Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise

Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions. Consistent modelling requires that piecewise-smooth and smooth dynamical systems have similar dynamics, but the conditions for such similarity are not well understood. Here we show that by smoothing out a piecewise-smooth system one may obtain dynamics that is inconsistent with the accepted wisdom --- so-called Filippov dynamics --- at a discontinuity, even in the piecewise-smooth limit. By subjecting the system to white noise, we show that these discrepancies can be understood in terms of potential wells that allow solutions to dwell at the discontinuity for long times. Moreover we show that spurious dynamics will revert to Filippov dynamics, with a small degree of stochasticity, when the noise magnitude is sufficiently large compared to the order of smoothing. We apply the results to a model of a dry-friction oscillator, where spurious dynamics (inconsistent with Filippov's convention or with Coulomb's model of friction) can account for different coefficients of static and kinetic friction, but under sufficient noise the system reverts to dynamics consistent with Filippov's convention (and with Coulomb-like friction).Comment: submitted to: Nonlinear Dynamic

Comparison of speech intelligibility in cockpit noise using SPH-4 flight helmet with and without active noise reduction

Active Noise Reduction (ANR) is a new technology which can reduce the level of aircraft cockpit noise that reaches the pilot's ear while simultaneously improving the signal to noise ratio for voice communications and other information bearing sound signals in the cockpit. A miniature, ear-cup mounted ANR system was tested to determine whether speech intelligibility is better for helicopter pilots using ANR compared to a control condition of ANR turned off. Two signal to noise ratios (S/N), representative of actual cockpit conditions, were used for the ratio of the speech to cockpit noise sound pressure levels. Speech intelligibility was significantly better with ANR compared to no ANR for both S/N conditions. Variability of speech intelligibility among pilots was also significantly less with ANR. When the stock helmet was used with ANR turned off, the average PB Word speech intelligibility score was below the Normally Acceptable level. In comparison, it was above that level with ANR on in both S/N levels

Use of solid-state NMR to probe the order, dynamics and conformations of poly(p-phenylene vinylene) and poly(2,5-dimethoxy-p-phenylene vinylene)/

Solid-state \sp{13}C cross-polarization magic-angle-spinning (CPMAS) nuclear magnetic resonance (NMR) spectra have been obtained for films of poly (p-phenylene vinylene) (PPV) and PPV-d\sb4, poly (p-2,3,5,6-tetradeutero-phenylene vinylene). All four phenylene and vinylene resonance have been assigned. The \sp{13}C CPMAS NMR spectra show the presence of phenylene ring 180\sp\circ rotation jumps. Solid-state \sp2H quadrupole-echo nuclear magnetic resonance spectra of PPV-d\sb4 films show that all the phenylene rings of PPV undergo 180\sp\circ rotational jumps about the 1,4 ring axis with a median activation energy, E\sb{\rm a} = 15 kcal/mol and a distribution of activation energies of less than $\pm$2 kcal/mol. The effects of concentrated sulfurice acid doping of PPV-d\sb4 have been examined with \sp2H quadrupole echo NMR spectroscopy. The activation energy for ring flips is observed to increase upon doping, as does the width of the jump rate distribution. Stretched PPV films have been prepared in which the vinylene protons have been substituted with deuterium (PPV-d\sb2). \sp2H spectra of aligned samples at high temperature show molecular motion. The observed chain motion is consistent with a 180\sp\circ rotational jump of the PPV chain about the crystallographic c axis. Inversion recovery quadrupole echo spectra also support a chain jump model and indicate the jump rate distribution is similar to that of the phenylene rings. \sp2H quadrupole echo NMR spectra of oriented PPV-d\sb4 aligned in the NMR magnetic field have been simulated and thereby have yielded the chain orientation distribution in these films. \sp2H spectra obtained at -58\sp\circC are well simulated by an orientation distribution consisting of two Gaussian components. In addition, the average tilt of the phenylene ring relative to the chain axis has been found to be 7.7\sp\circ, not the 9.2\sp\circ predicted for a trans-stilbene-like structure. PPV has been doped with sodium metal. The chemistry of this process has been examined with elemental analysis. ESR spectroscopy has followed the evolution of unpaired spins as the doping reaction proceeds. The \sp2H NMR line shape of sodium-doped PPV-d\sb4 is relatively insensitive to changes in temperature and consists of two distinct components. The origin of these components is considered. Two-dimensional \sp{13}C-\sp1H HETCOR CP-MAS NMR spectra of p-dimethoxybenzene (DMB) and poly(2,5-dimethoxy-p-phenylene vinylene) (PDMPV) with variable \sp1H dipolar mixing times have been analyzed to determine the rates of \sp1H magnetization transfer between chemically distinct protons. Internuclear distances have been obtained from these rates and the conformation of the PDMPV repeat unit has been calculated and discussed

