Rational extended thermodynamics:
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| Previous Title: | Müller/Ruggeri Extended thermodynamics |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
1998
|
| Edition: | 2. ed. |
| Series: | Springer tracts in natural philosophy
37 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 396 S. graph. Darst. |
| ISBN: | 0387983732 |
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MARC
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| 100 | 1 | |a Müller, Ingo |d 1936- |e Verfasser |0 (DE-588)128217863 |4 aut | |
| 245 | 1 | 0 | |a Rational extended thermodynamics |c Ingo Müller ; Tommaso Ruggeri |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |c 1998 | |
| 300 | |a XV, 396 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer tracts in natural philosophy |v 37 | |
| 650 | 4 | |a Fluids |x Thermal properties | |
| 650 | 4 | |a Gases |x Thermal properties | |
| 650 | 4 | |a Second sound | |
| 650 | 4 | |a Thermodynamics | |
| 650 | 0 | 7 | |a Kinetische Gastheorie |0 (DE-588)4163881-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtgleichgewichtsthermodynamik |0 (DE-588)4130850-5 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Kinetische Gastheorie |0 (DE-588)4163881-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Ruggeri, Tommaso |d 1947- |e Verfasser |0 (DE-588)1084792990 |4 aut | |
| 780 | 0 | 0 | |i 1. Aufl. u.d.T. |a Müller/Ruggeri |t Extended thermodynamics |
| 830 | 0 | |a Springer tracts in natural philosophy |v 37 |w (DE-604)BV000692404 |9 37 | |
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| _version_ | 1820851936300105728 |
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CONTENTS
PREFACE
V
1
TOUR
D
'
HORIZON
1
2
EARLY
VERSION
OF
EXTENDED
THERMODYNAMICS
AND
KINETIC
THEORY
OF
GASES
9
1
PARADOXES
OF
HEAT
CONDUCTION
AND
SHEAR
DIFFUSION
.
10
1.1
HEURISTIC
DERIVATION
OF
THE
LAWS
OF
FOURIER
AND
NAVIER-STOKES
.
10
1.2
PARABOLIC
LAWS
OF
HEAT
CONDUCTION
AND
SHEAR
DIFFUSION
.
11
2
PARADOX
REMOVED
.
12
2.1
THE
CATTANEO
EQUATION
.
12
2.2
EXTENDED
TIP
.
14
2.3
FINITE
PULSE
SPEEDS
IN
EXTENDED
TIP
.
16
2.4
CONCLUSION
AND
CRITICISM
.
18
3
KINETIC
THEORY
OF
MONATOMIC
GASES
.
19
3.1
BOLTZMANN
EQUATION
AND
MOMENTS
.
19
3.2
EQUATIONS
OF
BALANCE
FOR
MOMENTS
.
20
3.3
BALANCE
OF
ENTROPY
AND
POSSIBLE
EQUILIBRIA
.
22
3.4
THE
GRAD
DISTRIBUTION
.
23
3.5
ENTROPY
AND
ENTROPY
FLUX
IN
GRAD
'
S
13-MOMENT
THEORY
.
24
3.6
PHENOMENOLOGICAL
EQUATIONS
DERIVED
FROM
THE
KINETIC
THEORY
.
24
3.7
PULSE
SPEEDS
.
26
3.8
CONCLUSIONS
.
26
3
FORMAL
STRUCTURE
OF
EXTENDED
THERMODYNAMICS
27
1
FIELD
EQUATIONS
.
28
1.1
THERMODYNAMIC
PROCESSES
AND
PRINCIPLES
OF
THE
CONSTITUTIVE
THEORY
.
28
1.2
UNIVERSAL
PRINCIPLES
OF
THE
CONSTITUTIVE
THEORY
.
28
2
ENTROPY
INEQUALITY
AND
SYMMETRIC
HYPERBOLIC
SYSTEMS
.
29
2.1
EXPLOITATION
OF
THE
ENTROPY
INEQUALITY
.
29
2.2
SYMMETRIC
HYPERBOLIC
FIELD
EQUATIONS
.
31
2.3
DISCUSSION
.
31
2.4
CHARACTERISTIC
SPEEDS
.
32
3
MAIN
SUBSYSTEMS
.
33
3.1
CONSTRAINTS
ON
THE
MAIN
FIELD
.
33
3.2
A
MAIN
SUBSYSTEM
IMPLIES
AN
ENTROPY
INEQUALITY
.
33
3.3
A
MAIN
SUBSYSTEM
IS
SYMMETRIC
HYPERBOLIC
.
34
VIII
CONTENTS
3.4
CHARACTERISTIC
SPEEDS
OF
THE
SUBSYSTEMS
.
34
3.5
OTHER
SUBSYSTEMS
.
35
4
GALILEAN
INVARIANCE
.
35
4.1
TENSORS,
GALILEAN
TENSORS,
AND
EUCLIDEAN
TENSORS
.
35
4.2
PRINCIPLE
OF
RELATIVITY
.
36
4.3
EXPLOITATION
OF
THE
PRINCIPLE
OF
RELATIVITY
FOR
THE
ENTROPY
BALANCE
.
37
4.4
EXPLOITATION
OF
THE
PRINCIPLE
OF
RELATIVITY
FOR
THE
FIELD
EQUATIONS
.
37
4.5
FIELD
EQUATIONS
FOR
INTERNAL
QUANTITIES
.
38
4.6
GALILEI
INVARIANCE
FOR
SUBSYSTEMS
.
38
4.7
GALILEAN
INVARIANCE
AND
ENTROPY
PRINCIPLE
.
39
4.8
EXPLICIT
VELOCITY
DEPENDENCE
OF
CONSTITUTIVE
QUANTITIES.
THE
DETERMINA
TION
OF
A
R
40
5
THERMODYNAMICS
OF
AN
EULER
FLUID
.
42
5.1
THE
EULER
FLUID
.
43
5.2
LAGRANGE
MULTIPLIERS
.
44
5.3
INTERNAL
LAGRANGE
MULTIPLIERS
.
45
5.4
ABSOLUTE
TEMPERATURE
.
45
5.5
VECTOR
POTENTIAL
.
46
5.6
CONVEXITY
.
47
5.7
CHARACTERISTIC
SPEED
.
47
5.8
SUBSYSTEMS
.
47
5.9
DISCUSSION
.
49
4
EXTENDED
THERMODYNAMICS
OF
MONATOMIC
GASES
51
1
THE
EQUATIONS
OF
EXTENDED
THERMODYNAMICS
OF
MONATOMIC
GASES
.
52
1.1
THERMODYNAMIC
PROCESSES
.
52
1.2
DISCUSSION
.
53
1.3
GALILEAN
INVARIANCE.
CONVECTIVE
AND
NONCONVECTIVE
FLUXES
.
53
1.4
EUCLIDEAN
INVARIANCE.
INERTIAL
EFFECTS
.
55
2
CONSTITUTIVE
THEORY
.
56
2.1
RESTRICTIVE
PRINCIPLES
.
56
2.2
EXPLOITATION
OF
THE
PRINCIPLE
OF
MATERIAL
FLAME-INDIFFERENCE
.
58
2.3
EXPLOITATION
OF
THE
ENTROPY
PRINCIPLE
.
59
2.4
EXPLOITATION
OF
THE
REQUIREMENT
OF
CONVEXITY
AND
CAUSALITY
.
67
3
FIELD
EQUATIONS
AND
THE
THERMODYNAMIC
LIMIT
.
67
3.1
FIELD
EQUATIONS
.
67
3.2
THE
THERMODYNAMIC
LIMIT
.
69
3.3
THE
FRAME
DEPENDENCE
OF
THE
HEAT
FLUX
.
71
3.4
MATERIAL
FRAME
INDIFFERENCE
IN
ORDINARY
AND
EXTENDED
THERMODYNAMICS
73
4
THERMAL
EQUATIONS
OF
STATE
AND
IDEAL
GASES
.
73
4.1
THE
CLASSICAL
IDEAL
GAS
.
73
4.2
COMPARISON
WITH
THE
KINETIC
THEORY
.
74
4.3
COMPARISON
WITH
EXTENDED
TIP
.
75
4.4
DEGENERATE
IDEAL
GASES
.
75
CONTENTS
IX
5
THERMODYNAMICS
OF
MIXTURES
OF
EULER
FLUIDS
79
1
ORDINARY
THERMODYNAMICS
OF
MIXTURES
(TIP)
.
80
1.1
CONSTITUTIVE
EQUATIONS
.
80
1.2
PARADOX
OF
DIFFUSION
.
83
2
EXTENDED
THERMODYNAMICS
OF
MIXTURES
OF
EULER
FLUIDS
.
84
2.1
BALANCE
EQUATIONS
.
84
2.2
THERMODYNAMIC
PROCESSES
.
.
.
85
2.3
CONSTITUTIVE
THEORY
.
86
2.4
SUMMARY
OF
RESULTS
.
91
2.5
WAVE
PROPAGATION
IN
A
NONREACTING
BINARY
MIXTURE
.
92
2.6
LANDAU
EQUATIONS.
FIRST
AND
SECOND
SOUND
IN
HE
II
.
