| Introduction |
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1 | (6) |
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2 Geometry of deformations of solids |
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7 | (16) |
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7 | (4) |
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7 | (1) |
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2.1.2 Deformation gradient |
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7 | (1) |
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2.1.3 Measures of deformation |
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8 | (1) |
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2.1.4 Polar decomposition |
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9 | (2) |
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2.1.5 Homogeneous deformations |
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11 | (1) |
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11 | (4) |
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2.2.1 Families of universal solutions and corresponding geometric quantities |
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12 | (1) |
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2.2.1.1 Family 0: Homogeneous plane deformations |
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12 | (1) |
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2.2.1.2 Family 1: Deformation of a rectangular block |
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13 | (1) |
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2.2.1.3 Family 2: Sector of a circular-cylindrical tube |
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13 | (1) |
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2.2.1.4 Family 3: Deformation of an annular wedge |
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14 | (1) |
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2.2.1.5 Family 4: Inflation or eversion of a sector of a spherical shell |
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14 | (1) |
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2.2.1.6 Family 5: Deformation of a circular cylinder |
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15 | (1) |
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2.3 A few examples of universal deformations |
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15 | (8) |
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2.3.1 Isochoric extension |
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15 | (3) |
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18 | (3) |
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2.3.3 Pure torsion of a circular cylinder |
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21 | (2) |
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3 Kinematics of continua in different descriptions |
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23 | (10) |
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3.1 Summary: Kinematics of one-component media |
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23 | (5) |
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3.2 Two-component materials with the skeleton as reference |
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28 | (5) |
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3.2.1 Example clarifying the Lagrangian description of relative motion |
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28 | (5) |
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33 | (6) |
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5 Some solutions for fluids and solids |
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39 | (52) |
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39 | (1) |
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39 | (2) |
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41 | (30) |
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41 | (6) |
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47 | (1) |
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5.3.2.1 Navier-Stokes equation, uniqueness of solutions |
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47 | (8) |
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55 | (1) |
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56 | (2) |
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58 | (5) |
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5.3.3 Maxwell and N-th grade (Rivlin-Ericksen) fluids; viscometric flows |
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63 | (1) |
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63 | (2) |
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5.3.3.2 Viscometric flows |
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65 | (6) |
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5.4 Nonlinear elastic solids |
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71 | (8) |
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5.4.1 Rubber-like materials |
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71 | (3) |
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5.4.1.1 Homogeneous deformations |
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74 | (4) |
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5.4.1.2 Heterogeneous deformations |
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78 | (1) |
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79 | (12) |
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5.5.1 Differential constitutive relations |
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83 | (2) |
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5.5.2 Steady state processes and elastic-viscoelastic correspondence principle |
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85 | (6) |
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91 | (24) |
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91 | (2) |
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6.2 Stability of the torsional Couette flow |
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93 | (4) |
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6.3 Thermal instability of a layer of fluid heated from below -- Rayleigh-Benard problem |
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97 | (5) |
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6.4 Stability of a nonlinear elastic strip |
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102 | (4) |
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6.5 Stability of the thermodynamical equilibrium of second-grade fluids |
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106 | (9) |
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7 Thermodynamical problems |
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115 | (34) |
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7.1 Some heat conduction problems |
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115 | (13) |
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115 | (1) |
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7.1.1.1 Heat flow in a rectangular parallelepiped |
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116 | (2) |
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7.1.1.2 Radial heat flow in an infinite circular cylinder |
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118 | (2) |
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7.1.1.3 Radial heat flow in a sphere |
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120 | (2) |
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7.1.2 Variable temperature |
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122 | (1) |
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7.1.2.1 Cartesian coordinates |
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122 | (2) |
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7.1.2.2 Cylindrical coordinates |
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124 | (2) |
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7.1.2.3 Spherical polar coordinates |
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126 | (2) |
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7.2 Heat conduction in anisotropic solids |
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128 | (6) |
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7.2.1 Conduction in a thin crystal plate |
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131 | (3) |
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7.3 Thermal boundary layers |
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134 | (5) |
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7.4 Composite beams with embedded shape memory alloy |
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139 | (10) |
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7.4.1 Constitutive relations for a shape memory alloy |
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140 | (3) |
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7.4.2 Bending of a SMA composite beam |
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143 | (2) |
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145 | (4) |
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8 Extended thermodynamics of Jou--Casas-Vazquez--Lebon |
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149 | (18) |
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8.1 Summary of Extended Irreversible Thermodynamics (EIT) |
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150 | (7) |
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8.1.1 The generalized Gibbs equation |
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150 | (2) |
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8.1.2 The generalized entropy flux and entropy production |
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152 | (2) |
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8.1.3 Evolution equations of the fluxes |
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154 | (1) |
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8.1.4 Non-equilibrium equations of state and convexity requirements |
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155 | (2) |
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8.2 Microscopic foundations |
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157 | (8) |
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8.2.1 Kinetic theory of gases |
