Fundamentals of Maxwell's kinetic theory of a simple monatomic gas: treated as a branch of rational mechanics
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Pr.
1980
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| Edition: | 1. print. |
| Series: | Pure and applied mathematics
83 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 593 S. |
| ISBN: | 0127013504 |
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| 245 | 1 | 0 | |a Fundamentals of Maxwell's kinetic theory of a simple monatomic gas |b treated as a branch of rational mechanics |
| 250 | |a 1. print. | ||
| 264 | 1 | |a New York [u.a.] |b Acad. Pr. |c 1980 | |
| 300 | |a 593 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 83 | |
| 650 | 4 | |a Gaz, Théorie cinétique des | |
| 650 | 7 | |a Kinetische gastheorie |2 gtt | |
| 650 | 7 | |a Matematica Aplicada A Psicologia |2 larpcal | |
| 650 | 4 | |a Kinetic theory of gases | |
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| 830 | 0 | |a Pure and applied mathematics |v 83 |w (DE-604)BV010177228 |9 83 | |
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Record in the Search Index
| _version_ | 1804136121830998016 |
|---|---|
| adam_text | Contents
Prologue xv
Acknowledgments xxi
Notation xxiii
List of Special Symbols xxv
Part A Continuum Thermomechanics
Chapter I Continuum Theories of Fluids
(i) Basic concepts. Field equations 3
(ii) Constitutive relations. The Navier-Stokes-Fourier theory of viscous
fluids 4
(iii) Thermodynamic quantities. The Maxwell number and the caloric 7
(iv) More general constitutive assumptions and principles 8
(v) Thermodynamics: The Clausius-Duhem inequality and its special
cases and generalizations 12
Chapter II The Stokes-Kirchhoff Gas, Some of Its
Peculiarities, and Some of Its Flows
(i) The Stokes-Kirchhoff and Euler-Hadamard theories of ideal gases 19
(ii) Some parameters that control dynamical similarity 21
(iii) The caloric of an ideal gas 22
(iv) Equilibrium 22
(v) Some particular homo-energetic flows: dilatation, affine flow, simple
shearing, extension 23
vii
Viii CONTENTS
Part B Basic Structures of the Kinetic Theory
Chapter III The Molecular Density, the Definitions of Gross
Fields, and the Equation of Evolution
(i) The molecular density and the number density 39
(ii) Expectations. The thirteen basic fields 41
(iii) The higher moments 45
(iv) The retrogressors 46
(v) The equation of evolution 49
Chapter IV Some Limits of Agreement between Kinetic
Theories and Classical Fluid Mechanics
(i) Failure of constitutive relations in the sense of continuum mechanics 51
(ii) Limitations on the shear viscosity 52 ,
(iii) Vanishing of the bulk viscosity 57
(iv) Disagreement between the kinetic theory and the Stokes-Kirchhoff
theory for flows in which T fe 1 57
Chapter V The Differential Operators of the Kinetic Theory
(i) The retrogressor and the retrogression reviewed 61
(ii) Differentiation along a trajectory. Mild and strong derivatives 62
(iii) Local forms of the equation of evolution 64
(iv) Moments of the strong derivative of a function 66
Chapter VI The Dynamics of Molecular Encounters
(i) Binary encounters 69
(ii) Summational invariants and the Boltzmann-Gronwall theorem 71
(iii) The encounter problem and its solutions 74
(iv) The encounter operator and its properties 84
Appendix A Proof of the lemma 88
I
Chapter VII The Maxwell Collisions Operator. Kinetic
Constitutive Relations. The Total CoUisions
Operator and Bilinear Form
(i) The collisions operator 91 ,
(ii) Kinetic constitutive quantities 93 ;
CONTENTS ix
(iii) Alternative forms of the collisions operator 95
(iv) The bilinear form 98
(v) Orthogonal invariance of the collisions operator and the bilinear form 101
(vi) Inconsistency of Maxwell s kinetic theory with Newtonian mechanics 102
Chapter VIII Boltzmann s Monotonicity Theorem. The
Maxwellian Density. Analogues of the Caloric
and Its Flux
(i) The Boltzmann monotonicity theorem 105
(ii) Properties of the Maxwellian density 107
(iii) Degree to which a Maxwellian expectation approximates a general one 112
(iv) The caloric of a kinetic gas: Boltzmann s field h 116
(v) Bounds for h and for its flux s 119
(vi) Grossly determined functions, momentally determined functions 126
Part C The Maxwell—Boltzmann Equation and Its Elementary
Consequences
Chapter IX The Maxwell-Boltzmann Equation. Maxwell s
Consistency Theorem and Equation of Transfer 131
Chapter X Kinetic Equilibrium and Gross Equilibrium.
