Wilfried - Gille
The author is a physicist at the Martin-Luther-University Halle-Wittenberg. In 1979 he was confronted with small-angle scattering experiments. It is a nonsatisfactory objective fact that this field (experiments and data evaluation) has been developed independently of the results achieved in the field of stochastic geometry. It was a part of author's life to see the connections between both these sides and try to transform and introduce known mathematical results into the scattering theory.
Subjects: Materials Science, Mathematics, Nanoscience & Technology, Physics, Statistics
Biography
- born in Halle (1953)- school-leaving certificate (1970, special class with a concentration on mathematics and physics at Martin-Luther-University Halle-Wittenberg)
-diploma with the thesis: "X-ray emission spectra of vanadium and titanium oxides" (Martin-Luther-University, 1977)
- doctorate with the thesis "Stereological characterization of microparticle systems by use of SAS - applications in metal- and polymer physics (1983)
- postdoctoral thesis: "The concept of chord length distribution for reaching information from experimental small-angle scattering curves" (1995)
- scientific assistant in the field of physics since 1977
Education
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Dr. rer. nat . habil. (MLU 1995)
Areas of Research / Professional Expertise
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Application of scattering experiments in materials science;
The use of the chord length distribution of a particle;
Geometric models and data evaluation the field of Small-Angle Scattering;
Investigation of truncation errors, which result from the Fourier transformation of realistic data;
The influence of different norms for the approximation of a data set by a linear function y=ax+b; - approaches, which allow to exchange the variables y and x;
Personal Interests
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Physics, mathematics, sports
Books
Articles
Geometric parameters of isotropic ensembles of right cylinders from SAS
Published: Dec 20, 2010 by Acta Crystallographica; A66, 597-601 (2010)
Authors: Wilfried Gille & Mike Kraus
Subjects:
Materials Science, Nanoscience & Technology
The scattering intensity of ensembles of right homogeneous quasi-diluted cylinders with const. oval right section (RS) and volume fraction c are analyzed using the SAS correlation function and the correlation funtion. A relation between the correlation function of the RS and the correlation function of the single cylinder of height H allows the calculation of the cylinder parameters.
Relation between the CLD of an infinitely long cylinder and its base
Published: Dec 30, 2007 by Journal of Mathematical Physics; 48, 053305 (2007)
Authors: H.S. Sukiasan and W. Gille
Subjects:
Geoscience, Mathematics, Physics, Statistics
There exist connections between the chord length distribution (CLD) of a (three-dimensional) cylinder and its (two-dimensional) base. The corresponding integral transformation is derived from a pure mathematical point of view. The power series of the CLDs at the origin are discussed. The integral transform has been illustrated for the transition "triangle" to "triangular rod" and "rectangle" to "rectangular" rod.
Small-angle scattering analysis of the spherical half-shell
Published: Dec 30, 2007 by Journal of Applied Crystallography; (2007)
Authors: Wilfried Gille
Subjects:
Materials Science, Nanoscience & Technology, Physics, Statistics
For a spherical half-shell of diameter D, analytic expressions of the SAS correlation function, the chord length distribution and the scattering intensity are analyzed. The analytic terms are surprisingly simple. The size distribution (random variable D) of an ensemble of spherical half-shells can be detected from the scattering curve.
The chord length distribution of the hemisphere
Published: Dec 31, 2005 by Journal of Mathematics and Statistics; 1(1), 24-28 (2005)
Authors: Wilfried Gille
Subjects:
Mathematics, Nanoscience & Technology, Physics, Statistics
The distribution laws for two types of isotropic uniform random chords of the hemisphere, cap-chords and basic-chords, are investigated. From both distribution densities, the chord length ditribution density of the whole hemisphere is derived. Eq. (15) is the final analytic result.
SAS curves of two parallel, infinitely long circular cylinders
Published: Dec 30, 2005 by Computational Materials Science; 32 57-65 (2005)
Authors: Wilfried Gille
Subjects:
Materials Science, Nanoscience & Technology, Polymer Science
Based on the SAS Correlation function (CF) of two parallel, infinitely long circular cylinders of diameter d, wholse z-axes are separated by a distance s, scattering intensities I(h,d,s) have been determined numerically. As I(h,d,s) is not band limited here, for the step from the CF to I(h) highly oscillating integrands result. The Mathematica function SequenceLimit has been used. Normalized Porod plots have been obtained. The parameters d and s can be traced back to the behavior of I(h).
The SAS correlation function for packages of long parallel circular cylinders
Published: Dec 31, 2004 by Powder Technology; 149, 42-50 (2004)
Authors: Wilfried Gille
Subjects:
Materials Science, Nanoscience & Technology, Statistics
Expressions are given which define the isotropized SAS correlation function of an arrangement of homogeneous, parallel, infinitely long circular cylinders of diameter d in terms of the pair correlation function of the random distance between the cylinder axes. Features of the result in terms of the pair correlation function are discussed.
Linear simulation models for real-space interpretation of SAS experiments
Published: Dec 31, 2002 by Waves Random media; 12, 85-97 (2002)
Authors: W. Gille
Subjects:
Chemistry, Materials Science, Physics
A procedure is presented for modelling and interpreting SAS experiments of random isotropic two-phase media.
Chord length distributions of infinitely long geometric figures
Published: Dec 31, 2002 by Powder Technology; 123, 292-298 (2002)
Authors: Wilfried Gille
Subjects:
Materials Science, Polymer Science, Statistics
A transformation method for establishing chord length distributions for infinitely long "rods" of various right-sections is presented. Here, the transformation on the two-dimensional cross section of the object is used to define the chord length distribution of the three-dimensional "rod". Examples are given. The step from the "two-dimensional ellipse" to the corresponding "three-dimensional elliptic cylinder" is described.
The set covariance of a "Dead Leaves" model
Published: Dec 31, 2000 by Adv. Appl. Prob.(SGSA); 34, 11-20 (2002)
Authors: Wilfried Gille
Subjects:
Mathematics, Physics, Statistics
The set covariance of a DLm, constructed from hard spheres of constant diameter, is calculated analytically. A Mathematica program is given. There exist applications in the field of random sequential adsorption and the interpretation of small-angle scattering experiments. The calculation is based on the pair correlation function of the centers of the spheres.
Analysis of the chord length distribution of the cone for small chord lengths
Published: Dec 31, 2000 by computer & mathematics with applications; 40,1027-1035 (2000)
Authors: Wilfried Gille
Subjects:
Materials Science, Mathematics, Physics, Statistics
The chord length distribution of the cone near the origin is analized. A Mathematica program is given. There exists a logarithmic singularity in the origin. Connections to the small-angle scattering experiment are investigated. An expression for the asymptotic scattering intensity I(h) is formulated.
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