Spacetime without reference frames: An application to the kinetic theory

Spacetime structures defined in the language of manifolds admit an absolute formulation, i.e., a formulation which does not refer to observers (reference frames). We consider an affine structure for Galilean spacetime. As an application the Chapman-Enskog iteration for the solution of the Boltzmann equation is given in an absolute form. As a consequence, the second approximations of the stress tensor and the heat flux are obtained in a form independent of observers, which throws new light on material frame indifference.     

Numerical study of the unstable MHD spectrum of a small aspect ratio,flat current,non-circular tokamak

The Lausanne ideal MHD stability code ERATO is used to investigate spectral properties of Solovèv's equilibrium at small aspect ratios. Two different elongations are considered. Both free and rigid boundary models are computed and compared. Modes characterized by a large radial extension have been found which appear to be due to a coupling ofm=1 andm=2 modes due to toricity. The internal modes spectrum is compared with the predictions of the full mercier criterion, taking into account its spatial dependence, and with the ballooning modes stability criterion.

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Résumé Les propriétés spectrales des équilibres analytiques de Solov'èv à petit rapport d'aspect sont étudiées à l'aide du code numérique ERATO qui permet de calculer le spectre magnétohydrodynamique d'une configuration Tokomak quelconque. Nous avons examiné deux situations différentes: paroi conductrice collée contre la surface du plasma et vide infini ainsi que deux élongations. Nous avons trouvé que les modes instables ont une grande extension radiale, due au couplage torique entre les modesm=1 etm=2. Le spectre des modes internes est comparé aux prédictions du critère de Mercier, prenant en considération sa dépendance radiale. La limite de stabilité aux modes internes à basn est comprise entre la limite de Mercier correspondante et la limite ballooning.

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Presently at IBM Lausanne.

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Presently at General Atomics, San Diego.     

Quantization in generalized coordinates III-Lagrangian formulation

It is shown that if one incorporates the generalized coordinate quantum velocitiesQ ¹ as given byQ ¹=l[H,Q ¹](h=1) into the generalized classical Lagrangian for a free particle (the total energy),L=1/2Q ¹ g _tk Q ^k one does not obtain (no matter what ordering of the operatorsq ^l ,q ^k andg _lkwe choose the correct quantum Lagrangian operator which is a transformation from -1/2V² to generalized coordinates (Gruber, 1971, 1972).q ^l as given byq ^l=i[H,q ^l] turns out to be the Hermitian part of a more generaiized operator which we call the total generalized velocity operator similar to the notation in ear previous articles (Gruber, 1971, 1972). This total velocity operator really determines the fundamental structure governing our system in the Lagrangian formulation. We show that ft is through the total velocity operator that we make the transition from classical to quantum mechanics and through our procedure we arrive at the correct quantum Lagrangian operator.     

The space of compact subsets of E d

Let K be the space of compact subsets of E ^d, endowed with the Hausdorff-metric. It is shown that the isometries of K onto itself are the mappings generated by rigid motions of E ^d.     

Electronic control of chiral quaternary center creation in the intramolecular asymmetric heck reaction

The Boehringer-Ingelheim phosphinoimidazoline (BIPI) ligands were applied to the formation of chiral quaternary centers in the asymmetric Heck reaction. Several different substrates were examined in detail, using more than 70 members of this new ligand class. Hammett relationships were determined through systematic variation of the ligand electronics. All substrates showed essentially the same Hammett behavior, where enantioselectivity increased as the ligands were made more electron-deficient. Ligand optimization has led to catalysts which give the highest enantioselectivities reported to date for these difficult systems.