Morphometry of random spatial structures in physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Erlangen
FAU University Press
2016
|
| Series: | FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik
Band 10 |
| Subjects: | |
| Online Access: | Volltext Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | XXX, 342 Seiten Illustrationen, Diagramme |
| Format: | Langzeitarchivierung gewährleistet, LZA |
| ISBN: | 9783944057774 9783944057781 |
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| 100 | 1 | |a Klatt, Michael Andreas |e Verfasser |0 (DE-588)1115206729 |4 aut | |
| 245 | 1 | 0 | |a Morphometry of random spatial structures in physics |c Michael Andreas Klatt |
| 264 | 1 | |a Erlangen |b FAU University Press |c 2016 | |
| 300 | |a XXX, 342 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik |v Band 10 | |
| 502 | |b Dissertation |c Friedrich-Alexander-Universität Erlangen-Nürnberg |d 2016 | ||
| 538 | |a Langzeitarchivierung gewährleistet, LZA | ||
| 650 | 0 | 7 | |a Minkowski-Funktional |0 (DE-588)1121951953 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Ungeordnetes System |0 (DE-588)4124353-5 |2 gnd |9 rswk-swf |
| 653 | |a Morphology | ||
| 653 | |a Integral and stochastic geometry | ||
| 653 | |a Porous materials | ||
| 653 | |a Granular matter | ||
| 653 | |a Nuclear matter | ||
| 653 | |a Gamma rays | ||
| 653 | |a Data analysis | ||
| 653 | |a Image processing | ||
| 653 | |a Anisotropy | ||
| 653 | |a Percolation | ||
| 653 | |a Minkowski functionals and tensors | ||
| 653 | |a Morphologie | ||
| 653 | |a Integral- und stochastische Geometrie | ||
| 653 | |a Poröse Materialien | ||
| 653 | |a Granulare Materie | ||
| 653 | |a Minkowski Funktionale und Tensoren | ||
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Record in the Search Index
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CONTENTS
1 RANDOM SPATIAL STRUCTURES 1
2 MINKOWSKI TENSORS OF ANISOTROPIC RANDOM FIELDS 23
2.1 ORIENTATION BIASED RANDOM F IE LD S
. 26
2.1.1 THE BOOLEAN M O D
EL. 26
2.1.2 THE GAUSSIAN RANDOM FIELD
.
. 29
2.2 FABRIC TE N SO RS
.
32
2.3 MEAN INTERCEPT LENGTH OF BOOLEAN M O D E LS
. 35
2.3.1 ANALYTIC CALCULATION FOR ANISOTROPIC BOOLEAN MODELS . . . 36
2.3.2 MONTE CARLO S A M P LIN G
. 46
2.3.3 THE MIL TENSOR OF A BOOLEAN MODEL IS NOT A TENSOR . 47
2.3.4 INTENSITY DEPENDENCE AND ANISOTROPY INDEX
.
49
2.3.5 DEFICIENCIES OF THE MIL ANALYSIS
.
52
2.3.6 GENERALIZED INTERCEPT ANISOTROPY MEASURES
.
54
2.4 MINKOWSKI TENSORS AS METRICS OF ANISOTROPY AND ORIENTATION . 55
2.4.1 DEFINITION AND APPLICATIONS
.
56
2.4.2 CIRCULAR MINKOWSKI TENSORS . .
.
.
59
2.4.3 SENSITIVE MEASURES OF
ANISOTROPY. 62
2.5 MINKOWSKI TENSOR DENSITIES OF BOOLEAN MODELS
.
67
2.5.1 MINKOWSKI FUNCTIONAL DENSITIES
.
68
2.5.2 SURFACE TENSOR DENSITY . .
.
.
.
.
. . . 68
2.5.3 SIMULATIONS OF NONISOTROPIC BOOLEAN MODELS
.
69
2.5.4 NONUNIVERSAL VARIANCES AND COVARIANCES
.
78
2.5.5 UNIVERSAL PROBABILITY DENSITY FUNCTIONS
.
