The determination of the gravitational potential of axisymmetric mass distribution in spherical coordinates. II

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.

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Plastics. Determination of average molecular mass and molecular mass distribution of polymers using size-exclusion chromatography

10.3403/bseniso16014 ◽

2015 ◽

Keyword(s):

Molecular Mass ◽

Mass Distribution ◽

Size Exclusion Chromatography ◽

Molecular Mass Distribution ◽

Size Exclusion ◽

Average Molecular Mass ◽

Exclusion Chromatography

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New approaches for the determination of dextran in the sugar production process

Sugar Industry ◽

10.36961/si19321 ◽

2018 ◽

pp. 138-146 ◽

Cited By ~ 1

Author(s):

Karin Abraham ◽

Eckhard Flöter

Keyword(s):

Molecular Mass ◽

Mass Distribution ◽

Molecular Mass Distribution ◽

Molecular Size ◽

Mass Variation ◽

Negative Effects ◽

New Approaches ◽

Precise Knowledge ◽

Enzyme Application

The presence of polysaccharides in cane and beet raw juices causes several negative effects during the sugar manufacture. These are usually mitigated by enzymatic decomposition of dextrans. Such effects not only depend on the content, but also on the molecular mass distribution. This means that the different dextran fractions specifically affect the process. An accurate process control hence requires the most precise knowledge about the existing content and the molecular mass distribution present. A detailed understanding of the specific processing problems and also a targeted enzyme application hence requires the determination of a total dextran content and also its characterization including the differentiation between the different dextran fractions. An accurate analytical tool which equally satisfies industrial applicability is still lacking. To improve on this situation, two new approaches for the determination of dextran were developed and benchmarked against the commonly used and established Haze Method, which is rather inaccurate and also sensitive to molecular mass variation. The two new approaches are both based on polarimetry. These two methods indicate to be superior over the Haze Method with respect two molecular mass variation and hence enable the determination of a broader molecular size range including also low molecular mass dextrans.

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Solutions to the Vector Tetrahedron Equation

Journal of Engineering for Industry ◽

10.1115/1.3670802 ◽

1965 ◽

Vol 87 (2) ◽

pp. 228-234 ◽

Cited By ~ 11

Author(s):

Milton A. Chace

Keyword(s):

Closed Form ◽

Digital Computer ◽

Three Dimensional ◽

Dimensional Vector ◽

Spherical Coordinates ◽

Tetrahedron Equation ◽

Position Determination ◽

Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

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