Statistical mechanics of the nonlinear Schrödinger equation

We investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian $$H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}$$ is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL ² norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied.     

Solid-phase microextraction–capillary gas chromatography combined with microwave-induced plasma atomic-emission spectrometry for selenite determination

The use of solid-phase microextraction (SPME) with gas chromatography coupled to microwave-induced plasma atomic-emission detection (GC–MIP-AED) is described for selenite [Se(IV)] speciation. Aqueous standards were derivatised with sodium tetraethyl- or tetrapropylborate and extracted by SPME. Headspace extraction of the ethyl and propyl derivatives was studied. Relevant experimental conditions were optimised, including conditions for derivatisation and extraction and those of gas chromatographic analysis. The limits of detection achieved for headspace sampling of derivatised Se(IV) were in the low ng mL^–1 range for both ethylation and propylation. When the method was applied to analysis of selenite in selenised yeast reference material results were in good agreement with the indicated values.     

Neutron activation analysis of final molasses from Cuban sugar industry

Thermal and epithermal non-destructive activation analyses have been performed on samples of final molasses from 14 different sugar factories, covering the most important regions in Cuba. From the first measurement after irradiation at the Triga Mark reactor (VTT), the concentration of more than 15 elements is reported. The almost constant elemental composition shows that they can be used equally for different purposes as animal foodstuff and for the manufacture of biotechnological products. This work is part of a research project developed in order to establish a complete characterization of Cuban sugar molasses.     

Identification of odor signature chemicals in cocaine using solid-phase microextraction-gas chromatography and detector-dog response to isolated compounds spiked on U.S. paper currency

Solid-phase microextraction (SPME) combined with gas chromatography (GC) is optimized and applied to the analysis of street-cocaine samples followed by the field-testing of isolated chemicals using certified detector dogs. SPME proves to be a very sensitive and rapid method for isolating odor chemicals from street-cocaine samples. SPME-GC and activated charcoal strip (ACS)-SPME-GC signature profile methods are developed for the detection and quantitation of cocaine-odor chemicals, including the optimization of controllable variables such as fiber chemistry, extraction time, and desorption time. The volatile odor chemicals in representative illicit cocaine samples are identified and quantitated by the ACS-SPME-GC signature profile method and direct injection. Field tests with drug detector dogs show methyl benzoate to be the dominant signature odor chemical along with cocaine on U.S. currency at a threshold level of approximately 1-10 microg when spiked or when 10 ng/s methyl benzoate is diffused from polymer bottles, which is required in order to initiate an alert. No other substance studied initiated consistent responses by the drug dogs. The results indicate that the microgram levels of cocaine that have been reported on circulated U.S. currency are insufficient to signal an alert from law-enforcement trained drug detector dogs.     

Instrumental neutron activation analysis of rock samples from Ugep area of Cross River State,Nigeria

The theory and analytical procedures in Instrumental Neutron Activation Analysis (INAA) are discussed. Application of the method to the determination of sixteen trace elements: Na, K, Mn, Sm, La, Fe, Th, Sc, Co, Ba, Rb, Br, Sb, Cs and Ta in some rock samples from Ugep in the Lower Benue Region of Nigeria, is described. The high radioactivity observed in some of the samples analyzed has been associated with the higher-than-normal concentrations of Th and K in the samples. Also, Ba and Fe concentrations in some of the samples were found to be anomalous when compared with average expected values in normal sedimentary rocks.     

Dithiolate complexes of manganese and rhenium: X-ray structure and properties of an unusual mixed valence cluster Mn3(CO)6(mu-eta2-SCH2CH2CH2S)3

Treatment of Mn(2)(CO)(10) with 3,4-toluenedithiol and 1,2-ethanedithiol in the presence of Me(3)NO.2H(2)O in CH(2)Cl(2) at room temperature afforded the dinuclear complexes Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (1), and Mn(2)(CO)(6)(mu-eta(4)-SCH(2)CH(2)S-SCH(2)CH(2)S) (2), respectively. Similar reactions of Re(2)(CO)(10) with 3,4-toluenedithiol, 1,2-benzenedithiol, and 1,2-ethanedithiol yielded the dirhenium complexes Re(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (3), Re(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S) (4), and Re(2)(CO)(6)(SCH(2)CH(2)S-SCH(2)CH(2)S) (5), respectively. In contrast, treatment of Mn(2)(CO)(10) with 1,3-propanedithiol afforded the trimanganese compound Mn(3)(CO)(6)(mu-eta(2)-SCH(2)CH(2)CH(2)S)(3) (6), whereas Re(2)(CO)(10) gave only intractable materials. The molecular structures of 1, 3, and 6 have been determined by single-crystal X-ray diffraction studies. The dimanganese and dirhenium carbonyl compounds 1-5contain a binucleating disulfide ligand, formed by interligand disulfide bond formation between two dithiolate ligands identical in structure to that of the previously reported dimanganese complex Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S). Complex 6, on the other hand, forms a unique example of a mixed-valence trimangenese carbonyl compound containing three bridging 1,3-propanedithiolate ligands. The solution properties of 6 have been investigated by UV-vis and EPR spectroscopies as well as electrochemical techniques.     

THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method

The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.