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The demand for cast iron components, with weights ranging from a few kilograms to several tons, has increased significantly in recent years, both for technical and economic reasons. In fact, the lower cost compared to other alloys, and the good castability, which allow one to obtain near-net shape components in as-cast conditions, and the mechanical properties that can be obtained, are just some of the motivations that attract mechanical designers. However, correct design requires a good knowledge of the intrinsic correlation among alloy chemical composition, process parameters, microstructure (with casting defects) and mechanical properties. This book is aimed at collecting excellent and recent research experimental and theoretical works in this filed. Technological (say, wear resistance and weldability) and mechanical properties (say, Young modulus, static and fatigue strength) of different grades of cast irons, ranging from solution strengthened ferritic ductile iron to compacted graphite iron as well as white and nodular cast irons, are correlated with the alloy chemical composition, process parameters and casting dimension.

History of engineering & technology --- boundary element method (BEM) --- periodic boundary conditions --- representative volume elements (RVEs) --- effective elastic properties --- homogenization --- lamellar graphite iron --- ultimate tensile strength --- primary austenite --- gravity casting process simulation --- nodular cast iron --- effective Young's modulus --- computational homogenization --- multiscale numerical methods --- micro-CT --- finite elements --- silicon solution strengthened ferritic ductile iron --- thickness --- solidification time --- microstructure --- mechanical properties --- fatigue --- thermal analysis --- weldability --- pre-heating --- spheroidal graphite cast iron --- ductile cast irons --- tensile tests --- plasticity modelling --- compacted graphite iron --- minimum quantity lubrication (MQL) --- drilling machinability --- dry machining --- ductile iron --- cooling rate --- segregation --- cast iron --- high-chromium --- abrasive wear --- niobium alloying --- high chromium cast irons --- eutectic carbide --- carbide volume fraction --- chemical composition --- image analysis --- simulation --- MatCalc --- hardness --- boundary element method (BEM) --- periodic boundary conditions --- representative volume elements (RVEs) --- effective elastic properties --- homogenization --- lamellar graphite iron --- ultimate tensile strength --- primary austenite --- gravity casting process simulation --- nodular cast iron --- effective Young's modulus --- computational homogenization --- multiscale numerical methods --- micro-CT --- finite elements --- silicon solution strengthened ferritic ductile iron --- thickness --- solidification time --- microstructure --- mechanical properties --- fatigue --- thermal analysis --- weldability --- pre-heating --- spheroidal graphite cast iron --- ductile cast irons --- tensile tests --- plasticity modelling --- compacted graphite iron --- minimum quantity lubrication (MQL) --- drilling machinability --- dry machining --- ductile iron --- cooling rate --- segregation --- cast iron --- high-chromium --- abrasive wear --- niobium alloying --- high chromium cast irons --- eutectic carbide --- carbide volume fraction --- chemical composition --- image analysis --- simulation --- MatCalc --- hardness

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This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."

Schrödinger operator. --- Green's functions. --- Hamiltonian systems. --- Evolution equations. --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Operator, Schrödinger --- Differential equations --- Differentiable dynamical systems --- Potential theory (Mathematics) --- Differential operators --- Quantum theory --- Schrödinger equation --- Almost Mathieu operator. --- Analytic function. --- Anderson localization. --- Betti number. --- Cartan's theorem. --- Chaos theory. --- Density of states. --- Dimension (vector space). --- Diophantine equation. --- Dynamical system. --- Equation. --- Existential quantification. --- Fundamental matrix (linear differential equation). --- Green's function. --- Hamiltonian system. --- Hermitian adjoint. --- Infimum and supremum. --- Iterative method. --- Jacobi operator. --- Linear equation. --- Linear map. --- Linearization. --- Monodromy matrix. --- Non-perturbative. --- Nonlinear system. --- Normal mode. --- Parameter space. --- Parameter. --- Parametrization. --- Partial differential equation. --- Periodic boundary conditions. --- Phase space. --- Phase transition. --- Polynomial. --- Renormalization. --- Self-adjoint. --- Semialgebraic set. --- Special case. --- Statistical significance. --- Subharmonic function. --- Summation. --- Theorem. --- Theory. --- Transfer matrix. --- Transversality (mathematics). --- Trigonometric functions. --- Trigonometric polynomial. --- Uniformization theorem.