Locally Maxwellian Solutions 137
Chapter XI Boltzmann s ff-Theorem
(i) The formal broad H-theorem and the formal narrow //-theorem 146
(ii) Comparison and contrast of the formal //-theorem with the
Clausius-Duhem inequality and the heat-bath inequality of
thermomechanics 149
(iii) The concept of a solid boundary in the kinetic theory 152
(iv) The formal narrow //-theorem or the heat-bath inequality as a
consequence of boundary conditions 161
(v) Traditional interpretation of the formal narrow //-theorem. The
ultra-narrow trend to equilibrium. Statement of corresponding rigorous
propositions 166
(vi) Difficulties faced in interpretation of the more general narrow
//-theorem and the strict trend to equilibrium 168
(vii) Lack of interpretation for the broad//-theorem 171
X CONTENTS
Part D Particular Molecular Models and Exact Solutions for
Moments
Chapter XII The Collisions Operator for Some Special Kinetic
Constitutive Relations, Especially Maxwellian
Molecules 175
Chapter XIII The Pressures and the Energy Flux in a Gas of
Maxwellian Molecules. Maxwell s Relaxation
Theorem and Evaluation of Viscosity and
Thermal Conductivity
(i) General equations for the pressures and energy flux 187
(ii) Maxwell s relaxation theorem 189 j
(iii) Implications of Maxwell s relaxation theorem on constitutive relations !
in the sense of continuum mechanics 192 :
(iv) Maxwell s evaluation of viscosity and thermal conductivity 193 ]
Chapter XIV Homo-energetic Simple Shearing of a Gas of
Maxwellian Molecules
(i) Homo-energetic simple shearing 197
(ii) The pressures as functions of time 199
(iii) The dominant pressures and their gross determination 202
(iv) Definition and rigorous evaluation of the viscosity of the kinetic gas 203
(v) Reduced viscometric functions of the Maxwellian gas 204 (
(vi) Comparison of the pressures as functions of time with their
counterparts according to the Stokes-Kirchhoff theory 205
(vii) Asymptotic forms for fast shearing or rarefied gases 207
(viii) Solution for the energy flux. Instability 208
(ix) Entropy. Dissipation 212
(x) The principal solutions 214
Chapter XV General Solution for the Pressures hi
Homo-energetic Affine Flows of a Gas of
Maxwellian Molecules ¦
(i) Affine flows in general 219
(ii) Homo-energetic dilatation 222
(iii) Homo-energetic extension, I. The general solution for the pressures 224
(iv) Homo-energetic extension, II. The principal solutions 227
(v) Homo-energetic extension, III. Asymptotic status of the
Stokes- Kirchhoff solution 231
(vi) Retrospect 233
CONTENTS Xi
Part E The System of Equations for the Moments
Chapter XVI The General System of Equations for the
Moments hi a Gas of Maxwellian Molecules.
