Statistics for individual crystallographic orientation measurements:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Aachen
Shaker
2002
|
| Series: | Industriemathematik und angewandte Mathematik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erscheint: 23. Januar 2002 |
| Physical Description: | 159 S. Ill. : 21 cm |
| ISBN: | 3826597826 |
Staff View
MARC
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| 100 | 1 | |a Boogaart, Karl Gerald van den |d 1971- |e Verfasser |0 (DE-588)1116728516 |4 aut | |
| 245 | 1 | 0 | |a Statistics for individual crystallographic orientation measurements |c Karl Gerald van den Boogaart |
| 264 | 1 | |a Aachen |b Shaker |c 2002 | |
| 300 | |a 159 S. |b Ill. : 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Industriemathematik und angewandte Mathematik | |
| 500 | |a Erscheint: 23. Januar 2002 | ||
| 650 | 7 | |a Hochschulschrift |2 gtt | |
| 650 | 4 | |a Crystal lattices |x Measurement |x Statistical methods | |
| 650 | 4 | |a Crystals |x Analysis |x Statistical methods | |
| 650 | 4 | |a Electrons |x Diffraction |x Measurement |x Statistical methods | |
| 650 | 0 | 7 | |a Datenanalyse |0 (DE-588)4123037-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elektronenbeugung |0 (DE-588)4151862-7 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Kristallorientierung |0 (DE-588)4623755-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Kristallorientierung |0 (DE-588)4623755-0 |D s |
| 689 | 0 | 1 | |a Messung |0 (DE-588)4038852-9 |D s |
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Record in the Search Index
| _version_ | 1808227007787433984 |
|---|---|
| adam_text |
CONTENTS
PREFACE
.
7
1
INTRODUCTION
9
1.1
CRYSTALLOGRAPHIC
ORIENTATION
MEASUREMENTS
.
10
1.1.1
SHORT
HISTORY
OF
ORIENTATION
MEASUREMENTS
.
10
1.1.2
THE
OBJECT
OF
INTEREST:
CRYSTALLOGRAPHIC
ORIENTATIONS
AND
HOW
THEY
BEHAVE
.
13
1.1.3
THE
MEASUREMENT
METHOD
AND
ITS
PROBLEMS
.
18
1.2
MATHEMATICAL
TERMINOLOGY
.
21
1.2.1
PARAMETRISATIONS
OF
ORIENTATIONS
.
21
1.2.2
ORIENTATION
DENSITY
FUNCTION
(ODF)
.
23
1.2.3
POLE
DENSITY
FUNCTION
(PDF)
.
24
1.2.4
HARMONIC
FUNCTIONS
ON
50(3)
AND
5
2
.
24
1.2.5
TEXTURE
INDEX
AND
TEXTURE
ENTROPY
.
27
1.3
STATISTICS
.
28
1.3.1
PURPOSE,
OBJECTIVE
AND
METHODS
.
28
1.3.2
THE
THREE
SAMPLING
SITUATIONS
.
28
2
SPATIAL
STATISTICS
FOR
LINEAR
FUNCTIONALS
31
2.1
LINEAR
FUNCTIONALS
OF
THE
ODF
.
31
2.1.1
ESTIMATION
ERROR
WITH
A
SPARSE
MEASUREMENT
GRID
.
32
2.1.2
NON-INDEXING
CORRECTIONS
.
33
2.1.3
CALCULATING
THE
NUMBER
OF
MEASUREMENTS
REQUIRED
.
33
2.2
CORRELATION
MODEL
FROM
GEOSTATISTICS
.
34
2.2.1
MODELLING
STOCHASTIC
DEPENDENCE
.
34
2.2.2
THE
STATIONARY
CORRELATION
MODEL
.
35
2.2.3
ESTIMATION
OF
THE
COVARIANCE
FUNCTION
AND
ITS
GENERAL
PROBLEMS
NOT
TYPICAL
FOR
TEXTURE
DATA
.
38
2.2.4
ESTIMATION
OF
THE
ESTIMATION
VARIANCE
IN
THE
PRESENCE
OF
SPATIAL
CORRELATION
.