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157 | (1) |
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157 | (4) |
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161 | (1) |
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8.2.2.1 Second moments of equilibrium fluctuations |
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161 | (2) |
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163 | (2) |
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165 | (2) |
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167 | (12) |
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167 | (4) |
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9.2 Continuum with dislocations |
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171 | (4) |
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9.3 On plasticity of metals |
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175 | (2) |
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9.4 Dislocations in geophysics |
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177 | (2) |
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179 | (44) |
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179 | (3) |
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10.2 Propagation of acoustic waves in nonlinear materials with memory |
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182 | (2) |
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10.3 Bulk waves in nonlinear elasticity |
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184 | (6) |
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10.3.1 Modicum of the wave front description |
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184 | (3) |
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10.3.2 An approximate solution in the vicinity of the front |
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187 | (3) |
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10.4 Water waves and surface waves in linear solids |
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190 | (29) |
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190 | (1) |
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10.4.2 Water waves in an ideal incompressible fluid model |
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191 | (6) |
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10.4.3 Surface waves in linear elastic solids |
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197 | (1) |
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10.4.3.1 Plane boundaries of linear elastic homogeneous materials |
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198 | (7) |
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10.4.3.2 Rayleigh waves on cylindrical boundaries |
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205 | (3) |
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10.4.4 Waves in a layer of an ideal fluid and Love waves on plane boundaries |
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208 | (1) |
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10.4.4.1 Layer of a compressible fluid on a semiinfinite rigid body |
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208 | (1) |
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10.4.4.2 Love waves on plane boundaries |
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209 | (3) |
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10.4.5 Rayleigh waves in a layer of elastic material |
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212 | (2) |
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214 | (1) |
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10.4.6.1 Interface of two semiinfinite elastic solids |
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214 | (3) |
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10.4.6.2 Semiinfinite elastic solid and semiinfinite ideal fluid |
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217 | (2) |
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10.4.6.3 Semiinfinite elastic solid and a layer of an ideal fluid |
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219 | (1) |
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10.5 A few remarks on leaky waves |
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219 | (1) |
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10.6 Bulk and surface waves in viscoelastic solids |
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220 | (3) |
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11 Interactions of ponderable bodies with electromagnetic fields |
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223 | (50) |
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223 | (2) |
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11.2 Primer of Maxwell theory of electromagnetism |
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225 | (12) |
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11.2.1 Governing equations |
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225 | (9) |
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11.2.2 Lorentz invariance of the Maxwell equations |
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234 | (3) |
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11.3 On thermodynamics of coupled fields |
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237 | (2) |
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11.4 Magnetohydrodynamics of plasmas |
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239 | (15) |
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239 | (2) |
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11.4.2 Characteristic parameters |
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241 | (5) |
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11.4.3 MHD-model derived from the theory of miscible mixtures |
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246 | (4) |
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11.4.4 Two-component model |
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250 | (4) |
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11.5 Magnetohydrodynamics of a single component fluid |
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254 | (13) |
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11.5.1 Dimensionless notation, approximations |
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254 | (9) |
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11.5.2 Some steady state flows |
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263 | (1) |
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11.5.2.1 Poiseuille-Hartmann flow |
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264 | (2) |
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266 | (1) |
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11.6 A few remarks on the stability of plasmas |
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267 | (6) |
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11.6.1 Linear stability analysis of the ideal plasma model |
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267 | (3) |
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11.6.2 A few particular cases of instabilities |
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270 | (3) |
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12 Mechanics of porous materials |
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273 | (40) |
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12.1 Summary of two-component models |
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273 | (6) |
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12.1.1 Immiscible mixtures |
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273 | (1) |
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12.1.2 Lagrangian description of multi-component porous media |
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274 | (3) |
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12.1.3 Eulerian description of multi-component porous media |
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277 | (2) |
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12.2 Two-component models with constitutive relations for the porosity |
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279 | (11) |
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12.2.1 Fields and field equations |
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280 | (3) |
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12.2.2 Thermodynamic admissibility |
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283 | (1) |
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12.2.2.1 Second law of thermodynamics |
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283 | (1) |
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284 | (2) |
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286 | (4) |
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12.3 Double- and multi-porosity models |
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290 | (13) |
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12.3.1 Fissured rocks -- example of a model with double porosity |
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290 | (1) |
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12.3.1.1 Basic physical concepts |
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291 | (1) |
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12.3.1.2 Equation of motion of a uniform liquid in fissured rocks |
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292 | (2) |
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12.3.1.3 Homogeneous liquid in a medium with double porosity |
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294 | (1) |
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12.3.1.4 Non-steady-state flow of liquid in a gallery |
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295 | (4) |
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12.3.2 Multi-porosity models in bioengineering - swelling media |
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299 | (1) |
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12.3.2.1 Cardiovascular disease |
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299 | (1) |
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300 | (3) |
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12.4 Biomechanics of soft tissues |
