Solitons in a parametrically driven damped discrete nonlinear Schr\"odinger equation

We consider a parametrically driven damped discrete nonlinear Schr\"odinger (PDDNLS) equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental discrete bright solitons. We show that there are two types of onsite discrete soliton, namely onsite type I and II. We also show that there are four types of intersite discrete soliton, called intersite type I, II, III, and IV, where the last two types are essentially the same, due to symmetry. Onsite and intersite type I solitons, which can be unstable in the case of no dissipation, are found to be stabilized by the damping, whereas the other types are always unstable. Our further analysis demonstrates that saddle-node and pitchfork (symmetry-breaking) bifurcations can occur. More interestingly, the onsite type I, intersite type I, and intersite type III-IV admit Hopf bifurcations from which emerge periodic solitons (limit cycles). The continuation of the limit cycles as well as the stability of the periodic solitons are computed through the numerical continuation software Matcont. We observe subcritical Hopf bifurcations along the existence curve of the onsite type I and intersite type III-IV. Along the existence curve of the intersite type I we observe both supercritical and subcritical Hopf bifurcations.Comment: to appear in "Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations in Nonlinear Systems", B.A. Malomed, ed. (Springer, Berlin, 2012

Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically

Finite element optimizations for efficient non-linear electrical tomography reconstruction

Electrical Tomography can produce accurate results only if the underlying 2D or 3D volume discretization is chosen suitably for the applied numerical algorithm. We give general indications where and how to optimize a finite element discretization of a volume under investigation to enable efficient computation of potential distributions and the reconstruction of materials. For this, we present an error estimator and material-gradient indicator as a driver for adaptive mesh refinement and show how finite element mesh properties affect the efficiency and accuracy of the solutions

Archaic mitochondrial DNA inserts in modern day nuclear genomes

Traces of interbreeding of Neanderthals and Denisovans with modern humans in the form of archaic DNA have been detected in the genomes of present-day human populations outside sub-Saharan Africa. Up to now, only nuclear archaic DNA has been detected in modern humans; we therefore attempted to identify archaic mitochondrial DNA (mtDNA) residing in modern human nuclear genomes as nuclear inserts of mitochondrial DNA (NUMTs)

Discrete solitons in electromechanical resonators

We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrodinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein--Gordon system through the discrete Schrodinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e. oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein--Gordon equation are performed, confirming the relevance of our analysis

Small Energy Scale for Mixed-Valent Uranium Materials

We investigate a two-channel Anderson impurity model with a $5f^1$ magnetic and a $5f^2$ quadrupolar ground doublet, and a $5f^2$ excited triplet. Using the numerical renormalization group method, we find a crossover to a non-Fermi liquid state below a temperature $T^*$ varying as the $5f^2$ triplet-doublet splitting to the 7/2 power. To within numerical accuracy, the non-linear magnetic susceptibility and the $5f^1$ contribution to the linear susceptibility are given by universal one-parameter scaling functions. These results may explain UBe$_{13}$ as mixed valent with a small crossover scale $T^*$.Comment: 4 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let

Aerodynamic performance of conventional and advanced design labyrinth seals with solid-smooth abradable, and honeycomb lands

Labyrinth air seal static and dynamic performance was evaluated using solid, abradable, and honeycomb lands with standard and advanced seal designs. The effects on leakage of land surface roughness, abradable land porosity, rub grooves in abradable lands, and honeycomb land cell size and depth were studied using a standard labyrinth seal. The effects of rotation on the optimum seal knife pitch were also investigated. Selected geometric and aerodynamic parameters for an advanced seal design were evaluated to derive an optimized performance configuration. The rotational energy requirements were also measured to determine the inherent friction and pumping energy absorbed by the various seal knife and land configurations tested in order to properly assess the net seal system performance level. Results indicate that: (1) seal leakage can be significantly affected with honeycomb or abradable lands; (2) rotational energy absorption does not vary significantly with the use of a solid-smooth, an abradable, or a honeycomb land; and (3) optimization of an advanced lab seal design produced a configuration that had leakage 25% below a conventional stepped seal

The incidence of mid-infrared excesses in G and K giants

Using photometric data from the 2MASS and GLIMPSE catalogues, I investigate the incidence of mid-infrared excesses (~10 microns) of G and K stars of luminosity class III. In order to obtain a large sample size, stars are selected using a near-IR colour-magnitude diagram. Sources which are candidates for showing mid-IR excess are carefully examined and modelled to determined whether they are likely to be G/K giants. It is found that mid-IR excesses are present at a level of (1.8 +/- 0.4) x 10^-3. While the origin of these excesses remains uncertain, it is plausible that they arise from debris discs around these stars. I note that the measured incidence is consistent with a scenario in which dust lifetimes in debris discs are determined by Poynting-Robertson drag rather than by collisions.Comment: Accepted for publication in MNRAS. 13 pages, 5 figures, 2 tables (1 landscape table

A second-order class-D audio amplifier

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations

The Milky Way's stellar halo - lumpy or triaxial?

We present minimum chi-squared fits of power law and Hernquist density profiles to F-turnoff stars in eight 2.5 deg wide stripes of SDSS data: five in the North Galactic Cap and three in the South Galactic cap. Portions of the stellar Galactic halo that are known to contain large streams of tidal debris or other lumpy structure, or that may include significant contamination from the thick disk, are avoided. The data strongly favor a model that is not symmetric about the Galaxy's axis of rotation. If included as a free parameter, the best fit to the center of the spheroid is surprisingly approx 3 kpc from the Galactic center in the direction of the Sun's motion. The model fits favor a low value of the density of halo stars at the solar position. The alternative to a non-axisymmetric stellar distribution is that our fits are contaminated by previously unidentified lumpy substructure.Comment: 10 pages, 10 figs, to appear in proceedings of conference "Physics at the end of the Galactic Cosmic Ray Spectrum", Journal of Physics: Conf. series, eds. G. Thomson and P. Sokolsk