Methods for parallel integration of stiff systems of odes

This paper presents a class of parallel numerical integration methods for stiff systems of ordinary differential equations which can be partitioned into loosely coupled sub-systems. The formulas are called decoupled backward differentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagnonal sub-system. With one or several sub-systems allocated to each processor, information only has to be exchanged after completion of a step but not during the solution of the nonlinear algebraic equations.The main emphasis is on the formula of order 1, the decoupled implicit Euler formula. It is proved that this formula even for a wide range of multirate formulations has an asymptotic global error expansion permitting extrapolation. Besides, sufficient conditions for absolute stability are presented.     

The dipolar plasmon modes of a small metallic sphere

We consider here a treatment of the dipolar plasmon of a small metallic sphere, for which the radial extension of the surface profile is small compared with the radius of the sphere. We obtain the eigenvalues and damping by solving the classical equations for a non-uniform system. The theory is applicable also to the driven response. We compare our results with those recently reported by Apell and Ljungbert.     

Factorization of factorials

If factorials enter into product-quotient expressions, not allowing approximative calculation, the factorization into powers of primes is recommended. The paper describes a computer program for this process, based on a known formula, which should be applied differently, according as the primes are large or small. A discussion shows how to distinguish between large and small in order to minimize the computing time.     

Über eine Klasse von kubischen diophantischen Gleichungen mit drei Unbekannten

Ohne Zusammenfassung     

Absorber-induced features in the ac response of a He-Ne laser

The theoretically predicted pronounced ac-response of the laser intensity to the excitation current modulation of an intracavity saturable absorber has been experimentally verified in a He-Ne laser with a Ne-absorber. Good qualitative agreement with the theory is obtained.     

A CNDO/2 calculation on stilbene

The equilibrium conformations of trans- and cis-stilbene and the rotational barrier between the two isomers were calculated using the CNDO/2 method. The results for the equilibrium angles and distances are in good agreement with experimental data. However, according to the calculations the phenyl rings would have a nearly free rotation which is only limited by steric hindrance. This result obviously deviates from the current view. The results are discussed in relation to previous theoretical and experimental evidence.

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Zusammenfassung Die Gleichgewichtskonformation von trans- und cis-Stilben und die Rotationsbarriere zwischen zwei Isomeren wurde nach der CNDO/2-Methode berechnet. Die Ergebnisse in bezug auf die Geometrie stimmen mit experimentellen Daten gut überein, die Rotationsbarriere für die Drehung der Phenylringe dagegen ist praktisch Null.

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Résumé La méthode CNDO/2 a été employée pour calculer les conformations d'équilibre du trans- et du cis-stilbène ainsi que la barrière de rotation entre ces deux isomères. Angles d'équilibre et distances calculés sont en bon accord avec les données expérimentales. Cependant les calculs indiquent que les cycles phényles devraient posséder une rotation libre soumise seulement à l'empêchement stérique. Ce résultat s'écarte de l'opinion courante. Les résultats sont discutés en relation avec les données théoriques et expérimentales antérieures.

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This work was supported by grant No 2741-4 from The Swedish Natural Science Research Council and grant No 69-927/U 697 from The Swedish Board for Technical Development.     

Styrene and polystyrene microemulsions. I. Solubility in the W/O system

The solubility of styrene, its oligomers, and different molecular weight polymers was determined in W/O microemulsions stabilized by sodium dodecyl sulfate and pentanol. The results showed a complex pattern due to the interactions with pentanol, surfactant, and associated structures.     

On the absorption of electromagnetic radiation near a metal surface

We present a discussion on the absorptance of electromagnetic radiation per unit length in the surface region of a free electron like metal. We wish particularly to comment on recent work by Feibelman, Kliewer, Forstmann and Stenscke, who all considered different approximations of the jellium model. We are using a unified treatment from which the results in their models can easily be obtained. Our results confirm the general conclusions by Kliewer about a strong coupling to the electron-hole excitations which lead to a locally negative absorptance. In the model considered by Feibelman there is no such coupling to electron-hole excitations and he obtains the classical results for the absorptance. Forstmann and Stenschke have recently applied a hydrodynamical approach which gives results in disagreement with Kliewer's theory as well as with our own results, and we make some comments about their approach.