This book introduces groupoids and n-fold groupoids as powerful mathematical tools that unify and generalize local and distant symmetries observed in physical systems. While these concepts are typically discussed in highly specialized literature, this volume makes them accessible to a broader audience by grounding them in concrete applications to solid mechanics, including composite materials and metamaterials. No prior knowledge of the theory or its applications is assumed. The c...

An appealing and engaging introduction to Continuum Mechanics in BiosciencesThis book presents the elements of Continuum Mechanics to people interested in applications to biological systems. It is divided into two parts, the first of which introduces the basic concepts within a strictly one-dimensional spatial context. This policy has been adopted so as to allow the newcomer to Continuum Mechanics to appreciate how the theory can be applied to important issues in B...

This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The ...

Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics.Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constit...

Although the setting of this play is modern, it involves a fictitious encounter between Machiavelli and Richard Pace, a Tudor diplomat. It also involves John Keats and explores the meaning of poetry, love and life. Richard Pace was an important English diplomat during the Tudor period, a younger contemporary of Machiavelli. The meeting described in the play never took place, or did it? At any rate, the aging and broken Machiavelli opens his heart to Pace. This is the beginning of the story...

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 ...

Argentina is still reeling from the worst economic and political crisis to afflict the nation in its modern history. Since December 2001, the country has been through economic depression and bankruptcy, the impoverishment of half the population, a presidency that changed four times in the span of two weeks, and social protests met by state repression that left dozens dead and hundreds injured.What brought on this state of affairs? What are the primary features of this crisis? Who a...

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresse...