing (effect sizes for accuracy between d = 1 and d = 2), arithmetic (d≈1), and phonological processing (d>0.7). Except for spelling, these deficits were larger for speed related measures than for accuracy related measures. Students with dyslexia also performed slightly inferior on the KAIT tests of crystallized intelligence, due to the retrieval of verbal information from long-term memory. No significant differences were observed in the KAIT tests of fluid intelligence. The profile we obtained agrees with a recent meta-analysis of English findings suggesting that it generalizes to all alphabetic languages. Implications for special arrangements for students with dyslexia in higher education are outlined