Models for polymeric and anisotropic liquids:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
2005
|
| Series: | Lecture notes in physics
675 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 205 - 215 |
| Physical Description: | XIII, 229 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783540262107 3540262105 |
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MARC
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| 100 | 1 | |a Kröger, Martin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Models for polymeric and anisotropic liquids |c Martin Kröger |
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c 2005 | |
| 300 | |a XIII, 229 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in physics |v 675 | |
| 500 | |a Literaturverz. S. 205 - 215 | ||
| 650 | 7 | |a Física |2 larpcal | |
| 650 | 4 | |a Polymères cristallins - Modèles mathématiques | |
| 650 | 4 | |a Solutions de polymère - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Crystalline polymers |x Mathematical models | |
| 650 | 4 | |a Polymer solutions |x Mathematical models | |
| 650 | 0 | 7 | |a Polymere Flüssigkeit |0 (DE-588)4175229-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Computersimulation |0 (DE-588)4148259-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Anisotropie |0 (DE-588)4002073-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kinetische Theorie |0 (DE-588)4030669-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Polymere Flüssigkeit |0 (DE-588)4175229-6 |D s |
| 689 | 0 | 1 | |a Anisotropie |0 (DE-588)4002073-3 |D s |
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| adam_text | Contents
Part I Illustrations
&
Applications
1
Simple Models for Polymeric and
Anisotropie
Liquids
.............. 3
1.1
Section-by-Section Summary
................................. 7
2
Dumbbell Model for Dilute and Semi-Dilute Solutions
.............. 13
2.1
FENE-PMF Dumbbell in Finitely Diluted Solution
.............. 15
2.2
Introducing a Mean Field Potential
............................ 16
2.3
Relaxation Equation for the Tensor of Gyration
................. 16
2.4
Symmetry Adapted Basis
.................................... 18
2.5
Stress Tensor and Material Functions
.......................... 21
2.6
Reduced Description of Kinetic Models
........................ 23
3
Chain Model for Dilute Solutions
................................ 25
3.1
Hydrodynamic Interaction
................................... 25
3.2
Long Chain Limit, Cholesky Decomposition
.................... 27
3.3
NEBD Simulation Details
................................... 27
3.4
Universal Ratios
........................................... 29
4
Chain Model for Concentrated Solutions and Melts
................ 33
4.1
NEMD Simulation Method
.................................. 34
4.2
Stress Tensor
.............................................. 35
4.3
Lennard-Jones (LJ) Units
.................................... 35
4.4
Flow Curve and Dynamical Crossover for Polymer Melts
........ 35
4.5
Characteristic Lengths and Times
............................. 36
4.6
Linear Stress-Optic Rule
(SOR)
and Failures
................... 39
4.7
Nonlinear Stress-Optic-Rule
................................. 42
4.8
Stress-Optic Coefficient
..................................... 44
4.9
Interpretation of Dimensionless Simulation Numbers
............. 48
Contents
Chain Models
for Transient
and Semiflexible
Structures
..................................... 49
5.1 Conformational
Statistics of Wormlike Chains (WLC)
........... 49
5.1.1
Functional Integrals for WLCs
......................... 50
5.1.2
Properties of WLCs
.................................. 51
5.2
FENE
-С
Wormlike Micelles
................................. 53
5.2.1
Flow-Induced Orientation and Degradation
.............. 54
5.2.2
Length Distribution
.................................. 56
5.2.3
FENE
-С
Theory vs Simulation, Rheology, Flow Alignment
. 57
5.3
FENE-B
Semiflexible
Chains
................................ 61
5.3.1
Actin Filaments
..................................... 61
5.4
FENE-B Liquid Crystalline Polymers
