Interface and Transport Dynamics

by Emmerich, Heike; Nestler, Britta; Schreckenberg, Michael; Schreckenberg, Michael

• ISBN13: 9783540403678
• ISBN10: 3540403671
• Format: Hardcover
• Copyright: 2003-09-01
• Publisher: Springer Verlag

Summary

The book contains an overview of the recent progress of research in computational physics and materials science. Particular topics are modelling of traffic flow and complex multi-scale solidification phenomena. The sections introduce novel research results of experts from a considerable diversity of disciplines such as physics, mathematical and computational modelling, nonlinear dynamics, materials sciences, statistical mechanics and foundry technique. The book intends to create a comprehensive and coherent image of the current research status and illustrates new simulation results of transport and interface dynamics by high resolution graphics. Various possible perspectives are formulated for future activities. Special emphasis is laid on exchanging experiences concerning numerical tools and on the bridging of the scales as is necessary in a variety of scientific and engineering applications. An interesting possibility along this line was the coupling of different computational approaches leading to hybrid simulations.

Table of Contents

I INTERFACE DYNAMICS: Phenomenology and Modelling
Melting Kinetics of Prolate Spheroidal Crystals	3	(17)
M.E. Glicksman
A. Lupulescu
M.B. Koss
Introduction	3	(1)
Dendritic Growth	3	(1)
Isothermal Dendritic Growth Experiment (IDGE)	3	(1)
Mushy Zones	4	(1)
Video Melting Data	4	(1)
Data Analysis	5	(1)
Image Processing	5	(1)
Quasi-static Theory	6	(7)
Background	6	(1)
Potential Theoretic Formulation	6	(3)
Enthalpy Flux	9	(2)
Enthalpy Current	11	(1)
Kinematic Formulation	11	(2)
Results	13	(4)
Experimental Melting Rates	13	(2)
Thermal Data	15	(2)
Conclusions	17	(1)
Acknowledgements	17	(3)
Deterministic Behaviour in Sidebranching Development	20	(6)
Ricard Gonzalez-Cinca
Yves Couder
Introduction	20	(1)
Experimental Results	20	(2)
Model	22	(1)
Numerical Procedure and Results	23	(3)
Growth Dynamics during Solidification of Undercooled Melts	26	(21)
Dieter Herlach
Introduction	26	(1)
Experimental	27	(2)
Description of Dendrite Growth in Undercooled Melts	29	(3)
Experimental Results on Dendrite Growth in Undercooled Melts	32	(12)
Pure Metals	32	(2)
Solid Solutions	34	(1)
Dilute Multiphase Alloys	35	(2)
Intermetallics with Superlattice Structures	37	(2)
Complex Structures of Polytetrahedral Phases	39	(2)
Faceted and Non-Faceted Growth of Semiconductors	41	(3)
Summary and Conclusions	44	(3)
Thermodynamics of Diffuse Interfaces	47	(18)
G.J.Schmitz
Introduction	47	(2)
General Considerations	49	(1)
Thermodynamic Approaches to Interfacial Energy	50	(1)
Crystal Growth Models	50	(5)
Approaches from Theories of Phase Transitions	55	(2)
Statistical Approach	57	(4)
Conclusions	61	(2)
Acknowledgments	63	(2)
Computer Investigation of the Influence of the Internal Structure Topology on the Percolation Process in Two- and Three-Dimensional Inhomogeneous Systems	65	(10)
Aliaksei Konash
Sergey Bagnich
Introduction	65	(1)
Computational Technique	66	(1)
Results and Discussion	67	(6)
Conclusion	73	(2)
Electron Transport of Nanoperm Alloys	75	(7)
K. Pekala
Introduction	75	(1)
Experiments	75	(1)
Results and Discussion	76	(3)
Electrical Resistivity	76	(1)
Crystalline Fraction	77	(2)
Thermoelectric Power	79	(1)
Conclusion	79	(3)
Self-Organized Formation of Fractal and Regular Pores in Semiconductors	82	(6)
