A note on Volterra integral equations and topological dynamics

Topological dynamics theory applied to nonlinear Volterra equation

Exciton-magnon effects in the optical spectrum of MnF2

Exciton and magnon absorption, emission spectra, and fluorescence of antiferromagnetic manganese fluorid

Calcium-Rich Gap Transients: Tidal Detonations of White Dwarfs?

We hypothesize that at least some of the recently discovered class of calcium-rich gap transients are tidal detonation events of white dwarfs (WDs) by black holes (BHs) or possibly neutron stars. We show that the properties of the calcium-rich gap transients agree well with the predictions of the tidal detonation model. Under the predictions of this model, we use a follow-up X-ray observation of one of these transients, SN 2012hn, to place weak upper limits on the detonator mass of this system that include all intermediate-mass BHs (IMBHs). As these transients are preferentially in the stellar haloes of galaxies, we discuss the possibility that these transients are tidal detonations of WDs caused by random flyby encounters with IMBHs in dwarf galaxies or globular clusters. This possibility has been already suggested in the literature but without connection to the calcium-rich gap transients. In order for the random flyby cross-section to be high enough, these events would have to be occurring inside these dense stellar associations. However, there is a lack of evidence for IMBHs in these systems, and recent observations have ruled out all but the very faintest dwarf galaxies and globular clusters for a few of these transients. Another possibility is that these are tidal detonations caused by three-body interactions, where a WD is perturbed toward the detonator in isolated multiple star systems. We highlight a number of ways this could occur, even in lower-mass systems with stellar-mass BHs or neutron stars. Finally, we outline several new observational tests of this scenario, which are feasible with current instrumentation.Comment: 10 pages, 1 figure, accepted for publication in MNRA

Perturbations of Normally Hyperbolic Manifolds with Applications to the Navier–Stokes Equations

AbstractThere are two objectives in this paper. First we develop a theory which is valid in the infinite dimensional setting and which shows that, under reasonable conditions, if M is a normally hyperbolic, compact, invariant manifold for a semiflow S0(t) generated by a given evolutionary equation on a Banach space W, then for every small perturbation G of the given evolutionary equation, there is a homeomorphism hG:M→W such that MG=hG(M) is a normally hyperbolic, compact, invariant manifold for the perturbed semiflow SG(t), and that hG converges to the identity mapping (on M), as G converges to 0. The second objective is to develop a methodology which is rich enough to show that this theory can be easily applied to a wide range of applications, including the Navier–Stokes equations. It is noteworthy in this regard that, in order to be able to apply this theory in the analysis of numerical schemes used to study discretizations of partial differential equations, one needs to use a new measure or norm of the perturbation term G that arises in these schemes

Broadband Records of Earthquakes in Deep Gold Mines and a Comparison with Results from SAFOD, California

For one week during September 2007, we deployed a temporary network of field recorders and accelerometers at four sites within two deep, seismically active mines. The ground-motion data, recorded at 200 samples/sec, are well suited to determining source and ground-motion parameters for the mining-induced earthquakes within and adjacent to our network. Four earthquakes with magnitudes close to 2 were recorded with high signal/noise at all four sites. Analysis of seismic moments and peak velocities, in conjunction with the results of laboratory stick-slip friction experiments, were used to estimate source processes that are key to understanding source physics and to assessing underground seismic hazard. The maximum displacements on the rupture surfaces can be estimated from the parameter Rv, where v is the peak ground velocity at a given recording site, and R is the hypocentral distance. For each earthquake, the maximum slip and seismic moment can be combined with results from laboratory friction experiments to estimate the maximum slip rate within the rupture zone. Analysis of the four M 2 earthquakes recorded during our deployment and one of special interest recorded by the in-mine seismic network in 2004 revealed maximum slips ranging from 4 to 27 mm and maximum slip rates from 1.1 to 6:3 m=sec. Applying the same analyses to an M 2.1 earthquake within a cluster of repeating earthquakes near the San Andreas Fault Observatory at Depth site, California, yielded similar results for maximum slip and slip rate, 14 mm and 4:0 m=sec

The Effects of the Transition from Pre-nursing to Nursing on Mental Health

Mental health is an ever-growing crisis among adolescents and young adults, with suicide as second leading cause of death and the number of those negatively affected continually on the rise. Transitions are one of the major stressors prevalent among these age groups, placing individuals at risk for mental health deficits. This quantitative voluntary response comparative study assesses the transitional mental health of pre-nursing students and students in the nursing program at East Tennessee State University. Emailed to all with a declared major of pre-nursing or nursing, this study measured mental health using evidenced based assessment tools. The PHQ-9 for depression and the GAD-7 for anxiety, along with additional demographic information and mental health service usage questions, was sent to and completed by participants. A total of n = 173 responses were received. Of these responses n = 99 or 57.2 percent were nursing students, a participation rate of 9.6 percent, and n = 74 or 42.8 percent were pre-nursing students. The research revealed that depression and anxiety scores were above the cutoff for moderate depression and anxiety in both groups, as well as identified a deficit in availability of mental health resources, with over 10 percent of students unable to access counseling or psychiatric services. Contraindicatory to literature, which predicted improving mental health in the progression through university studies, this study reveals a variable and even worsening trajectory of mental health as students transition into the nursing program and progressed through college

Ultrahigh Bandwidth Spin Noise Spectroscopy: Detection of Large g-Factor Fluctuations in Highly n-Doped GaAs

We advance all optical spin noise spectroscopy (SNS) in semiconductors to detection bandwidths of several hundred gigahertz by employing an ingenious scheme of pulse trains from ultrafast laser oscillators as an optical probe. The ultrafast SNS technique avoids the need for optical pumping and enables nearly perturbation free measurements of extremely short spin dephasing times. We employ the technique to highly n-doped bulk GaAs where magnetic field dependent measurements show unexpected large g-factor fluctuations. Calculations suggest that such large g-factor fluctuations do not necessarily result from extrinsic sample variations but are intrinsically present in every doped semiconductor due to the stochastic nature of the dopant distribution.Comment: 5 pages, 3 figure