Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem

Developmental Differences in the Ability to Provide Temporal Information about Repeated Events

Children (n = 372) aged 4 - 8 years participated in 1 or 4 occurrences of a similar event and were interviewed 1 week later. Compared to 85% of children who participated once, less than 25% with repeated experience gave the exact number of times they participated, although all knew they participated more than once. Children with repeated experience were asked additional temporal questions and there were clear developmental differences. Older children were more able than younger children to judge relative order and temporal position of the four occurrences. They also demonstrated improved temporal memory for the first and last relative to the middle occurrences, while younger children did so only for the first. This is the first systematic demonstration of children’s memory for temporal information after a repeated event. We discuss implications for theories of temporal memory development and the practical implications of asking children to provide temporal information

A Push-Button Molecular Switch

The preparation, characterization, and switching mechanism of a unique single-station mechanically switchable hetero[2]catenane are reported. The facile synthesis utilizing a “threading-followed-by-clipping” protocol features Cu^(2+)-catalyzed Eglinton coupling as a mild and efficient route to the tetrathiafulvalene-based catenane in high yield. The resulting mechanically interlocked molecule operates as a perfect molecular switch, most readily described as a “push-button” switch, whereby two discrete and fully occupied translational states are toggled electrochemically at incredibly high rates. This mechanical switching was probed using a wide variety of experimental techniques as well as quantum-mechanical investigations. The fundamental distinctions between this single-station [2]catenane and other more traditional bi- and multistation molecular switches are significant

Short-Pulse, Compressed Ion Beams at the Neutralized Drift Compression Experiment

We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment (NDCX-II) at Lawrence Berkeley National Laboratory, with 1-mm beam spot size within 2.5 ns full-width at half maximum. The ion kinetic energy is 1.2 MeV. To enable the short pulse duration and mm-scale focal spot radius, the beam is neutralized in a 1.5-meter-long drift compression section following the last accelerator cell. A short-focal-length solenoid focuses the beam in the presence of the volumetric plasma that is near the target. In the accelerator, the line-charge density increases due to the velocity ramp imparted on the beam bunch. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including select topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Below the transition to melting, the short beam pulses offer an opportunity to study the multi-scale dynamics of radiation-induced damage in materials with pump-probe experiments, and to stabilize novel metastable phases of materials when short-pulse heating is followed by rapid quenching. First experiments used a lithium ion source; a new plasma-based helium ion source shows much greater charge delivered to the target.Comment: 4 pages, 2 figures, 1 table. Submitted to the proceedings for the Ninth International Conference on Inertial Fusion Sciences and Applications, IFSA 201

Nitric Oxide-Releasing Nanoparticles Prevent Propionibacterium acnes-Induced Inflammation by Both Clearing the Organism and Inhibiting Microbial Stimulation of the Innate Immune Response.

Propionibacterium acnes induction of IL-1 cytokines through the NLRP3 (NLR, nucleotide oligomerization domain-like receptor) inflammasome was recently highlighted as a dominant etiological factor for acne vulgaris. Therefore, therapeutics targeting both the stimulus and the cascade would be ideal. Nitric oxide (NO), a potent biological messenger, has documented broad-spectrum antimicrobial and immunomodulatory properties. To harness these characteristics to target acne, we used an established nanotechnology capable of generating/releasing NO over time (NO-np). P. acnes was found to be highly sensitive to all concentrations of NO-np tested, although human keratinocyte, monocyte, and embryonic zebra fish assays revealed no cytotoxicity. NO-np significantly suppressed IL-1β, tumor necrosis factor-α (TNF-α), IL-8, and IL-6 from human monocytes, and IL-8 and IL-6 from human keratinocytes, respectively. Importantly, silencing of NLRP3 expression by small interfering RNA did not limit NO-np inhibition of IL-1 β secretion from monocytes, and neither TNF-α nor IL-6 secretion, nor inhibition by NO-np was found to be dependent on this pathway. The observed mechanism by which NO-np impacts IL-1β secretion was through inhibition of caspase-1 and IL-1β gene expression. Together, these data suggest that NO-np can effectively prevent P. acnes-induced inflammation by both clearing the organism and inhibiting microbial stimulation of the innate immune response

Donor-Acceptor Oligorotaxanes Made to Order

Five donor–acceptor oligorotaxanes made up of dumbbells composed of tetraethylene glycol chains, interspersed with three and five 1,5-dioxynaphthalene units, and terminated by 2,6-diisopropylphenoxy stoppers, have been prepared by the threading of discrete numbers of cyclobis(paraquat-p-phenylene) rings, followed by a kinetically controlled stoppering protocol that relies on click chemistry. The well-known copper(I)-catalyzed alkyne–azide cycloaddition between azide functions placed at the ends of the polyether chains and alkyne-bearing stopper precursors was employed during the final kinetically controlled template-directed synthesis of the five oligorotaxanes, which were characterized subsequently by ^1H NMR spectroscopy at low temperature (233 K) in deuterated acetonitrile. The secondary structures, as well as the conformations, of the five oligorotaxanes were unraveled by spectroscopic comparison with the dumbbell and ring components. By focusing attention on the changes in chemical shifts of some key probe protons, obtained from a wide range of low-temperature spectra, a picture emerges of a high degree of folding within the thread protons of the dumbbells of four of the five oligorotaxanes—the fifth oligorotaxane represents a control compound in effect— brought about by a combination of C-H···O and π–π stacking interactions between the p-electron-deficient bipyridinium units in the rings and the π-electron-rich 1,5-dioxynaphthalene units and polyether chains in the dumbbells. The secondary structures of a foldamer-like nature have received further support from a solid-state superstructure of a related [3]pseudorotaxane and density functional calculations performed thereon

Massive scalar field in multiply connected flat spacetimes

The vacuum expectation value of the stress-energy tensor $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as $R^3 \times S^1$, $R^2 \times T^2$, $R^1 \times T^3$, the M\"{o}bius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.Comment: 19 pages, REVTeX, 5 figures in separate uuencoded compressed fil

Genetic and anatomical basis of the barrier separating wakefulness and anesthetic-induced unresponsiveness.

A robust, bistable switch regulates the fluctuations between wakefulness and natural sleep as well as those between wakefulness and anesthetic-induced unresponsiveness. We previously provided experimental evidence for the existence of a behavioral barrier to transitions between these states of arousal, which we call neural inertia. Here we show that neural inertia is controlled by processes that contribute to sleep homeostasis and requires four genes involved in electrical excitability: Sh, sss, na and unc79. Although loss of function mutations in these genes can increase or decrease sensitivity to anesthesia induction, surprisingly, they all collapse neural inertia. These effects are genetically selective: neural inertia is not perturbed by loss-of-function mutations in all genes required for the sleep/wake cycle. These effects are also anatomically selective: sss acts in different neurons to influence arousal-promoting and arousal-suppressing processes underlying neural inertia. Supporting the idea that anesthesia and sleep share some, but not all, genetic and anatomical arousal-regulating pathways, we demonstrate that increasing homeostatic sleep drive widens the neural inertial barrier. We propose that processes selectively contributing to sleep homeostasis and neural inertia may be impaired in pathophysiological conditions such as coma and persistent vegetative states