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303 | (10) |
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12.4.1 Structure of soft tissues -- collagen and elastin |
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304 | (1) |
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12.4.2 General mechanical characteristic of soft tissues |
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305 | (1) |
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306 | (2) |
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12.4.4 Example: A model for the artery |
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308 | (3) |
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12.4.5 Material parameters, numerical analysis and results |
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311 | (2) |
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13 Thermodynamics of porous materials with the porosity balance |
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313 | (60) |
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13.1 Summary: Balance equation of porosity and associated models |
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313 | (5) |
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13.1.1 Balance equation of porosity |
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313 | (1) |
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13.1.2 Full and simplified models with the balance equation of porosity |
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314 | (4) |
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13.2 Freezing and thawing |
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318 | (9) |
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318 | (1) |
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13.2.2 Modeling of the diffusion range (PE-range) without freezing |
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319 | (1) |
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13.2.2.1 Specification of the material parameters |
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320 | (3) |
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13.2.3 Governing equations for material damaged by freezing (F-range) |
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323 | (3) |
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13.2.4 Iterative procedure |
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326 | (1) |
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327 | (1) |
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13.3 Linear stability of a ID flow under transversal disturbance with adsorption |
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327 | (12) |
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327 | (2) |
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13.3.2 Adsorption/diffusion model |
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329 | (3) |
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13.3.3 Regular perturbation |
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332 | (3) |
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13.3.4 Wave ansatz for the disturbance |
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335 | (1) |
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13.3.5 Numerical investigation |
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336 | (1) |
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13.3.6 Properties of some other disturbances of the base flow |
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337 | (2) |
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339 | (1) |
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13.4 Wave propagation in porous media with anisotropic permeability |
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339 | (19) |
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13.4.1 Anisotropy of porous materials |
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339 | (1) |
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13.4.1.1 Anisotropy of the stress-strain relations |
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340 | (1) |
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13.4.1.2 Anisotropy of the permeability |
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340 | (2) |
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13.4.2 Governing equations accounting for anisotropic permeability |
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342 | (1) |
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13.4.3 Monochromatic waves |
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343 | (1) |
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13.4.4 Decoupled transversal wave |
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344 | (3) |
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347 | (6) |
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13.4.6 Shear polarization |
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353 | (4) |
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357 | (1) |
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13.5 Wave propagation in three-component porous media |
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358 | (15) |
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358 | (1) |
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358 | (2) |
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13.5.3 Material parameters |
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360 | (2) |
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13.5.4 General propagation condition of monochromatic waves |
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362 | (1) |
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13.5.4.1 Transversal wave |
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363 | (1) |
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13.5.4.2 Longitudinal waves |
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364 | (1) |
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13.5.5 Numerical analysis of the wave propagation |
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365 | (1) |
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13.5.5.1 Discussion of numerical results |
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366 | (4) |
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13.5.6 Comparison with suspensions and experiments |
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370 | (1) |
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370 | (3) |
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373 | (50) |
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374 | (27) |
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A.1 Mathematical basics shown on the example of polar decomposition |
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374 | (7) |
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A.2 Curvilinear coordinate systems |
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381 | (1) |
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A.2.1 General considerations |
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381 | (5) |
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A.2.2 Cylindrical coordinates |
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386 | (2) |
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A.2.3 Spherical coordinates |
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388 | (1) |
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A.2.4 Ellipsoidal coordinates |
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389 | (1) |
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A.2.4.1 Confocal ellipsoidal coordinates |
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389 | (2) |
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A.2.4.2 Elliptic cylindrical coordinates |
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391 | (1) |
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A.2.5 Paraboloidal coordinates |
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392 | (1) |
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A.2.5.1 Confocal paraboloidal coordinates |
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392 | (2) |
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A.2.5.2 Parabolic coordinates |
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394 | (1) |
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A.2.5.3 Parabolic cylindrical coordinates |
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394 | (1) |
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A.2.6 Bipolar coordinates |
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395 | (2) |
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A.2.7 Toroidal coordinates |
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397 | (2) |
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A.2.8 Non-orthogonal coordinates |
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399 | (2) |
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401 | (4) |
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401 | (1) |
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402 | (3) |
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405 | (13) |
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405 | (1) |
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C.2 Statics of isotropic elastic materials |
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405 | (3) |
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C.3 Dynamical Green function for isotropic elastic materials |
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408 | (4) |
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C.4 Some fundamental solutions for poroelastic and thermoelastic materials |
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412 | (6) |
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D Bessel functions and Bessel equation |
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418 | (2) |
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420 | (3) |
| Bibliography |
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423 | (30) |
| Index of Researchers |
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453 | (4) |
| Subject Index |
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457 | |
Lisainfo e-raamatute kohta