Mathematical models of granular matter:
Saved in:
| Other Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in mathematics
1937 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 212 S. Ill., graph. Darst. |
| ISBN: | 9783540782766 |
Staff View
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| 245 | 1 | 0 | |a Mathematical models of granular matter |c Gianfranco Capriz ... (eds.). With contributions by: A. Barrat ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XVI, 212 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
From Granular Matter to Generalized Continuum
J.D. Goddard
.................................................... 1
1
Introduction
.................................................. 1
1.1
Mathematical Preliminaries
................................ 3
1.2
Balances
................................................. 4
2
Micromechanics
.............................................. 5
2.1
Granular
Microstructure
and Rotation
....................... 5
2.2
Graph Theory for Extrinsic Modes
.......................... 7
2.3
Extrinsic Power
........................................... 12
3
Energy-Based Homogenization
.................................. 13
3.1
Intrinsic Moments and Continuum Fields
..................... 15
4
Conclusions
.................................................. 17
Appendix: Simplex and Edge-Complex Gradients
.................... 17
References
...................................................... 20
Generalized Kinetic Maxwell Type Models
of Granular Gases
A. V. Bobylev, C. Cercignani, and I.M.
Gamba
....................... 23
1
Introduction
.................................................. 23
2
Maxwell Models of the Boltzmann Equation
...................... 26
3
Isotropie
Maxwell Model in the Fourier Representation
............. 28
4
Models with Multiple Interactions
............................... 30
4.1
Statement of the General Problem
........................... 31
5
The General Problem in Fourier Representation
................... 33
5.1
Existence and Uniqueness of Solutions
....................... 33
5.2
Large Time Asymptotics
................................... 34
5.3
Existence of Self-Similar Solutions
........................... 41
5.4
Properties of Self-Similar Solutions
.......................... 42
XII Contents
6
Main Results for Maxwell Models with Multiple Interactions
........ 45
6.1
Self-Similar Asymptotics
................................... 45
6.2
Distribution Functions, Moments and Power-Like Tails
......... 47
6.3
Applications to the Conservative or Dissipative
Boltzmann Equation
....................................... 51
References
...................................................... 56
Hydrodynamics from the Dissipative Boltzmann Equation
Giuseppe
Toscani
................................................ 59
1
Introduction
.................................................. 59
2
Modeling Dissipative Boltzmann Equation
........................ 62
3
Hydrodynamic Limit and the
Euler
Equations
.................... 65
4
Hydrodynamics from Homogeneous Cooling States
................ 67
5
Conclusions
.................................................. 71
References
...................................................... 72
Bodies with Kinetic Substructure
Gianfranco
Capriz
............................................... 77
1
Kinetics
...................................................... 77
2
A Shadow Speck of Matter
..................................... 79
3
Straining and Allied Notions
.................................... 81
4
Balance Laws
................................................. 84
5
Balance of Kinetic Energy
...................................... 86
6
The First Principle
............................................ 89
References
...................................................... 90
Erom
Extended Thermodynamics to Granular Materials
Tommaso Ruggeri
................................................ 91
1
Introduction
.................................................. 91
2
Boltzmann Equation and Moments
.............................. 92
2.1
The Closure of Extended Thermodynamics
................... 93
2.2
Macroscopic Approach of
ET in
the
13
Fields
................. 93
3
Extended Thermodynamics of Moments
.......................... 94
4
Maximization of Entropy
....................................... 97
5
Maximum Characteristic Velocity in Classical Theory
.............. 98
6
Nesting Theories and Principal Subsystems
....................... 99
6.1
Example of 13-Moments Principal Subsystems
................ 99
6.2
Lower Bound Estimate and Characteristic Velocities
for Large
η
...............................................100
7
Qualitative Analysis
...........................................102
7.1
Shizuta-Kawashima Condition
..............................103
7.2
Global Existence of Smooth Solutions
........................103
8
Comparison with Experiments: Sound Waves and Light Scattering
.. 104
References
......................................................105
Contents XIII
Influence
of Contact Modelling on the Macroscopic Plastic
Response of Granular Soils Under Cyclic Loading
R.
García-Rojo,
S.
McN
amara,
and
H. J.
Herrmann
..................109
1
Introduction
..................................................109
2
Discrete Element Methods
......................................