.......................... 66
5.4.1
Static Structure Factor
................................ 69
5.5
FENE-CB Transient
Semiflexible
Networks, Ring Formation
...... 72
Primitive Path Models
.......................................... 77
6.1
Doi-Edwards Tube Model and Improvements
................... 77
6.2
Refined Tube Model
with
Anisotropie
Flow-Induced Tube Renewal
.................. 79
6.2.1
Linear Viscoelasticity of Melts and Concentrated Solutions
. 80
6.3
Nonlinear Viscoelasticity, Particular Closure
.................... 84
6.3.1
Example: Refined Tube Model, Stationary Shear Flow
..... 84
6.3.2
Example: Transient Viscosities for Rigid Polymers
........ 85
6.3.3
Example: Doi-Edwards Model as a Special Case
.......... 85
6.4
Nonlinear Viscoelasticity without Closure
...................... 86
6.4.1
Galerkin s Principle
.................................. 87
Elongated Particle Models
...................................... 91
7.1
Director Theory
............................................ 92
7.2
Structural Theories of Suspensions
........................... 93
7.2.1
Semi-Dilute Suspensions of Elongated Particles
.......... 95
7.2.2
Concentrated Suspensions of Rod-Like Polymers
......... 95
7.3
Uniaxial
Fluids, Micro-Macro Correspondence
................. 96
7.3.1
Concentrated Suspensions of Disks, Spheres, Rods
........ 97
7.3.2
Example: Tumbling
.................................. 97
7.3.3
Example: Miesowicz Viscosities
....................... 98
7.4
Uniaxial
Fluids: Decoupling Approximations
................... 99
7.4.1
Decoupling with Correct
Tensorial
Symmetry
............ 102
7.5
Ferrofluids: Dynamics and Rheology
.......................... 103
7.6
Liquid Crystals: Periodic and Irregular Dynamics
................ 105
7.6.1
Landau-
de Gennes
Potential
.......................... 108
7.6.2
In-Plane and Out-of-Plane States
....................... 109
Contents
XI
8
Connection
between Different Levels of Description
................
Ill
8.1
Boltzmann Equation
........................................
Ill
8.2
Generalized
Poisson
Structures
............................... 112
8.3
GENERIC Equations
....................................... 112
8.3.1
Building Block
L
.................................... 113
8.3.2
Building Block
M
.................................... 115
8.4
Dissipative Particles
........................................ 117
8.5
Langevin
and Fokker-Planck Equation, Brownian Dynamics
...... 117
8.5.1
Motivation
.......................................... 117
8.5.2
Interpretation, and
Langevin
Equation
................... 118
8.6
Projection Operator Methods
................................. 119
8.7
Stress Tensors: Giesekus
-
Kramers
-
GENERIC
................ 121
8.8
Generalized Canonical Ensemble and Friction Matrix
............ 123
8.9
Beyond-Equilibrium Molecular Dynamics (BEMD)
.............. 124
8.9.1
Multiplostatted Equations
............................. 128
8.9.2
Applicability of BEMD
............................... 130
8.9.3
DOLLS/SLLOD Analogy with Multiplostatted Equations
.. 132
8.10
Examples for Coarse-Graining
................................ 134
8.10.1
From Connected to Primitive Path
...................... 134
8.10.2
From Disconnected to Primitive Path
.................... 136
Part II Theory
&
Computational Recipes
9
Equilibrium Statistics: Monte Carlo Methods
..................... 145
9.1
Expectation Values, Metropolis Monte Carlo
.................... 146
9.2
Normalization Constants, Partition Function
.................... 148
9.2.1
Standard Monte Carlo
................................ 149
9.2.2
Direct Importance Sampling
........................... 150
9.2.3
Path Sampling
....................................... 150
9.3
Density of States Monte Carlo (DSMC)
........................ 151
9.4
Quasi Monte Carlo
......................................... 153
10
Irreducible and
Isotropie
Cartesian Tensors
....................... 155
10.1
Notation
.................................................. 155
10.2 Anisotropie
(Irreducible) Tensors
............................. 156
10.3
Differential Operators (V,
£
etc.)
