Preface |
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xi | |
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1 Introduction to materials modeling and simulation |
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1 | (10) |
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1.1 Modeling and simulation |
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1 | (1) |
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1.2 What is meant by computational materials science and engineering? |
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2 | (1) |
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1.3 Scales in materials structure and behavior |
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3 | (2) |
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1.4 How to develop models |
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5 | (2) |
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7 | (4) |
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11 | (16) |
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2.1 Random-walk model of diffusion |
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11 | (2) |
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2.2 Connection to the diffusion coefficient |
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13 | (5) |
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18 | (1) |
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2.4 A random-walk simulation |
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19 | (6) |
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2.5 Random-walk models for materials |
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25 | (1) |
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26 | (1) |
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3 Simulation of finite systems |
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27 | (18) |
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3.1 Sums of interacting pairs of objects |
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27 | (2) |
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29 | (2) |
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31 | (1) |
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3.4 Periodic boundary conditions |
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32 | (2) |
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34 | (1) |
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3.6 Long-ranged potentials |
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35 | (1) |
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36 | (1) |
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36 | (9) |
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PART TWO ATOMS AND MOLECULES |
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4 Electronic structure methods |
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45 | (17) |
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4.1 Quantum mechanics of multielectron systems |
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46 | (1) |
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4.2 Early density functional theories |
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47 | (4) |
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4.3 The Hohenberg-Kohn theorem |
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51 | (1) |
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51 | (3) |
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4.5 The exchange-correlation functional |
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54 | (1) |
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55 | (2) |
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57 | (2) |
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4.8 Use of density functional theory |
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59 | (2) |
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61 | (1) |
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62 | (34) |
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62 | (1) |
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5.2 Interatomic potentials |
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63 | (4) |
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67 | (9) |
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76 | (2) |
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78 | (6) |
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84 | (4) |
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5.7 Systems with mixed bonding |
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88 | (1) |
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89 | (2) |
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5.9 Determining parameters in potentials |
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91 | (1) |
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91 | (1) |
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92 | (4) |
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96 | (35) |
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6.1 Basics of molecular dynamics for atomic systems |
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96 | (11) |
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6.2 An example calculation |
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107 | (9) |
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116 | (1) |
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6.4 Molecular dynamics in other ensembles |
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117 | (3) |
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120 | (2) |
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6.6 Limitations of molecular dynamics |
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122 | (1) |
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6.7 Molecular dynamics in materials research |
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123 | (2) |
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125 | (1) |
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125 | (6) |
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131 | (27) |
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131 | (1) |
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132 | (2) |
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7.3 The Metropolis algorithm |
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134 | (5) |
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139 | (6) |
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7.5 Monte Carlo for atomic systems |
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145 | (5) |
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150 | (4) |
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7.7 Time in a Monte Carlo simulation |
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154 | (1) |
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7.8 Assessment of the Monte Carlo method |
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155 | (1) |
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7.9 Uses of the Monte Carlo method in materials research |
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155 | (1) |
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156 | (1) |
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156 | (2) |
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8 Molecular and macromolecular systems |
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158 | (25) |
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158 | (3) |
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8.2 Random-walk models of polymers |
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161 | (2) |
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8.3 Atomistic simulations of macromolecules |
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163 | (9) |
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8.4 Coarse-grained methods |
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172 | (3) |
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8.5 Lattice models for polymers and biomolecules |
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175 | (1) |
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8.6 Simulations of molecular and macromolecular materials |
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176 | (1) |
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177 | (1) |
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178 | (5) |
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PART THREE MESOSCOPIC METHODS |
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183 | (13) |
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9.1 The kinetic Monte Carlo method |
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183 | (4) |
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9.2 Time in the kinetic Monte Carlo method |
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187 | (2) |
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9.3 Kinetic Monte Carlo calculations |
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189 | (5) |
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194 | (1) |
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195 | (1) |
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10 Monte Carlo methods at the mesoscale |
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196 | (15) |
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10.1 Modeling Grain Growth |
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196 | (2) |
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10.2 The Monte Carlo Potts model |
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198 | (4) |
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202 | (3) |
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10.4 Example applications of the Potts model |
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205 | (3) |
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10.5 Applications in materials science and engineering |