Ikenberry s Theorem on the Structure of
Collisions Integrals
(i) Explicit collisions integrals for a gas of Maxwellian molecules 237
(ii) Ikenberry s theorem: The structure of collisions integrals 244
(iii) The general system of equations for the moments 249
Appendix A Integration formulae and the proof of Ikenberry s theorem 251
Appendix B Multi-indices 258
Chapter XVII Grad s Formal Evaluation of Collisions
Integrals, and His Method of Approximating
the Initial-value Problem
(i) Grad s expansion and equations of transfer for the Hermite coefficients 261
(ii) Contrast and comparison of Grad s formal expansion with Ikenberry s
theorem 270
(iii) Grad s method of truncation. His 13-moment system and his
20-moment system 272
(iv) Comparison of solutions of Grad s systems with corresponding exact
solutions for shearing 277
(v) The relaxation theorem for Grad s 13-moment system. Grad s
derivation of Enskog s first approximation to the viscosity and the
Maxwell number 278
Appendix A Conversion formulae 281
Appendix B Exact solutions of the Maxwell-Boltzmann equation for a gas
of Maxwellian molecules 284
Part F Existence, Uniqueness, and Qualitative Behavior
Chapter XVIII Existence Theory for the General
Initial-value Problem. Part I: Molecules with
Intermolecular Forces of Infinite Range
(i) Prolegomena to existence theory 295
(ii) Spatially homogeneous solutions for a gas of Maxwellian molecules:
existence, uniqueness, and the trend to equilibrium 297
(iii) Estimate of the rates of approach to equilibrium 299
(iv) Retrospect 302
Xii CONTENTS
Chapter XIX Convergence Theorems and the Domain of the
Collisions Operator
(i) Preliminaries 306
(ii) Restrictions on the growth of the integrand 307
(iii) Convergence theorems 309
(iv) Inverse Kth-power molecules 316
Chapter XX Existence Theory for the General Initial-value
Problem. Part II: Place-dependent Solutions
for Molecules with a Cut-off
(i) Integral forms of the Maxwell-Boltzmann equation 319
(ii) Survey of possibly place-dependent solutions 320
(iii) A class of body forces 323
(iv) Preliminary estimates 323
(v) Glikson s theorem 327
Chapter XXI Existence Theory for the General Initial-value
Problem. Part III: Spatially Homogeneous
Solutions for Molecules with a Cut-off
(i) Survey of spatially homogeneous solutions 335
(ii) General results on existence and regularity 338
(iii) A modified collisions operator and its properties 347
(iv) An existence theorem for spatially homogeneous solutions 349
(v) Proof of the ultra-narrow H-theorem 356
(vi) Proof of the ultra-narrow trend to equilibrium 363
Appendix A Estimation of fourth moments 368
Part G Grossly and Momentally Determined Solutions and
the Iterative Procedures of the Kinetic Theory
Chapter XXII Hilbert s Formal Iterative Procedure for
Calculating Gas-dynamic Solutions. The
Assertion of Gross Causality. The Hilbert
Mapping
(i) Hilbert s formal iterative procedure 375
(ii) Proof of effectiveness 380
(iii) Hilbert s assertion of gross causality 384
(iv) Properties of Hilbert s formal solutions. The Hilbert mapping 386
(v) Locally Maxwellian solutions 390
CONTENTS Xiii
(vi) Proof that Hilbert s solutions are grossly determined 394
(vii) Retrospect 395
Chapter XXIII Grossly Determined Solutions. The
Equations of Gross Determinism
(i) Gas-dynamic solutions. The importance of grossly determined
solutions 398
(ii) Methods of determining gas flows 401
(iii) The Maxwell-Boltzmann equation for grossly determined solutions 403
(iv) The equations of gross determinism and properties of gross determiners 405
(v) Principles of local action and the domain of the gross determiner 407
(vi) A space of functions for the principal moment 411
(vii) Gross determiners depending upon the body force. The generalized
equations of gross determinism and the equation of transfer for gross
determiners 413
(viii) Gross determinism for affine flows 420
Appendix A Calculus in Banach spaces 424
Chapter XXIV The Method of Stretched Fields for
Approximating Gross Determiners. Use of It
to Obtain the Results of Enskog s Procedure
(i) Enskog s procedure 430
(ii) The method of stretched fields 434
(iii) The basic expansion of gross determiners 437
(iv) Approximate gross determiners 441
(v) The expansion coefficients 445
(vi) Derivation of the iterative system for the gross determiner when b = 0 446
(vii) Structure of the iterative system. Proof of effectiveness 452
(viii) Properties of some of the expansion coefficients 455
(ix) The formulae of Enskog, Burnett, Chapman Cowling, and
Boltzmann 461
(x) Extension to take account of the body force 472
(xi) Explicit results for Maxwellian molecules 479
(xii) Explicit first approximations for general molecular models 481
(xiii) Retrospect 488
