Continuum physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2012
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| Series: | Graduate Texts in Physics
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVIII, 277 S. graph. Darst. |
| ISBN: | 3642294995 9783642294990 |
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IMAGE 1
CONTENTS
1 BALANCE EQUATIONS 1
1.1 MATERIAL POINTS 2
1.1.1 SUMMARY 3
1.2 DENSITIES FOR CONTENT, FLOW, AND PRODUCTION RATE 4
1.2.1 DENSITIES 4
1.2.2 CURRENT DENSITIES 4
1.2.3 PRODUCTION 5
1.2.4 GENERIC BALANCE EQUATION 6
1.2.5 SUMMARY 7
1.3 PARTICLE NUMBERS, MASS, AND ELECTRIC CHARGE 8
1.3.1 PARTICLE NUMBERS AND CURRENTS 8
1.3.2 CHEMICAL REACTIONS 8
1.3.3 MASS 9
1.3.4 ELECTRIC CHARGE 10
1.3.5 DIGRESSION ON ELECTROMAGNETISM 11
1.3.6 SUMMARY 12
1.4 CONVECTION AND CONDUCTION 13
1.4.1 CONDUCTION 13
1.4.2 TRANSFORMATION PROPERTIES OF CURRENTS 14
1.4.3 MATERIAL TIME DERIVATIVE 15
1.4.4 SPECIFIC QUANTITIES 16
1.4.5 SUMMARY 17
1.5 LINEAR AND ANGULAR MOMENTUM 17
1.5.1 STRESS AND EXTERNAL FORCES 17
1.5.2 ANGULAR MOMENTUM 18
1.5.3 NORMAL AND SHEAR FORCES 19
1.5.4 SUMMARY 2 0
1.6 ENERGY AND THE FIRST LAW OF THERMODYNAMICS 2 0
1.6.1 KINETIC ENERGY 2 0
1.6.2 POTENTIAL ENERGY 21
1.6.3 INTERNAL ENERGY 22
IX
HTTP://D-NB.INFO/1020805293
IMAGE 2
X CONTENTS
1.6.4 DIGRESSION ON TIME REVERSAL 23
1.6.5 FIRST LAW O F THERMODYNAMICS 2 4
1.6.6 SUMMARY 2 6
1.7 ENTROPY AND THE SECOND LAW O F THERMODYNAMICS 2 6
1.7.1 THERMODYNAMIC EQUILIBRIUM 27
1.7.2 BALANCE EQUATION FOR ENTROPY 27
1.7.3 SECOND LAW O F THERMODYNAMICS 29
1.7.4 SUMMARY 30
2 MATERIAL EQUATIONS 31
2.1 FLUID MEDIA 32
2.1.1 INCOMPRESSIBLE FLUIDS 32
2.1.2 IDEAL GAS 33
2.1.3 NEWTONIAN FLUID MEDIUM 3 4
2.1.4 HYDRODYNAMICS 35
2.1.5 AERODYNAMICS 36
2.1.6 SUMMARY 37
2.2 SOLID MEDIA 37
2.2.1 STRAIN 38
2.2.2 HOOKE'SLAW 39
2.2.3 STRUCTURAL MECHANICS 4 0
2.2.4 ELASTODYNAMICS 4 2
2.2.5 SUMMARY 4 2
2.3 HEAT CONDUCTION 4 2
2.3.1 FOURIER'S LAW 4 3
2.3.2 MORE ON HEAT CONDUCTION 4 4
2.3.3 HEAT EQUATION 4 4
2.3.4 SUMMARY 4 5
2.4 DIFFUSION 4 5
2.4.1 DIFFUSION CURRENTS 4 6
2.4.2 CHEMICAL POTENTIAL 4 6
2.4.3 DIFFUSION EQUATION 4 7
2.4.4 DIGRESSION ON OPEN SYSTEMS 47
2.4.5 SUMMARY 48
2.5 CHARGE TRANSPORT 4 9
2.5.1 THE ELECTROMAGNETIC FIELD IN MATTER 4 9
2.5.2 CONTRIBUTIONS TO THE ELECTRIC CURRENT DENSITY 51
2.5.3 OHM'S LAW 51
2.5.4 SUMMARY 52
2.6 THERMOELECTRIC EFFECTS 52
2.6.1 SIMULTANEOUS HEAT AND CHARGE TRANSPORT 53
2.6.2 FORCES AND FLUXES 53
2.6.3 KINETIC COEFFICIENTS FOR HEAT AND CHARGE TRANSPORT 5 4
