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A free boundary-value problem for a nonisothermal flow of two heavy viscous incompressible capillary liquids descibing a slot coating process is mathematically studied. The problem is stationary and two-dimensional and the Boussinesq approximation for the Navier-Stokes equations is used. The existence and uniqueness of a weak solution is proved in weighted Holder spaces for small data.
Deduktionssysteme
(1994)
Exact solutions of generalized three-particle Bargmann-Wigner equations in the strong-coupling limit
(1994)
In this paper a Petri net based methodology is outlined for an integrated qualitative and quantitative analysis of parallel software systems which is based on different (Petri) net representations of die software system under consideration. The software validation methodology starts from the source text of a set of communicating processes which specify the system under development. From this source text skeleton, a Petri net representation of the general control structure of the system is generated. On this basis a set of reduction steps is defined for transforming the net into different intermediate representations all owing the validation of both qualitative and qualitative properties. Particular attention is paid to the validation of quantitative properties which is performed using a transformation into locally Markovian Object Nets (MONs). Models of this new class of modular Petri nets are obtained by property-preserving structural compression and by enhancement with quantitative i nformation This information is obtained in the form of frequency and delay parameters by monitoring testing the software on the basis of prototypes. Compared to a previous paper on the same topic /Heiner94/ the methodology as well presentation have been improved. In particular, a new, more comprehensive running example been selected and the object net approach is explained in much more detail.
Small sodium and silver particles were generated on dielectric substrates like LiF, quartz and sapphire under ultrahigh vacuum conditions. The optical transmission spectra of the clusters were measured as a function of cluster size and shape, for low and high substrate temperatures as well as for s- and p- polarization of the incident light. Excitation of dipolar surface plasmon oscillations in the directions normal and parallel to the substrate surface could be identified. Furthermore, optical spectra for Na and Ag clusters were calculated with the classical Mie theory. The measured spectra vary strongly if the experimental conditions are changed and can be exploited, for example, to characterize the particles with regard to their size and shape. In particular, the axial ratio of the spheroidal clusters could be determined. Its value is considerably different for the two investigated metals and depends on the substrate material. Furthermore, the temperature of the substrate has a pronounced influence on the shape of the particles. At low temperature of T=100 K two-dimensional island growth is predominant. The particles extend only little in the direction perpendicular to the surface and coalesce readily at small coverage of metal atoms. In contrast, the clusters are truly three-dimensional at T=300 K. At this stage, sodium particles still exhibit a rather small axial ratio whereas silver clusters appear almost spherical. Thus, measurements of the optical spectra permit direct in situ monitoring of cluster growth during the nucleation of adsorbed atoms and of temperature induced shape variations. In addition to investigations of the shape of the particles, the quadrupolar surface plasmon mode was observed for Ag clusters.