
Interface and Transport Dynamics
Computational Modelling
By: Heike Ed Emmerich, Heike Emmerich (Editor), Britta Nestler (Editor)
Hardcover | 3 September 2003
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458 Pages
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| Interface Dynamics: Phenomenology and Modelling | |
| Melting Kinetics of Prolate Spheroidal Crystals | p. 3 |
| Introduction | p. 3 |
| Dendritic Growth | p. 3 |
| Isothermal Dendritic Growth Experiment (IDGE) | p. 3 |
| Mushy Zones | p. 4 |
| Video Melting Data | p. 4 |
| Data Analysis | p. 5 |
| Image Processing | p. 5 |
| Quasi-static Theory | p. 6 |
| Background | p. 6 |
| Potential Theoretic Formulation | p. 6 |
| Enthalpy Flux | p. 9 |
| Enthalpy Current | p. 11 |
| Kinematic Formulation | p. 11 |
| Results | p. 13 |
| Experimental Melting Rates | p. 13 |
| Thermal Data | p. 15 |
| Conclusions | p. 17 |
| Acknowledgements | p. 17 |
| Deterministic Behaviour in Sidebranching Development | p. 20 |
| Introduction | p. 20 |
| Experimental Results | p. 20 |
| Model | p. 22 |
| Numerical Procedure and Results | p. 23 |
| Growth Dynamics during Solidification of Undercooled Melts | p. 26 |
| Introduction | p. 26 |
| Experimental | p. 27 |
| Description of Dendrite Growth in Undercooled Melts | p. 29 |
| Experimental Results on Dendrite Growth in Undercooled Melts | p. 32 |
| Pure Metals | p. 32 |
| Solid Solutions | p. 34 |
| Dilute Multiphase Alloys | p. 35 |
| Intermetallics with Superlattice Structures | p. 37 |
| Complex Structures of Polytetrahedral Phases | p. 39 |
| Faceted and Non-Faceted Growth of Semiconductors | p. 41 |
| Summary and Conclusions | p. 44 |
| Thermodynamics of Diffuse Interfaces | p. 47 |
| Introduction | p. 47 |
| General Considerations | p. 49 |
| Thermodynamic Approaches to Interfacial Energy | p. 50 |
| Crystal Growth Models | p. 50 |
| Approaches from Theories of Phase Transitions | p. 55 |
| Statistical Approach | p. 57 |
| Conclusions | p. 61 |
| Acknowledgments | p. 63 |
| Computer Investigation of the Influence of the Internal Structure Topology on the Percolation Process in Two- and Three-Dimensional Inhomogeneous Systems | p. 65 |
| Introduction | p. 65 |
| Computational Technique | p. 66 |
| Results and Discussion | p. 67 |
| Conclusion | p. 73 |
| Electron Transport of Nanoperm Alloys | p. 75 |
| Introduction | p. 75 |
| Experiments | p. 75 |
| Results and Discussion | p. 76 |
| Electrical Resistivity | p. 76 |
| Crystalline Fraction | p. 77 |
| Thermoelectric Power | p. 79 |
| Conclusion | p. 79 |
| Self-Organized Formation of Fractal and Regular Pores in Semiconductors | p. 82 |
| Electrochemical Etching: Basic Experimental Setup | p. 82 |
| The Current-Burst Model | p. 83 |
| Consequences on Pore Geometries | p. 84 |
| Conclusions | p. 87 |
| Evolution and Shapes of Dunes | p. 88 |
| Introduction | p. 88 |
| Experimental Measurements of a Barchan Dune | p. 89 |
| Dune Morphology | p. 89 |
| Wind Velocity and Sand Flux | p. 92 |
| The Model | p. 94 |
| The Wind Shear Stress | p. 95 |
| The Sand Flux | p. 97 |
| The Surface Evolution | p. 98 |
| The Shape of the Dune and Outlook | p. 100 |
| Morphogenesis of Growing Amorphous Films | p. 103 |
| Introduction | p. 103 |
| Basic Concepts | p. 104 |
| Deposition Equation for Thin Film Growth | p. 109 |
| Conclusions and Perspectives | p. 117 |
| Interface Dynamics: Modelling and Simulation | |
| Density Effects and Fluid Flow in Phase-field Models | p. 121 |
| Introduction | p. 121 |
| Phase-field Model for a Pure Material | p. 123 |
| The Entropy Balance | p. 123 |
| The Thermodynamic Potential | p. 125 |
| Nondimensional Equations in one Dimension | p. 126 |
| Phase-field Model for a Binary Alloy | p. 127 |
| Numerical Solutions | p. 130 |
| Pure Substance | p. 130 |
| Binary Alloy | p. 133 |
| Conclusions | p. 134 |
| A Lattice Boltzmann Method for the Mesoscopic Calculation of Anisotropic Crystal Growth | p. 136 |
| Introduction | p. 136 |
| Lattice Phase-field Model | p. 136 |
| Results | p. 138 |
| Conclusions | p. 140 |
| A Phase-field Model for the Solidification Process in Multicomponent Alloys | p. 142 |
| Solidification Effects and Length Scales | p. 142 |
| Description of the Model | p. 143 |
| The Related Sharp Interface Model | p. 145 |
| Examples | p. 147 |
| Further Generalizations | p. 148 |
| Planar Solidification from Undercooled Melt: An Approximation of a Dilute Binary Alloy for a Phase-field Model | p. 150 |
| Introduction | p. 150 |
| The Model | p. 151 |
| An Approximation of a Small Impurity Concentration | p. 152 |
| Stationary Interface | p. 154 |
| Large-Velocity Asymptotics | p. 154 |
| Numerical Calculations | p. 155 |
| Conclusions | p. 158 |
| Initial Transients in the Symmetric Model for Directional Solidification | p. 160 |
| Introduction | p. 160 |
| The Sharp Interface Model | p. 160 |
| The Phase-field Model | p. 162 |
| Results and Discussion | p. 163 |
| Concluding Remarks | p. 164 |
| Dynamics of a Faceted Nematic-Smectic B Front in Thin-Sample Directional Solidification | p. 166 |
| Introduction | p. 166 |
| Results | p. 167 |
| Experiments | p. 167 |
| Linear Stability Analysis | p. 168 |
| Phase-field Simulations | p. 169 |
| Last Stage Solidification of Alloys: A Theoretical Study of Dendrite Arm and Grain Coalescence | p. 172 |
| Introduction and Theoretical Aspects | p. 172 |
| Results and Discussion | p. 175 |
| Conclusion | p. 179 |
| Acknowledgements | p. 180 |
| Phase-field Modeling of Eutectic Solidification: From Oscillations to Invasion | p. 182 |
| Introduction | p. 182 |
| Model | p. 183 |
| Simulations | p. 185 |
| Conclusion | p. 188 |
| Phase-field Theory of Nucleation and Growth in Binary Alloys | p. 190 |
| Introduction: Diffuse Interface and Nucleation | p. 190 |
| Phase-field Theory of Nucleation | p. 191 |
| Nucleation in 3D | p. 191 |
| Multi Particle Solidification in 2D | p. 192 |
| Results and Discussion | p. 193 |
| Modelling of Phase Transformations in Titanium Alloys with a Phase-field Model | p. 196 |
| Introduction | p. 196 |
| Which Model to Choose? | p. 197 |
| Can we Rely on the Model to Get Quantitative Predictions? | p. 198 |
| Spreading of Liquid Monolayers: From Kinetic Monte Carlo Simulations to Continuum Limit | p. 202 |
| Introduction | p. 202 |
| Model and KMC Simulations | p. 202 |
| Results and Discussion | p. 204 |
| Patterned Substrates | p. 206 |
| Summary and Conclusions | p. 207 |
| A Multi-mesh Finite Element Method for Phase-field Simulations | p. 208 |
| Models for Solidification | p. 208 |
| Sharp Interface Models | p. 209 |
| Diffuse Interface Models | p. 209 |
| Adaptive Finite Element Methods for Coupled Systems of PDE .... | p. 211 |
| Aspects of Implementation | p. 212 |
| Numerical Analysis and Adaptive Methods | p. 212 |
| Adaptive Method for Phase-field Models | p. 213 |
| Transport of Point Defects in Growing Si Crystals | p. 218 |
| Introduction | p. 218 |
| Point defect modeling | p. 219 |
| Finite element discretisation | p. 222 |
| Results | p. 223 |
| Conclusions | p. 224 |
| Acknowledgment | p. 225 |
| Atomistic Simulation of Transport Phenomena in Simple and Complex Fluids and Fluid Mixtures | p. 226 |
| Introduction | p. 226 |
| Interdiffusion and Selfdiffusion in Binary Mixtures (A,B) | p. 227 |
| Estimation of Selfdiffusion Coefficients in Various Models of Fluids | p. 233 |
| Estimation of the Shear Viscosity | p. 240 |
| Thermal Conductivity | p. 244 |
| Concluding Remarks | p. 245 |
| Unusual Viscosity Feature in Spinodal Decomposition Under Shear Flow | p. 249 |
| Introduction | p. 249 |
| Theory | p. 250 |
| Simulation Detail | p. 251 |
| Conclusion | p. 253 |
| Micro-macro Approach to Cluster Formation in Granular Media | p. 255 |
| Introduction | p. 255 |
| Models for Multi-particle Simulations | p. 256 |
| The Event-driven, Rigid Particle Method | p. 256 |
| The Time Driven, Soft Particle Technique | p. 257 |
| The Connection Between Hard- and Soft-sphere Models | p. 258 |
| Freely Cooling Granular Media | p. 258 |
| Homogeneous and Inhomogeneous Cooling | p. 260 |
| Cluster Structure | p. 261 |
| Cluster Growth | p. 261 |
| Micro-macro Transition | p. 263 |
| Summary and Conclusion | p. 265 |
| Transport | |
| Urban Transport Phenomena in the Street Canyon | p. 269 |
| The Field Models of Vehicles and Pollutants | p. 269 |
| The Governing Equations | p. 270 |
| Optimal Control Problems | p. 272 |
| Conclusions | p. 273 |
| Acknowledgements | p. 273 |
| Walker Behaviour Modelling by Differential Games | p. 275 |
| Introduction | p. 275 |
| Pedestrian Behaviour Framework | p. 276 |
| Theory of Walking | p. 278 |
| Conceptual Pedestrian Walking Task Model | p. 280 |
| Walking Subtask Hierarchy | p. 280 |
| Walking as a Feedback-oriented Control System | p. 281 |
| Pedestrian Kinematics (Internal Model) | p. 283 |
| Walking Discomfort (Resistance) | p. 284 |
| Cost Components | p. 285 |
| Cost L1 due to Deviation from Planned Route | p. 285 |
| Proximity Cost L2 | p. 285 |
| Acceleration and Deceleration Cost L3 | p. 286 |
| Derivation of Walker Model | p. 286 |
| Application of the Maximum Principle | p. 286 |
| Cooperative Walker Model | p. 289 |
| Relation to the Social-forces Model | p. 290 |
| Model Refinements | p. 290 |
| Approach to Model Calibration | p. 291 |
| Application Results | p. 292 |
| Conclusions and Future Research Directions | p. 293 |
| Investigations of Vibrations in the Complex Dynamical Systems of Transmission Pipelines | p. 295 |
| Introduction | p. 295 |
| Model | p. 296 |
| Method | p. 296 |
| Discussion of Results and Conclusions | p. 300 |
| Information in Intelligent Transportation System | p. 301 |
| Introduction | p. 301 |
| Two-route scenario | p. 302 |
| Simulation technique | p. 304 |
| Floating-Car Data | p. 305 |
| Influence of the dynamic drivers | p. 307 |
| Influence of the static drivers | p. 309 |
| Different criteria | p. 310 |
| Gradient of travel time | p. 310 |
| Global density and speed | p. 311 |
| Comparison | p. 313 |
| Summary and conclusion | p. 314 |
| Experiments on Route Choice Behaviour | p. 317 |
| Introduction | p. 317 |
| Experimental Setup | p. 318 |
| Equilibrium Predictions and Observed Behaviour | p. 318 |
| Response Mode | p. 319 |