Appendix A Derivation of the iterative system 488
Appendix B Computational formulae 494
Chapter XXV The Maxwellian Iteration of Ikenberry
Truesdell
(i) Exact results to which Maxwellian iteration is applied 508
(ii) The scheme of Maxwellian iteration 512
(iii) Illustration of the idea of Maxwellian iteration, applied to an ordinary
differential equation 514
Xiv CONTENTS
(iv) The first two stages of Maxwellian iteration: The Maxwell second
approximation to P and its companion for q 515
(v) Comments on the results, origin, and nature of Maxwellian iteration 518
(vi) The third stage of Maxwellian iteration 523
(vii) Proof of effectiveness 524
(viii) Example: Homo-energetic simple shearing of a gas of Maxwellian
molecules 526
(ix) Atemporal Maxwellian iteration 528
(x) Use of differential iteration to generate and improve Grad s method of
truncation 537
(xi) Retrospect upon formal methods of approximation 539
Chapter XXVI Convergence and Divergence of Atemporal
Maxwellian Iteration in Flows for Which an
Exact Solution Is Known. Failure of the
Higher Iterates to Improve the Asymptotic
Approximation
(i) Homo-energetic affine flows in general 542
(ii) Homo-energetic dilatation 546
(iii) Homo-energetic simple shearing 546
(iv) Homo-energetic extension 548
(v) Failure of the classical approach to approximate solution 549
(vi) Retrospect 556
Epilogue 559
List of Works Cited 569
Index of Authors Cited 579
Index of Matters Treated 582
|
| adam_txt |
Contents
Prologue xv
Acknowledgments xxi
Notation xxiii
List of Special Symbols xxv
Part A Continuum Thermomechanics
Chapter I Continuum Theories of Fluids
(i) Basic concepts. Field equations 3
(ii) Constitutive relations. The Navier-Stokes-Fourier theory of viscous
fluids 4
(iii) Thermodynamic quantities. The Maxwell number and the caloric 7
(iv) More general constitutive assumptions and principles 8
(v) Thermodynamics: The Clausius-Duhem inequality and its special
cases and generalizations 12
Chapter II The Stokes-Kirchhoff Gas, Some of Its
Peculiarities, and Some of Its Flows
(i) The Stokes-Kirchhoff and Euler-Hadamard theories of ideal gases 19
(ii) Some parameters that control dynamical similarity 21
(iii) The caloric of an ideal gas 22
(iv) Equilibrium 22
(v) Some particular homo-energetic flows: dilatation, affine flow, simple
shearing, extension 23
vii
Viii CONTENTS
Part B Basic Structures of the Kinetic Theory
Chapter III The Molecular Density, the Definitions of Gross
Fields, and the Equation of Evolution
(i) The molecular density and the number density 39
(ii) Expectations. The thirteen basic fields 41
(iii) The higher moments 45
(iv) The retrogressors 46
(v) The equation of evolution 49
Chapter IV Some Limits of Agreement between Kinetic
Theories and Classical Fluid Mechanics
(i) Failure of constitutive relations in the sense of continuum mechanics 51
(ii) Limitations on the shear viscosity 52 ,
(iii) Vanishing of the bulk viscosity 57
(iv) Disagreement between the kinetic theory and the Stokes-Kirchhoff
theory for flows in which T fe 1 57
Chapter V The Differential Operators of the Kinetic Theory
(i) The retrogressor and the retrogression reviewed 61
(ii) Differentiation along a trajectory. Mild and strong derivatives 62
(iii) Local forms of the equation of evolution 64
(iv) Moments of the strong derivative of a function 66
Chapter VI The Dynamics of Molecular Encounters
(i) Binary encounters 69
(ii) Summational invariants and the Boltzmann-Gronwall theorem 71
(iii) The encounter problem and its solutions 74
(iv) The encounter operator and its properties 84
Appendix A Proof of the lemma 88
I
Chapter VII The Maxwell Collisions Operator. Kinetic
Constitutive Relations. The Total CoUisions
Operator and Bilinear Form
(i) The collisions operator 91 ,
(ii) Kinetic constitutive quantities 93 ;
CONTENTS ix
(iii) Alternative forms of the collisions operator 95
(iv) The bilinear form 98
(v) Orthogonal invariance of the collisions operator and the bilinear form 101
(vi) Inconsistency of Maxwell's kinetic theory with Newtonian mechanics 102
Chapter VIII Boltzmann's Monotonicity Theorem. The
Maxwellian Density. Analogues of the Caloric
and Its Flux
(i) The Boltzmann monotonicity theorem 105
(ii) Properties of the Maxwellian density 107
(iii) Degree to which a Maxwellian expectation approximates a general one 112
(iv) The caloric of a kinetic gas: Boltzmann's field h 116
(v) Bounds for h and for its flux s 119
(vi) Grossly determined functions, momentally determined functions 126
Part C The Maxwell—Boltzmann Equation and Its Elementary
Consequences
Chapter IX The Maxwell-Boltzmann Equation. Maxwell's
Consistency Theorem and Equation of Transfer 131
Chapter X Kinetic Equilibrium and Gross Equilibrium.
