This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials. The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline. Sample Chapter(s) Preface Chapter 2: Continuum Mechanics: Elastic Simple Bodies Contents: Preface About the Authors Introduction Fundamentals: Continuum Mechanics: Elastic Simple Bodies Groupoids Algebroids Material Groupoid: Material Algebroid Characteristic Distributions and Material Bodies Appendices: Foliations and Distributions Covariant Derivatives Principal Bundles and Connections Bibliography Index Readership: Graduate and postgraduate students interested in Continuum Mechanics, Mathematical Physics and Differential Geometry. Researchers in Elasticity, Applied Mathematics and Differential Geometry. And those taking a master or doctorate course that seeks the interaction between mathematics and mechanical engineering.
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"Material and energy (M&E) balances are fundamental to biological, chemical, electrochemical, photochemical and environmental engineering disciplines and important in many fields related to sustainable development. This comprehensive compendium presents the basic M&E balance concepts and calculations in a format easily digested by students, engineering professionals and those concerned with related environmental issues. The useful reference text includes worked examples for each chapter and demonstrates process balances in the framework of M&E concerns of the 21st century. The additional problems and solutions in the Appendix embrace a wide range of subjects, from fossil fuels to fuel cells, solar energy, space stations, carbon dioxide capture and sodium-ion batteries. Request Inspection Copy Sample Chapter(s) An Introduction Contents: An Introduction The General Balance Equation Process Variables and Their Relationships Material and Energy Balances in Process Engineering Material Balances Energy Balances Simultaneous Material and Energy Balances Unsteady-State Material and Energy Balances Readership: Researchers, professionals, academics, undergraduate and graduate students in chemical engineering, environmental engineering and industrial chemistry."
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