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This lecture describes the methodology for physical modelling of materials problems, with particular emphasis on heat treatment and welding of age hardening alloys materials; it establishes mathematical relations between different process variables (e.g. alloy composition, heat treatment procedure, welding conditions) and the alloy strength or hardness, based on sound physical principles (e.g. thermodynamics, kinetic theory, dislocation mechanics); it motivates faster process development, optimization of process and properties and development of real-time control. Knowledge in metallurgy, materials science, materials engineering is assumed.