Enhancing energy conserving methods

Recent observations [5] indicate that energy-momentum methods might be better suited for the numerical integration of highly oscillatory Hamiltonian systems than implicit symplectic methods. However, the popular energy-momentum method, suggested in [3], achieves conservation of energy by a global scaling of the force field. This leads to an undesirable coupling of all degrees of freedom that is not present in the original problem formulation. We suggest enhancing this energy-momentum method by splitting the force field and using separate adjustment factors for each force. In case that the potential energy function can be split into a strong and a weak part, we also show how to combine an energy conserving discretization of the strong forces with a symplectic discretization of the weak contributions. We demonstrate the numerical properties of our method by simulating particles that interact through Lennard-Jones potentials and by integrating the Sine-Gordon equation.This work was partly supported by NIH Grant P41RR05969, DOE/NSF Grant DE-FG02-91-ER25099/DMS-9304268, and NSF GCAG/HPCC ASC-9318159.     

Some properties of complex matrix-variate generalized Dirichlet integrals

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.     

Wavelength stabilized 980 nm uncooled pump laser modules for erbium-doped fiber amplifiers

We review the development of wavelength stabilized 980 nm pump laser modules without active temperature stabilization for applications in erbium-doped fiber amplifiers. Operation over a wide temperature range with an output power exceeding 400 mW at an ambient temperature of 70°C is demonstrated. The overall reliability of uncooled modules is estimated to be well below 500 FIT at all operating conditions. Such devices are made possible by continuous development and steady improvement of the pump laser chip, the optimization of the fiber Bragg grating stabilization scheme, careful design of the module package, and extended reliability analysis on the basis of stress tests as well as field data.     

Thermodynamics in process development in the chemical industry - importance, benefits, current state and future development

Phase equilibrium thermodynamics is one of the most important fundamental sciences for process development in the chemical industry. The outstanding results achieved by thermodynamics in the last decades have let to a profound change in working methods for the development of thermal separation processes. However, there remains a large number of unsolved problems in the field of phase equilibrium thermodynamics which often represent a significant restriction to process development for the chemical engineer. Current deficiencies are illustrated with some significant examples and desired developments for the future are suggested.     

Interaction of aniline and benzidine with layered solids M n+(UO2XO4) n − ·z H2O[M = H3O+, Cu2+, VO2+, Fe2+; X = P,As]

The layered acid solids of formula H₃OUO₂XO₄· 3 H₂O (X = As, P) intercalate aniline and benzidine arylamines, by protonation of the guest molecules. The intercalates maintain the original laminar structure.The insertion of aniline and benzidinein the metal derivativesM(UO₂XO₄)₂·n H₂O (M = Cu, VO, Fe) requires rather drastic conditions. Near and medium infrared spectra of intercalates in which M = VO²⁺ and Cu²⁺, indicate that the polymerization and/or oxidation of sorbed amines occurs; however, the guest-host reactions for Fe²⁺-derivatives are of the acid-base type.     

Vapor—liquid equilibrium in ternary mixtures of hydrogen + carbon dioxide + 1-methylnaphthalene

Compositions of saturated vapor and liquid phases at equilibrium were measured for hydrogen + carbon dioxide + 1-methylnaphthalene mixtures at 543 and 704 K over a pressure range of 50–250 atm. Measurements were made at three relative concentrations of hydrogen to carbon dioxide at each condition of temperature and pressure. A significant variation of the K-value of 1-methylnaphthalene with gas composition was observed in the high pressure region.     

Formation Mechanism of the First Carbon–Carbon Bond and the First Olefin in the Methanol Conversion into Hydrocarbons

The elementary reactions leading to the formation of the first carbon–carbon bond during early stages of the zeolite‐catalyzed methanol conversion into hydrocarbons were identified by combining kinetics, spectroscopy, and DFT calculations. The first intermediates containing a C?C bond are acetic acid and methyl acetate, which are formed through carbonylation of methanol or dimethyl ether even in presence of water. A series of acid‐catalyzed reactions including acetylation, decarboxylation, aldol condensation, and cracking convert those intermediates into a mixture of surface bounded hydrocarbons, the hydrocarbon pool, as well as into the first olefin leaving the catalyst. This carbonylation based mechanism has an energy barrier of 80 kJ mol^?1 for the formation of the first C?C bond, in line with a broad range of experiments, and significantly lower than the barriers associated with earlier proposed mechanisms.     

Formamides as Lewis Base Catalysts in SN Reactions—Efficient Transformation of Alcohols into Chlorides,Amines, and Ethers

A simple formamide catalyst facilitates the efficient transformation of alcohols into alkyl chlorides with benzoyl chloride as the sole reagent. These nucleophilic substitutions proceed through iminium‐activated alcohols as intermediates. The novel method, which can be even performed under solvent‐free conditions, is distinguished by an excellent functional group tolerance, scalability (>100 g) and waste‐balance (E‐factor down to 2). Chiral substrates are converted with excellent levels of stereochemical inversion (99 %→≥95 % ee). In a practical one‐pot procedure, the primary formed chlorides can be further transformed into amines, azides, ethers, sulfides, and nitriles. The value of the method was demonstrated in straightforward syntheses of the drugs rac‐Clopidogrel and S‐Fendiline.