Jens Christian Claussen
Jurgen Carstensen
Marc Christophersen
Sergiu Langa
Helmut Foll
Electrochemical Etching: Basic Experimental Setup	82	(1)
The Current-Burst Model	83	(1)
Consequences on Pore Geometries	84	(3)
Conclusions	87	(1)
Evolution and Shapes of Dunes	88	(15)
Hans J. Herrmann
Gerd Sauermann
Introduction	88	(1)
Experimental Measurements of a Barchan Dune	89	(5)
Dune Morphology	89	(3)
Wind Velocity and Sand Flux	92	(2)
The Model	94	(6)
The Wind Shear Stress	95	(2)
The Sand Flux	97	(1)
The Surface Evolution	98	(2)
The Shape of the Dune and Outlook	100	(3)
Morphogenesis of Growing Amorphous Films	103	(18)
Stefan J. Linz
Martin Raible
Peter Hanggi
Introduction	103	(1)
Basic Concepts	104	(5)
Deposition Equation for Thin Film Growth	109	(8)
Conclusions and Perspectives	117	(4)
II INTERFACE DYNAMICS: Modelling and Simulation
Density Effects and Fluid Flow in Phase-field Models	121	(15)
Massimo Conti
Introduction	121	(2)
Phase-field Model for a Pure Material	123	(4)
The Entropy Balance	123	(2)
The Thermodynamic Potential	125	(1)
Nondimensional Equations in one Dimension	126	(1)
Phase-field Model for a Binary Alloy	127	(3)
Numerical Solutions	130	(4)
Pure Substance	130	(3)
Binary Alloy	133	(1)
Conclusions	134	(2)
A Lattice Boltzmann Method for the Mesoscopic Calculation of Anisotropic Crystal Growth	136	(6)
Wolfram Miller
Igor Rasin
Introduction	136	(1)
Lattice Phase-field Model	136	(2)
Results	138	(2)
Conclusions	140	(2)
A Phase-field Model for the Solidification Process in Multicomponent Alloys	142	(8)
H. Garcke
B. Nestler
B. Stinner
Solidification Effects and Length Scales	142	(1)
Description of the Model	143	(2)
The Related Sharp Interface Model	145	(2)
Examples	147	(1)
Further Generalizations	148	(2)
Planar Solidification from Undercooled Melt: An Approximation of a Dilute Binary Alloy for a Phase-field Model	150	(10)
Denis Danilov
Introduction	150	(1)
The Model	151	(1)
An Approximation of a Small Impurity Concentration	152	(2)
Stationary Interface	154	(1)
Large-Velocity Asymptotics	154	(1)
Numerical Calculations	155	(3)
Conclusions	158	(2)
Initial Transients in the Symmetric Model for Directional Solidification	160	(6)
Raul Benitez
Laureano Ramirez-Piscina
Introduction	160	(1)
The Sharp Interface Model	160	(2)
The Phase-field Model	162	(1)
Results and Discussion	163	(1)
Concluding Remarks	164	(2)
Dynamics of a Faceted Nematic-Smectic B Front in Thin-Sample Directional Solidification	166	(6)
Tamas Borzsonyi
Silvere Akamatsu
Gabriel Faivre
Introduction	166	(1)
Results	167	(1)
Experiments	167	(1)
Linear Stability Analysis	168	(1)
Phase-field Simulations	169	(3)
Last Stage Solidification of Alloys: A Theoretical Study of Dendrite Arm and Grain Coalescence	172	(10)
M. Rappaz
A. Jacot
W. J. Boettinger
Introduction and Theoretical Aspects	172	(3)
Results and Discussion	175	(4)
Conclusion	179	(1)
Acknowledgements	180	(2)
Phase-field Modeling of Eutectic Solidification: From Oscillations to Invasion	182	(8)
Roger Folch
Mathis Plapp
Introduction	182	(1)
Model	183	(2)
Simulations	185	(3)
Conclusion	188	(2)
Phase-field Theory of Nucleation and Growth in Binary Alloys	190	(6)
Laszlo Granasy
Tamas Borzsonyi
Tamas Pusztai
Introduction: Diffuse Interface and Nucleation	190	(1)
Phase-field Theory of Nucleation	191	(2)
Nucleation in 3D	191	(1)
Multi Particle Solidification in 2D	192	(1)
Results and Discussion	193	(3)
Modelling of Phase Transformations in Titanium Alloys with a Phase-field Model	196	(6)
