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Modelling and Optimisation of Flows on Networks: Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle 2013 ed. [Mīkstie vāki]

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  • Formāts: Paperback / softback, 497 pages, height x width: 235x155 mm, weight: 7723 g, 32 Illustrations, color; 109 Illustrations, black and white; XIV, 497 p. 141 illus., 32 illus. in color., 1 Paperback / softback
  • Sērija : Lecture Notes in Mathematics 2062
  • Izdošanas datums: 14-Dec-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642321593
  • ISBN-13: 9783642321597
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Modelling and Optimisation of Flows on Networks: Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle 2013 ed.Palielināt
  • Formāts: Paperback / softback, 497 pages, height x width: 235x155 mm, weight: 7723 g, 32 Illustrations, color; 109 Illustrations, black and white; XIV, 497 p. 141 illus., 32 illus. in color., 1 Paperback / softback
  • Sērija : Lecture Notes in Mathematics 2062
  • Izdošanas datums: 14-Dec-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642321593
  • ISBN-13: 9783642321597
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783642321597.html
Keywords:
In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.
A User's Guide to Optimal Transport
1(156)
Luigi Ambrosio
Nicola Gigli
1 Introduction
1(2)
2 The Optimal Transport Problem
3(25)
2.1 Monge and Kantorovich Formulations of the Optimal Transport Problem
3(4)
2.2 Necessary and Sufficient Optimality Conditions
7(6)
2.3 The Dual Problem
13(3)
2.4 Existence of Optimal Maps
16(10)
2.5 Bibliographical Notes
26(2)
3 The Wasserstein Distance W2
28(31)
3.1 X Polish Space
29(8)
3.2 X Geodesic Space
37(10)
3.3 X Riemannian Manifold
47(11)
3.4 Bibliographical Notes
58(1)
4 Gradient Flows
59(34)
4.1 Hilbertian Theory of Gradient Flows
59(2)
4.2 The Theory of Gradient Flows in a Metric Setting
61(20)
4.3 Applications to the Wasserstein Case
81(11)
4.4 Bibliographical Notes
92(1)
5 Geometric and Functional Inequalities
93(4)
5.1 Brunn-Minkowski Inequality
94(1)
5.2 Isoperimetric Inequality
94(1)
5.3 Sobolev Inequality
95(1)
5.4 Bibliographical Notes
96(1)
6 Variants of the Wasserstein Distance
97(6)
6.1 Branched Optimal Transportation
97(2)
6.2 Different Action Functional
99(1)
6.3 An Extension to Measures with Unequal Mass
100(2)
6.4 Bibliographical Notes
102(1)
7 More on the Structure of (P2(M), W2)
103(28)
7.1 "Duality" Between the Wasserstein and the Arnold Manifolds
103(3)
7.2 On the Notion of Tangent Space
106(1)
7.3 Second Order Calculus
107(23)
7.4 Bibliographical Notes
130(1)
8 Ricci Curvature Bounds
131(26)
8.1 Convergence of Metric Measure Spaces
134(3)
8.2 Weak Ricci Curvature Bounds: Definition and Properties
137(13)
8.3 Bibliographical Notes
150(7)
References
152(5)
Hyperbolic Conservation Laws: An Illustrated Tutorial
157(90)
Alberto Bressan
1 Conservation Laws
158(9)
1.1 The Scalar Conservation Law
158(2)
1.2 Strictly Hyperbolic Systems
160(1)
1.3 Linear Systems
161(2)
1.4 Nonlinear Effects
163(1)
1.5 Loss of Regularity
164(2)
1.6 Wave Interactions
166(1)
2 Weak Solutions
167(12)
2.1 Rankine-Hugoniot Conditions
168(4)
2.2 Construction of Shock Curves
172(1)
2.3 Admissibility Conditions
173(6)
3 The Riemann Problem
179(17)
