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.

• 1 Mathematics in Laser Processing; John Dowden.- 2 Simulation of Laser Cutting; Wolfgang Schulz, Markus Nießen, Urs Eppelt and Kerstin Kowalick.- 3 Glass Cutting; Wolfgang Schulz.- 4 Keyhole Welding: the Solid and Liquid Phases ; Alexander Kaplan.- 5 Laser Keyhole Welding: The Vapour Phase; John Dowden.- 6 Basic Concepts of Laser Drilling; Wolfgang Schulz and Urs Eppelt.- 7 Arc Welding and Hybrid Laser-Arc Welding; Ian Richardson. - 8 Metallurgy and Imperfections of Welding and Hardening; Alexander Kaplan.- 9 Laser Cladding; Frank Brückner and Dietrich Lepski.- 10 Laser Forming; Thomas Pretorius.- 11 Femtosecond Laser Pulse Interactions with Metals; Bernd Hüttner.- 12 Meta-Modelling and Visualisation of Multi-Dimensional Data for Virtual Production Intelligence; Wolfgang Schulz.- 13 Comprehensive Numerical Simulation of Laser Materials Processing; Markus Gross.- Index.

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.

• 1 Mathematics in Laser Processing; John Dowden.- 2 Simulation of Laser Cutting; Wolfgang Schulz, Markus Nießen, Urs Eppelt and Kerstin Kowalick.- 3 Glass Cutting; Wolfgang Schulz.- 4 Keyhole Welding: the Solid and Liquid Phases ; Alexander Kaplan.- 5 Laser Keyhole Welding: The Vapour Phase; John Dowden.- 6 Basic Concepts of Laser Drilling; Wolfgang Schulz and Urs Eppelt.- 7 Arc Welding and Hybrid Laser-Arc Welding; Ian Richardson. - 8 Metallurgy and Imperfections of Welding and Hardening; Alexander Kaplan.- 9 Laser Cladding; Frank Brückner and Dietrich Lepski.- 10 Laser Forming; Thomas Pretorius.- 11 Femtosecond Laser Pulse Interactions with Metals; Bernd Hüttner.- 12 Meta-Modelling and Visualisation of Multi-Dimensional Data for Virtual Production Intelligence; Wolfgang Schulz.- 13 Comprehensive Numerical Simulation of Laser Materials Processing; Markus Gross.- Index.

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.

• 1 Mathematics in Laser Processing; John Dowden.- 2 Simulation of Laser Cutting; Wolfgang Schulz, Markus Nießen, Urs Eppelt and Kerstin Kowalick.- 3 Glass Cutting; Wolfgang Schulz.- 4 Keyhole Welding: the Solid and Liquid Phases ; Alexander Kaplan.- 5 Laser Keyhole Welding: The Vapour Phase; John Dowden.- 6 Basic Concepts of Laser Drilling; Wolfgang Schulz and Urs Eppelt.- 7 Arc Welding and Hybrid Laser-Arc Welding; Ian Richardson. - 8 Metallurgy and Imperfections of Welding and Hardening; Alexander Kaplan.- 9 Laser Cladding; Frank Brückner and Dietrich Lepski.- 10 Laser Forming; Thomas Pretorius.- 11 Femtosecond Laser Pulse Interactions with Metals; Bernd Hüttner.- 12 Meta-Modelling and Visualisation of Multi-Dimensional Data for Virtual Production Intelligence; Wolfgang Schulz.- 13 Comprehensive Numerical Simulation of Laser Materials Processing; Markus Gross.- Index.