Relaxation and dephasing in a many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a fluctuating force generated by a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate Green's functions and discuss relaxation and dephasing of a single extra particle added above the Fermi sea. We also extend our analysis to a more generic coupling between system and bath that results in complete thermalization of the system.     

Spin determination of isobaric analogue resonances in209Bi and207Bi by proton polarization measurements

The polarization of elastically scattered protons from²⁰⁸Pb and²⁰⁶Pb was measured. The spins of some isobaric analogue resonances in²⁰⁹Bi and²⁰⁷Bi in the energy region from 16.2 to 17.8 MeV were determined.     

Advanced Geometrical Modeling of Focused Beam Reflectance Measurements (FBRM)

In the past decade the use of focused beam reflectance measurements (FBRM) has been established as an on line and in situ particle characterization technique. However, a model is required to obtain full information from the FBRM signal and to compare the results to other measurement techniques. Different modeling approaches can be found in the literature. All of these assume a laser focus of zero extension, motionless particles and fully opaque particles. It is shown in this work that these assumptions do not hold even for ideally spherical particles. For large, opaque particles, the particle velocity and a depth dependent laser velocity have to be considered. For highly transparent particles, backscattering only occurs near the edges of a crystal. Consequently, two more refined modeling approaches – the velocity model and the edge scattering model – based on Monte‐Carlo techniques are developed and verified in this work.     

Kinetic analysis of the decomposition of piperidinium hexathiocyanoatochromate(III)

Summary The decomposition of piperidinium hexathiocyanatochromate(III), (pipH)₃[Cr(NCS)₆](s), into Cr(NCS)₃(s) and pipHSCN(g) has been studied isothermally and nonisothermally using t.g.a. Data from isothermal studies were analysed according to 17 different kinetic models and the (, T) data from nonisothermal experiments were analysed using 12 rate laws by the procedure of Reich and Stivala. It was found that while a first-order rate law gave the best fit to the data obtained from isothermal and nonisothermal experiments most frequently, considerable variation exists for both types of experiments. Using the first order model, the activation energy was found to be 77.2 ±4.4kJ mol^–1.     

Pyrolysis of 1,1,2-trimethyl-1-silacyclobutane. Site of initial ring cleavage

The gas-phase, flow pyrolysis of 1,1,2-trimethyl-1-silacyclobutane (I) is described. A total of six products, containing two silicon atoms, have been analyzed with respect to relative yields (at 520°, 570°, 620° and 680°) and mechanistic origin. It is concluded that thermolysis of I occurs with predominant initial cleavage of the carboncarbon bond rather than the siliconcarbon bond and that further cleavage affords a silaalkene, Me₂Si=CHCH₃. The pyrolysis of 1,1,3,3-tetramethyl-1,3-disilacyclobutane at 700° leads to silaalkene production as shown through trapping with benzaldehyde.     

Isochinoline. 1. Mitteilung. Über die Umlagerung von α, α-Dialkylhomophtalimiden zu Derivaten des 1-Chlor-3, 4-dialkyl-isochinolins

On reinvestigation of the reaction of wet phosphorus oxychloride with α,α-dimethylhomophthalimide, 1-chloro-3-chloromethyl-4-methyl-isoquinoline and 1-chloro-4-chloromethyl-3-methyl-isoquinoline were isolated as the main products (aside from some substances resulting from a redox disproportionation). The production of these two substances can be rationalized by assuming a mechanism in which the rearrangement product is a protonated derivative of 3,4-dimethylene-3, 4-dihydroisoquinoline. With α, α-diethyl-homophthalimide the only isolated product was a derivative of 1-chloro-3, 4-diethyl-isoquinoline, with a chlorine atom in β-position of one of the ethyl groups, while with α-methyl-α-benzyl-homophthalimide the isolated product was 1,3-dichloro-4-methyl-isoquinoline, i.e. elimination had taken place instead of rearrangement. Also these results are in agreement with the proposed mechanism.     

Absolute Configuration from Different Multifragmentation Pathways in Light‐Induced Coulomb Explosion Imaging

The absolute configuration of individual small molecules in the gas phase can be determined directly by light‐induced Coulomb explosion imaging (CEI). Herein, this approach is demonstrated for ionization with a single X‐ray photon from a synchrotron light source, leading to enhanced efficiency and faster fragmentation as compared to previous experiments with a femtosecond laser. In addition, it is shown that even incomplete fragmentation pathways of individual molecules from a racemic CHBrClF sample can give access to the absolute configuration in CEI. This leads to a significant increase of the applicability of the method as compared to the previously reported complete break‐up into atomic ions and can pave the way for routine stereochemical analysis of larger chiral molecules by light‐induced CEI.     

Optimization of Discrete-Continuous Dynamic Systems Based on Disjunctive Programming

In this contribution, a novel approach for the modeling and optimization of discrete-continuous dynamic systems based on a disjunctive problem formulation is proposed. It will be shown that a disjunctive model representation, which constitutes an alternative to mixed-integer model formulations, provides a very flexible and intuitive way to formulate discrete-continuous dynamic optimization problems. Moreover, the structure and properties of the disjunctive process models can be exploited for an efficient and robust numerical solution by applying generalized disjunctive programming techniques. The proposed modeling and optimization approach will be illustrated by means of an optimal control problem that embeds a linear discretecontinuous dynamic system. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)