Locally Maxwellian Solutions 137
Chapter XI Boltzmann's ff-Theorem
(i) The formal broad H-theorem and the formal narrow //-theorem 146
(ii) Comparison and contrast of the formal //-theorem with the
Clausius-Duhem inequality and the heat-bath inequality of
thermomechanics 149
(iii) The concept of a solid boundary in the kinetic theory 152
(iv) The formal narrow //-theorem or the heat-bath inequality as a
consequence of boundary conditions 161
(v) Traditional interpretation of the formal narrow //-theorem. The
ultra-narrow trend to equilibrium. Statement of corresponding rigorous
propositions 166
(vi) Difficulties faced in interpretation of the more general narrow
//-theorem and the strict trend to equilibrium 168
(vii) Lack of interpretation for the broad//-theorem 171
X CONTENTS
Part D Particular Molecular Models and Exact Solutions for
Moments
Chapter XII The Collisions Operator for Some Special Kinetic
Constitutive Relations, Especially Maxwellian
Molecules 175
Chapter XIII The Pressures and the Energy Flux in a Gas of
Maxwellian Molecules. Maxwell's Relaxation
Theorem and Evaluation of Viscosity and
Thermal Conductivity
(i) General equations for the pressures and energy flux 187
(ii) Maxwell's relaxation theorem 189 j
(iii) Implications of Maxwell's relaxation theorem on constitutive relations !
in the sense of continuum mechanics 192 :
(iv) Maxwell's evaluation of viscosity and thermal conductivity 193 ]
Chapter XIV Homo-energetic Simple Shearing of a Gas of
Maxwellian Molecules
(i) Homo-energetic simple shearing 197
(ii) The pressures as functions of time 199
(iii) The dominant pressures and their gross determination 202
(iv) Definition and rigorous evaluation of the viscosity of the kinetic gas 203
(v) Reduced viscometric functions of the Maxwellian gas 204 (
(vi) Comparison of the pressures as functions of time with their '
counterparts according to the Stokes-Kirchhoff theory 205
(vii) Asymptotic forms for fast shearing or rarefied gases 207
(viii) Solution for the energy flux. Instability 208
(ix) Entropy. Dissipation 212
(x) The principal solutions 214
Chapter XV General Solution for the Pressures hi
Homo-energetic Affine Flows of a Gas of
Maxwellian Molecules ¦
(i) Affine flows in general 219
(ii) Homo-energetic dilatation 222
(iii) Homo-energetic extension, I. The general solution for the pressures 224
(iv) Homo-energetic extension, II. The principal solutions 227
(v) Homo-energetic extension, III. Asymptotic status of the
Stokes- Kirchhoff solution 231
(vi) Retrospect 233
CONTENTS Xi
Part E The System of Equations for the Moments
Chapter XVI The General System of Equations for the
Moments hi a Gas of Maxwellian Molecules.