42
2.2.5
DETAILS:
LIMITING
DISTRIBUTION
OF
THE
ESTIMATE
.
48
2.3
THE
GRAIN
MODEL
.
52
2.3.1
NUMBER
OF
MEASUREMENTS
PER
GRAIN
.
52
2.3.2
VARIANCE
CALCULATION
.
53
4
CONTENTS
2.3.3
VARIANCE
ESTIMATION
.
53
2.3.4
REDUCING
THE
NUMBER
OF
MEASUREMENTS
REQUIRED
.
55
2.3.5
APPLICATION
TO
MULTI
PHASE
MATERIAL
.
56
2.3.6
DETAILS:
LIMITING
DISTRIBUTION
OF
THE
ESTIMATE
.
56
2.4
APPLICATIONS
.
56
2.4.1
ESTIMATION
OF
C-COEFFICIENTS
.
56
2.4.2
ESTIMATION
OF
PROPERTY
TENSORS
.
62
2.4.3
ESTIMATION
OF
THE
TEXTURE
INDEX
.
65
2.4.4
ESTIMATION
OF
VOLUME
FRACTIONS
.
67
2.4.5
THE
SIMPLE
APPROACH
TO
ODF-ESTIMATION
.
68
2.5
SPATIAL
COHERENCE
FUNCTIONS
.
70
2.5.1
THE
DISORIENTATION
CORRELATION
FUNCTION
(DCF)
.
70
2.5.2
TOTAL
ORIENTATION
VARIOGRAMS
.
70
2.5.3
HOW
TO
USE
SPATIAL
COHERENCE
FUNCTIONS
.
71
2.6
CONCLUSIONS
FOR
LINEAR
STATISTICS
.
71
3
STANDARD
ORIENTATION
DENSITY
FUNCTIONS
73
3.1
UNIMODAL
DENSITY
MODELS
.
73
3.1.1
ROTATIONAL
BROWNIAN
DISTRIBUTION
.
73
3.1.2
VON
MISES-FISHER
MATRIX
DISTRIBUTION
.
74
3.1.3
ORIENTATION
DENSITIES
DEPENDING
ON
THE
ROTATION ANGLE
ONLY
.
.
76
3.1.4
MODELLING
ODFS
WITH
MORE
THAN
ONE
PREFERRED
ORIENTATION
.
.
77
3.2
CRYSTALLOGRAPHIC
EXPONENTIAL
FAMILY
(CEF)
.
77
3.2.1
DEFINITION
OF
CEF
.
77
3.2.2
PROPERTIES
OF
CEF
.
78
3.2.3
MODELLING
SPECIAL
TEXTURES
USING
CEF
.
80
3.2.4
THE
THREE
CANONICAL
CHARACTERISATIONS
.
81
3.3
SIMULATION
OF
CEF
DISTRIBUTIONS
.
82
3.3.1
REJECTION
SAMPLING
.
82
3.3.2
A
METHOD
WITH
PROVISION
FOR
LARGE
SAMPLES
.
83
4
KERNEL
DENSITY
ESTIMATION
85
4.1
HOW
KERNEL
DENSITY
ESTIMATION
WORKS
.
85
4.1.1
INTRODUCTION
.
85
4.1.2
DEFINITION
OF
KERNEL
DENSITY
ESTIMATIONS
FOR
ORIENTATIONS
.
.
86
4.1.3
ADJUSTING
FOR
SAMPLE
SYMMETRY
.
87
4.1.4
C-COEFFICIENTS
.
88
4.1.5
WHAT
DO
WE
ESTIMATE
WITH
MEASUREMENT
ERRORS?
.
89
4.2
THE
ESTIMATION
ERROR
.
90
4.2.1
EXPECTED
SQUARED
ESTIMATION
ERROR
.
90
4.2.2
ESTIMATION
OF
THE
TEXTURE
INDEX
.
92
4.2.3
ESTIMATION
ERROR
IN
THE
GRAIN
MODEL
.
92
4.3
CONFIDENCE
INTERVALS
.
93
CONTENTS
5
4.3.1
TSCHEBYSCHEFF
POINTWISE
CONFIDENCE
INTERVALS
.
94
4.3.2
NORMAL
APPROXIMATION
POINTWISE
CONFIDENCE
INTERVALS
.
94
4.3.3
THE
JOINT
CONFIDENCE
BAND
.
96
5
PARAMETRIC
STATISTICS
101
5.1
PARAMETRIC
STATISTICS
WITH
ONE
SAMPLE
.
101
5.1.1
MAXIMUM
LIKELIHOOD
ESTIMATION
.
102
5.1.2
ESTIMATION
ERROR
.
103
5.1.3
DEALING
WITH
SMALL
MEASUREMENT
ERRORS
.
104
5.2
TESTS
.
104
5.2.1
THE
GENERAL
TEST
PROBLEM
.
104
5.2.2
LIKELIHOOD
RATIO
TEST
.
105
5.2.3
TESTING
IN
CASE
OF
THE
GRAIN
MODEL
.
105
5.2.4
TESTING
IN
CASE
OF
THE
STATIONARY
CORRELATION
MODEL
.
106
5.2.5
UNIVARIATE
MODELS
.
109
5.3
TEXTURE
REGRESSION
.
ILL
5.3.1
THE
GENERAL
IDEAS
OF
TEXTURE
REGRESSION
.
112
5.3.2
GENERALISING
R
2
.
113
5.3.3
BUILDING
DEPENDENCE
MODELS
.
115
5.3.4
TEXTURE
REGRESSION
TABLES
.
117
5.3.5
TEXTURE
GRADIENTS
.
119
5.3.6
DIAGNOSTIC
STATISTICS
.
119
5.3.7
OUTLOOK:
POSSIBLE
EXTENSION
.
121
5.4
OUTLOOK:
SPATIAL
INTERACTION
OF
GRAINS
.
122
5.4.1
DEPENDENCE
ON
THE
GRAIN
SHAPE
.
122
5.4.2
DEPENDING
ON
THE
ORIENTATION
OF
OTHER
GRAINS
.
123
5.4.3
ESTIMATION
AND
TESTING
.
123
5.4.4
CONCLUSIONS
FOR
DEPENDENCE
MODELS
.
124
5.5
TEXTURE
DISCRIMINATION
ANALYSIS
.
125
5.5.1
THE
SCENARIO
OF
DISCRIMINATION
ANALYSIS
.
125
5.5.2
ESTIMATION
OF
MEAN
AND
VARIANCE
.
125
5.5.3
ESTIMATION
OF
A-POSTERIORI
PROBABILITIES
.
127
5.6
INVERSE
REGRESSION
FOR
PARAMETER
ESTIMATION
.
129
5.7
PARAMETRIC
STATISTICS:
CONCLUSIONS
.
130
6
CONCLUSIONS
AND
OUTLOOK
133
6.1
THE
GENERAL
TASK
.
133
6.2
BASIC
IDEAS
.
133
6.2.1
THE
SCALE
OF
CRYSTALLOGRAPHIC
ORIENTATIONS
.
133
6.2.2
VARIANCE
ESTIMATION
IN
PRESENCE
OF
SPATIAL
DEPENDENCE
.
133
6.2.3
CRYSTALLOGRAPHIC
EXPONENTIAL
FAMILY
AND
TEXTURE
REGRESSION
.
.
134
6.3
RESULTS
.
134
6
CONTENTS
A
SHORT
INTRODUCTION
OF
TOOLS
137
A.L
SPHERICAL
AND
ROTATIONAL
HARMONIC
FUNCTIONS
.
137
A.2
PROBABILITY
AND
MOMENTS
.
141
A.2.1
RANDOM
VARIABLES
.
141
A.2.2
MEAN,
VARIANCE,
COVARIANCE
.
142
A.2.3
CALCULATING
WITH
MOMENTS
.
143
A.3
GENERATING
ORIENTATIONS
WITH
UNIFORM
DISTRIBUTION
.