2.6.4 SUMMARY 55
IMAGE 3
CONTENTS XI
3 LINEAR RESPONSE THEORY 57
3.1 STATISTICAL THERMODYNAMICS 57
3.1.1 QUANTUM THEORY 57
3.1.2 ENTROPY 6 0
3.1.3 EQUILIBRIUM 61
3.1.4 SUMMARY 63
3.2 PERTURBATIONS 63
3.2.1 INTERACTION PICTURE 6 3
3.2.2 LINEAR RESPONSE 65
3.2.3 PERTURBATION BY LIGHT 66
3.2.4 SUSCEPTIBILITY TENSOR 67
3.2.5 SUMMARY 68
3.3 DISPERSION RELATIONS 68
3.3.1 CAUSAL FUNCTIONS 69
3.3.2 KRAMERS-KRONIG RELATIONS 7 0
3.3.3 SUMMARY 72
3.4 FLUCTUATIONS AND DISSIPATION 72
3.4.1 WIENER-KHINCHIN THEOREM 72
3.4.2 KUBO-MARTIN-SCHWINGER FORMULA 7 4
3.4.3 CALLEN-WELTON THEOREM 75
3.4.4 INTERACTION WITH AN ELECTROMAGNETIC FIELD 77
3.4.5 SUMMARY 78
3.5 ONSAGER RELATIONS 78
3.5.1 TIME REVERSAL 7 9
3.5.2 SYMMETRIES FOR SUSCEPTIBILITIES 80
3.5.3 SYMMETRIES FOR CONDUCTIVITIES 82
3.5.4 SYMMETRIES FOR KINETIC COEFFICIENTS 83
3.5.5 SUMMARY 85
4 EXAMPLES 87
4.1 ARCHIMEDES'PRINCIPLE 88
4.1.1 ERRONEOUS REASONING 89
4.1.2 INCOMPRESSIBLE FLUID 9 0
4.1.3 COMPRESSIBLE FLUID 91
4.2 BEAM BENDING AND BUCKLING 92
4.2.1 BEAM THEORY 9 2
4.2.2 EQUILIBRIUM 9 6
4.2.3 AN EXAMPLE 97
4.2.4 BUCKLING INSTABILITY 98
4.3 BERNOULLI'S LAW 100
4.4 BROWNIAN MOTION 101
4.4.1 EINSTEIN'S EXPLANATION 103
4.4.2 THE DIFFUSION COEFFICIENT 105
4.4.3 LANGEVIN'S APPROACH 106
IMAGE 4
XII CONTENTS
4.5 BULK AND SURFACE ACOUSTIC WAVES IN SOLIDS 109
4.5.1 WAVE EQUATION 109
4.5.2 BULK ACOUSTIC WAVES 110
4.5.3 ATTENUATION I L L
4.5.4 RAYLEIGH WAVES 112
4.5.5 MORE ON SAW 114
4.6 CRYSTAL OPTICS 115
4.6.1 SUSCEPTIBILITY 115
4.6.2 PLANAR WAVES 116
4.6.3 OPTICAL ISOTROPY 117
4.6.4 BIREFRINGENCE 118
4.6.5 POLARIZATION CHANGE DUE TO BIREFRINGENCE 119
4.6.6 ABSORPTION 120
4.6.7 DISPERSION 121
4.7 DIELECTRIC PLANAR WAVEGUIDES 121
4.7.1 T E MODES 123
4.7.2 T M MODES 124
4.7.3 GRADED INDEX WAVEGUIDES 125
4.7.4 SLAB WAVEGUIDES 127
4.8 ELASTICITY MODULI 129
4.8.1 STRAIN AND STRESS 129
4.8.2 UNIAXIAL STRESS 130
4.8.3 HYDROSTATIC PRESSURE 131
4.8.4 TORSION 132
4.8.5 EXAMPLES: STEEL AND RUBBER 133
4.9 FARADAY EFFECT 134
4.9.1 SUSCEPTIBILITY AND ONSAGER'S RELATION 134
4.9.2 ROTATION O F THE POLARIZATION VECTOR 135
4.9.3 DRUDE MODEL 137
4.9.4 OPTICAL ISOLATOR 139
4.9.5 YTTRIUM IRON GARNET 140
4.10 FOURIER'S SOLUTION O F A HEAT CONDUCTION PROBLEM 140
4.10.1 REPRESENTATION OF A PERIODIC FUNCTION 141
4.10.2 ORDINARY INSTEAD O F PARTIAL DIFFERENTIAL EQUATIONS 141
4.10.3 INITIAL CONDITIONS 141
4.11 HAGEN-POISEUILLE LAW 142
4.11.1 EXPLOITING SYMMETRY 143
4.11.2 FLUX 143
4.11.3 PUMP POWER 144
