Multiple Transitions to Chaos in a Damped Parametrically Forced Pendulum

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving force). As $A$ is increased, the SP will restabilize after its instability, destabilize again, and so {\it ad infinitum} for any given $\omega_0$. Its destabilizations (restabilizations) occur via alternating supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork bifurcations, except the first destabilization at which a supercritical or subcritical bifurcation takes place depending on the value of $\omega_0$. For each case of the supercritical destabilizations, an infinite sequence of PDB's follows and leads to chaos. Consequently, an infinite series of period-doubling transitions to chaos appears with increasing $A$. The critical behaviors at the transition points are also discussed.Comment: 20 pages + 7 figures (available upon request), RevTex 3.

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights

We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure

Prominence seismology using small amplitude oscillations

Quiescent prominences are thin slabs of cold, dense plasma embedded in the much hotter and rarer solar corona. Although their global shape is rather irregular, they are often characterised by an internal structure consisting of a large number of thin, parallel threads piled together. Prominences often display periodic disturbances mostly observed in the Doppler displacement of spectral lines and with an amplitude typically of the order of or smaller than 2--3 km s$^{-1}$, a value which seems to be much smaller than the characteristic speeds of the prominence plasma (namely the Alfv\'en and sound velocities). Two particular features of these small amplitude prominence oscillations is that they seem to damp in a few periods and that they seem not to affect the whole prominence structure. In addition, in high spatial resolution observations, in which threads can be discerned, small amplitude oscillations appear to be clearly associated to these fine structure constituents. Prominence seismology tries to bring together the results from these observations (e.g. periods, wavelengths, damping times) and their theoretical modeling (by means of the magnetohydrodynamic theory) to gain insight into physical properties of prominences that cannot be derived from direct observation. In this paper we discuss works that have not been described in previous reviews, namely the first seismological application to solar prominences and theoretical advances on the attenuation of prominence oscillations

The Boundary-spanning Role of Democratic Learning Communities: Implementing the IDEALS

This multi-case study investigates characteristics and practices in schools that expand the traditional boundaries of school leadership and transform schools into democratic learning communities based on the level of implementation of the IDEALS framework. This investigation serves as a modus to illuminate democratic processes that change schools and address the needs of the students, not the needs of the adults in the system. A sample of five purposefully selected high schools, from the Midwest USA, was utilized. The schools serve Grade 9—12 students, but vary in size, residential area and socioeconomic status of the students. This study illuminates some of the challenges and strategies that facilitate or impede the process of creating more democratic schools that expand the boundaries of inquiry and discourse to include a broader range of community stakeholders and that respect and embrace issues of equity.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Constraints on dark matter-nucleon effective couplings in the presence of kinematically distinct halo substructures using the DEAP-3600 detector

DEAP-3600 is a single-phase liquid argon detector aiming to directly detect weakly interacting massive particles (WIMPs), located at SNOLAB (Sudbury, Canada). After analyzing data taken during the first year of operation, a null result was used to place an upper bound on the WIMP-nucleon, spin-independent, isoscalar cross section. This study reinterprets this result within a nonrelativistic effective field theory framework and further examines how various possible substructures in the local dark matter halo may affect these constraints. Such substructures are hinted at by kinematic structures in the local stellar distribution observed by the Gaia satellite and other recent astronomical surveys. These include the Gaia Sausage (or Enceladus), as well as a number of distinct streams identified in recent studies. Limits are presented for the coupling strength of the effective contact interaction operators O1, O3, O5, O8, and O11, considering isoscalar, isovector, and xenonphobic scenarios, as well as the specific operators corresponding to millicharge, magnetic dipole, electric dipole, and anapole interactions. The effects of halo substructures on each of these operators are explored as well, showing that the O5 and O8 operators are particularly sensitive to the velocity distribution, even at dark matter masses above 100 GeV=c

Altered white matter microstructural organization in posttraumatic stress disorder across 3047 adults: results from the PGC-ENIGMA PTSD consortium

A growing number of studies have examined alterations in white matter organization in people with posttraumatic stress disorder (PTSD) using diffusion MRI (dMRI), but the results have been mixed which may be partially due to relatively small sample sizes among studies. Altered structural connectivity may be both a neurobiological vulnerability for, and a result of, PTSD. In an effort to find reliable effects, we present a multi-cohort analysis of dMRI metrics across 3047 individuals from 28 cohorts currently participating in the PGC-ENIGMA PTSD working group (a joint partnership between the Psychiatric Genomics Consortium and the Enhancing NeuroImaging Genetics through Meta-Analysis consortium). Comparing regional white matter metrics across the full brain in 1426 individuals with PTSD and 1621 controls (2174 males/873 females) between ages 18-83, 92% of whom were trauma-exposed, we report associations between PTSD and disrupted white matter organization measured by lower fractional anisotropy (FA) in the tapetum region of the corpus callosum (Cohen's d = -0.11, p = 0.0055). The tapetum connects the left and right hippocampus, for which structure and function have been consistently implicated in PTSD. Results were consistent even after accounting for the effects of multiple potentially confounding variables: childhood trauma exposure, comorbid depression, history of traumatic brain injury, current alcohol abuse or dependence, and current use of psychotropic medications. Our results show that PTSD may be associated with alterations in the broader hippocampal network.New methods for child psychiatric diagnosis and treatment outcome evaluatio