Benoit Appolaire
Elisabeth Gautier
Introduction	196	(1)
Which Model to Choose?	197	(1)
Can we Rely on the Model to Get Quantitative Predictions?	198	(4)
Spreading of Liquid Monolayers: From Kinetic Monte Carlo Simulations to Continuum Limit	202	(6)
M. N. Popescu
S. Dietrich
Introduction	202	(1)
Model and KMC Simulations	202	(2)
Results and Discussion	204	(2)
Patterned Substrates	206	(1)
Summary and Conclusions	207	(1)
A Multi-mesh Finite Element Method for Phase-field Simulations	208	(10)
Alfred Schmidt
Models for Solidification	208	(3)
Sharp Interface Models	209	(1)
Diffuse Interface Models	209	(2)
Adaptive Finite Element Methods for Coupled Systems of PDE	211	(2)
Aspects of Implementation	212	(1)
Numerical Analysis and Adaptive Methods	212	(1)
Adaptive Method for Phase-field Models	213	(5)
Transport of Point Defects in Growing Si Crystals	218	(8)
Axel Voigt
Christian Weichmann
Introduction	218	(1)
Point defect modeling	219	(3)
Finite element discretisation	222	(1)
Results	223	(1)
Conclusions	224	(1)
Acknowledgment	225	(1)
Atomistic Simulation of Transport Phenomena in Simple and Complex Fluids and Fluid Mixtures	226	(23)
Kurt Binder
Jurgen Horbach
Walter Kob
Fathollah Varnik
Introduction	226	(1)
Interdiffusion and Selfdiffusion in Binary Mixtures (A,B)	227	(6)
Estimation of Selfdiffusion Coefficients in Various Models of Fluids	233	(7)
Estimation of the Shear Viscosity	240	(4)
Thermal Conductivity	244	(1)
Concluding Remarks	245	(4)
Unusual Viscosity Feature in Spinodal Decomposition Under Shear Flow	249	(6)
Jian Wang
Wolfram Gronski
Christian Friedrich
Peter Galenko
Dieter Herlach
Introduction	249	(1)
Theory	250	(1)
Simulation Detail	251	(2)
Conclusion	253	(2)
Micro-macro Approach to Cluster Formation in Granular Media	255	(14)
S. Luding
Introduction	255	(1)
Models for Multi-particle Simulations	256	(2)
The Event-driven, Rigid Particle Method	256	(1)
The Time Driven, Soft Particle Technique	257	(1)
The Connection Between Hard- and Soft-sphere Models	258	(1)
Freely Cooling Granular Media	258	(7)
Homogeneous and Inhomogeneous Cooling	260	(1)
Cluster Structure	261	(1)
Cluster Growth	261	(2)
Micro-macro Transition	263	(2)
Summary and Conclusion	265	(4)
III Transport
Urban Transport Phenomena in the Street Canyon	269	(6)
Maciej M. Duras
The Field Models of Vehicles and Pollutants	269	(1)
The Governing Equations	270	(2)
Optimal Control Problems	272	(1)
Conclusions	273	(1)
Acknowledgements	273	(2)
Walker Behaviour Modelling by Differential Games	275	(20)
Serge P. Hoogendoorn
Introduction	275	(1)
Pedestrian Behaviour Framework	276	(2)
Theory of Walking	278	(2)
Conceptual Pedestrian Walking Task Model	280	(6)
Walking Subtask Hierarchy	280	(1)
Walking as a Feedback-oriented Control System	281	(2)
Pedestrian Kinematics (Internal Model)	283	(1)
Walking Discomfort (Resistance)	284	(1)
Cost Components	285	(1)
Cost L1 due to Deviation from Planned Route	285	(1)
Proximity Cost L2	285	(1)
Acceleration and Deceleration Cost L3	286	(1)
Derivation of Walker Model	286	(5)
Application of the Maximum Principle	286	(3)
Cooperative Walker Model	289	(1)
Relation to the Social-forces Model	290	(1)
Model Refinements	290	(1)
Approach to Model Calibration	291	(1)
Application Results	292	(1)
Conclusions and Future Research Directions	293	(2)
Investigations of Vibrations in the Complex Dynamical Systems of Transmission Pipelines	295	(6)
Elena Mul
Vladimir Kravchenko
Introduction	295	(1)
Model	296	(1)
Method	296	(4)
Discussion of Results and Conclusions	300	(1)