143
A.3.1
SIMULATION
IN
EULER
ANGLES
.
143
A.3.2
SIMULATION
IN
RODRIGUES
PARAMETERISATION
.
143
A.4
NUMERICAL
INTEGRATION
OF
ODFS
.
143
A.4.1
MONTE
CARLO
METHOD
OF
INTEGRATION
.
144
A.4.2
EULER
SPACE
METHOD
.
144
BIBLIOGRAPHY
145
LIST
OF
FIGURES
151
LIST
OF
SYMBOLS
153 |
| any_adam_object | 1 |
| author | Boogaart, Karl Gerald van den 1971- |
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| author_facet | Boogaart, Karl Gerald van den 1971- |
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| ctrlnum | (OCoLC)50978746 (DE-599)BVBBV014112121 |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV014112121 |
| illustrated | Illustrated |
| indexdate | 2024-08-24T00:34:15Z |
| institution | BVB |
| isbn | 3826597826 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009668972 |
| oclc_num | 50978746 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 159 S. Ill. : 21 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Shaker |
| record_format | marc |
| series2 | Industriemathematik und angewandte Mathematik |
| spelling | Boogaart, Karl Gerald van den 1971- Verfasser (DE-588)1116728516 aut Statistics for individual crystallographic orientation measurements Karl Gerald van den Boogaart Aachen Shaker 2002 159 S. Ill. : 21 cm txt rdacontent n rdamedia nc rdacarrier Industriemathematik und angewandte Mathematik Erscheint: 23. Januar 2002 Hochschulschrift gtt Crystal lattices Measurement Statistical methods Crystals Analysis Statistical methods Electrons Diffraction Measurement Statistical methods Datenanalyse (DE-588)4123037-1 gnd rswk-swf Elektronenbeugung (DE-588)4151862-7 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Kristallorientierung (DE-588)4623755-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kristallorientierung (DE-588)4623755-0 s Messung (DE-588)4038852-9 s Elektronenbeugung (DE-588)4151862-7 s Datenanalyse (DE-588)4123037-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009668972&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boogaart, Karl Gerald van den 1971- Statistics for individual crystallographic orientation measurements Hochschulschrift gtt Crystal lattices Measurement Statistical methods Crystals Analysis Statistical methods Electrons Diffraction Measurement Statistical methods Datenanalyse (DE-588)4123037-1 gnd Elektronenbeugung (DE-588)4151862-7 gnd Messung (DE-588)4038852-9 gnd Kristallorientierung (DE-588)4623755-0 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4151862-7 (DE-588)4038852-9 (DE-588)4623755-0 (DE-588)4113937-9 |
| title | Statistics for individual crystallographic orientation measurements |
| title_auth | Statistics for individual crystallographic orientation measurements |
| title_exact_search | Statistics for individual crystallographic orientation measurements |
| title_full | Statistics for individual crystallographic orientation measurements Karl Gerald van den Boogaart |
| title_fullStr | Statistics for individual crystallographic orientation measurements Karl Gerald van den Boogaart |
| title_full_unstemmed | Statistics for individual crystallographic orientation measurements Karl Gerald van den Boogaart |
| title_short | Statistics for individual crystallographic orientation measurements |
| title_sort | statistics for individual crystallographic orientation measurements |
| topic | Hochschulschrift gtt Crystal lattices Measurement Statistical methods Crystals Analysis Statistical methods Electrons Diffraction Measurement Statistical methods Datenanalyse (DE-588)4123037-1 gnd Elektronenbeugung (DE-588)4151862-7 gnd Messung (DE-588)4038852-9 gnd Kristallorientierung (DE-588)4623755-0 gnd |
| topic_facet | Hochschulschrift Crystal lattices Measurement Statistical methods Crystals Analysis Statistical methods Electrons Diffraction Measurement Statistical methods Datenanalyse Elektronenbeugung Messung Kristallorientierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009668972&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boogaartkarlgeraldvanden statisticsforindividualcrystallographicorientationmeasurements |