A Journey Around the Different Scales Involved in the Description of Matter and Complex Systems - A Brief Overview with Special Emphasis on Kinetic Theory Approaches

This SpringerBrief covers the main scales of description of matter, starting at its finest level, the quantum scale, moving through ab-initio, molecular dynamics, coarse grained approaches, to finish at the scale of kinetic theory models that allows a nice compromise between the rich but expensive microscopic descriptions and the computationally cheap but sometimes too coarse macroscopic descriptions. The book addresses undergraduate and graduate students, as well as beginners in multi-scale modeling of materials.

List of contents

1 The Schrödinger equation.- 1.1 The history of quantum mechanics in small bits.- 1.2 Planck versus the ultraviolet catastrophe.- 1.3 An intuitive approach to the Schrödinger equation.- 1.4 The Feynman approach.- 1.5 The Schrödinger equation.- 1.6 Relations between position and momentum wavefunctions.- 1.7 Heisenberg uncertainty principle.- 1.8 Observable and its time evolution.- 1.9 The Hellmann-Feynman theorem.- 1.10 The Pauli exclusion principle.- 1.11 On the numerical solution of the Schrödinger equation.- 2 Ab-initio calculations.- 2.1 The Hartree-Fock description.- 2.2 Density Functional Theory.- 2.3 Concluding remarks on the quantum scale.- 3 Coarse-grained descriptions.- 3.1 Molecular dynamics.- 3.2 Brownian dynamics.- 4 Kinetic theory models. 4.1 Motivation.- 4.2 Kinetic theory description of simple liquids and gases.- 4.3 Complex fluids.- 4.4 The Chemical Master Equation.- References.

Summary

This SpringerBrief covers the main scales of description of matter, starting at its finest level, the quantum scale, moving through ab-initio, molecular dynamics, coarse grained approaches, to finish at the scale of kinetic theory models that allows a nice compromise between the rich but expensive microscopic descriptions and the computationally cheap but sometimes too coarse macroscopic descriptions. The book addresses undergraduate and graduate students, as well as beginners in multi-scale modeling of materials.

Product details

• Authors: Emmanuelle Abisset-Chavanne, Francisc Chinesta, Francisco Chinesta
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 31.01.2018
• EAN: 9783319700007
• ISBN: 978-3-31-970000-7
• No. of pages: 125
• Dimensions: 168 mm x 9 mm x 239 mm
• Weight: 219 g
• Illustrations: X, 125 p. 16 illus.
• Series: SpringerBriefs in Applied Sciences and Technology; SpringerBriefs in Applied Sciences and Technology
• Subjects: Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering; C, engineering, Civil Engineering, Theoretical and Applied Mechanics, Quantum Physics, Quantum physics (quantum mechanics & quantum field theory), Testing of materials, Characterization and Analytical Technique, Materials science, Characterization and Evaluation of Materials, Mechanics, Mechanics, Applied