A collection of arithmetic exercises designed particularly for the superior child in grade three of four to supplement the standard program at those grade levels

Thesis (Ed.M.)--Boston Universit

Spacetime perspective of Schwarzschild lensing

We propose a definition of an exact lens equation without reference to a background spacetime, and construct the exact lens equation explicitly in the case of Schwarzschild spacetime. For the Schwarzschild case, we give exact expressions for the angular-diameter distance to the sources as well as for the magnification factor and time of arrival of the images. We compare the exact lens equation with the standard lens equation, derived under the thin-lens-weak-field assumption (where the light rays are geodesics of the background with sharp bending in the lens plane, and the gravitational field is weak), and verify the fact that the standard weak-field thin-lens equation is inadequate at small impact parameter. We show that the second-order correction to the weak-field thin-lens equation is inaccurate as well. Finally, we compare the exact lens equation with the recently proposed strong-field thin-lens equation, obtained under the assumption of straight paths but without the small angle approximation, i.e., with allowed large bending angles. We show that the strong-field thin-lens equation is remarkably accurate, even for lightrays that take several turns around the lens before reaching the observer.Comment: 22 pages, 6 figures, to appear in Phys. Rev.

Combined grazing incidence RBS and TEM analysis of luminescent nano-SiGe/SiO2 multilayers.

Multilayer structures with five periods of amorphous SiGe nanoparticles/SiO2 layers with different thickness were deposited by Low Pressure Chemical Vapor Deposition and annealed to crystallize the SiGe nanoparticles. The use of grazing incidence RBS was necessary to obtain sufficient depth resolution to separate the signals arising from the individual layers only a few nm thick. The average size and areal density of the embedded SiGe nanoparticles as well as the oxide interlayer thickness were determined from the RBS spectra. Details of eventual composition changes and diffusion processes caused by the annealing processes were also studied. Transmission Electron Microscopy was used to obtain complementary information on the structural parameters of the samples in order to check the information yielded by RBS. The study revealed that annealing at 900 °C for 60 s, enough to crystallize the SiGe nanoparticles, leaves the structure unaltered if the interlayer thickness is around 15 nm or higher

Nanoplasmonic near-field synthesis

The temporal response of resonances in nanoplasmonic structures typically converts an incoming few-cycle field into a much longer near-field at the spot where non-linear physical phenomena including electron emission, recollision and high-harmonic generation can take place. We show that for practically useful structures pulse shaping of the incoming pulse can be used to synthesize the plasmon-enhanced field and enable single-cycle driven nonlinear physical phenomena. Our method is demonstrated for the generation of an isolated attosecond pulse by plasmon-enhanced high harmonic generation. We furthermore show that optimal control techniques can be used even if the response of the plasmonic structure is not known a priori.Comment: 6 page

Fermat Potentials for Non-Perturbative Gravitational Lensing

The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which relates the placement and distortion of the images to the real source position in the thin-lens scenario, is obtained by extremizing the time of arrival among all the null paths from the source to the observer (Fermat's principle). We show that the construction of envelopes of certain families of null surfaces consitutes an alternative variational principle or version of Fermat's principle that leads naturally to a lens equation in a generic spacetime with any given metric. We illustrate the construction by deriving the lens equation for static asymptotically flat thin lens spacetimes. As an application of the approach, we find the bending angle for moving thin lenses in terms of the bending angle for the same deflector at rest. Finally we apply this construction to cosmological spacetimes (FRW) by using the fact they are all conformally related to Minkowski space.Comment: accepted for publication in Phys. Rev.

Continuous image distortion by astrophysical thick lenses

Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The method we develop continuously changes the shape of the pencil of rays from the source to the observer with no reference to lens planes in astrophysically relevant scenarios. We compare the projected area and the ratio of semi-major to semi-minor axes of the observed elliptical image shape for circular sources from the continuous, thick-lens method with the commonly assumed thin-lens approximation. We find that for truncated singular isothermal sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens approximation is accurate to better than 1 part in 10^4 in predicting the image area and axes ratios. For asymmetric thick lenses consisting of two massive clusters separated along the line of sight in redshift up to \Delta z = 0.2, we find that modeling the image distortion as two clusters in a single lens plane does not produce relative errors in image area or axes ratio more than 0.5%Comment: accepted to GR

Inhibition of fungal infection using sulfite pads prior to initiation of callus from Vitis labruscana cv. Concord

Research NoteIncubation of plant material with potassium metabisulfite was found to inhibit fungal infections of explants from grapevines. Grapevine tissue of Vitis labruscana cv. Concord was incubated with sulfite pads containing 0.4 g of potassium metabilsufite for one and two days prior to culturing and evaluated against a control that had been surface sterilized with 0.5 % NaOCI and 70 % ethanol after one week for losses due to microbial contamination. Sulfite fumigation of plant material reduced the incidence of mold infection, particularly in tissue cultures developed from fruit explants which had reductions in contamination as high as 10 fold. Continued attempts to isolate contaminants from cultures intitiated from these explants showed no signs of infection

Phase- and intensity-resolved measurements of above threshold ionization by few-cycle pulses

We investigate the carrier-envelope phase (CEP) and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750 nm is varied in a range between 0.7 × 1014 and . Our measurements reveal a prominent maximum in the CEP-dependent asymmetry at photoelectron energies of 2 U P (U P being the ponderomotive potential), that is persistent over the entire intensity range. Further local maxima are observed around 0.3 and 0.8 U P. The experimental results are in good agreement with theoretical results obtained by solving the three-dimensional time-dependent Schrödinger equation. We show that for few-cycle pulses, the amplitude of the CEP-dependent asymmetry provides a reliable measure for the peak intensity on target. Moreover, the measured asymmetry amplitude exhibits an intensity-dependent interference structure at low photoelectron energy, which could be used to benchmark model potentials for complex atoms