1 Mathematics in Laser Processing; John Dowden. 1.1 Mathematics and its Application. 1.2 Formulation in Terms of Partial Differential Equations. 1.3 Boundary and Interface Conditions. 1.4 Fick's Laws. 1.5 Electromagnetism.
2 Simulation of Laser Cutting; Wolfgang Schulz, Markus Nießen, Urs Eppelt and Kerstin Kowalick. 2.1 Introduction. 2.2 Mathematical Formulation and Analysis. 2.3 Outlook. 2.4 Acknowledgements.
3 Glass Cutting; Wolfgang Schulz. 3.1 Introduction. 3.2 Phenomenology of Glass Processing with Ultrashort Laser Radiation. 3.3 Modelling the Propagation of Radiation and the Dynamics of Electron Density. 3.4 Radiation Propagation Solved by BPM Methods. 3.5 The Dynamics of Electron Density Described by Rate Equations. 3.6 Properties of the Solution with Regard to Ablation and Damage. 3.7 Electronic Damage versus Thermal Damage. 3.8 Glass Cutting by Direct Ablation or Filamentation?. 3.9 Acknowledgements.4 Keyhole Welding: the Solid and Liquid Phases; Alexander Kaplan. 4.1 Heat Generation and Heat Transfer. 4.2 Melt Flow.
5 Laser Keyhole Welding: The Vapour Phase; John Dowden. 5.1 Notation. 5.2 The Keyhole. 5.3 The Keyhole Wall. 5.4 The Role of Convection in the Transfer of Energy to the Keyhole Wall. 5.5 Fluid Flow in the Keyhole. 5.6 Further Aspects of Fluid Flow. 5.7 Electromagnetic Effects.
6 Basic Concepts of Laser Drilling; Wolfgang Schulz and Urs Eppelt. 6.1 Introduction. 6.2 Technology and Laser Systems. 6.3 Diagnostics and Monitoring for s Pulse Drilling. 6.4 Phenomena of Beam-Matter Interaction. 6.5 Phenomena of the Melt Expulsion Domain. 6.6 Mathematical Formulation of Reduced Models. 6.7 Analysis. 6.8 Outlook. 6.9 Acknowledgements
7 Arc Welding and Hybrid Laser-Arc Welding; Ian Richardson. 7.1 The Structure of the Welding Arc. 7.2 The Arc Electrodes. 7.3 Fluid Flow in the Arc-Generated Weld Pool . 7.4 Unified Arc and Electrode Models. 7.5 Arc Plasma-Laser Interactions. 7.6 Laser-Arc Hybrid Welding. 8 Metallurgy and Imperfections of Welding and Hardening; Alexander Kaplan. 8.1 Thermal Cycle and Cooling Rate. 8.2 Resolidification. 8.3 Metallurgy. 8.4 Imperfections.
9 Laser Cladding; Frank Brückner and Dietrich Lepski. 9.1 Introduction. 9.2 Beam-Particle Interaction. 9.3 Formation of the Weld Bead. 9.4 Thermal Stress and Distortion. 9.5 Conclusions and Future Work.
10 Laser Forming; Thomas Pretorius. 10.1 History of Thermal Forming. 10.2 Forming Mechanisms. 10.3 Applications.
11 Femtosecond Laser Pulse Interactions with Metals; Bernd Hüttner. 11.1. Introduction. 11.2. What is Different Compared to Longer Pulses? 11.3. Material Properties under Exposure to Femtosecond Laser Pulses. 11.4. Determination of the Electron and Phonon Temperature Distribution. 11.5. Summary and Conclusions. 12 Meta-Modelling and Visualisation of Multi-Dimensional Data for Virtual Production Intelligence; Wolfgang Schulz. 12.1 Introduction. 12.2 Implementing Virtual Production Intelligence. 12.3 Meta-Modelling Providing Operative Design Tools. 12.4 Meta-Modelling by Smart Sampling with Discontinuous Response. 12.5 Global Sensitivity Analysis and Variance Decomposition. 12.6 Reduced Models and Emulators. 12.7 Summary and Advances in Meta-Modelling.
13 Comprehensive Numerical Simulation of Laser Materials Processing; Markus Gross. 13.1 Motivation - The Pursuit of Ultimate Understanding. 13.2 Review. 13.3 Correlation, the Full Picture. 13.4 Introduction to Numerical Techniques. 13.5 Solution of the Energy Equation and Phase Changes. 13.6 Program Development and Best Practice when Using Analysis Tools. 13.7 Introduction to High Performance Computing. 13.8 Visualisation Tools. 13.9 Summary and Concluding Remarks.
Index.
About the Author: Prof. John Dowden was educated at Bedford School and Cambridge University, UK, where he graduated with a First Class degree in Mathematics in 1962. He became the first student of the new University of Essex obtaining a PhD in Mathematical Oceanography in 1967. He was appointed to the staff of the Mathematics Department of the university and subsequently changed his main research interests to the mathematics and physics of laser technology while retaining interests in mathematically related applications of heat and mass transfer. Before retirement he was Head of the university's Department of Mathematical Sciences, a member of the Institute of Physics and of the Laser Institute of America. He is still a Fellow of the Institute of Mathematics and its Applications and is now an Emeritus Professor of the University.
Prof. Dr. Wolfgang Schulz studied physics at Braunschweig University of Technology. He graduated from the Institute for Theoretical Physics and received a postgraduate scholarship in 1986 on the topic of "Hot electrons in metals". In 1987, he accepted an invitation to the department Laser Technology at RWTH Aachen University. He received the "Borchers Medal" award in 1992 in recognition of his PhD thesis. In 1997, he joined the Fraunhofer Institute for Laser Technology in Aachen and, in 1999, received the "Venia Legendi" in the field "Principles of Continuum Physics applied to Laser Technology". His postdoctoral lecture qualification (habilitation) was awarded with distinction in 1999 with the prize of the Friedrich-Wilhelm Foundation at RWTH Aachen University. Since March 2005, he has represented the newly founded department "Nonlinear Dynamics of Laser Processing" at RWTH Aachen University and is the head of the newly founded department of "Modelling and Simulation" at the Fraunhofer Institute for Laser Technology in Aachen. Since 2007, he is the coordinator of the Excellence Cluster Domain "Virtual Production" at RWTH Aachen University.
His current work is focused on developing and improving laser systems and their industrial applications by combination of mathematical, physical and experimental methods. In particular, he applies the principles of optics, continuum physics and thermodynamics to analyse the phenomena involved in laser processing. The mathematical objectives are modelling, analysis and dynamical simulation of Free Boundary Problems, which are systems of nonlinear partial differential equations. Analytical and numerical methods for model reduction are developed and applied. The mathematical analysis yields approximate dynamical systems of small dimensions in the phase space and is based on asymptotic properties such as the existence of inertial manifolds.