............................. 158
10.4 Isotropie
Tensors
........................................... 159
10.4.1
Construction of the
Isotropie
Tensors A{l)
................ 160
10.4.2
Generalized Cross Product
4( ·Μ)
...................... 160
10.4.3
Generalized Tensor
Λ
(w)
............................ 161
10.4.4
Implications (Summary)
.............................. 161
10.5
Differential Operations (Tabular Form)
........................ 162
10.6
Nematic Order Parameters
................................... 163
10.6.1
Uniaxial
Phase
...................................... 163
XII Contents
10.6.2
Biaxial Phase
....................................... 164
10.7
Tensor Invariants
........................................... 165
10.8
Solutions of the Laplace Equation
............................. 167
10.9
The Reverse
Д(/)
Operation
.................................. 168
lO.lOIntegrating Irreducible Tensors
............................... 168
11
Nonequilibrium Dynamics of
Anisotropie
Fluids
................... 169
11.1
Orientational Distribution Function
............................ 169
11.1.1
Alignment Tensors
................................... 170
11.1.2
Uniaxial
Distribution Function
......................... 170
11.2
Fokker-Planck Equation, Smoluchowski Equation
............... 170
11.2.1
Spatial Inhomogeneous Distribution
.................... 172
11.2.2
Row Field
.......................................... 172
11.2.3
Spatial Homogeneous Distribution, Mh Order Potential
___ 173
11.2.4
Examples for Potentials and Applications
................ 174
11.3
Coupled Equations of Change for Alignment Tensors
............ 174
11.3.1
Dynamical Closures
.................................. 176
11.3.2
Equations of Change for Order Parameters
............... 176
11.4
Langevin
Equation
......................................... 178
11.4.1
Brownian Dynamics Simulation
........................ 179
12
Simple Simulation Algorithms
and Sample Applications
........................................ 181
12.1
Index of Programs
.......................................... 182
12.2
Recipes
................................................... 182
12.2.1
Random Vectors, Random Paths (2D,
3D) ............... 182
12.2.2
Periodic and Reflecting Boundary Conditions (nD)
........ 183
12.2.3
Useful Initial Phase Space Coordinates (nD)
............. 184
12.2.4
Visualization, Animation
&
Movies (nD)
................ 184
12.3
Montecarlo
............................................... 185
12.3.1
Standard Monte Carlo Integration (nD)
.................. 185
12.3.2
Ising Model via Metropolis Monte Carlo (2D)
............ 186
12.4
Molecular Dynamics
........................................ 187
12.4.1
Molecular Dynamics of a Lennard-Jones System (nD)
..... 187
12.4.2
Associating Equilibrium
FENE
Polymers (2D.3D)
........ 188
12.5
NonEquilibrium Molecular Dynamics
......................... 190
12.5.1
NonEquilibrium Molecular Dynamics (nD)
.............. 190
12.5.2
Flow through Nanopore
(3D).......................... 191
12.6
Brownian Dynamics
........................................ 194
12.6.1
Brownian Dynamics of a Lennard-Jones System (nD)
..... 194
12.6.2
Hydrodynamic Interaction via Chebyshev Polynomials
(3D) 194
12.7
Coarse-Graining
........................................... 195
12.7.1
Coarse-Graining Polymer Chains (nD)
.................. 195
Contents XIII
Concluding Remarks
............................................... 197
13.1
Acknowledgement
.......................................... 198
Notation
........................................................... 199
14.1
Special Symbols
........................................... 199
14.2
Tensor Symbols
............................................ 199
14.3
Upper Case Roman Symbols
................................. 200
14.4
Lower Case Roman Symbols
................................. 201
14.5
Greek Symbols
............................................ 202
14.6
Caligraphic Symbols
........................................ 202
14.7
FENE
Models
............................................. 203
14.8
Gaussian Integrals
.......................................... 204
References
......................................................... 205
Author Index
...................................................... 217
Index
............................................................. 223
