Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Sonic crystal lenses that obey Lensmaker's formula

This paper presents a theoretical study of the phenomenon of acoustic imaging by sonic crystals, which are made of two-dimensional regular arrays of rigid cylinders placed in parallel in air. The scattering of acoustic waves is computed using the standard multiple scattering theory, and the band structures are computed by the plane-wave expansion method. It is shown that properly arranged arrays not only can behave as acoustic lenses, but also the focusing effect can be well described by Lensmaker's formula. Possible applications are also discussed.Comment: 4 pages, 5 figure

A peculiar multi-wavelength flare in the Blazar 3C 454.3

The blazar 3C454.3 exhibited a strong flare seen in gamma-rays, X-rays, and optical/NIR bands during 3--12 December 2009. Emission in the V and J bands rose more gradually than did the gamma-rays and soft X-rays, though all peaked at nearly the same time. Optical polarization measurements showed dramatic changes during the flare, with a strong anti-correlation between optical flux and degree of polarization (which rose from ~ 3% to ~ 20%) during the declining phase of the flare. The flare was accompanied by large rapid swings in polarization angle of ~ 170 degree. This combination of behaviors appear to be unique. We have cm-band radio data during the same period but they show no correlation with variations at higher frequencies. Such peculiar behavior may be explained using jet models incorporating fully relativistic effects with a dominant source region moving along a helical path or by a shock-in-jet model incorporating three-dimensional radiation transfer if there is a dominant helical magnetic field. We find that spectral energy distributions at different times during the flare can be fit using modified one-zone models where only the magnetic field strength and particle break frequencies and normalizations need change. An optical spectrum taken at nearly the same time provides an estimate for the central black hole mass of ~ 2.3 * 10^9 M_sun. We also consider two weaker flares seen during the $\sim 200$ d span over which multi-band data are available. In one of them, the V and J bands appear to lead the $\gamma$-ray and X-ray bands by a few days; in the other, all variations are simultaneous.Comment: 11 pages, 4 figures, 2 tables; MNRAS in pres

Remarkable enhancement in crystalline perfection, second harmonic generation efficiency, optical transparency, and laser damage threshold in potassium dihydrogen phosphate crystals by L-threonine doping

Effect of L-threonine (LT) doping on crystalline perfection, second harmonic generation (SHG) efficiency, optical transparency, and laser damage threshold (LDT) in potassium dihydrogen phosphate (KDP) crystals grown by slow evaporation solution technique (SEST) has been investigated. The influence of doping on growth rate and morphology of the grown crystals has also been studied. Powder x-ray diffraction data confirms the crystal structure of KDP and shows a systematic variation in intensity of diffraction peaks in correlation with morphology due to varying LT concentration. No extra phase formation was observed which is further confirmed by Fourier transform Raman (FT-Raman) studies. High-resolution x-ray diffraction curves indicate that crystalline perfection has been improved to a great extent at low concentrations with a maximum perfection at 1 mol % doping. At higher concentrations (5 to 10 mol %), it is slightly reduced due to excess incorporation of dopants at the interstitial sites of the crystalline matrix. LDT has been increased considerably with increase in doping concentration, whereas SHG efficiency was found to be maximum at 1 mol % in correlation with crystalline. The optical transparency for doped crystals has been increased as compared to that of pure KDP with a maximum value at 1 mol % doping

Water wave propagation and scattering over topographical bottoms

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps

Multiband optical variability of the blazar OJ 287 during its outbursts in 2015 -- 2016

We present recent optical photometric observations of the blazar OJ 287 taken during September 2015 -- May 2016. Our intense observations of the blazar started in November 2015 and continued until May 2016 and included detection of the large optical outburst in December 2016 that was predicted using the binary black hole model for OJ 287. For our observing campaign, we used a total of 9 ground based optical telescopes of which one is in Japan, one is in India, three are in Bulgaria, one is in Serbia, one is in Georgia, and two are in the USA. These observations were carried out in 102 nights with a total of ~ 1000 image frames in BVRI bands, though the majority were in the R band. We detected a second comparably strong flare in March 2016. In addition, we investigated multi-band flux variations, colour variations, and spectral changes in the blazar on diverse timescales as they are useful in understanding the emission mechanisms. We briefly discuss the possible physical mechanisms most likely responsible for the observed flux, colour and spectral variability.Comment: 11 pages, 6 figures, 4 tables; Accepted for publication in MNRA