Modelling stochastic fibrous materials with Mathematica:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
2009
|
| Schriftenreihe: | Engineering materials and processes
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 277 S. graph. Darst. |
| ISBN: | 9781848009905 |
Internformat
MARC
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| 245 | 1 | 0 | |a Modelling stochastic fibrous materials with Mathematica |c William W. Sampson |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
1
Introduction
............................................... 1
1.1
Random, Near-Random and Stochastic
..................... 3
1.2
Reasons for Theoretical Analysis
.......................... 9
1.3
Modelling with
Mathematica
.............................. 11
2
Statistical Tools and Terminology
.......................... 15
2.1
Introduction
............................................ 15
2.2
Discrete and Continuous Random Variables
................. 15
2.2.1
Characterising Statistics
............................ 16
2.3
Common Probability Functions
........................... 29
2.3.1
Bernoulli Distribution
.............................. 29
2.3.2
Binomial Distribution
.............................. 31
2.3.3
Poisson
Distribution
............................... 35
2.4
Common Probability Density Functions
.................... 37
2.4.1
Uniform Distribution
.............................. 38
2.4.2
Normal Distribution
............................... 39
2.4.3 Lognormal
Distribution
............................ 42
2.4.4
Exponential distribution
........................... 45
2.4.5
Gamma Distribution
............................... 46
2.5
Multivariate Distributions
................................ 49
2.5.1
Divariate
Normal Distribution
...................... 51
3
Planar
Poisson
Point and Line Processes
.................. 55
3.1
Introduction
............................................ 55
3.2
Point
Poisson
Processes
.................................. 55
3.2.1
Clustering
........................................ 56
3.2.2
Separation of Pairs of Points
........................ 63
3.3
Poisson
Line Processes
................................... 71
3.3.1
Process Intensity
.................................. 73
3.3.2
Inter-crossing Distances
............................ 81
Contents
3.3.3
Statistics of Polygons
.............................. 83
3.3.4
Intrinsic Correlation
............................... 94
Poisson
Fibre Processes I: Fibre Phase
....................105
4.1
Introduction
............................................105
4.2
Planar Fibre Networks
...................................105
4.2.1
Probability of Crossing
.............................110
4.2.2
Fractional Contact Area
............................115
4.2.3
Fractional Between-zones Variance
...................117
4.3
Layered Fibre Networks
..................................132
4.3.1
Fractional Contact Area
............................132
4.3.2
In-plane Distribution of Fractional Contact Area
......137
4.3.3
Intensity of Contacts
...............................146
4.3.4
Absolute Contact States
............................150
Poisson
Fibre Processes II: Void Phase
....................159
5.1
Introduction
............................................159
5.2
In-plane Pore Dimensions
.................................160
5.3
Out-of-plane Pore Dimensions
.............................171
5.4
Porous Anisotropy
.......................................174
5.5
Tortuosity
..............................................182
5.6
Distribution of Porosity
..................................184
5.6.1
Bivariate Normal Distribution
......................185
5.6.2
Implications for Network Permeability
...............191
Stochastic Departures from Randomness
..................195
6.1
Introduction
............................................195
6.2
Fibre Orientation Distributions
............................196
6.2.1
One-parameter Cosine Distribution
..................196
6.2.2 von
Mises
Distribution
.............................199
6.2.3
Wrapped Cauchy Distribution
......................201
6.2.4
Comparing Orientation Distribution Functions
........202
6.2.5
Fibre Crossings
...................................206
6.2.6
Crossing Area Distribution
.........................211
6.2.7
Mass Distribution
.................................216
6.3
Fibre Clumping and Dispersion
...........................217
6.3.1
Influence on Network Parameters
....................222
Three-dimensional Networks
...............................241
7.1
Introduction
............................................241
7.2
Network Density
........................................244
7.2.1
Crowding Number
.................................246
7.3
Intensity of Contacts
.....................................248
7.4
Variance of Porosity
.....................................250
Contents xi
7.5
Variance of
Areal
Density
................................253
7.6
Sphere Caging
..........................................258
References
.....................................................265
Index
..........................................................275
|
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| discipline | Physik Technik Informatik Werkstoffwissenschaften / Fertigungstechnik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:08Z |
| institution | BVB |
| isbn | 9781848009905 |
| language | English |
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| oclc_num | 255068252 |
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| owner_facet | DE-29T DE-703 DE-M347 |
| physical | XI, 277 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Engineering materials and processes |
| spelling | Sampson, William W. Verfasser (DE-588)140071105 aut Modelling stochastic fibrous materials with Mathematica William W. Sampson London Springer 2009 XI, 277 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering materials and processes Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Mathematica 6 (DE-588)7581228-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Faser (DE-588)4127566-4 gnd rswk-swf Faser (DE-588)4127566-4 s Stochastisches Modell (DE-588)4057633-4 s Mathematisches Modell (DE-588)4114528-8 s Mathematica 6 (DE-588)7581228-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017078131&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sampson, William W. Modelling stochastic fibrous materials with Mathematica Stochastisches Modell (DE-588)4057633-4 gnd Mathematica 6 (DE-588)7581228-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Faser (DE-588)4127566-4 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)7581228-9 (DE-588)4114528-8 (DE-588)4127566-4 |
| title | Modelling stochastic fibrous materials with Mathematica |
| title_auth | Modelling stochastic fibrous materials with Mathematica |
| title_exact_search | Modelling stochastic fibrous materials with Mathematica |
| title_full | Modelling stochastic fibrous materials with Mathematica William W. Sampson |
| title_fullStr | Modelling stochastic fibrous materials with Mathematica William W. Sampson |
| title_full_unstemmed | Modelling stochastic fibrous materials with Mathematica William W. Sampson |
| title_short | Modelling stochastic fibrous materials with Mathematica |
| title_sort | modelling stochastic fibrous materials with mathematica |
| topic | Stochastisches Modell (DE-588)4057633-4 gnd Mathematica 6 (DE-588)7581228-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Faser (DE-588)4127566-4 gnd |
| topic_facet | Stochastisches Modell Mathematica 6 Mathematisches Modell Faser |
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