82
2.5.6 ANALYTIC BOUNDS VIA CONCENTRATION INEQUALITIES . 86
2.5.7 OUTLOOK: INHOMOGENEOUS BOOLEAN M ODELS
.
88
2.6 MINKOWSKI TENSOR DENSITIES OF GAUSSIAN RANDOM FIELDS
.
89
2.6.1 GLOBAL AND LOCAL AVERAGES
.
89
2.6.2 DISTRIBUTION OF THE GRADIENT
.
.
. 91
2.6.3 MINKOWSKI FUNCTIONAL DENSITIES
.
93
2.6.4 MINKOWSKI TENSOR
DENSITIES. 94
2.6.5 ANISOTROPY INDICES OF RANK TWO AND F O U R
. 98
2.6.6 EXTENDED GAUSSIAN IMAGE D E N S ITY
.
99
2.7 GRAY-SCALE MINKOWSKI TE N S O R S
. 104
2.8 C
ONCLUSIONS.107
3 ANISOTROPIC CONTINUUM PERCOLATION 113
3.1 UNIVERSAL SCALING IN TOPOLOGY AND TRANSPORT
.115
3.2 ANISOTROPIC PERCOLATION AND ISOTROPIC THRESHOLD
.
118
3.2.1 CONNECTIVITY AND EFFECTIVE PERCOLATION TH RESH O LD S
.
120
3.2.2 ISOTROPIC PERCOLATION TH RESHOLD
.
123
3.2.3 THRESHOLD ESTIMATES FOR DIFFERENTLY ANISOTROPIC MODELS . . 127
3.3 PERCOLATION THRESHOLD APPROXIMATIONS
.
128
3.3.1 EXCLUDED AREA APPROXIMATION
.
129
3.3.2 EULER CHARACTERISTIC APPROXIM
ATION.133
3.3.3 SECOND-MOMENT APPROXIM
ATIONS.136
3.4 C ONCLUSIONS
.
139
4 MINKOWSKI CORRELATION FUNCTIONS OF RANDOM TESSELLATIONS 141
4.1 ORDERED AND DISORDERED HARD-SPHERE P A C K IN G S
.
142
4.2 LOCAL DISTRIBUTIONS OF MINKOWSKI FUNCTIONALS AND TE N S O RS
.146
4.3 GLOBAL CORRELATION FUNCTIONS AND PROBABILITY DENSITY FUNCTIONS . .
153
4.3.1 CORRELATION FUNCTIONS OF MINKOWSKI
FUNCTIONALS.153
4.3.2 CELL-CELL PROBABILITY DENSITY FU N CTIO N S
.
155
4.4 CORRELATION FUNCTIONS OF MINKOWSKI FU N CTIO N ALS
.
156
4.4.1 ONE-DIMENSIONAL POISSON POINT P R O C E S S
.
156
4.4.2 THREE-DIMENSIONAL POISSON POINT P R O C E S S
.
159
4.4.3 EQUILIBRIUM HARD-SPHERE LIQ U ID
.
160
4.4.4 MRJ SPHERE
PACKINGS.
160
4.4.5 MIXED CORRELATION FU N C TIO N S
.
162
4.5 CELL-CELL PROBABILITY DENSITY FU N C TIO N S
.
167
4.6 N-POINT INFORMATION IN MINKOWSKI CORRELATION
FUNCTIONS.170
4.6.1 CLUSTERING PLANAR POINT PROCESSES
.
171
4.6.2 DISTINGUISHING POINT PATTERNS BY THEIR GLOBAL STRUCTURE . . . 173
4.7 C ONCLUSIONS. 176
5 SHAPE INDICES FOR NUCLEAR MATTER 181
5.1 NUCLEAR P A S T A
.
182
5.2 NUMERICAL SIMULATION SCHEM
E.184
5.3 SHAPE CH ARACTERIZATION
.
188
5.4 CLASSIFICATION AND MAP OF PASTA SHAPES AND FLUCTUATIONS
.
