Condensate formation and vortex generation in Bose gas upon cooling

The mechanism of transition of a Bose gas to the superfluid state via thermal fluctuations under the condition of external cooling at a temperature above the transition point is considered. The probability of formation of such critical fluctuations (instantons) is calculated; it is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.     

Study of the dynamic structure factor of strong glasses

The dynamic structure factors (DSFs) of several strong glasses (SF6, SF10, BK7, SUPRASIL) measured by Brillouin light scattering spectroscopy are reported. Spectra have been collected, at and above room temperature, at two scattering angles, θ=90° and θ=180° corresponding to exchanged wavevector q values ranging from 0.0256 to 0.0448 nm⁻¹. In particular we find that the isotropic spectral lineshapes are in all cases well described by the simple hydrodynamic theory of an amorphous solid. The width of the Brillouin peaks are found to be consistent with the predicted q² dependence at both investigated temperatures. This damping is however found to account only partially for the strong asymmetry of the Brillouin line clearly visible on a logarithmic intensity scale. As a matter of fact there is an excess intensity in the very low frequency plateau underlying the central component. The height of this plateau and hence the entire lineshape is well reproduced if a relaxation process is taken into account in the hydrodynamic equations. Owing to the intense elastic scattering we are able to determine unambiguously only the ratio between amplitude and characteristic time of this process which quantifies the sound dispersion to be of the order of a few percent in all samples. The temperature dependence of the parameters indicates that this relaxation cannot be attributed to thermally activated relaxation phenomena. These general findings favorably compare with molecular dynamics simulation results on similar systems.     

On the Validity of Clauser and Horne Factorizability

The Clauser–Horne approach used to derive experimentally measurable quantities for performing experiments on EPR paradox based on Type-I Spontaneous Parametric Down Conversion (SPDC) sources is discussed. It is proved that in this case the deduced Bell's type inequality does not correctly express separability and causality. A deeper analysis of the problem shows that the Clauser–Horne hypothesis of factorizability of joint detection probability cannot be considered so general as to describe this physical situation.     

Scattering of excited atoms due to ion bombardment of metals

The spectrum and the spatial distribution of the emission of scattered particles upon bombardment of Be, Ti, Ta, and W with H and He ions were studied. The quantum yield and the velocity and angular distributions of the scattered excited particles were measured. Computer simulation of the scattering of H ions and He ions from the metals under study was performed with the use of the program TRIM-95. Agreement is observed between the calculated and experimentally measured angular distributions of the scattered particles.     

Rheological and Electrical Properties of Oxidized Carbon Black Suspensions in Vaseline Oil under Shear and Vibration

The results of investigations of the rheological characteristics and electrical resistance of the suspensions of carbon black in vaseline oil under the effects of shear and vibration were presented. The investigations are carried out on an original unit that allowed one to simultaneously subject the suspensions to shear deformation and orthogonal vibration. The electrical resistance was also measured in an ac pulsed low-voltage mode. Possible mechanisms of the suspension conductivity were considered depending on the regime of dynamic action.     

The honors class: hilbert’s problems and their solvers

Feel like writing a review for The Mathematical Intelligencer? You are welcome to submit an unsolicited review of a book of your choice; or, if you would welcome being assigned a book to review, please write us, telling us your expertise and your predilections.     

Gaussian Beams,the Hamilton-Jacobi Equations,and Finsler Geometry

Relationships between Gaussian beams and geometry are considered in the paper. We show that the main properties of the Gaussian beam solutions are determined by the natural geometry related to the problem under consideration. The geometry is determined by the Hamilton-Jacobi equation and the corresponding Hamiltonian. In particular, we find a geometric interpretation of the Riccati equation for the quadratic form of the phase function corresponding to a Gaussian beam in the case of Finsler geometry. Bibliography: 2 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 66–92.     

Polarized Lidar Reflectance Measurements of Vegetation at Near-Infrared and Green Wavelengths

There is growing interest in the use of lidar for remote sensing of vegetation owing to the emergence of reliable and rugged lasers and highly sensitive detectors. Lidar remote sensing has a distinct advantage over conventional techniques in vegetation remote sensing due to its capability for three-dimensional characterization of vegetative targets. The Multiwavelength Airborne Polarimetric Lidar (MAPL) system was developed primarily for vegetation remote sensing applications from an airborne platform of up to 1,000 -m altitude. The lidar system has full waveform capture and polarimetric measurement capability at two wavelengths in the near-infrared (1064 nm) and the green (532 nm) spectral regions. This study presents preliminary ground-based lidar reflectance measurements on a variety of deciduous and coniferous trees under fully foliated conditions with a view towards tree species discrimination. Variations in the reflectance characteristics of selected deciduous trees under unfoliated and fully foliated conditions were also investigated. Our study reveals distinct differences in the reflectance characteristics of various trees.