96
3
ORDINARY
AND
EXTENDED
THERMODYNAMICS
OF
MIXTURES
.
99
3.1
THE
LAWS
OF
FICK
AND
FOURIER
IN
EXTENDED
THERMODYNAMICS
.
99
3.2
ONSAGER
RELATIONS
.
101
3.3
INERTIAL
CONTRIBUTION
TO
THE
LAWS
OF
DIFFUSION
.
103
6
RELATIVISTIC
THERMODYNAMICS
105
1
BALANCE
EQUATIONS
AND
CONSTITUTIVE
RESTRICTIONS
.
106
1.1
THERMODYNAMIC
PROCESSES
.
106
1.2
PRINCIPLES
OF
THE
CONSTITUTIVE
THEORY
.
107
2
CONSTITUTIVE
THEORY
.
108
2.1
SCOPE
AND
STRUCTURE
.
108
2.2
LAGRANGE
MULTIPLIERS
AND
THE
VECTOR
POTENTIAL.
STEP
I
.
108
2.3
PRINCIPLE
OF
RELATIVITY
AND
LINEAR
REPRESENTATIONS.
STEP
II
.
110
2.4
STRESS
DEVIATOR,
HEAT
FLUX,
AND
DYNAMIC
PRESSURE.
STEP
III
.
ILL
2.5
FUGACITY
AND
ABSOLUTE
TEMPERATURE.
STEP
IV
.
112
2.6
LINEAR
RELATIONS
BETWEEN
LAGRANGE
MULTIPLIERS
AND
N,
U
A
,T^
AB
\7R,Q
A
,E.
STEP
V
.
114
2.7
THE
LINEAR
FLUX
TENSOR.
STEP
VI
.
116
2.8
THE
ENTROPY
FLUX
VECTOR.
STEP
VII
.
117
2.9
RESIDUAL
INEQUALITY.
STEP
VIII
.
118
2.10
CAUSALITY
AND
CONVEXITY.
STEP
IX
.
118
2.11
SUMMARY
OF
RESULTS.
STEP
X
.
120
3
IDENTIFICATION
OF
VISCOSITIES
AND
HEAT-CONDUCTIVITY
.
123
3.1
EXTENDED
THERMODYNAMICS
AND
ORDINARY
THERMODYNAMICS
.
123
3.2
TRANSITION
FROM
EXTENDED
TO
ORDINARY
THERMODYNAMICS
.
124
4
SPECIFIC
RESULTS
FOR
RELATIVISTIC
AND
DEGENERATE
GASES
.
126
4.1
EQUILIBRIUM
DISTRIBUTION
FUNCTION
.
126
4.2
THE
DEGENERATE
RELATIVISTIC
GAS
.
127
4.3
NONDEGENERATE
RELATIVISTIC
GAS
.
131
4.4
DEGENERATE
NONRELATIVISTIC
GAS
.
133
4.5
NONDEGENERATE
NONRELATIVISTIC
GAS
.
135
4.6
STRONGLY
DEGENERATE
RELATIVISTIC
FERMI
GAS
.
137
4.7
A
REMARK
ON
THE
STRONGLY
DEGENERATE
RELATIVISTIC
BOSE
GAS
.
139
4.8
EQUILIBRIUM
PROPERTIES
OF
AN
ULTRARELATIVISTIC
GAS
.
140
5
AN
APPLICATION:
THE
MASS
LIMIT
OF
A
WHITE
DWARF
.
140
6
THE
RELATIVISTIC
KINETIC
THEORY
FOR
NONDEGENERATE
GASES
.
145
X
CONTENTS
6.1
BOLTZMANN-CHERNIKOV
EQUATION
.
145
6.2
EQUATIONS
OF
TRANSFER
.
146
6.3
EQUATIONS
OF
BALANCE
FOR
PARTICLE
NUMBER,
ENERGY-MOMENTUM,
FLUXES,
AND
ENTROPY
.
147
6.4
MAXWELL-JIITTNER
DISTRIBUTION,
EQUILIBRIUM
PROPERTIES
.
147
6.5
POSSIBLE
THERMODYNAMIC
FIELDS
IN
EQUILIBRIUM
.
148
7
THE
NONRELATIVISTIC
LIMIT
OF
RELATIVISTIC
THERMODYNAMICS
.
149
7.1
THE
PROBLEM
.
149
7.2
VARIABLES
AND
CONSTITUTIVE
QUANTITIES
.
150
7.3
THE
DYNAMIC
PRESSURE
.
152
7.4
ORDER
OF
MAGNITUDE
OF
THE
DYNAMIC
PRESSURE
.