191
5.5 THE SINGLE GYROID NETWORK P H A S E
.
194
5.5.1 CONSTANT MEAN-CURVATURE (CMC) SU RFACES
.
195
5.5.2 STATIONARY S TRU C TU RE S
. 197
5.5.3 DYNAMICAL
STABILITY.199
5.6 C
ONCLUSIONS.203
6 MINKOWSKI SKY MAPS IN GAMMA-RAY ASTRONOMY 207
6.1 STRUCTURE
CHARACTERIZATION.209
6.1.1 MORPHOLOGICAL DATA ANALYSIS IN ASTRONOM
Y.209
6.1.2 SHAPE OF COUNTS M APS
.
210
6.2 SOURCE
DETECTION.
214
6.2.1 GLOBAL NULL HYPOTHESIS T E S T
. 214
6.2.2 LOCAL MINKOWSKI SKY MAPS
.217
6.2.3 MARCHING SQUARE ALGORITHM AND
PIXELATION.220
6.3 TRIAL C O RRE C TIO N
.221
6.4 DETECTOR ACCEPTANCE CO RRECTIO N
.
224
6.4.1 MONTE CARLO OBSERVATIONS
.
225
6.4.2 P
OSTSELECTION.
225
6.4.3 COMBINED POSTSELECTION AND MC OBSERVATIONS
.
226
6.4.4 LOCAL DETECTOR ACCEPTANCE CORRECTION
.
226
6.5 STRUCTURE PROBABILITY DISTRIBUTIONS
. 229
6.5.1 WANG-LANDAU ALGORITHM COMBINED WITH ANALYTIC DOS . . . 230
6.5.2 SATURATION OF E R R O R
.232
6.5.3 THE DENSITY OF STATES FOR LARGE OBSERVATION WINDOWS . 235
6.6 SENSITIVITY INCREASE VIA STRUCTURE
CHARACTERIZATION.235
6.6.1 EXAMPLES OF MINKOWSKI SKY M A P S
.
236
6.6.2 SYSTEMATIC ANALYSIS OF INCREASE IN SENSITIVITY
.
238
6.7 COMBINING DIFFERENT THRESHOLDS
.
241
6.7.1 EMPIRICAL CUMULATIVE
DISTRIBUTIONS.242
6.7.2 SENSITIVITY INCREASE FOR DIFFUSE RAD IATIO N
.
243
6.8 COMPARISON TO A STANDARD COUNTING METHOD
.
243
6.8.1 DEPENDENCE ON EXPERIMENTAL D E TA ILS
.
244
6.8.2 SCAN WINDOW SIZE DEPENDENCE AND LOW STATISTICS
.
246
6.9 EXPERIMENTAL DATA FROM H.E.S.S. SKY M AP S
.
249
6.9.1 THE SUPERNOVA REMNANT RX J1713.7-3946 . 249
6.9.2 THE GALACTIC CENTER R I D G E
.
252
6.10 COVARIANCE A P P RO A C H
.
253
6.10.1 VARIANCES AND COVARIANCES OF MINKOWSKI FUNCTIONALS . . . 253
6.10.2 TESTING
PROCEDURE.
257
6.10.3 SENSITIVE TEST FOR INHOM
OGENEITIES.260
6.11 CONCLUSION
.
264
6.12 O U TLO O K
.
265
6.12.1 OTHER SHAPE DESCRIPTORS
.
266
6.12.2 CORRELATIONS BETWEEN P I X E L S
.
