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Thermal treatment of materials occupies a significant, increasing proportion of MSE activity and is an integral component of modern curricula as well as a highly monetized component of industrial production. Laser processing of materials offers advantages over conventional methods of processing. Some of these advantages include fast processing, precision of operation, low cost and local treatment. Analytical modelling of laser processing gives insight into the physical and mathematical aspects of the problem and provides useful information on process optimization. However the impor

Heat engineering - Instruments. --- Laser heating. --- Laser processing. --- Lasers - Industrial applications. --- Thermal treatment. --- Lasers --- Heat engineering --- Engineering & Applied Sciences --- Applied Physics --- Industrial applications --- Instruments --- Industrial applications. --- Instruments. --- Instruments, Heat engineering

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The characterization of the physical and chemical properties of transition metals and their compounds under extreme conditions of pressure and temperature has always attracted the interest of a wide scientific community. Their properties have numerous implications in fields ranging from solid-state physics, chemistry, and materials science to Earth and planetary science. The present Special Issue represents a good example of such a broad interest and shows some of the latest advancements in the investigation of transition metals under extreme conditions of pressure and temperature.

Technology: general issues --- vanadate --- kagome compound --- high pressure --- X-ray diffraction --- equation of state --- iodate --- infrared spectroscopy --- phase transitions --- grain refinement --- mechanical properties --- commercial purity aluminum --- zirconium --- Nb3Sn --- local atomic structure --- XAFS --- melting curves --- laser-heated diamond anvil cell --- extreme conditions --- synchrotron radiation --- transition metals --- iridium --- laser heating --- density-functional theory --- melting --- radial-distribution function --- quantum molecular dynamics --- melting curve --- solid-solid phase transition boundary --- multi-phase materials --- phase relation --- Earth's core --- iron alloys --- high-pressure --- high-temperature --- thermodynamics --- eutectic spacing --- Al-Si alloy --- superheat --- electrical resistivity --- iron sulfides --- high temperature --- Ganymede --- thermal convection --- creep testing --- ME21 --- magnesium alloy --- size effects --- miniature specimen --- PbTe --- substitutional disorder --- thermal expansion --- bulk modulus --- atomic displacement --- low temperature --- compression --- Debye temperature --- vanadate --- kagome compound --- high pressure --- X-ray diffraction --- equation of state --- iodate --- infrared spectroscopy --- phase transitions --- grain refinement --- mechanical properties --- commercial purity aluminum --- zirconium --- Nb3Sn --- local atomic structure --- XAFS --- melting curves --- laser-heated diamond anvil cell --- extreme conditions --- synchrotron radiation --- transition metals --- iridium --- laser heating --- density-functional theory --- melting --- radial-distribution function --- quantum molecular dynamics --- melting curve --- solid-solid phase transition boundary --- multi-phase materials --- phase relation --- Earth's core --- iron alloys --- high-pressure --- high-temperature --- thermodynamics --- eutectic spacing --- Al-Si alloy --- superheat --- electrical resistivity --- iron sulfides --- high temperature --- Ganymede --- thermal convection --- creep testing --- ME21 --- magnesium alloy --- size effects --- miniature specimen --- PbTe --- substitutional disorder --- thermal expansion --- bulk modulus --- atomic displacement --- low temperature --- compression --- Debye temperature

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The characterization of the physical and chemical properties of transition metals and their compounds under extreme conditions of pressure and temperature has always attracted the interest of a wide scientific community. Their properties have numerous implications in fields ranging from solid-state physics, chemistry, and materials science to Earth and planetary science. The present Special Issue represents a good example of such a broad interest and shows some of the latest advancements in the investigation of transition metals under extreme conditions of pressure and temperature.

vanadate --- kagome compound --- high pressure --- X-ray diffraction --- equation of state --- iodate --- infrared spectroscopy --- phase transitions --- grain refinement --- mechanical properties --- commercial purity aluminum --- zirconium --- Nb3Sn --- local atomic structure --- XAFS --- melting curves --- laser-heated diamond anvil cell --- extreme conditions --- synchrotron radiation --- transition metals --- iridium --- laser heating --- density-functional theory --- melting --- radial-distribution function --- quantum molecular dynamics --- melting curve --- solid–solid phase transition boundary --- multi-phase materials --- phase relation --- Earth’s core --- iron alloys --- high-pressure --- high-temperature --- thermodynamics --- eutectic spacing --- Al-Si alloy --- superheat --- electrical resistivity --- iron sulfides --- high temperature --- Ganymede --- thermal convection --- creep testing --- ME21 --- magnesium alloy --- size effects --- miniature specimen --- PbTe --- substitutional disorder --- thermal expansion --- bulk modulus --- atomic displacement --- low temperature --- compression --- Debye temperature --- n/a --- solid-solid phase transition boundary --- Earth's core

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This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering

delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation