Preface |
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ix | |
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Random Variables and Generating Functions |
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1 | (28) |
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Introduction to Random Variables |
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1 | (6) |
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7 | (3) |
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The Characteristic Function |
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10 | (3) |
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13 | (1) |
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Probability Generating Functions |
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14 | (3) |
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Cumulants and Cumulant Generating Functions |
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17 | (2) |
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Probability Weighted Moments |
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19 | (1) |
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19 | (1) |
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Experimental and Theoretical Moments |
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20 | (9) |
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21 | (1) |
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22 | (1) |
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22 | (4) |
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Appendix A: Exponential Distributions |
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26 | (1) |
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Appendix B: Maximum Likelihood Estimation |
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27 | (2) |
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Laplace Transforms for Solute Transport Models |
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29 | (28) |
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Definition of the Transform and its Inverse |
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29 | (3) |
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Singularities of the Laplace Transform |
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32 | (2) |
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Green's Functions for Initial Value Problems |
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34 | (1) |
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Solute Transport by Diffusion |
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35 | (3) |
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Advective -- Dispersive Solute Transport Model |
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38 | (5) |
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Role of Boundary Conditions |
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43 | (3) |
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The Mobile -- Immobile Water Model |
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46 | (3) |
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The Physical Nonequilibrium Model |
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49 | (3) |
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The Chemical Nonequilibrium Model |
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52 | (2) |
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Nonequilibrium Sorption by Diffusion into Spherical Grains |
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54 | (3) |
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Fourier Transforms for Solute Transport Models |
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57 | (20) |
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Solute Transport by Diffusion |
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57 | (3) |
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60 | (1) |
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Fourier Transform of the Diffusion Equation |
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61 | (2) |
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Fourier Transforms of Derivatives |
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63 | (2) |
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Fourier Sine and Cosine Transforms |
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65 | (5) |
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Fourier Transform Solution for Advection-Dispersion Equation Over an Infinite Domain |
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70 | (1) |
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Fourier Sine Transform for Advection-Dispersion Equation Over Semi-Infinite Domains |
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71 | (1) |
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Fourier Transforms in Higher Dimensions |
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72 | (5) |
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Transfer Function Approaches |
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77 | (28) |
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Residence Time Distributions |
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77 | (1) |
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Models of Solute Transport |
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78 | (5) |
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Depth Moments of the Advection-Dispersion Equation |
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83 | (4) |
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Depth-Moments for Stochastic-Convective Models |
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87 | (1) |
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Transfer Functions for Layered Soils |
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88 | (3) |
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Stochastic Stream Tube Models |
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91 | (2) |
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A Stochastic Stream Tube Model for Contaminant Dissolution and Transport with Degradation |
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93 | (12) |
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93 | (12) |
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Temporal Moment Analysis for Solute Transport in Porous Media |
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105 | (38) |
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Model Descriptions and Governing Differential Equations |
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106 | (3) |
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Temporal Moment Definitions |
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109 | (2) |
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Aris's Method of Moment Analysis |
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111 | (5) |
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Computing Time Moments from Experimental Data |
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116 | (7) |
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116 | (1) |
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Computing Moments from Observed Data |
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117 | (2) |
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119 | (4) |
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Applications of the Method of Moments |
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123 | (11) |
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Estimating Parameters of the Transport Equation |
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123 | (5) |
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128 | (1) |
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129 | (5) |
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134 | (1) |
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Appendix: Sample BTC Data |
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135 | (8) |
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Spatial Moment Analysis for Solute Transport in Porous Media |
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143 | (12) |
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143 | (2) |
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145 | (1) |
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Spatial Moments to Describe Solute Plume Behavior |
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146 | (3) |
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Spatial Moments for the PNE Model |
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149 | (2) |
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Spatial Moments for First-Order Rate Model |
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151 | (4) |
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Moment Analysis for Volatile Compounds |
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155 | (28) |
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155 | (2) |
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Immobile Vapor Phase Model |
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157 | (5) |
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Description of Loss Fractions |
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162 | (1) |
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Effective Parameter Definitions |
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163 | (10) |
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173 | (8) |
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Spatial Moments for Mobile Vapor Phase Model |
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181 | (2) |
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Moment Generating Differential Equations |
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183 | (24) |
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183 | (2) |
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Temporal MGDEs for Solute Transport in Soil |
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185 | (4) |
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Analysis with Degradation |
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186 | (1) |
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Analysis without Degradation |
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187 | (2) |
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Spatial MGDEs for PNE Model of Solute Transport in Soil |
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189 | (10) |
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192 | (5) |
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197 | (1) |
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198 | (1) |
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Spatial Moments for a Two-Layer Aquifer |
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199 | (4) |
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Perfectly Stratified Aquifer with Velocity Variation |
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203 | (4) |
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Momemt Analysis for Compounds Undergoing Sequential Decay Chain Reactions |
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207 | (16) |
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207 | (1) |
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Governing Differential Equations |
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207 | (2) |
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209 | (1) |
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210 | (5) |
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Temporal Moments for Advective Transport |
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215 | (2) |
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Spatial Moments for Compounds Undergoing Sequential First-Order Decay Chain |
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217 | (6) |
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Applications of Moments in Interval Computing Methods |
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223 | (24) |
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223 | (1) |
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Interval Arithmetic Operations |
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224 | (1) |
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Interval Distribution Functions |
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225 | (2) |
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Defining Moments from Interval Distribution Functions |
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227 | (1) |
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Application to a Remediation Example |
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227 | (10) |
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First-Order Degradation Model |
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228 | (1) |
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Statistical Distributions of Degradation Rates and Initial Concentrations |
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229 | (2) |
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231 | (2) |
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233 | (4) |
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Application to Solute Transport Experiment |
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237 | (10) |
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Description of the Solute Transport Experiment |
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238 | (1) |
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Advective Solute Transport in Vadose Zone |
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238 | (2) |
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Field-Scale Model using Interval Computing Method |
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240 | (1) |
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Stochastic Advective Solute Transport |
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241 | (3) |
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244 | (3) |
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Moment Analysis for Subsurface Storm Flow |
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247 | (18) |
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247 | (2) |
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Moments For Linearized Subsurface Drainage with No Recharge |
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249 | (3) |
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Subsurface Drainage with Lateral Inflow |
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252 | (4) |
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Transfer Function Approach for Subsurface Drainage |
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256 | (9) |
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256 | (4) |
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Moments and Experimental Results |
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260 | (5) |
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Constructing Concentration Distributions from Moments |
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265 | (12) |
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265 | (2) |
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267 | (1) |
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Polynomial Summation Methods |
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267 | (4) |
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Gram-Charlier and Edgeworth Series Approach |
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267 | (3) |
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Expansion Methods Based on other Polynomials |
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270 | (1) |
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Maximum Entropy (Maxent) Method |
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271 | (3) |
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273 | (1) |
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274 | (3) |
References |
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277 | (12) |
Index |
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289 | |