Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems

We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations. We can compute branches of solutions with limit points, bifurcation points, etc. Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations

Mechanisms of superconductivity investigated by nuclear radiation

Investigation focused on the behavior of superconducting magnet and its constituent materials during and after exposure to nuclear radiation. The results will indicate the feasibility of their use in diverse applications and various environments

Reconstruction of potential energy profiles from multiple rupture time distributions

We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an energy barrier, can be easily extracted from a single first passage time (FPT) distribution, the reconstruction of finer structure is ill-conditioned. More careful analysis shows the existence of optimal bond potential amplitudes (represented by an effective Peclet number) and initial bond configurations that yield the most efficient numerical reconstruction of simple potentials. Furthermore, we show that reconstruction of more complex potentials containing multiple minima can be achieved by simultaneously using two or more measured FPT distributions, obtained under different physical conditions. For example, by changing the effective potential energy surface by known amounts, additional measured FPT distributions improve the reconstruction. We demonstrate the possibility of reconstructing potentials with multiple minima, motivate heuristic rules-of-thumb for optimizing the reconstruction, and discuss further applications and extensions.Comment: 20 pages, 9 figure

Ptychographic reconstruction of attosecond pulses

We demonstrate a new attosecond pulse reconstruction modality which uses an algorithm that is derived from ptychography. In contrast to other methods, energy and delay sampling are not correlated, and as a result, the number of electron spectra to record is considerably smaller. Together with the robust algorithm, this leads to a more precise and fast convergence of the reconstruction.Comment: 12 pages, 7 figures, the MATLAB code for the method described in this paper is freely available at http://figshare.com/articles/attosecond_Extended_Ptychographyc_Iterative_Engine_ePIE_/160187

Inelastic resonant tunneling through single molecules and quantum dots: spectrum modification due to nonequilibrium effects

Resonant electron transport through a mesoscopic region (quantum dot or single molecule) with electron-phonon interaction is considered at finite voltage. In this case the standard Landauer-B\"uttiker approach cannot be applied. Using the nonequilibrium Green function method we show that due to a nonequilibrium distribution function of electrons in the mesoscopic region, the inelastic scattering rate and spectral function of the dot become functions of the voltage and have to be calculated self-consistently.Comment: 4 pages, 3 figure

Modeling of mode-locking in a laser with spatially separate gain media

We present a novel laser mode-locking scheme and discuss its unusual properties and feasibility using a theoretical model. A large set of single-frequency continuous-wave lasers oscillate by amplification in spatially separated gain media. They are mutually phase-locked by nonlinear feedback from a common saturable absorber. As a result, ultra short pulses are generated. The new scheme offers three significant benefits: the light that is amplified in each medium is continuous wave, thereby avoiding issues related to group velocity dispersion and nonlinear effects that can perturb the pulse shape. The set of frequencies on which the laser oscillates, and therefore the pulse repetition rate, is controlled by the geometry of resonator-internal optical elements, not by the cavity length. Finally, the bandwidth of the laser can be controlled by switching gain modules on and off. This scheme offers a route to mode-locked lasers with high average output power, repetition rates that can be scaled into the THz range, and a bandwidth that can be dynamically controlled. The approach is particularly suited for implementation using semiconductor diode laser arrays.Comment: 13 pages, 5 figures, submitted to Optics Expres

Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential

We examine numerically vortex families near band edges of the Bloch wave spectrum in the Gross--Pitaevskii equation with a two-dimensional periodic potential and in the discrete nonlinear Schroedinger equation. We show that besides vortex families that terminate at a small distance from the band edges via fold bifurcations there exist vortex families that are continued all way to the band edges.Comment: 12 pages, 8 figure

The color dependent morphology of the post-AGB star HD161796

Context. Many protoplanetary nebulae show strong asymmetries in their surrounding shell, pointing to asymmetries during the mass loss phase. Questions concerning the origin and the onset of deviations from spherical symmetry are important for our understanding of the evolution of these objects. Here we focus on the circumstellar shell of the post-AGB star HD 161796. Aims. We aim at detecting signatures of an aspherical outflow, as well as to derive the properties of it. Methods. We use the imaging polarimeter ExPo (the extreme polarimeter), a visitor instrument at the William Herschel Telescope, to accurately image the dust shell surrounding HD 161796 in various wavelength filters. Imaging polarimetry allows us to separate the faint, polarized, light from circumstellar material from the bright, unpolarized, light from the central star. Results. The shell around HD 161796 is highly aspherical. A clear signature of an equatorial density enhancement can be seen. This structure is optically thick at short wavelengths and changes its appearance to optically thin at longer wavelengths. In the classification of the two different appearances of planetary nebulae from HST images it changes from being classified as DUPLEX at short wavelengths to SOLE at longer wavelengths. This strengthens the interpretation that these two appearances are manifestations of the same physical structure. Furthermore, we find that the central star is hotter than often assumed and the relatively high observed reddening is due to circumstellar rather than interstellar extinction.Comment: Accepted for publication in A&