153
7
EXTENDED
THERMODYNAMICS
OF
REACTING
MIXTURES
155
1
MOTIVATION,
RESULTS,
AND
DISCUSSION
.
156
1.1
MOTIVATION
.
156
1.2
RESULTS
.
157
1.3
DISCUSSION
.
159
2
FIELDS
.
160
2.1
A
CONVENTIONAL
CHOICE
.
160
2.2
ABSOLUTE
TEMPERATURE,
FUGACITIES,
AND
CHEMICAL
AFFINITY
.
160
2.3
SUMMARY
OF
FIELDS
.
162
3
FIELD
EQUATION
.
163
3.1
BALANCE
LAWS
.
163
3.2
CONSTITUTIVE
THEORY
.
163
3.3
PRINCIPLE
OF
RELATIVITY
.
164
4
ENTROPY
INEQUALITY
.
164
4.1
LAGRANGE
MULTIPLIERS
.
164
4.2
EXPLOITATION
.
165
5
NONRELATIVISTIC
LIMIT
.
.
.
165
5.1
DISCUSSION
.
165
5.2
DYNAMIC
PRESSURE
AND
BULK
VISCOSITY
.
167
5.3
THERMAL
CONDUCTIVITY
AND
VISCOSITY
.
168
8
WAVES
IN
EXTENDED
THERMODYNAMICS
171
1
HYPERBOLICITY
AND
SYMMETRIC
HYPERBOLIC
SYSTEMS
.
172
1.1
HYPERBOLICITY
IN
THE
T-DIRECTION
.
172
1.2
SYMMETRIC
HYPERBOLIC
SYSTEMS
.
172
2
LINEAR
WAVES
.
173
2.1
PLANE
HARMONIC
WAVES,
THE
DISPERSION
RELATION
.
173
2.2
THE
HIGH-FREQUENCY
LIMIT
.
174
2.3
HIGHER-ORDER
TERMS
.
175
2.4
LINEAR
WAVES
IN
EXTENDED
THERMODYNAMICS
.
176
3
HYPERBOLICITY
AND
NONLINEAR
WAVES
.
178
3.1
THE
CHARACTERISTIC
POLYNOMIAL
.
178
3.2
REGION
OF
HYPERBOLICITY
.
179
4
ACCELERATION
WAVES
.
181
4.1
AMPLITUDE
OF
DISCONTINUITY
WAVES
.
181
CONTENTS
XI
4.2
GROWTH
AND
DECAY
.
183
4.3
EVOLUTION
OF
AMPLITUDE
IN
EXTENDED
THERMODYNAMICS
.
184
4.4
ACCELERATION
WAVES
IN
RELATIVISTIC
EXTENDED
THERMODYNAMICS
.
186
5
WEAK
SOLUTIONS
AND
SHOCK
WAVES
.
187
5.1
WEAK
SOLUTIONS
.
187
5.2
RANKINE-HUGONIOT
EQUATIONS
.
187
5.3
SHOCKS
IN
EXTENDED
THERMODYNAMICS
.
189
5.4
SELECTION
RULES
FOR
PHYSICAL
SHOCKS.
THE
ENTROPY
GROWTH
CONDITION.
.
.
.
193
5.5
SELECTION
RULES
FOR
PHYSICAL
SHOCKS.
THE
LAX
CONDITIONS
.
193
5.6
LAX
CONDITION
IN
EXTENDED
THERMODYNAMICS
.
194
9
EXTENDED
THERMODYNAMICS
OF
MOMENTS
197
1
FIELD
EQUATIONS
FOR
MOMENTS
.
198
1.1
DENSITIES,
FLUXES,
AND
PRODUCTIONS
AS
MOMENTS
OF
THE
PHASE
DENSITY
.
198
1.2
EXTENDED
THERMODYNAMICS
OF
MOMENTS
.
199
1.3
SPECIFIC
PHASE
DENSITIES
.
201
1.4
FIELD
EQUATIONS
FOR
A
Q
AND
EQUATIONS
FOR
U
A
NEAR
EQUILIBRIUM
.
201
1.5
THE
CASE
N=3:
AN
ILLUSTRATION
.
203
1.6
FIELD
EQUATIONS
FOR
N=13,
14,
20,
21,
26,
35
.
205
2
CHARACTERISTIC
SPEEDS
.
208
2.1
FIELD
EQUATIONS
NEAR
EQUILIBRIUM
.
208
2.2
PULSE
SPEED
.
208
2.3
DISCUSSION
.
211
2.4
THE
RELATIVISTIC
CASE;
SPEEDS
SMALLER
THAN
C
.
211
3
MEAN
EIGENFUNCTIONS
.
