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Mathematical Point (mathematical + point)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Supershells in deformed harmonic oscillators and atomic clusters

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2002
Dennis Bonatsos
Abstract From the mathematical point of view, the appearance of supershells is a general feature of potentials having relatively sharp edges. In physics, supershells have been observed in systems of metal clusters, which are also known to exhibit an underlying shell structure with magic numbers intermediate between the magic numbers of the 3-D isotropic harmonic oscillator and those of the 3-D square well. In the present study, Nilsson's modified harmonic oscillator (without any spin,orbit interaction), as well as the 3-D q -deformed harmonic oscillator with uq(3) , soq(3) symmetry, are considered. The former model has been used for an early schematic description of shell structure in metal clusters, while the latter has been found to successfully reproduce the magic numbers of metal clusters up to 1500 atoms, the expected limit of validity for theories based on the filling of electronic shells. The systematics of the appearance of supershells in the two models will be considered, putting emphasis on the differences between the spectra of the two oscillators. While the validity of Nilsson's modified harmonic oscillator framework is limited to relatively low particle numbers, the 3-D q -deformed harmonic oscillator gives reliable descriptions of the first supershell in metal clusters, which lies within its region of validity. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source]

On the hyperbolic system of a mixture of Eulerian fluids: a comparison between single- and multi-temperature models

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007
Tommaso Ruggeri
Abstract The first rational model of homogeneous mixtures of fluids was proposed by Truesdell in the context of rational thermodynamics. Afterwards, two different theories were developed: one with a single-temperature (ST) field of the mixture and the other one with several temperatures. The two systems are from the mathematical point of view completely different and the relationship between their solutions was not clarified. In this paper, the hyperbolic multi-temperature (MT) system of a mixture of Eulerian fluids will be explained and it will be shown that the corresponding single-temperature differential system is a principal subsystem of the MT one. As a consequence, the subcharacteristic conditions for characteristic speeds hold and this gives an upper-bound esteem for pulse speeds in an ST model. Global behaviour of smooth solutions for large time for both systems will also be discussed through the application of the Shizuta,Kawashima condition. Finally, as an application, the particular case of a binary mixture is considered. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Basic aspects of geopotential field approximation from satellite-to-satellite tracking data

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2001
W. Freeden
Abstract The satellite-to-satellite tracking (SST) problems are characterized from mathematical point of view. Uniqueness results are formulated. Moreover, the basic relations are developed between (scalar) approximation of the earth's gravitational potential by ,scalar basis systems' and (vectorial) approximation of the gravitational field by ,vectorial basis systems'. Finally, the mathematical justification is given for approximating the external geopotential field by finite linear combinations of certain gradient fields (for example, gradient fields of multi-poles) consistent to a given set of SST data. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Correctness of a particular solution of inverse problem in rocking curve imaging

PHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 8 2009
Isabella Huber
Abstract Local lattice misorientations on crystalline substrates can be visualized by rocking curve imaging. Local deviations from Bragg peak positions are extracted from a series of digital topographs recorded by a CCD detector under different azimuths. Bragg peaks from surface regions such as crystallites with a larger local misorientation overlap on the detector, which requires a back-projection method in order to reconstruct the misorientation components on the sample surface from the measured angular position on the detector planes. From mathematical point of view, the reconstruction problem is an inverse problem. In this paper, we formulate the forward and back-projection problems and we prove the correctness of a particular solution. The usability of the method is demonstrated on a phantom data set. [source]

Local and non-local ductile damage and failure modelling at large deformation with applications to engineering

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Bob Svendsen Prof. Dr.
The numerical analysis of ductile damage and failure in engineering materials is often based on the micromechanical model of Gurson [1]. Numerical studies in the context of the finite-element method demonstrate that, as with other such types of local damage models, the numerical simulation of the initiation and propagation of damage zones is strongly mesh-dependent and thus unreliable. The numerical problems concern the global load-displacement response as well as the onset, size and orientation of damage zones. From a mathematical point of view, this problem is caused by the loss of ellipticity of the set of partial di.erential equations determining the (rate of) deformation field. One possible way to overcome these problems with and shortcomings of the local modelling is the application of so-called non-local damage models. In particular, these are based on the introduction of a gradient type evolution equation of the damage variable regarding the spatial distribution of damage. In this work, we investigate the (material) stability behaviour of local Gurson-based damage modelling and a gradient-extension of this modelling at large deformation in order to be able to model the width and other physical aspects of the localization of the damage and failure process in metallic materials. [source]

Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose,Response Analysis

BIOMETRICS, Issue 1 2009
Björn Bornkamp
Summary In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose,response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose,response analysis. [source]