4.12 ICE LAYER 145
4.12.1 PHASE TRANSITION ENTHALPY 145
4.12.2 THE PROBLEM 146
4.12.3 CRUDE APPROXIMATION 147
4.12.4 DIMENSIONLESS QUANTITIES 148
4.12.5 THE EXACT SOLUTION 149
4.12.6 DISCUSSION 150
IMAGE 5
CONTENTS XIII
4.13 METAMATERIALS 150
4.13.1 RESONANCES 151
4.13.2 WAVE PROPAGATION 152
4.13.3 NORMAL REFRACTION 153
4.13.4 REFRACTION IN A BACKWARD MEDIUM 155
4.13.5 A NEW TYPE OF OPTICAL MICROSCOPE 156
4.13.6 PHOTONIC CRYSTALS 157
4.14 MODEL ATMOSPHERE 159
4.14.1 ADIABATIC PROCESS FOR A DIATOMIC IDEAL GAS 159
4.14.2 CONVECTION NEUTRAL ATMOSPHERE 160
4.15 NATURAL UNITS 162
4.15.1 SI AND ATOMIC UNITS 162
4.15.2 REMARKS 164
4.16 OHM'S LAW AND HALL EFFECT 165
4.16.1 DRUDE MODEL 166
4.16.2 ONSAGER RELATIONS 167
4.16.3 HALL EFFECT 168
4.16.4 ELECTRO-CHEMICAL POTENTIAL 169
4.17 OPTICALLY ACTIVE MEDIA 169
4.17.1 SPATIAL DISPERSION 170
4.17.2 OPTICAL ACTIVITY 171
4.17.3 QUARTZ 172
4.17.4 NATURAL GRAPE SUGAR 173
4.18 POCKELS AND KERR EFFECT 174
4.18.1 DIELECTRIC SUSCEPTIBILITY 175
4.18.2 POCKELS EFFECT 176
4.18.3 CRYSTAL SYMMETRY 3M 176
4.18.4 SYMMETRY COMPATIBLE TENSORS 177
4.18.5 DIGRESSION ON ORDERS O F MAGNITUDE 179
4.18.6 HOW LIGHT PROPAGATION IS AFFECTED 180
4.18.7 KERR EFFECT 181
4.19 REACTIONS AND DIFFUSION 182
4.19.1 GRAY-SCOTT MODEL 183
4.19.2 SIMILARITY CONSIDERATIONS 183
4.19.3 HOMOGENEOUS SOLUTIONS 184
4.19.4 PATTERN FORMATION 186
4.19.5 FURTHER REMARKS 188
4.20 REYNOLD'S NUMBER 188
4.20.1 NAVIER-STOKES EQUATION 188
4.20.2 SIMILARITY CONSIDERATIONS 189
4.20.3 LAMINAR FLOW AND TURBULENCE 190
4.21 SOUND IN AIR 190
4.21.1 WAVE EQUATION 191
4.21.2 SOUND GENERATION 193
IMAGE 6
XIV CONTENTS
4.22 STOKES' LAW 196
4.22.1 THE PROBLEM 196
4.22.2 VORTICITY AND STREAM FUNCTION 197
4.22.3 THE SOLUTION 199
4.22.4 STOKE'S FORMULA 199
4.23 STRESS CONCENTRATION 201
4.23.1 CIRCULAR HOLE IN A THIN PLATE 201
4.23.2 AIRY'S STRESS FUNCTION FOR PLANAR PROBLEMS 203
4.23.3 THE SOLUTION 203
4.23.4 DISCUSSION 205
4.24 SURFACE PLASMON POLARITONS 206
4.24.1 THE DRUDE MODEL 206
4.24.2 GUIDED T M MODE 207
4.24.3 T E POLARIZATION 210
4.25 THERMAL NOISE O F A RESISTOR 210
4.25.1 LANGEVIN EQUATION 211
4.25.2 NYQUIST FORMULA 212
4.25.3 REMARKS 214
4.26 THOMSON, SEEBECK AND PELTIER EFFECT 215
4.26.1 SOLID CONDUCTORS 215
4.26.2 CHARGE AND HEAT TRANSPORT 216
4.26.3 THOMSON EFFECT 217
4.26.4 SEEBECK AND PELTIER EFFECT 218
4.27 VIBRATING STRINGS AND MEMBRANES 219
4.27.1 STRINGS 219
4.27.2 MEMBRANES 220
4.27.3 STRING EIGENMODES 221
4.27.4 MEMBRANE EIGENMODES 225
4.28 WHITE DWARFS 228
