Continuous Restricted Radial Motion of a Gas under the Action of a Piston

The possibility of continuous conjugation of the straightline radial motion of a gas sphere toward the center and away from the center with the motion where the gas in the entire sphere stops simultaneously is shown. The motion is described by an invariant submodel of rank 1. Time reflections allow one to construct a solution that describes a periodic continuous restricted motion of the gas sphere under the action of a piston.     

Homology classes that can be represented by embedded spheres in rational surfaces

The problem of embedding spheres in rational surfaces CP~2#nCP~2 is studied.For homology classes u=(b_1+k, b_2,…, b_n) with positive self-intersection numbers, anecessary and sufficient condition to detect its representability is given when k≤5.     

Schopenhauer's Prolegomenon to Fuzziness

Prolegomenon means something said in advance of something else. In this study, we posit that part of the work by Arthur Schopenhauer (1788–1860) can be thought of as a prolegomenon to the existing concept of fuzziness. His epistemic framework offers a comprehensive and surprisingly modern framework to study individual decision making and suggests a bridgeway from the Kantian program into the concept of fuzziness, which may have had its second prolegomenon in the work by Frege, Russell, Wittgenstein, Peirce and Black. In this context, Zadeh's seminal contribution can be regarded as the logical consequence of the Kant-Schopenhauer representation framework.     

Thermodynamics and Hydrodynamics (Statistical Foundations): 2. Thermodynamic Equilibrium

We show that the BBGKY hierarchy in thermodynamic equilibrium degenerates into an equilibrium hierarchy. In turn, the latter can be used to obtain both the fundamental system of equations describing the state of matter inside a correlation sphere of the radius R10^-7cm and the canonical Gibbs distribution, which, according to the current concepts, describes the state of the entire macroscopic system. We show that the Gibbs distribution is indeed also local, i.e., describes the state of matter only inside the correlation sphere; in the thermostat surrounding this sphere, the Gibbs distribution degenerates into a constant. We state that these two approaches are equivalent to each other.     

Collisional, Nonuniform Plasma Sphere Scattering Calculation by FDTD Employing a Drude Model

In a collisional plasma, the collision frequency between electrons and neutrals may be equal to or greater than incident electromagnetic wave frequency. The complex permittivity can not represent the dielectric property of the plasma perfectly used in the finite difference in time domain (FDTD). Drude model is adopted to characterize a collisional plasma. Using a commercial FDTD package, XFDTD 6.0, the electromagnetic scattering of plasma sphere is calculated. By comparison with Mie method, Drude mode is proven to be suitable. Radar cross-section (RCS) of nonuniform plasma spheres and conductor spheres coated by plasma layer are calculated.     

Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

On the paper “Symmetry analysis of wave equation on sphere” by H. Azad and M.T. Mustafa

Using the scalar curvature of the product manifold S²×R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M.T. Mustafa [H. Azad, M.T. Mustafa, Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl. 333 (2007) 1180-1188] to nonlinear Klein-Gordon equations on the two-dimensional sphere.     

Infrared diffuse reflectance instrumentation and standards at NIST

A spectrophotometer system for spectral characterization of materials in the infrared has been built around a bench-top Fourier transform instrument. Its capabilities include the measurement of directional-hemispherical reflectance from 1 to 18 μm. The spectral reflectance measurement is performed with an integrating sphere with an incidence angle of 8°. Both relative and absolute measurements can be made. Several methods can be used to determine the absolute value of the directional-hemispherical reflectance of samples. The primary method used is independent of the integrating sphere theory and the requisite assumptions associated with its use. The calibration of a standard reference material (SRM) is described. This SRM has a reflectance value near 0.9 over the complete calibration range 2–18 μm. As part of the calibration procedure the spatial uniformity of the sphere throughput and the bi-directional reflectance distribution function (BRDF) of the SRM material are evaluated.     

Finite-Difference Time-Domain Analysis of the Interaction of Gaussian Evanescent Light with a Single Dielectric Sphere or Ordered Dielectric Spheres

The interaction of gaussian evanescent light with a single dielectric sphere or ordered dielectric spheres in an attenuated total reflection (ATR) geometry was analyzed by the finite-difference time-domain method. Various aspects of this interaction were investigated in terms of spatial visualizations of light intensity, reflectance vs. wavelength characteristics, the transient behavior of reflectances, and so forth. In the case of a single sphere, it was evident that the whispering gallery mode can be excited in ATR geometries, but such excitation cannot be easily confirmed only through the observation of wavelength-scanned ATR spectra. In the case of a closely packed two-dimensional array of dielectric spheres, it was found that an easy axis and also a difficult axis for light propagation exist.This paper was originally presented at the 5th International Conference on NEAR FIELD OPTICS and RELATED TECHNOLOGIES (NFO-5), which was held on December 6–10, 1998 at Coganoi Bay Hotel, Shirahama, Japan, in cooperation with the Japan Society of Applied Phisics and Mombusho Grantin Aid for Scientific Research on Priority Areas “Near-field Nano-optics” Project, sponsored by Japan Society for the Promotion of Science.