1,969 research outputs found
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
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