A note on Sommerfeld's diffraction problem

A direct transform technique is found to be most suitable for attacking two-dimensional diffraction problems. As a first example of the application of the technique, the well-known Sommerfeld problem is reconsidered and the solution of the problem of diffraction, by a half-plane, of a cylindrical pulse is made use of in deducing the solution of the problem of diffraction of a plane wave by a soft half-plane. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Note: Dynamic point spread function for single and multiphoton fluorescence microscopy

We propose and demonstrate a dynamic point spread function (PSF) for single and multiphoton fluorescence microscopy. The goal is to generate a PSF whose shape and size can be maneuvered from highly localized to elongated one, thereby allowing shallow-to-depth excitation capability during active imaging. The PSF is obtained by utilizing specially designed spatial filter and dynamically altering the filter parameters. We predict potential applications in nanobioimaging and fluorescence microscopy.

Note: Dynamic point spread function for single and multiphoton fluorescence microscopy

We propose and demonstrate a dynamic point spread function (PSF) for single and multiphoton fluorescence microscopy. The goal is to generate a PSF whose shape and size can be maneuvered from highly localized to elongated one, thereby allowing shallow-to-depth excitation capability during active imaging. The PSF is obtained by utilizing specially designed spatial filter and dynamically altering the filter parameters. We predict potential applications in nanobioimaging and fluorescence microscopy.

A note on the effect of wall compliance on lowest?order mode propagation in fluid?filled/submerged impedance tubes

Wave propagation in fluid?filled/submerged tubes is of interest in large HVAC ducts, and also in understanding and interpreting the experimental results obtained from fluid?filled impedance tubes. Based on the closed form analytical solution of the coupled wave equations, an eigenequation, which is the determinant of an 8×8 matrix, is derived and solved to obtain the axial wave number of the lowest?order longitudinal modes for cylindrical ducts of various diameter and wall thickness. The dispersion behavior of the wave motion is analyzed. It is observed that the larger the diameter of the duct and/or the smaller its wall thickness, the more flexible the impedance tube leading to more coupling between the waves in the elastic media. Also, it is shown that the wave motion in water?filled ducts submerged in water exhibits anomalous dispersion behavior. The axial attenuation characteristics of plane waves along water?filled tubes submerged in water or air are also investigated. Finally, investigations on the sound intensity level difference characteristics of the wall of the air?filled tubes are reported.

A Note On The Effect Of Short And Long Laminar Separation-Bubbles On Desinent Cavitation

Earlier desinent cavitation studies on a 1/8 caliber ogive by one of the authors (J. W. H.) showed a sudden change in the magnitude of the desinent cavitation number at a critical velocity. In the present work it is shown by means of oil-film flow visualization that below the critical velocity a long laminar separation bubble exists whereas above the critical velocity the laminar separation bubble is short. Thus the desinent cavitation characteristics of a 1/8 caliber ogive are governed by the nature of the viscous flow around the body.

Note: Effect of fluid phase compositions on the formation of substitutionally ordered solid phases from a binary mixture of oppositely charged colloidal suspensions

A binary mixture of oppositely charged colloidal particles can self-assemble into either a substitutionally ordered or substitutionally disordered crystalline phase depending on the nature and strength of interactions among the particles. An earlier study had mapped out favorable inter-particle interactions for the formation of substitutionally ordered crystalline phases from a fluid phase using Monte Carlo molecular simulations along with the Gibbs-Duhem integration technique. In this paper, those studies are extended to determine the effect of fluid phase composition on formation of substitutionally ordered solid phases.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.