267
7 SUMMARY 269
A FORMAL DEFINITION OF THE MORPHOMETRIC ANALYSIS 273
B LOOK-UP TABLES FOR MINKOWSKI TENSORS 275
BIBLIOGRAPHY 297 |
| any_adam_object | 1 |
| author | Klatt, Michael Andreas |
| author_GND | (DE-588)1115206729 |
| author_facet | Klatt, Michael Andreas |
| author_role | aut |
| author_sort | Klatt, Michael Andreas |
| author_variant | m a k ma mak |
| building | Verbundindex |
| bvnumber | BV043809574 |
| collection | ebook |
| ctrlnum | (OCoLC)960019688 (DE-599)DNB1114990000 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV043809574 |
| illustrated | Illustrated |
| indexdate | 2024-12-04T13:00:49Z |
| institution | BVB |
| isbn | 9783944057774 9783944057781 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029220849 |
| oclc_num | 960019688 |
| open_access_boolean | 1 |
| owner | DE-384 DE-473 DE-BY-UBG DE-703 DE-1051 DE-824 DE-29 DE-12 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-1049 DE-92 DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-706 DE-20 DE-1102 DE-29T |
| owner_facet | DE-384 DE-473 DE-BY-UBG DE-703 DE-1051 DE-824 DE-29 DE-12 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-1049 DE-92 DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-706 DE-20 DE-1102 DE-29T |
| physical | XXX, 342 Seiten Illustrationen, Diagramme |
| psigel | ebook |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | FAU University Press |
| record_format | marc |
| series | FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik |
| series2 | FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik |
| spelling | Klatt, Michael Andreas Verfasser (DE-588)1115206729 aut Morphometry of random spatial structures in physics Michael Andreas Klatt Erlangen FAU University Press 2016 XXX, 342 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik Band 10 Dissertation Friedrich-Alexander-Universität Erlangen-Nürnberg 2016 Langzeitarchivierung gewährleistet, LZA Minkowski-Funktional (DE-588)1121951953 gnd rswk-swf Integralgeometrie (DE-588)4161911-0 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 gnd rswk-swf Morphology Integral and stochastic geometry Porous materials Granular matter Nuclear matter Gamma rays Data analysis Image processing Anisotropy Percolation Minkowski functionals and tensors Morphologie Integral- und stochastische Geometrie Poröse Materialien Granulare Materie Minkowski Funktionale und Tensoren (DE-588)4113937-9 Hochschulschrift gnd-content Ungeordnetes System (DE-588)4124353-5 s Integralgeometrie (DE-588)4161911-0 s Minkowski-Funktional (DE-588)1121951953 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:29-opus4-76542 FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik Band 10 (DE-604)BV041959107 10 https://open.fau.de/handle/openfau/7654 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-76542 Resolving-System kostenfrei Volltext http://d-nb.info/1114990000/34 Langzeitarchivierung Nationalbibliothek kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029220849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klatt, Michael Andreas Morphometry of random spatial structures in physics FAU Forschungen. Reihe B, Medizin, Naturwissenschaft, Technik Minkowski-Funktional (DE-588)1121951953 gnd Integralgeometrie (DE-588)4161911-0 gnd Ungeordnetes System (DE-588)4124353-5 gnd |
| subject_GND | (DE-588)1121951953 (DE-588)4161911-0 (DE-588)4124353-5 (DE-588)4113937-9 |
| title | Morphometry of random spatial structures in physics |
| title_auth | Morphometry of random spatial structures in physics |
| title_exact_search | Morphometry of random spatial structures in physics |
| title_full | Morphometry of random spatial structures in physics Michael Andreas Klatt |
| title_fullStr | Morphometry of random spatial structures in physics Michael Andreas Klatt |
| title_full_unstemmed | Morphometry of random spatial structures in physics Michael Andreas Klatt |
| title_short | Morphometry of random spatial structures in physics |
| title_sort | morphometry of random spatial structures in physics |
| topic | Minkowski-Funktional (DE-588)1121951953 gnd Integralgeometrie (DE-588)4161911-0 gnd Ungeordnetes System (DE-588)4124353-5 gnd |
| topic_facet | Minkowski-Funktional Integralgeometrie Ungeordnetes System Hochschulschrift |
| url | https://open.fau.de/handle/openfau/7654 https://nbn-resolving.org/urn:nbn:de:bvb:29-opus4-76542 http://d-nb.info/1114990000/34 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029220849&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV041959107 |
| work_keys_str_mv | AT klattmichaelandreas morphometryofrandomspatialstructuresinphysics |