212
3.1
EIGENFUNCTIONS
AND
EIGENVALUES
.
212
3.2
MEAN
EIGENFUNCTIONS
AS
THE
MAIN
FIELD
.
215
3.3
LINEAR
FIELD
EQUATIONS
FOR
THE
MEAN
EIGENFUNCTIONS
.
217
4
MAXIMIZATION
OF
ENTROPY
.
218
4.1
MAXIMIZING
ENTROPY
.
219
4.2
MAXIMIZING
ENTROPY
IS
EQUIVALENT
TO
EXTENDED
THERMODYNAMICS
OF
MOMENTS219
10
EXTENDED
THERMODYNAMICS
AND
LIGHT
SCATTERING
221
1
BASIC
ELECTRODYNAMICS
.
222
1.1
DISTANT
FIELD
APPROXIMATION
.
222
1.2
INCIDENT
PLANE
HARMONIC
WAVE
.
223
2
A
MODICUM
OF
FLUCTUATION
THEORY
.
225
2.1
EXPECTATION
VALUES
.
225
2.2
TEMPORAL
EVOLUTION
OF
A
FLUCTUATION
.
230
2.3
AUTOCORRELATION
OF
E
'
(R,T)
.
231
3
MEASURING
THE
SPECTRAL
DENSITY
.
233
3.1
SIGNAL
AND
SPECTRAL
DENSITY
.
233
3.2
MEASURED
DATA
AND
THEIR
DEPENDENCE
ON
PRESSURE
.
236
4
NAVIER-STOKES-FOURIER
FLUID
.
237
4.1
DYNAMIC
FORM
FACTOR
.
237
4.2
AN
ALTERNATIVE
FORM
OF
THE
DYNAMIC
FORM
FACTOR.
ALSO:
AN
APPROXIMATE
FORM
FOR
FORWARD
SCATTERING
.
239
XII
CONTENTS
4.3
GRAPHICAL
REPRESENTATION
OF
THE
DYNAMIC
FORM
FACTOR
FOR
A
MONATOMIC
IDEAL
GAS
.
240
4.4
COMPARISON
WITH
EXPERIMENTAL
DATA
.
242
4.5
AUTOCORRELATION
.
243
4.6
HEAT
AND
SOUND
MODES
.
243
5
EXTENDED
THERMODYNAMICS
.
245
5.1
INTRODUCING
EXTENDED
THERMODYNAMICS.
THE
CASE
OF
13
MOMENTS
.
245
5.2
DYNAMIC
FORM
FACTORS
FOR
N=20,
35,
84
.
247
5.3
HEAT
AND
SOUND
MODES
IN
EXTENDED
THERMODYNAMICS
.
250
5.4
HIGHER
MOMENTS
BY
METHOD
OF
EIGENFUNCTIONS
.
250
5.5
DYNAMIC
FORM
FACTORS
FOR
MANY
MOMENTS
.
254
5.6
EVALUATION
OF
MOMENT
THEORIES
.
254
5.7
CHARACTERISTIC
SPEEDS
.
257
5.8
MORE
EXPERIMENTAL
AND
THEORETICAL
EVIDENCE
.
258
6
EXTRAPOLATION
OF
S(Q,U?)
FOR
Y
-
YY
0
.
258
6.1
THE
PROBLEM
.
258
6.2
THE
BOLTZMANN
EQUATION
IN
THE
KROOK
APPROXIMATION
.
261
6.3
THE
DYNAMIC
FORM
FACTOR
S(Q,
W);
GENERAL
FORMULA
.
261
6.4
FLUCTUATIONS
IN
PHASE
SPACE
.
261
6.5
THE
DYNAMIC
FORM
FACTOR
S(Q,UI);
SPECIFIC
FORM
.
263
6.6
DISCUSSION
.
264
11
TESTING
EXTENDED
THERMODYNAMICS
BY
SOUND
265
1
BASIC
ACOUSTICS
.
266
1.1
HOW
THE
ACOUSTIC
RESONATOR
MEASURES
PHASE
SPEEDS
IN
PRINCIPLE
.
266
1.2
PIEZOELECTRIC
TRANSDUCER
AND
THE
MECHANICAL
IMPEDANCE
.
267
1.3
EXTERNAL
MECHANICAL
IMPEDANCE
AND
WAVELENGTH
.
269
1.4
DIFFICULTIES
WITH
MANY
MODES
AND
DAMPING
.
269
2
DISPERSION
RELATIONS
.
270
2.1
NAVIER-STOKES-FOURIER
THEORY
.
270
2.2
EXTENDED
THERMODYNAMICS
OF
13
FIELDS
.