Ikenberry's Theorem on the Structure of
Collisions Integrals
(i) Explicit collisions integrals for a gas of Maxwellian molecules 237
(ii) Ikenberry's theorem: The structure of collisions integrals 244
(iii) The general system of equations for the moments 249
Appendix A Integration formulae and the proof of Ikenberry's theorem 251
Appendix B Multi-indices 258
Chapter XVII Grad's Formal Evaluation of Collisions
Integrals, and His Method of Approximating
the Initial-value Problem
(i) Grad' s expansion and equations of transfer for the Hermite coefficients 261
(ii) Contrast and comparison of Grad's formal expansion with Ikenberry's
theorem 270
(iii) Grad's method of truncation. His 13-moment system and his
20-moment system 272
(iv) Comparison of solutions of Grad's systems with corresponding exact
solutions for shearing 277
(v) The relaxation theorem for Grad's 13-moment system. Grad's
derivation of Enskog's first approximation to the viscosity and the
Maxwell number 278
Appendix A Conversion formulae 281
Appendix B Exact solutions of the Maxwell-Boltzmann equation for a gas
of Maxwellian molecules 284
Part F Existence, Uniqueness, and Qualitative Behavior
Chapter XVIII Existence Theory for the General
Initial-value Problem. Part I: Molecules with
Intermolecular Forces of Infinite Range
(i) Prolegomena to existence theory 295
(ii) Spatially homogeneous solutions for a gas of Maxwellian molecules:
existence, uniqueness, and the trend to equilibrium 297
(iii) Estimate of the rates of approach to equilibrium 299
(iv) Retrospect 302
Xii CONTENTS
Chapter XIX Convergence Theorems and the Domain of the
Collisions Operator
(i) Preliminaries 306
(ii) Restrictions on the growth of the integrand 307
(iii) Convergence theorems 309
(iv) Inverse Kth-power molecules 316
Chapter XX Existence Theory for the General Initial-value
Problem. Part II: Place-dependent Solutions
for Molecules with a Cut-off
(i) Integral forms of the Maxwell-Boltzmann equation 319
(ii) Survey of possibly place-dependent solutions 320
(iii) A class of body forces 323
(iv) Preliminary estimates 323
(v) Glikson's theorem 327
Chapter XXI Existence Theory for the General Initial-value
Problem. Part III: Spatially Homogeneous
Solutions for Molecules with a Cut-off
(i) Survey of spatially homogeneous solutions 335
(ii) General results on existence and regularity 338
(iii) A modified collisions operator and its properties 347
(iv) An existence theorem for spatially homogeneous solutions 349
(v) Proof of the ultra-narrow H-theorem 356
(vi) Proof of the ultra-narrow trend to equilibrium 363
Appendix A Estimation of fourth moments 368
Part G Grossly and Momentally Determined Solutions and
the Iterative Procedures of the Kinetic Theory
Chapter XXII Hilbert's Formal Iterative Procedure for
Calculating Gas-dynamic Solutions. The
Assertion of Gross Causality. The Hilbert
Mapping
(i) Hilbert's formal iterative procedure 375
(ii) Proof of effectiveness 380
(iii) Hilbert's assertion of gross causality 384
(iv) Properties of Hilbert's formal solutions. The Hilbert mapping 386
(v) Locally Maxwellian solutions 390
CONTENTS Xiii
(vi) Proof that Hilbert's solutions are grossly determined 394
(vii) Retrospect 395
Chapter XXIII Grossly Determined Solutions. The
Equations of Gross Determinism
(i) Gas-dynamic solutions. The importance of grossly determined
solutions 398
(ii) Methods of determining gas flows 401
(iii) The Maxwell-Boltzmann equation for grossly determined solutions 403
(iv) The equations of gross determinism and properties of gross determiners 405
(v) Principles of local action and the domain of the gross determiner 407
(vi) A space of functions for the principal moment 411
(vii) Gross determiners depending upon the body force. The generalized
equations of gross determinism and the equation of transfer for gross
determiners 413
(viii) Gross determinism for affine flows 420
Appendix A Calculus in Banach spaces 424
Chapter XXIV The Method of Stretched Fields for
Approximating Gross Determiners. Use of It
to Obtain the Results of Enskog's Procedure
(i) Enskog's procedure 430
(ii) The method of stretched fields 434
(iii) The basic expansion of gross determiners 437
(iv) Approximate gross determiners 441
(v) The expansion coefficients 445
(vi) Derivation of the iterative system for the gross determiner when b = 0 446
(vii) Structure of the iterative system. Proof of effectiveness 452
(viii) Properties of some of the expansion coefficients 455
(ix) The formulae of Enskog, Burnett, Chapman Cowling, and
Boltzmann 461
