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Table of Contents
Preface; Contents; Part I Methods; Calculation of Chemical Equilibria in Multi-Phase: Multicomponent Systems; 1 Introduction; 2 Problem Formulation; 2.1 Non-Ideal Gibbs Function; 2.2 Stoichiometric Constraints; 2.3 The Optimization Problem; 3 Methodology for the Calculation of Chemical Equilibria; 3.1 Reformulation of the Minimization Problem; 3.2 Discretization of the H-Problem; 3.3 Corrector Step; 4 Automated Detection of Miscibility Gaps; 5 Results; 5.1 Gibbs Free Energy Minimization Using BePhaSys
5.2 Calculation of Two-Dimensional Phase Diagrams: Interpolation and ParallelizationAppendix: The Gibbs Free Energy Function; References; LC-GAP: Localized Coulomb Descriptors for the Gaussian Approximation Potential; 1 Introduction; 2 Potential Energy Prediction Through Machine Learning; 2.1 The GAP Framework and Gaussian Process Regression; 2.2 Localized Coulomb Matrix Descriptors; 3 Results; 3.1 Comparison of Descriptor Functions on QM7; 3.2 Larger Datasets and Prediction of Multiple Properties
3.3 Distribution of Individual Atomic Contributions4 Conclusions and Future Work; References; River Bed Morphodynamics: Metamodeling, Reliability Analysis, and Visualization in a Virtual Environment; 1 Introduction; 2 RBF Metamodel; 3 Quantile Estimation; 3.1 Sensitivity-Based Approach; 3.1.1 First-Order Approximation; 3.1.2 Second-Order Approximation; 3.2 Monte Carlo; 3.3 Weighted Monte Carlo; 3.4 Quasi-Monte Carlo (QMC); 3.5 Quasi-Random Splines (QRS); 4 Numerical Tests; 5 Visualization in Virtual Environment; 6 Conclusion
3.1 The First Documented AMG Application3.2 The Basics of `Classical' AMG; 4 The Renaissance of AMG (1995-2000); 4.1 Resumption of Major Research on AMG; 4.2 Towards Industry; 4.2.1 Computational Fluid Dynamics; 4.2.2 Streamline Approach in Oil Reservoir Simulation; 5 The Main AMG Development Phase (2000-Today); 5.1 The General Trend; 5.2 Bridging the Gap; 5.3 SAMG for Coupled PDE Systems; 5.3.1 Unknown-Based Approach; 5.3.2 Point-Based Approach; 5.3.3 Status of the Solver Framework SAMG; 6 Industry-Driven Applications
5.2 Calculation of Two-Dimensional Phase Diagrams: Interpolation and ParallelizationAppendix: The Gibbs Free Energy Function; References; LC-GAP: Localized Coulomb Descriptors for the Gaussian Approximation Potential; 1 Introduction; 2 Potential Energy Prediction Through Machine Learning; 2.1 The GAP Framework and Gaussian Process Regression; 2.2 Localized Coulomb Matrix Descriptors; 3 Results; 3.1 Comparison of Descriptor Functions on QM7; 3.2 Larger Datasets and Prediction of Multiple Properties
3.3 Distribution of Individual Atomic Contributions4 Conclusions and Future Work; References; River Bed Morphodynamics: Metamodeling, Reliability Analysis, and Visualization in a Virtual Environment; 1 Introduction; 2 RBF Metamodel; 3 Quantile Estimation; 3.1 Sensitivity-Based Approach; 3.1.1 First-Order Approximation; 3.1.2 Second-Order Approximation; 3.2 Monte Carlo; 3.3 Weighted Monte Carlo; 3.4 Quasi-Monte Carlo (QMC); 3.5 Quasi-Random Splines (QRS); 4 Numerical Tests; 5 Visualization in Virtual Environment; 6 Conclusion
3.1 The First Documented AMG Application3.2 The Basics of `Classical' AMG; 4 The Renaissance of AMG (1995-2000); 4.1 Resumption of Major Research on AMG; 4.2 Towards Industry; 4.2.1 Computational Fluid Dynamics; 4.2.2 Streamline Approach in Oil Reservoir Simulation; 5 The Main AMG Development Phase (2000-Today); 5.1 The General Trend; 5.2 Bridging the Gap; 5.3 SAMG for Coupled PDE Systems; 5.3.1 Unknown-Based Approach; 5.3.2 Point-Based Approach; 5.3.3 Status of the Solver Framework SAMG; 6 Industry-Driven Applications