271
2.3
EXTENDED
THERMODYNAMICS
WITH
MANY
VARIABLES
.
273
2.4
CONCLUSION
AND
ESTIMATE
.
273
3
MAXIMUM
SPEED
.
274
3.1
MODES
OF LEAST
DAMPING
.
274
3-2
THE
MAXIMUM
SPEED
.
275
12
STRUCTURE
OF
SHOCK
WAVES
277
1
EXPERIMENTAL
EVIDENCE
.
278
2
REVIEW
OF
PREVIOUS
WORK
.
279
2.1
RANKINE-HUGONIOT
RELATIONS
.
279
2.2
BECKER
'
S
SOLUTIONS
.
281
2.3
SINGULAR
PERTURBATION
ANALYSIS
.
283
2.4
NUMERICAL
SOLUTION
BY
GILBARG
AND
PAOLUCCI
.
284
2.5
THE
13-MOMENT
THEORY
BY
GRAD
.
284
2.6
THE
13-MOMENT
THEORY
BY
ANILE
&
MAJORANA
.
285
2.7
CRITICISM
OF
MOMENT
METHODS
FOR
SHOCK
STRUCTURE
.
285
CONTENTS
XIII
2.8
ALTERNATIVE
METHODS
FOR
SHOCK
STRUCTURE
CALCULATIONS
.
286
3
PRELIMINARIES
ON
SINGULAR
POINTS
AND
CHARACTERISTIC
SPEEDS
.
286
3.1
FIELD
EQUATIONS
AND
BOUNDARY
VALUES
.
286
3.2
SINGULAR
POINTS
AND
STATIONARY
POINTS
.
287
3.3
THE
SINGULARITIES
D
=
0
.
288
3.4
REGULAR
AND
IRREGULAR
SINGULARITIES
.
289
4
NUMERICAL
CALCULATION
OF
THE
SHOCK
STRUCTURE
.
290
4.1
INITIAL
AND
BOUNDARY
VALUE
PROBLEMS
.
290
4.2
ALGORITHM
FOR
THE
INITIAL
VALUE
PROBLEM
.
291
4.3
ALGORITHM
FOR
THE
BOUNDARY
VALUE
PROBLEM
.
294
4.4
THE
13-MOMENT
CASE
.
294
4.5
THE
14-MOMENT
CASE
.
297
4.6
THE
21-MOMENT
CASE
.
302
5
CONCLUSION
.
305
6
ADDENDUM
ON
INITIAL
VALUE
PROBLEM
FOR
13
MOMENTS
.
305
7
QUANTITATIVE
RESULTS
AND
CONCLUSIONS
.
307
13
EXTENDED
THERMODYNAMICS
OF
RADIATION
309
1
STRUCTURE
OF
EXTENDED
THERMODYNAMICS
OF
PHOTONS
.
310
1.1
ENERGY
AND
MOMENTUM
OF
INDIVIDUAL
PHOTONS
.
310
1.2
RADIATIVE
TRANSFER
EQUATION
.
310
1.3
MOMENTS
AND
MOMENT
EQUATIONS.
THE
CLOSURE
PROBLEM
.
311
1.4
ENTROPY
AND
MAXIMIZATION
OF
ENTROPY
.
311
1.5
CLOSURE
.
312
2
EQUILIBRIUM
.
313
2.1
THE
FIRST
FEW
MOMENTS
.
313
2.2
EQUILIBRIUM
OF
RADIATION
WITH
MATTER
.
313
3
NEAR
EQUILIBRIUM
.
316
3.1
PHASE
DENSITY
IN
NEAR-EQUILIBRIUM
.
316
3.2
APPROXIMATE
LAGRANGE
MULTIPLIERS
.
316
4
FIELD
EQUATIONS
.
317
4.1
CLOSURE
FOR
MOMENTS
.
317
4.2
CLOSURE
FOR
PRODUCTIONS
.
317
4.3
THE
HIERARCHIES
OF
FIELD
EQUATIONS
.
318
4.4
ABSORPTION
AND
EMISSION
OF
BREMSSTRAHLUNG.'THOMSON
SCATTERING
.
318
5
LOCAL
RADIATIVE
EQUILIBRIUM
.
319
5.1
THE
ROSSELAND
MEAN
VALUE
OF
THE
ABSORPTION
COEFFICIENT
.
319
5.2
MAXWELL
ITERATION
.
320
5.3
CONCLUSION
.
321
6
COMPRESSION
OF
RADIATION
.
321
6.1
A
THOUGHT
EXPERIMENT
.
321
6.2
SOLUTION
OF
THE
RADIATIVE
TRANSFER
EQUATION
.
