Hydrodynamic theory of plasma oscillations in quasi-two-dimensional systems

We show that a hydrodynamic theory can be applied to calculate the dispersion relation of plasma oscillations in a quasi-two-dimensional system. It also leads to the conclusion that additional “multipole” modes may exist in the system.     

Exact solution of damped nonlinear Schrödinger equation for a parabolic density profile

An exact single envelope soliton solution of the damped nonlinear Schrödinger equation in a medium with a parabolic density profile has been obtained. It is found that the condition of reflection of the soliton from the density hump is determined by its initial velocity and the scale lengths of the inhomogeneity.     

Measurement of mercaptans in gasoline

In an r-FIA single-line manifold, 10-l portions of 5,5-dithiobis (2-nitrobenzoic acid) and 2% (v/v) ethylenediamine in 80 20 inethanol: acetone are injected from pressurized containers via high-speed on/off valves into a flowing gasoline stream. The reaction product, 2-nitro-5-mercaptobenzoate, is detected optically at 412 nm after a reaction time of 15s. The system is intended for the measurement of mercaptans in the 0–2 mM (0–64 ppm S) concentration range. The response for C1–C10n-mercaptans ranges from 0.766–0.159 mAU/mM, the response to C1–C5n-mercaptans is 630 mAU/mM (±18.5% RSD). The response ratio of C1 and C5 mercaptans is 1 0.653. The system permits extreme conservation of reagents; only 10 l of each reagent is consumed per determination.     

Borel complexity of the space of probability measures

Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if is any non-Polish Borel subspace of a Polish space, then , the space of probability Borel measures on with the weak topology, is always true , where is the least ordinal such that is .

     

Fusion suppression and sub-barrier breakup of weakly bound nuclei

The mechanism for the large suppression of complete fusion in the 9Be+208Pb reaction has been investigated through measurement of sub-barrier breakup of 9Be. Excluding breakup through the 8Be ground state, whose lifetime is too long, a prompt breakup component remains, having sufficient probability to explain the observed suppression of complete fusion. This appears to be associated with interactions at the nuclear surface. The fusion suppression is predicted to be almost proportional to the charge of the target nucleus, making it most significant in reactions with heavy nuclei.     

Experimental persistence probability for fluctuating steps

The persistence behavior for fluctuating steps on the Si(111)-(sqrt[3]xsqrt[3])R30 degrees -Al surface was determined by analyzing time-dependent STM images for temperatures between 770 and 970 K. Using the standard persistence definition, the measured persistence probability displays power-law decay with an exponent of theta=0.77+/-0.03. This is consistent with the value of theta=3/4 predicted for attachment-detachment limited step kinetics. If the persistence analysis is carried out in terms of return to a fixed-reference position, the measured probability decays exponentially. Numerical studies of the Langevin equation used to model step motion corroborate the experimental observations.     

A universal coanalytic linear ordering

We construct a linear ordering in which every (coanalytic) linear ordering can be order embedded.

     

Photo-stability of laser dye solutions under Copper-vapour-laser excitation

The photo-stability of laser dyes, Rhodamine-6G, Rhodamine-B, and Kiton-Red, under high repetition rate (6.3 kHz) Copper-vapour-laser (CVL) irradiation has been investigated. Exhaustive photo-bleaching of these dyes in different solvents has been carried out to study the extent to which the dye photo-degraded products would interfere with the lasing process in high-power CVL-pumped dye lasers. Our results indicate that the photo-degradation of dyes occurs predominantly through excited-state intermolecular reactions, involving the singlet state, rather than the process of nonlinear optical absorption in individual molecules. Received: 13 March 2000 / Revised version: 2 August 2000 / Published online: 21 March 2001     

Tutorial: Simulating chromatography with Microsoft Excel Macros

Chromatography is one of the cornerstones of modern analytical chemistry; developing an instinctive feeling for how chromatography works will be invaluable to future generation of chromatographers. Specialized software programs exist that handle and manipulate chromatographic data; there are also some that simulate chromatograms. However, the algorithm details of such software are not transparent to a beginner. In contrast, how spreadsheet tools like Microsoft Excel™ work is well understood and the software is nearly universally available. We show that the simple repetition of an equilibration process at each plate (a spreadsheet row) followed by discrete movement of the mobile phase down by a row, easily automated by a subroutine (a “Macro” in Excel), readily simulates chromatography. The process is readily understood by a novice. Not only does this permit simulation of isocratic and simple single step gradient elution, linear or multistep gradients are also easily simulated. The versatility of a transparent and easily understandable computational platform further enables the simulation of complex but commonly encountered chromatographic scenarios such as the effects of nonlinear isotherms, active sites, column overloading, on-column analyte degradation, etc. These are not as easily simulated by available software. Views of the separation as it develops on the column and as it is seen by an end-column detector are both available in real time. Excel 2010™ also permits a 16-level (4-bit) color gradation of numerical values in a column/row; this permits visualization of a band migrating down the column, much as Tswett may have originally observed, but in a numerical domain. All parameters of relevance (partition constants, elution conditions, etc.) are readily changed so their effects can be examined. Illustrative Excel spreadsheets are given in the Supporting Information; these are easily modified by the user or the user can write his/her own routine.