(x) Extension to take account of the body force 472
(xi) Explicit results for Maxwellian molecules 479
(xii) Explicit first approximations for general molecular models 481
(xiii) Retrospect 488
Appendix A Derivation of the iterative system 488
Appendix B Computational formulae 494
Chapter XXV The Maxwellian Iteration of Ikenberry
Truesdell
(i) Exact results to which Maxwellian iteration is applied 508
(ii) The scheme of Maxwellian iteration 512
(iii) Illustration of the idea of Maxwellian iteration, applied to an ordinary
differential equation 514
Xiv CONTENTS
(iv) The first two stages of Maxwellian iteration: The Maxwell second
approximation to P and its companion for q 515
(v) Comments on the results, origin, and nature of Maxwellian iteration 518
(vi) The third stage of Maxwellian iteration 523
(vii) Proof of effectiveness 524
(viii) Example: Homo-energetic simple shearing of a gas of Maxwellian
molecules 526
(ix) Atemporal Maxwellian iteration 528
(x) Use of differential iteration to generate and improve Grad's method of
truncation 537
(xi) Retrospect upon formal methods of approximation 539
Chapter XXVI Convergence and Divergence of Atemporal
Maxwellian Iteration in Flows for Which an
Exact Solution Is Known. Failure of the
Higher Iterates to Improve the Asymptotic
Approximation
(i) Homo-energetic affine flows in general 542
(ii) Homo-energetic dilatation 546
(iii) Homo-energetic simple shearing 546
(iv) Homo-energetic extension 548
(v) Failure of the classical approach to approximate solution 549
(vi) Retrospect 556
Epilogue 559
List of Works Cited 569
Index of Authors Cited 579
Index of Matters Treated 582 |
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| author | Truesdell, Clifford 1919-2000 Muncaster, Robert G. |
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| edition | 1. print. |
| format | Book |
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| id | DE-604.BV022147865 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:18:01Z |
| indexdate | 2024-07-09T20:51:22Z |
| institution | BVB |
| isbn | 0127013504 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015362503 |
| oclc_num | 4638938 |
| open_access_boolean | |
| owner | DE-12 DE-706 DE-83 |
| owner_facet | DE-12 DE-706 DE-83 |
| physical | 593 S. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Acad. Pr. |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Truesdell, Clifford 1919-2000 Verfasser (DE-588)121263983 aut Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics 1. print. New York [u.a.] Acad. Pr. 1980 593 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 83 Gaz, Théorie cinétique des Kinetische gastheorie gtt Matematica Aplicada A Psicologia larpcal Kinetic theory of gases Kinetische Gastheorie (DE-588)4163881-5 gnd rswk-swf Kinetische Gastheorie (DE-588)4163881-5 s DE-604 Muncaster, Robert G. Verfasser aut Pure and applied mathematics 83 (DE-604)BV010177228 83 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015362503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Truesdell, Clifford 1919-2000 Muncaster, Robert G. Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics Pure and applied mathematics Gaz, Théorie cinétique des Kinetische gastheorie gtt Matematica Aplicada A Psicologia larpcal Kinetic theory of gases Kinetische Gastheorie (DE-588)4163881-5 gnd |
| subject_GND | (DE-588)4163881-5 |
| title | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_auth | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_exact_search | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_exact_search_txtP | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_full | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_fullStr | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_full_unstemmed | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_short | Fundamentals of Maxwell's kinetic theory of a simple monatomic gas |
| title_sort | fundamentals of maxwell s kinetic theory of a simple monatomic gas treated as a branch of rational mechanics |
| title_sub | treated as a branch of rational mechanics |
| topic | Gaz, Théorie cinétique des Kinetische gastheorie gtt Matematica Aplicada A Psicologia larpcal Kinetic theory of gases Kinetische Gastheorie (DE-588)4163881-5 gnd |
| topic_facet | Gaz, Théorie cinétique des Kinetische gastheorie Matematica Aplicada A Psicologia Kinetic theory of gases Kinetische Gastheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015362503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010177228 |
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