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2.5.5 Discussion of the Flutter Phenomenon for the Tacoma Narrows Bridge
2.6 The Galloping of the Bridge and the Stall Flutter Phenomenon
2.7 Letter from W.P. Rodden to R. Scanlan About Tacoma
2.8 Answer from R. Scanlan to W.P. Rodden About Tacoma
2.9 The Stall Flutter Phenomenon in the Torsion of the Bridge
3 Generalization of the Apparent Wind Method
4 Assembly of Several Rigid Structures
5 Control Strategy for the Full System
5.1 The Cooperative Strategy
5.2 How to Compute the Limit of the Optimal Control When →0
5.3 The Non-cooperative Strategy
5.3.1 Existence (and Uniqueness) of an Exact Decentralized Control with Coordination
5.4 A Coordination Algorithm for the Decentralized Control
6 Limit Cycle of Oscillations
6.1 Definition of a Limit Cycle of Oscillations
6.2 Localisation of Limit Cycles of Oscillations
6.3 How to Find Invariant Sets?
7 Computation of the Limit Cycle
7.1 Canonical Formulation for (98)
7.2 Second Step: Elimination of Second Order Terms
7.3 Partial Elimination of Terms of Order 3
8 The Stall Flutter of a Model in a Wind Tunnel
8.1 The Measures from the Wind Tunnel
8.2 The Simple Mathematical Model Used
9 About the Added Mass Method
10 Conclusion
References
Computational Treatment of Interface Dynamics via Phase-Field Modeling
1 Introduction
1.1 Interface Dynamics in Computational Mechanics and the Phase-Field Method
1.2 Notational Conventions
2 Derivation of Phase-Field Models via Diffusification
2.1 A Classical Moving Boundary Problem for Solidification of Pure Materials
2.2 The Basis of Diffusification
2.3 The Phase-Field Model for Solidification
2.4 The Diffuse-Interface Transition Profile: Asymptotic Analysis
3 General Framework of Thermomechanics and Energy Dissipation for Phase-Field Models
3.1 The Idea Behind Thermomechanically-Consistent Phase-Field Modeling
3.2 Allen-Cahn and Cahn-Hilliard
3.2.1 Allen-Cahn Equation
3.2.2 Cahn-Hilliard Equation
3.3 Navier-Stokes-Cahn-Hilliard
4 The Diffuse Domain Approach
4.1 Derivation of a Diffuse Domain Model for a Standard Convection-Diffusion Problem
4.2 Diffuse Domain Method for Problems Posed on Evolving Surfaces
5 Numerical Examples
5.1 Solidification Model
5.2 Cahn-Hilliard Equation
5.3 Diffuse Domain Model
2.6 The Galloping of the Bridge and the Stall Flutter Phenomenon
2.7 Letter from W.P. Rodden to R. Scanlan About Tacoma
2.8 Answer from R. Scanlan to W.P. Rodden About Tacoma
2.9 The Stall Flutter Phenomenon in the Torsion of the Bridge
3 Generalization of the Apparent Wind Method
4 Assembly of Several Rigid Structures
5 Control Strategy for the Full System
5.1 The Cooperative Strategy
5.2 How to Compute the Limit of the Optimal Control When →0
5.3 The Non-cooperative Strategy
5.3.1 Existence (and Uniqueness) of an Exact Decentralized Control with Coordination
5.4 A Coordination Algorithm for the Decentralized Control
6 Limit Cycle of Oscillations
6.1 Definition of a Limit Cycle of Oscillations
6.2 Localisation of Limit Cycles of Oscillations
6.3 How to Find Invariant Sets?
7 Computation of the Limit Cycle
7.1 Canonical Formulation for (98)
7.2 Second Step: Elimination of Second Order Terms
7.3 Partial Elimination of Terms of Order 3
8 The Stall Flutter of a Model in a Wind Tunnel
8.1 The Measures from the Wind Tunnel
8.2 The Simple Mathematical Model Used
9 About the Added Mass Method
10 Conclusion
References
Computational Treatment of Interface Dynamics via Phase-Field Modeling
1 Introduction
1.1 Interface Dynamics in Computational Mechanics and the Phase-Field Method
1.2 Notational Conventions
2 Derivation of Phase-Field Models via Diffusification
2.1 A Classical Moving Boundary Problem for Solidification of Pure Materials
2.2 The Basis of Diffusification
2.3 The Phase-Field Model for Solidification
2.4 The Diffuse-Interface Transition Profile: Asymptotic Analysis
3 General Framework of Thermomechanics and Energy Dissipation for Phase-Field Models
3.1 The Idea Behind Thermomechanically-Consistent Phase-Field Modeling
3.2 Allen-Cahn and Cahn-Hilliard
3.2.1 Allen-Cahn Equation
3.2.2 Cahn-Hilliard Equation
3.3 Navier-Stokes-Cahn-Hilliard
4 The Diffuse Domain Approach
4.1 Derivation of a Diffuse Domain Model for a Standard Convection-Diffusion Problem
4.2 Diffuse Domain Method for Problems Posed on Evolving Surfaces
5 Numerical Examples
5.1 Solidification Model
5.2 Cahn-Hilliard Equation
5.3 Diffuse Domain Model