Characteristic features of microlensing by noncompact objects of dark matter

A theory of microlensing by nonbaryonic bodies is developed. The characteristic features of lensing by noncompact transparent objects with a singular density distribution are investigated. The conditions under which additional peaks appear in the brilliance curve and the characteristics of these peaks are determined. The effect of a compact baryonic nucleus on the brilliance curve is studied.     

Absolute intensities for the Q-branch of the 3ν2-ν1 (465.161 cm) band of nitrous oxide

The absolute intensities of four lines, Q15–Q18 in the 03¹0–10⁰0 band, of N₂O have been measured using a tunable diode laser spectrometer at temperatures between 380 and 420 K and pressures between 4 and 15 torr. Even though these transitions are weak and produced only about 2% of absorption at the line center for a pathlength of 52m, they were measured with a signal to noise ratio of about 20 due to the high sensitivity of the instrument. The band strength derived is 1.03 × 10^-24cm molec^-1 at 296 K.     

The complete infinite series solution of systems governed by the wave equation with boundary damping

A common method of solving initial boundary value problems is separation of variables, denoted as modal analysis in the field of flexible structures. For systems with undamped boundary conditions the method is well-established, but for systems with boundary damping it does not provide closed form solutions. In this paper the exact modal series solution for second order systems with damped boundaries is derived with explicit expressions for the series coefficients. Knowledge of these coefficients enables practical applications of the solution, such as finite dimension approximation. The key element of the derivation is a new orthogonality condition for the damped eigenfunctions. The modal series is also transformed into a traveling wave form. The solution, which is the extension of the classical D’Alembert formula, is represented by a single equivalent propagating wave. A component of the solution, denoted by “end waves”, is identified to provide the continuity of the systems displacement response.     

Heating and convection associated with alkaline electrophoresis

Alkaline version of the single-cell gel electrophoresis (Comet assay) is widely used in toxicological, environmental, and monitoring studies to assess the DNA damage levels in individual cells. The change in the temperature of the electrophoretic solution is one of the reasons leading to interlaboratory variation of Comet assay results. In this work, changes of surface temperature of the solution during electrophoresis were studied using technique of real-time thermal imaging. It has been found that the electrophoresis is accompanied by nonuniform temperature rise in different areas of the electrophoretic chamber. The maximum of heating was observed in the central region of the chamber, where temperature increased by an average of 7°C. The minimum temperature rise in other parts of the chamber was about 5°C. After removing the solution, the temperature on the surface of slides was higher than that on the surface of the solution. We believe that (1) nonuniform heating of the electrophoretic solution and convection could be the reasons responsible for the variability of results both in inter- and intralaboratory studies; (2) the spatial distribution of heating of the solution depends on the size and configuration of the electrophoretic chambers used.     

Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables

We derive exponential bounds for the tail of the distribution of normalized sums of triangular arrays of random variables, not necessarily independent, under the law of ordinary logarithm.

Furthermore, we provide estimates for partial sums of triangular arrays of independent random variables belonging to suitable grand Lebesgue spaces and having heavy-tailed distributions.

     

Lamellar gels and spontaneous vesicles in catanionic surfactant mixtures

Caillé analysis of the small-angle X-ray line shape of the lamellar phase of 7:3 wt/wt cetyltrimethylammonium tosylate (CTAT)/sodium dodecylbenzene sulfonate (SDBS) bilayers shows that the bending elastic constant is kappa = (0.62 +/- 0.09)k(B)T. From this and previous results, the Gaussian curvature constant is kappa = (-0.9 +/- 0.2)k(B)T. For 13:7 wt/wt CTAT/SDBS bilayers, the measured bending elasticity decreases with increasing water dilution, in good agreement with predictions based on renormalization theory, giving kappa(o) = 0.28k(B)T. These results show that surfactant mixing is sufficient to make kappa approximately k(B)T, which promotes strong, Helfrich-type repulsion between bilayers that can dominate the van der Waals attraction. These are necessary conditions for spontaneous vesicles to be equilibrium structures. The measurements of the bending elasticity are confirmed by the transition of the lamellar phase of CTAT/SDBS from a turbid, viscoelastic gel to a translucent fluid as the water fraction is decreased below 40 wt %. Freeze-fracture electron microscopy shows that the gel is characterized by spherulite defects made possible by spontaneous bilayer curvature and low bending elasticity. This lamellar gel phase is common to a number of catanionic surfactant mixtures, suggesting that low bending elasticity and spontaneous curvature are typical of these mixtures that form spontaneous vesicles.     

Lagrangian structure functions in hydrodynamic turbulence

Based on a solution of the Navier-Stokes equations for the inertial range of fully developed turbulence, a statistical theory is developed to determine the Lagrangian structure functions K _n (τ). Over times τ shorter than the large-scale correlation time τ_c, they obey scaling relations of the form K _n (τ) ∞ \(\tau ^{\zeta _n } \). Analytical expressions are derived for ζ _n . A detailed comparison between the theory and the experimental results presented in [1] demonstrates complete quantitative agreement. A new concept is introduced in turbulence theory: the correlation R _n (τ) between tracer-particle positions on a Lagrangian trajectory. It is shown that the position correlation functions R _n exhibit universal scaling behavior for n > 3.