| Preface |
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xi | |
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Thermodynamics of Discrete Systems |
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1 | (46) |
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The representational bases of a material system |
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1 | (14) |
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1 | (7) |
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Systems analysis and thermodynamics |
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8 | (3) |
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11 | (2) |
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13 | (2) |
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15 | (6) |
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15 | (1) |
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16 | (4) |
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20 | (1) |
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Consequences of the axioms of thermostatics |
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21 | (8) |
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21 | (2) |
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23 | (6) |
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Out-of-equilibrium states |
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29 | (18) |
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29 | (1) |
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30 | (15) |
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Application to heat engines |
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45 | (2) |
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Thermodynamics of Continuous Media |
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47 | (54) |
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Thermostatics of continuous media |
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47 | (16) |
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Reduced extensive quantities |
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47 | (1) |
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Local thermodynamic equilibrium |
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48 | (2) |
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Flux of extensive quantities |
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50 | (4) |
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Balance equations in continuous media |
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54 | (3) |
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57 | (6) |
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63 | (9) |
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General equations of fluid statics |
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63 | (5) |
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Pressure forces on solid boundaries |
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68 | (4) |
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72 | (1) |
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72 | (1) |
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Thermal boundary conditions |
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72 | (1) |
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73 | (28) |
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73 | (4) |
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77 | (3) |
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Choice of reference frame |
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80 | (5) |
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Binary isothermal mixture |
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85 | (12) |
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Coupled phenomena with diffusion |
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97 | (2) |
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99 | (2) |
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Physics of Energetic Systems in Flow |
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101 | (50) |
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Dynamics of a material point |
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101 | (6) |
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Galilean reference frames in traditional mechanics |
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101 | (1) |
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Isolated mechanical system and momentum |
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102 | (1) |
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103 | (1) |
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104 | (2) |
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The fundamental law of dynamics (closed systems) |
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106 | (1) |
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106 | (1) |
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Mechanical material system |
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107 | (12) |
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Dynamic properties of a material system |
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107 | (2) |
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Kinetic energy of a material system |
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109 | (2) |
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Mechanical system in thermodynamic equilibrium: the rigid solid |
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111 | (1) |
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The open mechanical system |
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112 | (4) |
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Thermodynamics of a system in motion |
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116 | (3) |
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Kinematics of continuous media |
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119 | (13) |
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Lagrangian and Eulerian variables |
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119 | (2) |
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Trajectories, streamlines, streaklines |
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121 | (1) |
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Material (or Lagrangian) derivative |
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122 | (7) |
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129 | (3) |
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Phenomenological laws of viscosity |
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132 | (19) |
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132 | (3) |
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135 | (11) |
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146 | (5) |
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151 | (48) |
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151 | (3) |
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Balance of an extensive quantity G |
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151 | (2) |
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Interpretation of an equation in terms of the balance equation |
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153 | (1) |
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154 | (6) |
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Conservation of mass and its consequences |
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154 | (6) |
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160 | (1) |
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Balance of mechanical and thermodynamic quantities |
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160 | (18) |
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160 | (4) |
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164 | (7) |
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171 | (1) |
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172 | (5) |
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Balance of chemical species |
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177 | (1) |
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178 | (4) |
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178 | (1) |
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Geometric boundary conditions |
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179 | (2) |
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181 | (1) |
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Global form of the balance equations |
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182 | (7) |
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The interest of the global form of a balance |
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182 | (2) |
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Equation of mass conservation |
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184 | (1) |
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184 | (1) |
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The momentum flux theorem |
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184 | (2) |
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186 | (1) |
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187 | (1) |
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The balance equation for chemical species |
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188 | (1) |
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Similarity and non-dimensional parameters |
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189 | (10) |
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189 | (10) |
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Transport and Propagation |
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199 | (58) |
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199 | (4) |
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199 | (3) |
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The Cauchy problem for differential equations |
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202 | (1) |
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First order quasi-linear partial differential equations |
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203 | (4) |
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203 | (1) |
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Geometric interpretation of the solutions |
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204 | (2) |
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206 | (1) |
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The Cauchy problem for partial differential equations |
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206 | (1) |
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Systems of first order partial differential equations |
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207 | (18) |
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The Cauchy problem for n unknowns and two variables |
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207 | (3) |
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Applications in fluid mechanics |
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210 | (6) |
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Cauchy problem with n unknowns and p variables |
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216 | (2) |
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Partial differential equations of order n |
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218 | (2) |
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220 | (3) |
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Physical interpretation of propagation |
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223 | (2) |
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Second order partial differential equations |
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225 | (14) |
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225 | (1) |
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Characteristic curves of hyperbolic equations |
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226 | (3) |
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Reduced form of the second order quasi-linear partial equation |
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229 | (3) |
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Second order partial differential equations in a finite domain |
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232 | (1) |
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Second order partial differential equations and their boundary conditions |