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The demand for cast iron components, with weights ranging from a few kilograms to several tons, has increased significantly in recent years, both for technical and economic reasons. In fact, the lower cost compared to other alloys, and the good castability, which allow one to obtain near-net shape components in as-cast conditions, and the mechanical properties that can be obtained, are just some of the motivations that attract mechanical designers. However, correct design requires a good knowledge of the intrinsic correlation among alloy chemical composition, process parameters, microstructure (with casting defects) and mechanical properties. This book is aimed at collecting excellent and recent research experimental and theoretical works in this filed. Technological (say, wear resistance and weldability) and mechanical properties (say, Young modulus, static and fatigue strength) of different grades of cast irons, ranging from solution strengthened ferritic ductile iron to compacted graphite iron as well as white and nodular cast irons, are correlated with the alloy chemical composition, process parameters and casting dimension.

History of engineering & technology --- boundary element method (BEM) --- periodic boundary conditions --- representative volume elements (RVEs) --- effective elastic properties --- homogenization --- lamellar graphite iron --- ultimate tensile strength --- primary austenite --- gravity casting process simulation --- nodular cast iron --- effective Young’s modulus --- computational homogenization --- multiscale numerical methods --- micro-CT --- finite elements --- n/a --- silicon solution strengthened ferritic ductile iron --- thickness --- solidification time --- microstructure --- mechanical properties --- fatigue --- thermal analysis --- weldability --- pre-heating --- spheroidal graphite cast iron --- ductile cast irons --- tensile tests --- plasticity modelling --- compacted graphite iron --- minimum quantity lubrication (MQL) --- drilling machinability --- dry machining --- ductile iron --- cooling rate --- segregation --- cast iron --- high-chromium --- abrasive wear --- niobium alloying --- high chromium cast irons --- eutectic carbide --- carbide volume fraction --- chemical composition --- image analysis --- simulation --- MatCalc --- hardness --- effective Young's modulus

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This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While originating in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity.Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players, as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit.This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Convergence. --- Mean field theory. --- Many-body problem --- Statistical mechanics --- Functions --- A priori estimate. --- Approximation. --- Bellman equation. --- Boltzmann equation. --- Boundary value problem. --- C0. --- Chain rule. --- Compact space. --- Computation. --- Conditional probability distribution. --- Continuous function. --- Convergence problem. --- Convex set. --- Cooperative game. --- Corollary. --- Decision-making. --- Derivative. --- Deterministic system. --- Differentiable function. --- Directional derivative. --- Discrete time and continuous time. --- Discretization. --- Dynamic programming. --- Emergence. --- Empirical distribution function. --- Equation. --- Estimation. --- Euclidean space. --- Folk theorem (game theory). --- Folk theorem. --- Heat equation. --- Hermitian adjoint. --- Implementation. --- Initial condition. --- Integer. --- Large numbers. --- Linearization. --- Lipschitz continuity. --- Lp space. --- Macroeconomic model. --- Markov process. --- Martingale (probability theory). --- Master equation. --- Mathematical optimization. --- Maximum principle. --- Method of characteristics. --- Metric space. --- Monograph. --- Monotonic function. --- Nash equilibrium. --- Neumann boundary condition. --- Nonlinear system. --- Notation. --- Numerical analysis. --- Optimal control. --- Parameter. --- Partial differential equation. --- Periodic boundary conditions. --- Porous medium. --- Probability measure. --- Probability theory. --- Probability. --- Random function. --- Random variable. --- Randomization. --- Rate of convergence. --- Regime. --- Scientific notation. --- Semigroup. --- Simultaneous equations. --- Small number. --- Smoothness. --- Space form. --- State space. --- State variable. --- Stochastic calculus. --- Stochastic control. --- Stochastic process. --- Stochastic. --- Subset. --- Suggestion. --- Symmetric function. --- Technology. --- Theorem. --- Theory. --- Time consistency. --- Time derivative. --- Uniqueness. --- Variable (mathematics). --- Vector space. --- Viscosity solution. --- Wasserstein metric. --- Weak solution. --- Wiener process. --- Without loss of generality.