Generalized solutions and distributional shadows for Dirac equations

We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated distributional limits and derive their explicit form in case of free Dirac fields with regularizations of initial values corresponding to point-like probability densities

Generalized Fourier Integral Operators on spaces of Colombeau type

Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data

Dipole trap model for the metallic state in gated silicon-inversion layers

In order to investigate the metallic state in high-mobility Si-MOS structures, we have further developed and precised the dipole trap model which was originally proposed by B.L. Altshuler and D.L. Maslov [Phys. Rev. Lett.\ 82, 145 (1999)]. Our additional numerical treatment enables us to drop several approximations and to introduce a limited spatial depth of the trap states inside the oxide as well as to include a distribution of trap energies. It turns out that a pronounced metallic state can be caused by such trap states at appropriate energies whose behavior is in good agreement with experimental observations.Comment: 16 pages, 10 figures, submitte

Classes of generalized functions with finite type regularities

We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities

Application of a virtual watershed in academic education

International audienceHydrologic models of watersheds often represent complex systems which are difficult to understand regarding to their structure and dynamics. Virtual watersheds, i.e. watersheds which exist only in the virtual reality of a computer system, are an approach to simplify access to this real-world complexity. In this study we present the virtual watershed KIELSHED-1, a 117 km2 v-shaped valley with grassland on a "Cambisol" soil type. Two weather scenarios are delivered with the watershed: a simplified artificial weather scenario based on long-term data of a German weather station as well as an unmodified data record. The input data and parameters are compiled according to the conventions of the SWAT 2000 hydrological model. KIELSHED-1 is mainly used for education, and illustrative application examples, i.e. calculation of water balance, model calibration, development of land use scenarios, give an insight to the capabilities of the virtual watershed

Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Stabilization of the γ-Sn phase in tin nanoparticles and nanowires

Structures of Sn nanoparticles and nanowires are studied using density functional theory in conjunction with thermodynamic considerations. Besides the low-temperature α and room-temperature β phases, the high-temperature γ phase is considered. Results show that at ambient temperatures for sizes smaller than 50 nm, metallic β- and γ-Sn nanoparticles are more stable than semimetallic α-Sn ones because of their lower surface energies. Moreover, very small Sn nanostructures, exemplified by nanowires, are expected to exhibit the γ phase even at 0 K