|
| adam_txt |
Contents
Part I Illustrations
&
Applications
1
Simple Models for Polymeric and
Anisotropie
Liquids
. 3
1.1
Section-by-Section Summary
. 7
2
Dumbbell Model for Dilute and Semi-Dilute Solutions
. 13
2.1
FENE-PMF Dumbbell in Finitely Diluted Solution
. 15
2.2
Introducing a Mean Field Potential
. 16
2.3
Relaxation Equation for the Tensor of Gyration
. 16
2.4
Symmetry Adapted Basis
. 18
2.5
Stress Tensor and Material Functions
. 21
2.6
Reduced Description of Kinetic Models
. 23
3
Chain Model for Dilute Solutions
. 25
3.1
Hydrodynamic Interaction
. 25
3.2
Long Chain Limit, Cholesky Decomposition
. 27
3.3
NEBD Simulation Details
. 27
3.4
Universal Ratios
. 29
4
Chain Model for Concentrated Solutions and Melts
. 33
4.1
NEMD Simulation Method
. 34
4.2
Stress Tensor
. 35
4.3
Lennard-Jones (LJ) Units
. 35
4.4
Flow Curve and Dynamical Crossover for Polymer Melts
. 35
4.5
Characteristic Lengths and Times
. 36
4.6
Linear Stress-Optic Rule
(SOR)
and Failures
. 39
4.7
Nonlinear Stress-Optic-Rule
. 42
4.8
Stress-Optic Coefficient
. 44
4.9
Interpretation of Dimensionless Simulation Numbers
. 48
Contents
Chain Models
for Transient
and Semiflexible
Structures
. 49
5.1 Conformational
Statistics of Wormlike Chains (WLC)
. 49
5.1.1
Functional Integrals for WLCs
. 50
5.1.2
Properties of WLCs
. 51
5.2
FENE
-С
Wormlike Micelles
. 53
5.2.1
Flow-Induced Orientation and Degradation
. 54
5.2.2
Length Distribution
. 56
5.2.3
FENE
-С
Theory vs Simulation, Rheology, Flow Alignment
. 57
5.3
FENE-B
Semiflexible
Chains
. 61
5.3.1
Actin Filaments
. 61
5.4
FENE-B Liquid Crystalline Polymers
. 66
5.4.1
Static Structure Factor
. 69
5.5
FENE-CB Transient
Semiflexible
Networks, Ring Formation
. 72
Primitive Path Models
. 77
6.1
Doi-Edwards Tube Model and Improvements
. 77
6.2
Refined Tube Model
with
Anisotropie
Flow-Induced Tube Renewal
. 79
6.2.1
Linear Viscoelasticity of Melts and Concentrated Solutions
. 80
6.3
Nonlinear Viscoelasticity, Particular Closure
. 84
6.3.1
Example: Refined Tube Model, Stationary Shear Flow
. 84
6.3.2
Example: Transient Viscosities for Rigid Polymers
. 85
6.3.3
Example: Doi-Edwards Model as a Special Case
. 85
6.4
Nonlinear Viscoelasticity without Closure
. 86
6.4.1
Galerkin's Principle
. 87
Elongated Particle Models
. 91
7.1
Director Theory
. 92
7.2
Structural Theories of Suspensions
. 93
7.2.1
Semi-Dilute Suspensions of Elongated Particles
. 95
7.2.2
Concentrated Suspensions of Rod-Like Polymers
. 95
7.3
Uniaxial
Fluids, Micro-Macro Correspondence
. 96
7.3.1
Concentrated Suspensions of Disks, Spheres, Rods
. 97
7.3.2
Example: Tumbling
. 97
7.3.3
Example: Miesowicz Viscosities
. 98
7.4
Uniaxial
Fluids: Decoupling Approximations
. 99
7.4.1
Decoupling with Correct
Tensorial
Symmetry
. 102
7.5
Ferrofluids: Dynamics and Rheology
. 103
7.6
Liquid Crystals: Periodic and Irregular Dynamics
. 105
7.6.1
Landau-
de Gennes
Potential
. 108
7.6.2
In-Plane and Out-of-Plane States
. 109
Contents
XI
8
Connection
between Different Levels of Description
.
Ill
8.1
Boltzmann Equation
.
Ill
8.2
Generalized
Poisson
Structures
. 112
8.3
GENERIC Equations
. 112
8.3.1
Building Block
L
. 113
8.3.2
Building Block
M
. 115
8.4
Dissipative Particles
. 117
8.5
Langevin
and Fokker-Planck Equation, Brownian Dynamics
. 117
8.5.1
Motivation
. 117
8.5.2
Interpretation, and
Langevin
Equation
. 118
8.6
Projection Operator Methods
. 119
8.7
Stress Tensors: Giesekus
-
Kramers
-
GENERIC
. 121
8.8
Generalized Canonical Ensemble and Friction Matrix
. 123
8.9
Beyond-Equilibrium Molecular Dynamics (BEMD)
. 124
8.9.1
Multiplostatted Equations
. 128
8.9.2
Applicability of BEMD
. 130
8.9.3
DOLLS/SLLOD Analogy with Multiplostatted Equations
. 132
8.10
Examples for Coarse-Graining
. 134
8.10.1
From Connected to Primitive Path
. 134
8.10.2
From Disconnected to Primitive Path
. 136
Part II Theory
&
Computational Recipes
9
Equilibrium Statistics: Monte Carlo Methods
. 145
9.1
Expectation Values, Metropolis Monte Carlo
. 146
9.2
Normalization Constants, Partition Function
. 148
9.2.1
Standard Monte Carlo
. 149
9.2.2
Direct Importance Sampling
. 150
9.2.3
Path Sampling
. 150
9.3
Density of States Monte Carlo (DSMC)
. 151
9.4
Quasi Monte Carlo
. 153
10
Irreducible and
Isotropie
Cartesian Tensors
. 155
10.1
Notation
. 155
10.2 Anisotropie
(Irreducible) Tensors
. 156
10.3
Differential Operators (V,
£
etc.)