| Payoffs and Road Changes | p. 320 |
| Conclusion | p. 320 |
| Transport Out of a Gravitationally Stable Layer with the Help of a Faster Diffusing Substance: PDE Simulations and Scaling Laws | p. 322 |
| Introduction | p. 322 |
| Analytical Estimates | p. 323 |
| Experiments | p. 324 |
| PDE Simulations | p. 325 |
| Conclusion | p. 326 |
| Microscopic Parameters and Macroscopic Features of Traffic Flow | p. 329 |
| Microscopic Parameters of Traffic Flow | p. 329 |
| Stochastic and Deterministic Microscopic Description | p. 330 |
| A Cellular Automata Model | p. 330 |
| Car-following Models | p. 331 |
| Optimal-velocity Car-following Models | p. 331 |
| Derivation of Macroscopic Counterparts | p. 332 |
| Similarity of Flow Patterns | p. 334 |
| More Realistic Models | p. 335 |
| Multi-species Traffic; Temporal and Spatial Variations of Driver Behaviour | p. 337 |
| Reaction Time | p. 339 |
| Multiple Look-ahead Models | p. 339 |
| Multi-lane Flow | p. 340 |
| Synchronised Flow | p. 341 |
| Outlook | p. 341 |
| An Adaptive Smoothing Method for Traffic State Identification from Incomplete Information | p. 343 |
| Introduction | p. 343 |
| Description of the Method | p. 344 |
| Application to German Freeways | p. 350 |
| Summary and Outlook | p. 357 |
| Probabilistic Description of Nucleation in Vapours and on Roads | p. 361 |
| Introduction | p. 361 |
| Stochastic Master Equation Approach | p. 363 |
| Nucleation in Supersaturated Vapours | p. 368 |
| Car Cluster Formation on Roads | p. 376 |
| An Advanced Model of Car Cluster Formation | p. 382 |
| Conclusion | p. 385 |
| Appendix: Derivation of Thermodynamic Potential and Corresponding Transition Rate | p. 385 |
| Cellular Automata Simulation of Collective Phenomena in Pedestrian Dynamics | p. 390 |
| Introduction | p. 390 |
| Collective Effects | p. 390 |
| Modelling Approaches | p. 392 |
| Basic Principles of the Model | p. 393 |
| Definition of the Model | p. 395 |
| Collective Phenomena | p. 397 |
| Influence of the Floor Fields | p. 399 |
| Friction Effects | p. 401 |
| Conclusions | p. 403 |
| Modeling, Simulation and Observations for Freeway Traffic and Pedestrian | p. 406 |
| Introduction | p. 406 |
| Brief Review of OV Model (Traffic in Circuit) | p. 406 |
| Observations in the Bottleneck | p. 408 |
| OV Model with a Bottleneck | p. 410 |
| Modelling and Simulation | p. 410 |
| The Structure of Flow Upstream of Bottleneck | p. 412 |
| Summary and Conjecture | p. 417 |
| Modeling Pedestrians in 2-dimensional OV Models | p. 418 |
| Testing Traffic Flow Models | p. 422 |
| So Much Models, so Little Time | p. 422 |
| Theory | p. 422 |
| Testing Dynamical Models | p. 423 |
| The Trouble with the Data | p. 426 |
| Daganzo's Data | p. 426 |
| The Contest | p. 427 |
| Building a Reference Model | p. 427 |
| Technicalities | p. 428 |
| The Rest of the Pack | p. 429 |
| Finally, the Rest (Preliminary Results!!!) | p. 430 |
| Conclusions & Further Plans | p. 431 |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9783540403678
ISBN-10: 3540403671
Series: Lecture Notes in Computational Science and Engineering, 32
Published: 3rd September 2003
Format: Hardcover
Language: English
Number of Pages: 458
Audience: Professional and Scholarly
Publisher: Springer Nature B.V.
Country of Publication: DE
Dimensions (cm): 23.5 x 15.88 x 1.91
Weight (kg): 0.78
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