3.1 Some Examples
179(3)
3.2 A Class of Hyperbolic Systems
182(2)
3.3 Elementary Waves
184(3)
3.4 General Solution of the Riemann Problem
187(3)
3.5 The Riemann Problem for the p-System
190(4)
3.6 Error and Interaction Estimates
194(2)
4 Global Solutions to the Cauchy Problem
196(9)
4.1 Front Tracking Approximations
197(3)
4.2 Bounds on the Total Variation
200(3)
4.3 Convergence to a Limit Solution
203(2)
5 The Glimm Scheme
205(5)
6 Continuous Dependence on the Initial Data
210(6)
6.1 Unique Solutions to the Scalar Conservation Law
211(1)
6.2 Linear Hyperbolic Systems
212(1)
6.3 Nonlinear Systems
213(3)
7 Uniqueness of Solutions
216(7)
7.1 An Error Estimate for Front Tracking Approximations
217(1)
7.2 Characterization of Semigroup Trajectories
218(3)
7.3 Uniqueness Theorems
221(2)
8 The Vanishing Viscosity Approach
223(15)
8.1 Local Decomposition by Traveling Waves
226(4)
8.2 Evolution of Gradient Components
230(1)
8.3 Lyapunov Functionals
231(5)
8.4 Continuous Dependence on the Initial Data
236(1)
8.5 The Semigroup of Vanishing Viscosity Limit Solutions
237(1)
9 Extensions and Open Problems
238(9)
9.1 Compactness Theorems
239(1)
9.2 An Elementary Error Estimate
240(1)
9.3 The Center Manifold Theorem
241(6)
References
243(4)
Derivation of Non-local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models
247(24)
Dirk Helbing
1 Introduction
247(1)
2 The Gradient Expansion Approach
248(2)
3 The Linear Interpolation Approach
250(3)
4 An Approach Reminding of Smooth Particle Hydrodynamics
253(13)
4.1 Derivation of the Continuity Equation
253(2)
4.2 Derivation of the Macroscopic Velocity Equation
255(5)
4.3 Discussion of the Non-locality
260(1)
4.4 Comparison with Other Macroscopic Traffic Models
260(6)
5 Summary, Discussion, and Conclusions
266(5)
References
268(3)
On the Controversy Around Daganzo's Requiem for and Aw-Rascle's Resurrection of Second-Order Traffic Flow Models
271(32)
Dirk Helbing
Anders Johansson
1 Introduction
272(1)
2 Summary of the Controversy Regarding Second-Order Traffic Flow Models
273(2)
3 Linear Instability of Macroscopic Traffic Models
275(6)
3.1 Derivation of the Instability Condition
278(1)
3.2 Characteristic Speeds, Phase, and Group Velocities
279(2)
4 Discussion
281(5)
4.1 Characteristic Speeds in the Aw-Rascle Model
281(1)
4.2 Payne's Traffic Model
282(2)
4.3 Characteristic Speeds Vs. Vehicle Speeds
284(2)
5 Linear Instability and Characteristic Speeds of the Optimal Velocity Model
286(3)
6 Summary, Conclusions, and Outlook
289(14)
Appendix 1 Hyperbolic Sets of Partial Differential Equations and Characteristic Speeds
291(2)
Appendix 2 Stability Analysis for Macroscopic Traffic Models
293(1)
Appendix 3 Derivation of Formula (19)
294(2)
Appendix 4 Meaning of the Group Velocity
296(1)
Appendix 5 Linear Stability Analysis of the Optimal Velocity Model
297(2)
Appendix 6 Correspondence of the Optimal Velocity Model with the Macroscopic Payne Model
299(1)
References
300(3)
Theoretical vs. Empirical Classification and Prediction of Congested Traffic States
303(32)
Dirk Helbing
Martin Treiber
Arne Kesting
Martin Schonhof
1 Introduction
303(3)
2 On the Definition of Traffic Phases
306(1)
3 Congested Traffic States
307(2)
4 Derivation and Explanation of the Phase Diagram of Traffic States
309(9)
4.1 Transition to Congested Traffic for Small Bottlenecks