Ill
2.1
Boundary Conditions: Biaxial Test
..........................112
2.2
Molecular Dynamics
.......................................113
2.3
The Normal-Dashpot Model
................................114
2.4
Contact Dynamics
........................................115
3
Results
......................................................116
3.1
Comparing MD and CD
...................................117
3.2
Comparing Different Visco-Elastic Laws
......................118
4
Conclusions
..................................................123
References
......................................................123
Fluctuations in Granular Gases
A. Barrat,
A. Puglisi, E. Trizac, P.
Visco,
and F. van Wijland
........125
1
Introduction
..................................................125
2
A Brief Introduction to Granular Gases
..........................127
2.1
Boundary Driven Gases
....................................128
2.2
Randomly Driven Gases
...................................129
3
Total Energy Fluctuations in Vibrated
and Driven Granular Gases
.....................................131
3.1
The Inhomogeneous Boundary Driven Gas
...................131
3.2
The Homogeneously Driven Case
............................135
4
A Large Deviation Theory for the Injected Power Fluctuations
in the Homogeneous Driven Granular Gas
........................138
4.1
The
Cumulants
...........................................141
4.2
The Solvable Infinite Dimension Limit
.......................145
5
Fluctuations of Injected Power at Finite Times: Two Examples
.....146
5.1
The Homogeneous Driven Gas of Inelastic Hard Disks
.........146
5.2
The Boundary Driven Gas of Inelastic Hard Disks
.............153
6
The Dynamics of a Tracer Particle as a Non-Equilibrium
Markov Process
...............................................157
6.1
Detailed Balance
..........................................158
6.2
Action Functionals
........................................160
7
Conclusions
..................................................161
References
......................................................162
An Extended Continuum Theory for Granular Media
Pasquale Giovine................................................
167
1
Introduction
..................................................167
2
A First Model
................................................169
3
Rotations
....................................................171
XIV Contents
4 Balance
of Interactions for Material Bodies
with
Affine
Microstructure
.....................................173
5
Observers
....................................................175
6
Dilatant
Granular Materials with Rotating Grains
.................177
7
Inertia Forces and Balance of Granular Energy
....................179
8
Constitutive Restrictions in the Thermoelastic Case
...............182
9
Suspension of Rigid Granules in a Fluid Matrix
...................185
Appendix: Kinetic Energy Coefficients
..............................187
References
......................................................190
Slow Motion in Granular Matter
Paolo Maria Mariano
............................................193
1
Introduction
..................................................193
2
Representation of the Granularity
...............................194
3
Balance of Interactions: R3
к
SO(3)
Invariance
...................200
4
Evolution of the Local Numerosity of Granules
....................204
5
A Single Granule Coinciding with the Generic Material Element
.... 207
References
......................................................209
Index
..........................................................211
|
| adam_txt |
Contents
From Granular Matter to Generalized Continuum
J.D. Goddard
. 1
1
Introduction
. 1
1.1
Mathematical Preliminaries
. 3
1.2
Balances
. 4
2
Micromechanics
. 5
2.1
Granular
Microstructure
and Rotation
. 5
2.2
Graph Theory for Extrinsic Modes
. 7
2.3
Extrinsic Power
. 12
3
Energy-Based Homogenization
. 13
3.1
Intrinsic Moments and Continuum Fields
. 15
4
Conclusions
. 17
Appendix: Simplex and Edge-Complex Gradients
. 17
References
. 20
Generalized Kinetic Maxwell Type Models
of Granular Gases
A. V. Bobylev, C. Cercignani, and I.M.
Gamba
. 23
1
Introduction
. 23
2
Maxwell Models of the Boltzmann Equation
. 26
3
Isotropie
Maxwell Model in the Fourier Representation
. 28
4
Models with Multiple Interactions
. 30
4.1
Statement of the General Problem
. 31
5
The General Problem in Fourier Representation
. 33
5.1
Existence and Uniqueness of Solutions
. 33
5.2
Large Time Asymptotics
. 34
5.3
Existence of Self-Similar Solutions
. 41
5.4
Properties of Self-Similar Solutions
. 42
XII Contents
6
Main Results for Maxwell Models with Multiple Interactions
. 45
6.1
Self-Similar Asymptotics
. 45
6.2
Distribution Functions, Moments and Power-Like Tails
. 47
6.3
Applications to the Conservative or Dissipative
Boltzmann Equation
. 51
References
. 56
Hydrodynamics from the Dissipative Boltzmann Equation
Giuseppe
Toscani
. 59
1
Introduction
. 59
2
Modeling Dissipative Boltzmann Equation
. 62
3
Hydrodynamic Limit and the
Euler
Equations
. 65
4
Hydrodynamics from Homogeneous Cooling States
. 67
5
Conclusions
. 71
References
. 72
Bodies with Kinetic Substructure
Gianfranco
Capriz
. 77
1
Kinetics
. 77
2
A Shadow Speck of Matter
. 79
3
Straining and Allied Notions
. 81
4
Balance Laws
. 84
5
Balance of Kinetic Energy
. 86
6
The First Principle
. 89
References
. 90
Erom
Extended Thermodynamics to Granular Materials
Tommaso Ruggeri
. 91
1
Introduction
. 91
2
Boltzmann Equation and Moments
. 92
2.1
The Closure of Extended Thermodynamics
. 93
2.2
Macroscopic Approach of
ET in
the
13
Fields
. 93
3
Extended Thermodynamics of Moments
. 94
4
Maximization of Entropy
. 97
5
Maximum Characteristic Velocity in Classical Theory
. 98
6
Nesting Theories and Principal Subsystems
. 99
6.1
Example of 13-Moments Principal Subsystems
. 99
6.2
Lower Bound Estimate and Characteristic Velocities
for Large
η
.100
7
Qualitative Analysis
.102
7.1
Shizuta-Kawashima Condition
.103
7.2
Global Existence of Smooth Solutions
.103
8
Comparison with Experiments: Sound Waves and Light Scattering
. 104
References
.105
Contents XIII
Influence
of Contact Modelling on the Macroscopic Plastic
Response of Granular Soils Under Cyclic Loading
R.