4.28.1 THE MODEL 229
4.28.2 EQUATION O F STATE 229
4.28.3 ORDERS OF MAGNITUDE 231
4.28.4 NUMERICAL SOLUTION 231
4.28.5 REMARKS 232
A FIELDS 235
A . L COVARIANCE 236
A. 1.1 INERTIAL SYSTEMS O F REFERENCE 236
A. 1.2 TENSOR FIELDS 238
A.2 DIFFERENTIATING FIELDS 239
A.2.1 TIME DERIVATIVE 239
A.2.2 GRADIENT 240
A.2.3 DIVERGENCE 240
A.2.4 CURL 240
IMAGE 7
CONTENTS XV
A.3 PATHS, SURFACES AND VOLUMES 241
A.3.1 PATHS 241
A.3.2 SURFACES 243
A.3.3 VOLUMES 246
A.4 INTEGRATING FIELDS 247
A.4.1 PATH INTEGRALS 247
A.4.2 SURFACE INTEGRALS 248
A.4.3 VOLUME INTEGRALS 249
A.4.4 STOKES' AND GAUSS' THEOREMS 250
A.5 MORE ON FIELDS 252
A.5.1 DENSITIES AND CURRENT DENSITIES 252
A.5.2 TIME DERIVATIVES 254
GLOSSARY 255
REFERENCES 277 |
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| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
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| id | DE-604.BV040235642 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:34:38Z |
| institution | BVB |
| isbn | 3642294995 9783642294990 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025091956 |
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| physical | XVIII, 277 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| publisher | Springer |
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| series2 | Graduate Texts in Physics |
| spelling | Hertel, Peter 1938-2017 Verfasser (DE-588)132343789 aut Continuum physics Peter Hertel Heidelberg [u.a.] Springer 2012 XVIII, 277 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate Texts in Physics Kontinuumsphysik (DE-588)4165166-2 gnd rswk-swf Kontinuumsphysik (DE-588)4165166-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-29500-3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3994673&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025091956&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hertel, Peter 1938-2017 Continuum physics Kontinuumsphysik (DE-588)4165166-2 gnd |
| subject_GND | (DE-588)4165166-2 |
| title | Continuum physics |
| title_auth | Continuum physics |
| title_exact_search | Continuum physics |
| title_full | Continuum physics Peter Hertel |
| title_fullStr | Continuum physics Peter Hertel |
| title_full_unstemmed | Continuum physics Peter Hertel |
| title_short | Continuum physics |
| title_sort | continuum physics |
| topic | Kontinuumsphysik (DE-588)4165166-2 gnd |
| topic_facet | Kontinuumsphysik |
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