Self Consistent
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Self-Consistent Fields in Atoms
Self-Consistent Fields in Atoms: Hartree and Thomas-Fermi Atoms covers the various aspects of atomic properties, including energy levels, binding energies, X-ray scattering activity, and magnetic properties. This book emphasizes the Hartree field concept. This book is organized into two parts encompassing 13 chapters. Part I examines first the concepts of central field wave functions and angular momentum operators. This part also deals with the concept of self-consistent field, Thomas-Fermi atom, energies of atoms and ions, and other atomic properties. The electron-electron correlation and the relativistic effects in heavy atoms are reviewed in this part. Part II presents the applications of the theory and methods used for determining the characteristic values and functions of Schrödinger’s wave equations for a non-Coulomb central field of force. This part also looks into the simplification of the Hartree-Fock method. This book will prove useful to physicists and researchers in the allied fields.
Material Modeling with the Visco-Plastic Self-Consistent (VPSC) Approach
Material Modeling with the Visco-Plastic Self-Consistent (VPSC) Approach: Theory and Practical Applications provides readers with knowledge of material viscoplasticity and robust modeling approaches for predicting plastic deformation of crystal aggregates. Visco-Plastic Self-Consistent (VPSC) is the identifier of a computer code developed for the specific mechanical regime addressed (visco-plastic: VP) and the approach used (self-consistent: SC) meant to simulate large plastic deformation of aggregates, thermo-elastic material deformation, as well as predict stress-strain response, texture evolution of aggregates and stress-strain state inside grains. This approach is very versatile and able to tackle arbitrary material symmetry (cubic, hexagonal, trigonal, orthorhombic, triclinic), twinning, and multiphase aggregates. It accounts for hardening, reorientation and shape change of individual grains, and can be applied to the deformation of metals, inter-metallics and geologic aggregates. Readers will have access to a companion website where they can download code and modify its input/output or add subroutines covering specific simulation research needs. - Highlights a modeling approach that allows readers to accurately predict stress-strain response, texture evolution of aggregates, and internal stress states inside grains while also accounting for hardening, reorientation and shape change of individual grains - Features modeling techniques that can be applied to the deformation of metals, inter-metallics and geologic aggregates - Covers the theoretical aspects of homogeneous effective medium models as they apply to the simulation of plasticity and elasticity - Provides several practical examples and applications of materials of different symmetry subjected to different deformation conditions