García-Rojo,
S.
McN
amara,
and
H. J.
Herrmann
.109
1
Introduction
.109
2
Discrete Element Methods
.
Ill
2.1
Boundary Conditions: Biaxial Test
.112
2.2
Molecular Dynamics
.113
2.3
The Normal-Dashpot Model
.114
2.4
Contact Dynamics
.115
3
Results
.116
3.1
Comparing MD and CD
.117
3.2
Comparing Different Visco-Elastic Laws
.118
4
Conclusions
.123
References
.123
Fluctuations in Granular Gases
A. Barrat,
A. Puglisi, E. Trizac, P.
Visco,
and F. van Wijland
.125
1
Introduction
.125
2
A Brief Introduction to Granular Gases
.127
2.1
Boundary Driven Gases
.128
2.2
Randomly Driven Gases
.129
3
Total Energy Fluctuations in Vibrated
and Driven Granular Gases
.131
3.1
The Inhomogeneous Boundary Driven Gas
.131
3.2
The Homogeneously Driven Case
.135
4
A Large Deviation Theory for the Injected Power Fluctuations
in the Homogeneous Driven Granular Gas
.138
4.1
The
Cumulants
.141
4.2
The Solvable Infinite Dimension Limit
.145
5
Fluctuations of Injected Power at Finite Times: Two Examples
.146
5.1
The Homogeneous Driven Gas of Inelastic Hard Disks
.146
5.2
The Boundary Driven Gas of Inelastic Hard Disks
.153
6
The Dynamics of a Tracer Particle as a Non-Equilibrium
Markov Process
.157
6.1
Detailed Balance
.158
6.2
Action Functionals
.160
7
Conclusions
.161
References
.162
An Extended Continuum Theory for Granular Media
Pasquale Giovine.
167
1
Introduction
.167
2
A First Model
.169
3
Rotations
.171
XIV Contents
4 Balance
of Interactions for Material Bodies
with
Affine
Microstructure
.173
5
Observers
.175
6
Dilatant
Granular Materials with Rotating Grains
.177
7
Inertia Forces and Balance of Granular Energy
.179
8
Constitutive Restrictions in the Thermoelastic Case
.182
9
Suspension of Rigid Granules in a Fluid Matrix
.185
Appendix: Kinetic Energy Coefficients
.187
References
.190
Slow Motion in Granular Matter
Paolo Maria Mariano
.193
1
Introduction
.193
2
Representation of the Granularity
.194
3
Balance of Interactions: R3
к
SO(3)
Invariance
.200
4
Evolution of the Local Numerosity of Granules
.204
5
A Single Granule Coinciding with the Generic Material Element
. 207
References
.209
Index
.211 |
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| id | DE-604.BV023294256 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:44:16Z |
| indexdate | 2024-07-09T21:15:10Z |
| institution | BVB |
| isbn | 9783540782766 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016478815 |
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| physical | XVI, 212 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Mathematical models of granular matter Gianfranco Capriz ... (eds.). With contributions by: A. Barrat ... Berlin [u.a.] Springer 2008 XVI, 212 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1937 Granular materials - Mathematical models blmsh Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Granulärer Stoff (DE-588)4256351-3 gnd rswk-swf Granulärer Stoff (DE-588)4256351-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Barrat, Alain ctb Capriz, Gianfranco 1925- (DE-588)135621232 edt Lecture notes in mathematics 1937 (DE-604)BV000676446 1937 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016478815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematical models of granular matter Lecture notes in mathematics Granular materials - Mathematical models blmsh Mathematisches Modell (DE-588)4114528-8 gnd Granulärer Stoff (DE-588)4256351-3 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4256351-3 |
| title | Mathematical models of granular matter |
| title_auth | Mathematical models of granular matter |
| title_exact_search | Mathematical models of granular matter |
| title_exact_search_txtP | Mathematical models of granular matter |
| title_full | Mathematical models of granular matter Gianfranco Capriz ... (eds.). With contributions by: A. Barrat ... |
| title_fullStr | Mathematical models of granular matter Gianfranco Capriz ... (eds.). With contributions by: A. Barrat ... |
| title_full_unstemmed | Mathematical models of granular matter Gianfranco Capriz ... (eds.). With contributions by: A. Barrat ... |
| title_short | Mathematical models of granular matter |
| title_sort | mathematical models of granular matter |
| topic | Granular materials - Mathematical models blmsh Mathematisches Modell (DE-588)4114528-8 gnd Granulärer Stoff (DE-588)4256351-3 gnd |
| topic_facet | Granular materials - Mathematical models Mathematisches Modell Granulärer Stoff |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016478815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT barratalain mathematicalmodelsofgranularmatter AT caprizgianfranco mathematicalmodelsofgranularmatter |