322
6.3
SOLUTION
OF
MOMENT
EQUATIONS
.
323
6.4
CONCLUSION
.
324
7
PENETRATION
OF
A
BEAM
OF
RADIATION
INTO
MATTER
.
324
7.1
FIELD
EQUATIONS
.
324
7.2
CHARACTERISTIC
SPEEDS
AND
AMPLITUDES
OF
THE
PROPAGATING
BEAM
.
325
XIV
CONTENTS
7.3
PLANE
HARMONIC
WAVES
AND
DISPERSION
RELATION
(GENERAL)
.
326
7.4
INTENSE
ABSORPTION.
THE
DAMPED
WAVE
LIMIT
.
328
7.5
INTENSE
SCATTERING.
THE
DIFFUSION
LIMIT
.
329
7.6
GENERAL
CASE
AND
A
SIMPLE
EXAMPLE
.
330
8
RADIATIVE
ENTROPY
IN
GRAY
BODIES
.
331
8.1
PHOTON
GAS
AND
AN
EULERIAN
FLUID
.
331
8.2
EQUILIBRIUM
OF
RADIATION
WITH
MATTER
AT
REST
.
332
8.3
ENTROPY
PRODUCTION
DUE
TO
MATTER-PHOTON
INTERACTION
.
332
8.4
THERMODYNAMIC
FIELDS
OF
RADIATION
IN
THE
NEIGHBORHOOD
OF
A
SPHERICAL
SOURCE
.
333
8.5
ABSORPTION
OF
RADIATION
FROM
A
SPHERICAL
SOURCE
IN
AN
EULERIAN
FLUID
AT
TEMPERATURE
T
.
335
8.6
ENTROPIC
PRODUCTION
FOR
INCIDENT
RAYS
.
337
8.7
PSEUDO-TEMPERATURE
.
338
8.8
ENTROPY
FLUX
AND
ENTROPY
.
340
14
EXTENDED
THERMODYNAMICS
OF
PHONONS
343
1
PHONON
TRANSFER
EQUATION
.
344
1.1
ENERGY
AND
MOMENTUM
OF
PHONONS
.
344
1.2
PHONON
TRANSFER
EQUATION,
ENERGY
AND
MOMENTUM
.
344
1.3
THE
PHASE
DENSITY
OF
PRODUCTION
.
344
2
MOMENTS
AND
MOMENT
EQUATIONS
.
346
2.1
MOMENTS
AND
THEIR
EQUILIBRIUM
VALUES
.
346
2.2
MOMENT
EQUATIONS
AND
CONSERVATION
LAWS
.
346
2.3
CLOSURE
PROBLEM
.
347
3
THE
HEAT
PULSE
EXPERIMENT
.
348
3.1
EXPERIMENTAL
RESULTS
AND
ONE-DIMENSIONAL
EQUATIONS
.
348
3.2
BALLISTIC
PHONONS
.
349
3.3
SECOND
SOUND
IN
ITS
PUREST
FORM
.
350
3.4
DAMPED
SECOND
SOUND
AND
PURE
DIFFUSION
.
351
3.5
THE
9-FIELD
THEORY
OF
EXTENDED
THERMODYNAMICS
.
351
3.6
HEAT
PULSES.
NUMERICAL
SOLUTIONS
.
353
15
THERMODYNAMICS
OF
METAL
ELECTRONS
357
1
EQUATIONS
OF
BALANCE
.
358
1.1
KINETIC
THEORY
OF
METAL
ELECTRONS
.
358
1.2
EQUATIONS
OF
BALANCE
OF
MASS,
MOMENTUM,
ENERGY,
AND
ENERGY
FLUX
.
359
1.3
ENTROPY
PRINCIPLE
AND
PHASE
DENSITY
CLOSE
TO
EQUILIBRIUM
.
360
2
EXTENDED
THERMODYNAMICS
AND
KINETIC
THEORY
.
361
2.1
TOWARD
EXTENDED
THERMODYNAMICS
OF
ELECTRONS
IN
METALS
.
361
2.2
A
CONVENIENT
SHORTCUT
VIA
THE
KINETIC
THEORY
OF
ELECTRONS
.
362
2.3
CHARACTERISTIC
SPEEDS
.
363
2.4
THE
LAWS
OF
OHM
AND
FOURIER
.
363
2.5
HALL
AND
CORIOLIS
EFFECTS
.
365
2.6
DISCUSSION
.
365
CONTENTS
XV
16
VISCOELASTIC
FLUIDS
367
1
VISCOELASTIC
FLUIDS
OF
SECOND
GRADE
.