The most metal-poor Galactic globular cluster: the first spectroscopic observations of ESO280-SC06

We present the first spectroscopic observations of the very metal-poor Milky Way globular cluster ESO280-SC06. Using spectra acquired with the 2dF/AAOmega spectrograph on the Anglo-Australian Telescope, we have identified 13 members of the cluster, and estimate from their infrared calcium triplet lines that the cluster has a metallicity of $\mathrm{[Fe/H]}=-2.48\substack{+0.06 \\ -0.11}$. This would make it the most metal-poor globular cluster known in the Milky Way. This result was verified with comparisons to three other metal-poor globular clusters that had been observed and analyzed in the same manner. We also present new photometry of the cluster from EFOSC2 and SkyMapper and confirm that the cluster is located $22.9\pm2.1$ kpc from the Sun and $15.2\pm2.1$ kpc from the Galactic centre, and has a radial velocity of $92.5\substack{+2.4 \\ -1.6}$ km s$^{-1}$. These new data finds the cluster to have a radius about half that previously estimated, and we find that the cluster has a dynamical mass of the cluster of $(12\pm2)\times10^3$ solar masses. Unfortunately, we lack reliable proper motions to fully characterize its orbit about the Galaxy. Intriguingly, the photometry suggests that the cluster lacks a well-populated horizontal branch, something that has not been observed in a cluster so ancient or metal-poor.Comment: 12 pages, 12 figures. Accepted for publication in MNRA

Fast phase randomisation via two-folds

A two-fold is a singular point on the discontinuity surface of a piecewise-smooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If an orbit passes through an invisible two-fold (also known as a Teixeira singularity) before settling to regular periodic motion, then the phase of that motion cannot be determined from initial conditions, and, in the presence of small noise, the asymptotic phase of a large number of sample solutions is highly random. In this paper, we show how the probability distribution of the asymptotic phase depends on the global nonlinear dynamics. We also show how the phase of a smooth oscillator can be randomized by applying a simple discontinuous control law that generates an invisible two-fold. We propose that such a control law can be used to desynchronize a collection of oscillators, and that this manner of phase randomization is fast compared with existing methods (which use fixed points as phase singularities), because there is no slowing of the dynamics near a two-fold

Projectile deformation effects on single-nucleon removal reactions

We discuss intermediate-energy single-nucleon removal reactions from deformed projectile nuclei. The removed nucleon is assumed to originate from a given Nilsson model single-particle state and the inclusive cross sections, to all rotational states of the residual nucleus, are calculated. We investigate the sensitivity of both the stripping cross sections and their momentum distributions to the assumed size of the model space in the Nilsson model calculations and to the shape of the projectile and residue. We show that the cross sections for small deformations follow the decomposition of the Nilsson state in a spherical basis. In the case of large and prolate projectile deformations the removal cross sections from prolate-like Nilsson states, having large values for the asymptotic quantum number n z, are reduced. For oblate-like Nilsson states, with small n z, the removal cross sections are increased. Whatever the deformation, the residue momentum distributions are found to remain robustly characteristic of the orbital angular momentum decomposition of the initial state of the nucleon in the projectile. � 2012 American Physical Society

Intermittent immersion vessel apparatus and process for plant propagation

A plant micropropagation apparatus and process is provided in which a support platform for vessels containing a liquid growth media are periodically pivoted which brings about an intermittent immersion of the plant tissue/growth substrate in the growth media. The motion of the support platform may optionally be used to engage a piston operated dispenser for supplying aseptic media to the sealed vessel. The intermittent immersion also provides for an improved method of separating viable embryos from culture materials using a separation matrix in conjunction with the intermittent wave motion of the plant media when suspended in a liquid culture