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Conclusion
It is useful to construct slow invariant manifolds. Effective model reduction becomes unfeasible without them for complex kinetic systems.
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Dimension of Attractors Estimation
How can we prove that all the attractors of an infinite-dimensional system belong to a finite-dimensional manifold? How can we estimate the...
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Newton Method with Incomplete Linearization
The Newton method with incomplete linearization is developed for solving the invariance equation. It is the basis of an iterative construction of the...
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The Source of Examples
The Boltzmann equation is the first and the most celebrated nonlinear kinetic equation introduced by the great Austrian scientist Ludwig Boltzmann in...
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Introduction
In this book, we present a collection of constructive methods to study slow (stable) positively invariant manifolds of dynamic systems. The main...
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Hydrodynamics From Grad’s Equations: What Can We Learn From Exact Solutions?
A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad’s moment equations. Grad’s systems...
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14 Quantum Mechanical and Classical State Densities
Regardless of its rather problematic foundation (see Chap. 4), Boltzmann’s “recipe” to calculate thermodynamic behavior from a classical Hamilton...
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9 Quantum Thermodynamic Equilibrium
A very important characterization of thermodynamic systems concerns the kind of contact between the observed system and its environment. In classical...
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Electrons and Phonons
The aim of this Chapter is not to produce a complete course on electrons and phonons, but rather to give a concise outline of a certain number of...
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Exploring Multicomponent Phase Space to Discover New Materials
Multicomponent phase space has been shown to consist of an enormous number of materials with different compositions, the vast majority of which have...
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Phase Equilibria of the Er-Al-Zr Ternary System at 500 °C
The phase equilibria of the Er-Al-Zr ternary system at 500 °C were investigated using a combination of electron probe microanalyzer and x-ray...
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The 500 °C Isothermal Section of the Al-Fe-Pr Ternary System
Phases and equilibria involved in the isothermal section at 500 °C of the ternary Al-Fe-Pr system have been here investigated in the whole...
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Thermodynamic Assessments of Ti-Al, Ti-Fe, and Ti-Al-Fe Systems with Four-Sublattice Description of Ordered Body-Centered Cubic Phase and Density Functional Theory Data
A thermodynamic description of the Ti-Al-Fe system was established with reassessed Ti-Al and Ti-Fe binary systems using density function theory (DFT)...
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Mats Hillert’s Invaluable Contributions to Cast Irons
The microstructures and properties of foundry alloys designated by the generic term “cast irons” are highly diverse, even if we limit ourselves to...
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Measurement of Diffusion Coefficients and Assessment of Atomic Mobilities in HCP Mg-Ag-Sn Alloys
Reliable thermodynamic and kinetic databases are essential for designing and develo** novel magnesium (Mg) alloys for elevated-temperature...
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Inter-property Correlation of Al2O3-CaO-MgO-SiO2 Quaternary Slag System in Blast Furnace Ironmaking
Exploring the correlation between the density and the thermo-physical properties of the Al 2 O 3 -CaO-MgO-SiO 2 quaternary slag system is a subject of...
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Phase Equilibria in the Ag2S–Sb2S3–SnS2 System and the Novel Quaternary Chalcogenide Ag11Sb3SnS12
Interactions of Ag and Sb(III) and Sn(IV) sulfides were investigated by x-ray diffraction, differential thermal analysis and microstructure analysis...
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Thermodynamic Description of the Gadolinium-Cadmium Phase Diagram
The thermodynamic optimization of the Gd-Cd binary system was carried out with the help of CALPHAD (CALculation of PHAse Diagram) method., GdCd 3 , Gd 13 Cd...
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On the U-Fe-C Isothermal Section at 1100 °C
The energy crisis and climate change have promoted a growing interest in non-fossil sources, such as nuclear, with uranium carbides being seen as...