Information in Intelligent Transportation System	301	(16)
J. Wahle
M. Schreckenberg
Introduction	301	(1)
Two-route scenario	302	(3)
Simulation technique	304	(1)
Floating-Car Data	305	(5)
Influence of the dynamic drivers	307	(2)
Influence of the static drivers	309	(1)
Different criteria	310	(4)
Gradient of travel time	310	(1)
Global density and speed	311	(2)
Comparison	313	(1)
Summary and conclusion	314	(3)
Experiments on Route Choice Behaviour	317	(5)
Reinhard Selten
Michael Schreckenberg
Thomas Pitz
Thorsten Chmura
Joachim Wahle
Introduction	317	(1)
Experimental Setup	318	(1)
Equilibrium Predictions and Observed Behaviour	318	(1)
Response Mode	319	(1)
Payoffs and Road Changes	320	(1)
Conclusion	320	(2)
Transport Out of a Gravitationally Stable Layer with the Help of a Faster Diffusing Substance: PDE Simulations and Scaling Laws	322	(7)
Karsten Koetter
Malte Schmick
Mario Markus
Introduction	322	(1)
Analytical Estimates	323	(1)
Experiments	324	(1)
PDE Simulations	325	(1)
Conclusion	326	(3)
Microscopic Parameters and Macroscopic Features of Traffic Flow	329	(14)
Peter Berg
Eddie Wilson
Microscopic Parameters of Traffic Flow	329	(1)
Stochastic and Deterministic Microscopic Description	330	(1)
A Cellular Automata Model	330	(1)
Car-following Models	331	(1)
Optimal-velocity Car-following Models	331	(1)
Derivation of Macroscopic Counterparts	332	(2)
Similarity of Flow Patterns	334	(1)
More Realistic Models	335	(6)
Multi-species Traffic; Temporal and Spatial Variations of Driver Behaviour	337	(2)
Reaction Time	339	(1)
Multiple Look-ahead Models	339	(1)
Multi-lane Flow	340	(1)
Synchronised Flow	341	(1)
Outlook	341	(2)
An Adaptive Smoothing Method for Traffic State Identification from Incomplete Information	343	(18)
Martin Treiber
Dirk Helbing
Introduction	343	(1)
Description of the Method	344	(6)
Application to German Freeways	350	(7)
Summary and Outlook	357	(4)
Probabilistic Description of Nucleation in Vapours and on Roads	361	(29)
Reinhard Mahnke
Introduction	361	(2)
Stochastic Master Equation Approach	363	(5)
Nucleation in Supersaturated Vapours	368	(8)
Car Cluster Formation on Roads	376	(6)
An Advanced Model of Car Cluster Formation	382	(3)
Conclusion	385	(1)
Appendix: Derivation of Thermodynamic Potential and Corresponding Transition Rate	385	(5)
Cellular Automata Simulation of Collective Phenomena in Pedestrian Dynamics	390	(16)
Andreas Schadschneider
Ansgar Kirchner
Katsuhiro Nishinari
Introduction	390	(3)
Collective Effects	390	(2)
Modelling Approaches	392	(1)
Basic Principles of the Model	393	(2)
Definition of the Model	395	(2)
Collective Phenomena	397	(2)
Influence of the Floor Fields	399	(2)
Friction Effects	401	(2)
Conclusions	403	(3)
Modeling, Simulation and Observations for Freeway Traffic and Pedestrian	406	(16)
Yuki Sugiyama
Akihiro Nakayama
Introduction	406	(1)
Brief Review of OV Model (Traffic in Circuit)	406	(2)
Observations in the Bottleneck	408	(2)
OV Model with a Bottleneck	410	(8)
Modelling and Simulation	410	(2)
The Structure of Flow Upstream of Bottleneck	412	(5)
Summary and Conjecture	417	(1)
Modeling Pedestrians in 2-dimensional OV Models	418	(4)
Testing Traffic Flow Models	422
Elmar Brockfeld
Peter Wagner
So Much Models, so Little Time	422
Theory	422
Testing Dynamical Models	423
The Trouble with the Data	426
Daganzo's Data	426
The Contest	427
Building a Reference Model	427
Technicalities	428
The Rest of the Pack	429
Finally, the Rest (Preliminary Results!!!)	430
Conclusions & Further Plans	431