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208 | (2) |
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210 | (1) |
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211 | (18) |
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11.1 Basics of cellular automata |
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211 | (4) |
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11.2 Examples of cellular automata in two dimensions |
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215 | (3) |
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218 | (1) |
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11.4 Examples of cellular automata in materials research |
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219 | (8) |
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11.5 Relation to Monte Carlo |
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227 | (1) |
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227 | (2) |
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229 | (20) |
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12.1 Conserved and non-conserved order parameters |
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229 | (1) |
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230 | (3) |
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12.3 A one-dimensional phase-field calculation |
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233 | (4) |
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12.4 Free energy of an interface |
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237 | (1) |
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12.5 Local free-energy functions |
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238 | (3) |
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241 | (3) |
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12.7 Other applications in materials research |
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244 | (1) |
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244 | (1) |
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244 | (5) |
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249 | (20) |
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249 | (2) |
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251 | (1) |
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13.3 Simulation "entities" at the mesoscale |
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252 | (1) |
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13.4 Dynamic models of grain growth |
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253 | (3) |
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13.5 Discrete dislocation dynamics simulations |
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256 | (9) |
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265 | (4) |
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PART FOUR SOME FINAL WORDS |
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14 Materials selection and design |
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269 | (12) |
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14.1 Integrated computational materials engineering |
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269 | (2) |
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14.2 Concurrent materials design |
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271 | (2) |
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273 | (2) |
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14.4 Materials informatics |
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275 | (3) |
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278 | (3) |
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A Energy units, fundamental constants, and conversions |
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281 | (2) |
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A.1 Fundamental constants |
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281 | (1) |
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A.2 Units and energy conversions |
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281 | (2) |
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B A brief introduction to materials |
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283 | (27) |
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283 | (1) |
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284 | (7) |
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291 | (1) |
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291 | (1) |
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292 | (10) |
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B.6 Polycrystalline materials |
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302 | (4) |
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306 | (4) |
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310 | (14) |
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310 | (4) |
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314 | (1) |
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315 | (2) |
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317 | (1) |
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318 | (3) |
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321 | (3) |
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D A brief summary of classical mechanics |
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324 | (6) |
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324 | (2) |
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326 | (1) |
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D.3 Example: the harmonic oscillator |
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327 | (1) |
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D.4 Central-force potentials |
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328 | (2) |
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330 | (4) |
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330 | (1) |
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E.2 Electrostatic potentials and energies |
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330 | (1) |
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E.3 Distribution of charges: the multipole expansion |
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331 | (3) |
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F Elements of quantum mechanics |
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334 | (17) |
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334 | (1) |
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335 | (1) |
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F.3 The Schrodinger equation |
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336 | (1) |
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336 | (1) |
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337 | (5) |
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F.6 Atoms with more than one electron |
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342 | (4) |
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F.7 Eigenvalues and eigenvectors |
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346 | (2) |
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F.8 Multielectron systems |
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348 | (1) |
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F.9 Quantum mechanics of periodic systems |
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349 | (1) |
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349 | (2) |
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G Statistical thermodynamics and kinetics |
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351 | (24) |
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G.1 Basic thermodynamic quantities |
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351 | (1) |
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G.2 Introduction to statistical thermodynamics |
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352 | (1) |
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G.3 Macrostates versus microstates |
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352 | (1) |
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G.4 Phase space and time averages |
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353 | (2) |
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355 | (7) |
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362 | (2) |
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G.7 Correlation functions |
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364 | (4) |
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368 | (6) |
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374 | (1) |
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375 | (8) |
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375 | (3) |
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378 | (1) |
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H.3 Engineering stress and strain |
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378 | (1) |
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379 | (2) |
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381 | (2) |
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I Introduction to computation |
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383 | (9) |
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383 | (1) |
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I.2 Random-number generators |
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383 | (3) |
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386 | (2) |
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I.4 Numerical derivatives |
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388 | (3) |
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391 | (1) |
References |
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392 | (17) |
Index |
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409 | |