. 158
10.4 Isotropie
Tensors
. 159
10.4.1
Construction of the
Isotropie
Tensors A{l)
. 160
10.4.2
Generalized Cross Product
4('·Μ)
. 160
10.4.3
Generalized Tensor
Λ
(w)
. 161
10.4.4
Implications (Summary)
. 161
10.5
Differential Operations (Tabular Form)
. 162
10.6
Nematic Order Parameters
. 163
10.6.1
Uniaxial
Phase
. 163
XII Contents
10.6.2
Biaxial Phase
. 164
10.7
Tensor Invariants
. 165
10.8
Solutions of the Laplace Equation
. 167
10.9
The Reverse
Д(/)
Operation
. 168
lO.lOIntegrating Irreducible Tensors
. 168
11
Nonequilibrium Dynamics of
Anisotropie
Fluids
. 169
11.1
Orientational Distribution Function
. 169
11.1.1
Alignment Tensors
. 170
11.1.2
Uniaxial
Distribution Function
. 170
11.2
Fokker-Planck Equation, Smoluchowski Equation
. 170
11.2.1
Spatial Inhomogeneous Distribution
. 172
11.2.2
Row Field
. 172
11.2.3
Spatial Homogeneous Distribution, Mh Order Potential
_ 173
11.2.4
Examples for Potentials and Applications
. 174
11.3
Coupled Equations of Change for Alignment Tensors
. 174
11.3.1
Dynamical Closures
. 176
11.3.2
Equations of Change for Order Parameters
. 176
11.4
Langevin
Equation
. 178
11.4.1
Brownian Dynamics Simulation
. 179
12
Simple Simulation Algorithms
and Sample Applications
. 181
12.1
Index of Programs
. 182
12.2
Recipes
. 182
12.2.1
Random Vectors, Random Paths (2D,
3D) . 182
12.2.2
Periodic and Reflecting Boundary Conditions (nD)
. 183
12.2.3
Useful Initial Phase Space Coordinates (nD)
. 184
12.2.4
Visualization, Animation
&
Movies (nD)
. 184
12.3
Montecarlo
. 185
12.3.1
Standard Monte Carlo Integration (nD)
. 185
12.3.2
Ising Model via Metropolis Monte Carlo (2D)
. 186
12.4
Molecular Dynamics
. 187
12.4.1
Molecular Dynamics of a Lennard-Jones System (nD)
. 187
12.4.2
Associating Equilibrium
FENE
Polymers (2D.3D)
. 188
12.5
NonEquilibrium Molecular Dynamics
. 190
12.5.1
NonEquilibrium Molecular Dynamics (nD)
. 190
12.5.2
Flow through Nanopore
(3D). 191
12.6
Brownian Dynamics
. 194
12.6.1
Brownian Dynamics of a Lennard-Jones System (nD)
. 194
12.6.2
Hydrodynamic Interaction via Chebyshev Polynomials
(3D) 194
12.7
Coarse-Graining
. 195
12.7.1
Coarse-Graining Polymer Chains (nD)
. 195
Contents XIII
Concluding Remarks
. 197
13.1
Acknowledgement
. 198
Notation
. 199
14.1
Special Symbols
. 199
14.2
Tensor Symbols
. 199
14.3
Upper Case Roman Symbols
. 200
14.4
Lower Case Roman Symbols
. 201
14.5
Greek Symbols
. 202
14.6
Caligraphic Symbols
. 202
14.7
FENE
Models
. 203
14.8
Gaussian Integrals
. 204
References
. 205
Author Index
. 217
Index
. 223 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kröger, Martin |
| author_facet | Kröger, Martin |
| author_role | aut |
| author_sort | Kröger, Martin |
| author_variant | m k mk |
| building | Verbundindex |
| bvnumber | BV021263806 |
| callnumber-first | Q - Science |
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| callnumber-sort | QC 13 |
| callnumber-subject | QC - Physics |
| classification_rvk | UD 8220 |
| ctrlnum | (OCoLC)61715044 (DE-599)BVBBV021263806 |
| dewey-full | 547/.70454 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 547 - Organic chemistry |
| dewey-raw | 547/.70454 |
| dewey-search | 547/.70454 |
| dewey-sort | 3547 570454 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik |
| discipline_str_mv | Chemie / Pharmazie Physik |
| format | Book |
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| id | DE-604.BV021263806 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:42:42Z |