313(2)
4.2 Conditions for Different Kinds of Congested Traffic After the Breakdown of Traffic Flow
315(3)
5 Combinations of On-and Off-Ramps
318(3)
6 Other Phase Diagrams and Universality Classes of Models
321(3)
7 Empirical Phase Diagram
324(4)
7.1 Reply to Criticisms of Phase Diagrams for Traffic Models with a Fundamental Diagram
325(1)
7.2 On the Validity of Traffic Models
326(2)
8 Summary, Conclusions, and Outlook
328(7)
Appendix 1 Modeling of Source and Sink Terms (In- and Outflows)
329(1)
Appendix 2 Parameter Dependence of the Instability Thresholds in the Intelligent Driver Model
330(1)
References
331(4)
Self-Organized Network Flows
335(22)
Dirk Helbing
Jan Siegmeier
Stefan Lammer
1 Introduction
335(1)
2 Flows in Networks
336(8)
2.1 Flow Conservation Laws
337(2)
2.2 Two Views on Traffic Jams
339(5)
3 Treatment of Merging, Diverging and Intersection Points
344(7)
3.1 Diverging Flows: One Inflow and Several Outflows
345(1)
3.2 Merging Flows: Two Inflows and One Outflow
345(1)
3.3 A Side Road Merging with a Main Road
346(1)
3.4 Intersection-Free Designs of Road Networks
347(1)
3.5 Two Inflows and Two Outflows
348(2)
3.6 Inefficiencies Due to Coordination Problems
350(1)
4 Towards a Self-Organized Traffic Light Control
351(2)
5 Summary and Outlook
353(4)
References
354(3)
Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections
357(38)
Dirk Helbing
Amin Mazloumian
1 Introduction
357(2)
1.1 Paradoxical Behavior of Transport Systems
358(1)
2 Specification of the Traffic System Under Consideration
359(3)
3 Consideration of Traffic Flows
362(2)
4 Travel-Time-Oriented Signal Operation
364(12)
4.1 The Optimize-One-Phase Approach
365(3)
4.2 Transformation to Dimensionless Variables and Parameters
368(3)
4.3 Control Strategies and Slower-is-Faster Effect
371(1)
4.4 Operation Regimes for Periodic Operation
372(3)
4.5 Minimization of Vehicle Queues
375(1)
4.6 Complexity of Traffic Light Control
375(1)
5 Optimize-Multiple-Phases Approach
376(7)
5.1 Combined Flow-and-Delay Time Optimization
377(6)
6 Summary, Discussion, and Outlook
383(12)
6.1 Self-Organized Traffic Light Control
385(10)
Appendix 1 Considering the Price of Stopping Vehicles
387(2)
Appendix 2 More Than Two Traffic Phases
389(2)
Appendix 3 Limited Forecast Time Horizon
391(1)
References
392(3)
Modeling and Optimization of Scalar Flows on Networks
395(68)
Simone Gottlich
Axel Klar
1 Introduction
395(2)
2 Traffic Flow Networks
397(40)
2.1 Network Models Based on Scalar Partial Differential Equations
397(13)
2.2 Simplified Dynamics on the Network
410(5)
2.3 Optimization
415(21)
2.4 Summary
436(1)
3 Modeling Supply Networks
437(26)
3.1 Network Models Based on Scalar Conservation Laws
437(5)
3.2 Optimization Problems
442(9)
3.3 Numerical Results
451(8)
3.4 Summary
459(4)
References
459(4)
Control and Stabilization of Waves on 1-d Networks
463
Enrique Zuazua
1 Introduction and Main Results
464(4)
2 The Wave Equation on a Network
468(6)
3 Main Results on Observability and Controllability
474(4)
3.1 Summary of Known Results
474(3)
3.2 The Weighted Observability Inequality
477(1)
4 Stabilization
478(9)
4.1 Problem Formulation
478(4)
4.2 Observability for the Damped System
482(2)
4.3 The Interpolation Inequality
484(2)
4.4 The Main Result
486(1)
5 Further Comments and Open Problems
487
References
491