4 research outputs found
Minkowski Tensors of Anisotropic Spatial Structure
- Author
- Aste T
- Aste T
- B Breidenbach
- Berg M
- Breidenbach B
- Chavel I
- Cohn D L
- D Hug
- Delaney G W
- Durand G
- Eberly D H
- Evans L C
- F M Schaller
- G E Schröder-Turk
- Hansen-Goos H
- Heijmans H J A M
- Hörrmann J Hug D Klatt M Mecke K
- K Mecke
- Kapfer S
- Kapfer S C
- Krsek P
- König P-M
- Liu J
- Marlow C
- Materon G
- McMullen P
- Mecke K
- Mecke K
- Mickel W
- Neher R A
- S C Kapfer
- Santaló L A
- Schaller F M Neudecker M Saadatfar M Delaney G Mecke K Schröder-Turk G E Schröter M
- Schaller F M Schröder-Turk G E
- Schröder-Turk G E
- Schröder-Turk G E Schielein R Kapfer S C Schaller F M Delaney G W Senden T Saadatfar M Aste T Mecke K
- Serra J
- Stoyan D
- Sung Y-J
- Tunák M
- W Mickel
- Zhao S-C
- Publication venue
- 'IOP Publishing'
- Publication date
- 01/01/2013
- Field of study
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
Minkowski tensors and local structure metrics: Amorphous and crystalline sphere packings
- Author
- Publication venue
- 'AIP Publishing'
- Publication date
- 12/12/2015
- Field of study
Robust and sensitive tools to characterise local structure are essential for investigations of granular or particulate matter. Often local structure metrics derived from the bond network are used for this purpose, in particular Steinhardt's bond-orientational order parameters ql . Here we discuss an alternative method, based on the robust characterisation of the shape of the particles' Voronoi cells, by Minkowski tensors and derived anisotropy measures. We have successfully applied these metrics to quantify structural changes and the onset of crystallisation in random sphere packs. Here we specifically discuss the expectation values of these metrics for simple crystalline unimodal packings of spheres, consisting of single spheres on the points of a Bravais lattice. These data provide an important reference for the discussion of anisotropy values of disordered structures that are typically of relevance in granular systems. This analysis demonstrates that, at least for sufficiently high packing fractions above φ > 0.61, crystalline sphere packs exist whose Voronoi cells are more anisotropic with respect to a volumetric moment tensor than the average value of Voronoi cell anisotropy in random sphere packs
Local Anisotropy of Fluids using Minkowski Tensors
- Author
- Binder K
- C Goll
- Dress C
- Durand G
- F M Schaller
- Frenkel D
- G E Schröder-Turk
- Goll C
- Hadwiger H
- Hansen-Goos H
- K Mecke
- Kalikmanov V I
- Krauth W
- M Spanner
- Matsumoto S Nogawa T Shimada T Ito Nobuyasu
- Meijering J L
- N Ito
- Okabe A
- Rapaport D C
- S C Kapfer
- Santaló L A
- Schröder-Turk G E
- Schröder-Turk G E Mickel W Kapfer S C Schaller F M Hug D Breidenbach B Mecke K
- T Nogawa
- W Mickel
- Publication venue
- 'IOP Publishing'
- Publication date
- 01/01/2010
- Field of study
Statistics of the free volume available to individual particles have
previously been studied for simple and complex fluids, granular matter,
amorphous solids, and structural glasses. Minkowski tensors provide a set of
shape measures that are based on strong mathematical theorems and easily
computed for polygonal and polyhedral bodies such as free volume cells (Voronoi
cells). They characterize the local structure beyond the two-point correlation
function and are suitable to define indices 0≤βνa,b≤1 of
local anisotropy. Here, we analyze the statistics of Minkowski tensors for
configurations of simple liquid models, including the ideal gas (Poisson point
process), the hard disks and hard spheres ensemble, and the Lennard-Jones
fluid. We show that Minkowski tensors provide a robust characterization of
local anisotropy, which ranges from βνa,b≈0.3 for vapor
phases to βνa,b→1 for ordered solids. We find that for fluids,
local anisotropy decreases monotonously with increasing free volume and
randomness of particle positions. Furthermore, the local anisotropy indices
βνa,b are sensitive to structural transitions in these simple
fluids, as has been previously shown in granular systems for the transition
from loose to jammed bead packs
Enzyme Handbook
- Author
- 339-349
- [10]Siffert O., Emöd, I.
- [11] Fricker L.D., Snyder, S.H.
- [11] Taylor A., Volz, K.W., Lipscomb, W.N., Takemoto, L. J.
- [3] Schmidt U., Weller, D., Holder, A.
- [9]Fujiwara K., Tsuru, D.
- [hie J.N., Dure, L.S.
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- TA Bicsak
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- Xin-Ii Lin Wong, R.N.S., Tang, J.
- Y Agrawal
- Y Agrawal
- Y Atsumi
- Y Bai
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- Y Bando
- Y Banno
- Y Birk
- Y Dasarathy
- Y Dupont
- Y Ethoh
- Y Etoh
- Y Hara
- Y Hashitani
- Y Hirashima
- Y Hirashima
- Y Hojima
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- Y Ishizaki
- Y Isowa
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- Y Kawaguchi
- Y Kido
- Y Kido
- Y Kim
- Y Kohama
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- Y Kubota
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- Y Kuriyama
- Y Levin
- Y Looze
- Y Minami
- Y Miura
- Y Mizuno
- Y Mukohata
- Y Nagai
- Y Nagai
- Y Nagai
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- Y Nakagawa
- Y Nakajima
- Y Narahashi
- Y Nishimura
- Y Nishimura
- Y Ohba
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- Y Ohno-Iwashita
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- Y Otsuka
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- Y Tiffon
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- Y Tsujita
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- “ (Turk V., Neville, M.
- Publication venue
- 'Springer Science and Business Media LLC'
- Publication date
- 01/01/1991
- Field of study