| indexdate | 2024-07-09T20:34:10Z |
| institution | BVB |
| isbn | 9783540262107 3540262105 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014585015 |
| oclc_num | 61715044 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-11 |
| owner_facet | DE-384 DE-703 DE-11 |
| physical | XIII, 229 S. Ill., graph. Darst. 24 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Kröger, Martin Verfasser aut Models for polymeric and anisotropic liquids Martin Kröger Berlin ; Heidelberg ; New York Springer 2005 XIII, 229 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 675 Literaturverz. S. 205 - 215 Física larpcal Polymères cristallins - Modèles mathématiques Solutions de polymère - Modèles mathématiques Mathematisches Modell Crystalline polymers Mathematical models Polymer solutions Mathematical models Polymere Flüssigkeit (DE-588)4175229-6 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Anisotropie (DE-588)4002073-3 gnd rswk-swf Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Polymere Flüssigkeit (DE-588)4175229-6 s Anisotropie (DE-588)4002073-3 s Kinetische Theorie (DE-588)4030669-0 s Computersimulation (DE-588)4148259-1 s DE-604 Lecture notes in physics 675 (DE-604)BV000003166 675 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014585015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kröger, Martin Models for polymeric and anisotropic liquids Lecture notes in physics Física larpcal Polymères cristallins - Modèles mathématiques Solutions de polymère - Modèles mathématiques Mathematisches Modell Crystalline polymers Mathematical models Polymer solutions Mathematical models Polymere Flüssigkeit (DE-588)4175229-6 gnd Computersimulation (DE-588)4148259-1 gnd Anisotropie (DE-588)4002073-3 gnd Kinetische Theorie (DE-588)4030669-0 gnd |
| subject_GND | (DE-588)4175229-6 (DE-588)4148259-1 (DE-588)4002073-3 (DE-588)4030669-0 |
| title | Models for polymeric and anisotropic liquids |
| title_auth | Models for polymeric and anisotropic liquids |
| title_exact_search | Models for polymeric and anisotropic liquids |
| title_exact_search_txtP | Models for polymeric and anisotropic liquids |
| title_full | Models for polymeric and anisotropic liquids Martin Kröger |
| title_fullStr | Models for polymeric and anisotropic liquids Martin Kröger |
| title_full_unstemmed | Models for polymeric and anisotropic liquids Martin Kröger |
| title_short | Models for polymeric and anisotropic liquids |
| title_sort | models for polymeric and anisotropic liquids |
| topic | Física larpcal Polymères cristallins - Modèles mathématiques Solutions de polymère - Modèles mathématiques Mathematisches Modell Crystalline polymers Mathematical models Polymer solutions Mathematical models Polymere Flüssigkeit (DE-588)4175229-6 gnd Computersimulation (DE-588)4148259-1 gnd Anisotropie (DE-588)4002073-3 gnd Kinetische Theorie (DE-588)4030669-0 gnd |
| topic_facet | Física Polymères cristallins - Modèles mathématiques Solutions de polymère - Modèles mathématiques Mathematisches Modell Crystalline polymers Mathematical models Polymer solutions Mathematical models Polymere Flüssigkeit Computersimulation Anisotropie Kinetische Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014585015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT krogermartin modelsforpolymericandanisotropicliquids |