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233 | (6) |
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Discontinuities: Shock waves |
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239 | (11) |
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239 | (1) |
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Unsteady 1D flow of an inviscid compressible fluid |
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239 | (5) |
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Plane steady supersonic flow |
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244 | (1) |
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244 | (4) |
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248 | (1) |
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Other discontinuity categories |
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248 | (1) |
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Balance equations across a discontinuity |
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249 | (1) |
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Some comments on methods of numerical solution |
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250 | (7) |
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Characteristic curves and numerical discretization schemes |
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250 | (3) |
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253 | (2) |
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Boundary conditions of flow problems |
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255 | (2) |
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General Properties of Flows |
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257 | (82) |
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257 | (12) |
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Kinematic properties of the rotation vector |
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257 | (4) |
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Equation and properties of the rotation vector |
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261 | (8) |
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269 | (19) |
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269 | (1) |
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Bernoulli's second theorem |
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269 | (1) |
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Flow of compressible inviscid fluid |
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270 | (1) |
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Nature of equations in inviscid flows |
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271 | (2) |
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Elementary solutions in irrotational flows |
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273 | (11) |
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Surface waves in shallow water |
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284 | (4) |
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288 | (8) |
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Introduction and discussion of a simple example |
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288 | (3) |
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Obtaining approximate values of a solution |
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291 | (5) |
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Small parameters and perturbation phenomena |
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296 | (13) |
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296 | (1) |
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296 | (9) |
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305 | (4) |
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309 | (18) |
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309 | (5) |
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314 | (5) |
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The boundary layer in steady flow |
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319 | (8) |
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Unsteady flows and steady flows |
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327 | (12) |
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327 | (1) |
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The existence of steady flows |
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328 | (2) |
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Transitional regime and permanent solution |
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330 | (4) |
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Non-existence of a steady solution |
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334 | (5) |
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Measurement, Representation and Analysis of Temporal Signals |
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339 | (66) |
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Introduction and position of the problem |
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339 | (1) |
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Measurement and experimental data in flows |
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340 | (17) |
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340 | (1) |
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341 | (1) |
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342 | (4) |
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346 | (1) |
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Measurements of concentration |
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347 | (1) |
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Fields of quantities and global measurements |
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347 | (4) |
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Errors and uncertainties of measurements |
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351 | (6) |
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Representation of signals |
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357 | (32) |
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Objectives of continuous signal representation |
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357 | (3) |
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Analytical representation |
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360 | (1) |
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Signal decomposition on the basis of functions; series and elementary solutions |
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361 | (2) |
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363 | (11) |
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Time-frequency (or timescale) representations |
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374 | (7) |
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381 | (4) |
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385 | (4) |
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Choice of representation and obtaining pertinent information |
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389 | (16) |
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389 | (1) |
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An example: analysis of sound |
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390 | (3) |
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Analysis of musical signals |
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393 | (9) |
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Signal analysis in aero-energetics |
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402 | (3) |
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Thermal Systems and Models |
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405 | (72) |
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405 | (7) |
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Introduction and definitions |
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405 | (3) |
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Modeling by state representation and choice of variables |
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408 | (2) |
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410 | (1) |
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411 | (1) |
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Thermodynamics and state representation |
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412 | (10) |
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General principles of modeling |
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412 | (8) |
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Linear time-invariant system (LTIS) |
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420 | (2) |
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Modeling linear invariant thermal systems |
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422 | (24) |
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Modeling discrete systems |
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422 | (9) |
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Thermal models in continuous media |
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431 | (15) |
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External representation of linear invariant systems |
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446 | (5) |
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446 | (1) |
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External description of linear invariant systems |
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446 | (5) |
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451 | (14) |
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Definition of model parameters |
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451 | (2) |
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Established regimes of linear invariant systems |
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453 | (5) |
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Established regimes in continuous media |
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458 | (7) |
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465 | (9) |
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465 | (1) |
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Model reduction of discrete systems |
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466 | (8) |
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Application in fluid mechanics and transfer in flows |
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474 | (3) |
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Appendix
1. Laplace Transform |
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477 | (4) |
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477 | (1) |
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477 | (1) |
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478 | (1) |
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Application to the solution of constant coefficient differential equations |
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479 | (2) |
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Appendix
2. Hilbert Transform |
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481 | (2) |
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Appendix
3. Cepstral Analysis |
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483 | (4) |
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483 | (1) |
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483 | (1) |
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Example of echo suppression |
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484 | (1) |
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485 | (2) |
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Appendix
4. Eigenfunctions of an Operator |
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487 | (2) |
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Eigenfunctions of an operator |
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487 | (1) |
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487 | (2) |
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487 | (1) |
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Expression of a function off using an eigenfunction basis-set |
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488 | (1) |
| Bibliography |
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489 | (8) |
| Index |
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497 | |
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