368
1.1
THE
STRESS
OF
A
SECOND
GRADE
FLUID
.
368
1.2
ORDINARY
THERMODYNAMICS
OF
SECOND
GRADE
FLUIDS
.
368
1.3
DISCUSSION
.
370
2
RATE-TYPE
VERSUS
DIFFERENTIAL-TYPE
CONSTITUTIVE
EQUATIONS
.
371
2.1
CATTANEO
AND
STABILITY
.
371
2.2
VISCOELASTICITY
AND
STABILITY
.
371
2.3
CONCLUSION
.
372
3
TOWARD
EXTENDED
THERMODYNAMICS
OF
VISCOELASTICITY
.
372
3.1
FIELDS
AND
FIELD
EQUATIONS
.
372
3.2
INCOMPRESSIBLE
ADIABATIC
FLUID
.
374
3.3
ENTROPY
INEQUALITY
.
374
3.4
PARTIAL
EXPLOITATION
OF
THE
ENTROPY
INEQUALITY
.
375
3.5
EVALUATION
.
376
3.6
CRITICISM
AND
OUTLOOK
.
377
INDEX
389 |
| any_adam_object | 1 |
| author | Müller, Ingo 1936- Ruggeri, Tommaso 1947- |
| author_GND | (DE-588)128217863 (DE-588)1084792990 |
| author_facet | Müller, Ingo 1936- Ruggeri, Tommaso 1947- |
| author_role | aut aut |
| author_sort | Müller, Ingo 1936- |
| author_variant | i m im t r tr |
| building | Verbundindex |
| bvnumber | BV012058160 |
| callnumber-first | Q - Science |
| callnumber-label | QC311 |
| callnumber-raw | QC311 |
| callnumber-search | QC311 |
| callnumber-sort | QC 3311 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 2000 |
| ctrlnum | (OCoLC)37696325 (DE-599)BVBBV012058160 |
| dewey-full | 536/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 536 - Heat |
| dewey-raw | 536/.7 |
| dewey-search | 536/.7 |
| dewey-sort | 3536 17 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV012058160 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T09:02:05Z |
| institution | BVB |
| isbn | 0387983732 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008161199 |
| oclc_num | 37696325 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-706 |
| owner_facet | DE-703 DE-83 DE-706 |
| physical | XV, 396 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| record_format | marc |
| series | Springer tracts in natural philosophy |
| series2 | Springer tracts in natural philosophy |
| spelling | Müller, Ingo 1936- Verfasser (DE-588)128217863 aut Rational extended thermodynamics Ingo Müller ; Tommaso Ruggeri 2. ed. New York [u.a.] 1998 XV, 396 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer tracts in natural philosophy 37 Fluids Thermal properties Gases Thermal properties Second sound Thermodynamics Kinetische Gastheorie (DE-588)4163881-5 gnd rswk-swf Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd rswk-swf Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 s DE-604 Kinetische Gastheorie (DE-588)4163881-5 s Ruggeri, Tommaso 1947- Verfasser (DE-588)1084792990 aut 1. Aufl. u.d.T. Müller/Ruggeri Extended thermodynamics Springer tracts in natural philosophy 37 (DE-604)BV000692404 37 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161199&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Müller, Ingo 1936- Ruggeri, Tommaso 1947- Rational extended thermodynamics Springer tracts in natural philosophy Fluids Thermal properties Gases Thermal properties Second sound Thermodynamics Kinetische Gastheorie (DE-588)4163881-5 gnd Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd |
| subject_GND | (DE-588)4163881-5 (DE-588)4130850-5 |
| title | Rational extended thermodynamics |
| title_auth | Rational extended thermodynamics |
| title_exact_search | Rational extended thermodynamics |
| title_full | Rational extended thermodynamics Ingo Müller ; Tommaso Ruggeri |
| title_fullStr | Rational extended thermodynamics Ingo Müller ; Tommaso Ruggeri |
| title_full_unstemmed | Rational extended thermodynamics Ingo Müller ; Tommaso Ruggeri |
| title_old | Müller/Ruggeri Extended thermodynamics |
| title_short | Rational extended thermodynamics |
| title_sort | rational extended thermodynamics |
| topic | Fluids Thermal properties Gases Thermal properties Second sound Thermodynamics Kinetische Gastheorie (DE-588)4163881-5 gnd Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd |
| topic_facet | Fluids Thermal properties Gases Thermal properties Second sound Thermodynamics Kinetische Gastheorie Nichtgleichgewichtsthermodynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161199&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000692404 |
| work_keys_str_mv | AT mulleringo rationalextendedthermodynamics AT ruggeritommaso rationalextendedthermodynamics |