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Frameworks, Tensegrities, and Symmetry

Frameworks, Tensegrities, and Symmetry
Author: Robert Connelly
Publisher: Cambridge University Press
Total Pages:
Release: 2022-01-27
Genre: Mathematics
ISBN: 1009234226
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This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.

Tensegrity Structures

Tensegrity Structures
Author: Jing Yao Zhang
Publisher: Springer
Total Pages: 307
Release: 2015-03-17
Genre: Science
ISBN: 4431548130
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To facilitate a deeper understanding of tensegrity structures, this book focuses on their two key design problems: self-equilibrium analysis and stability investigation. In particular, high symmetry properties of the structures are extensively utilized. Conditions for self-equilibrium as well as super-stability of tensegrity structures are presented in detail. An analytical method and an efficient numerical method are given for self-equilibrium analysis of tensegrity structures: the analytical method deals with symmetric structures and the numerical method guarantees super-stability. Utilizing group representation theory, the text further provides analytical super-stability conditions for the structures that are of dihedral as well as tetrahedral symmetry. This book not only serves as a reference for engineers and scientists but is also a useful source for upper-level undergraduate and graduate students. Keeping this objective in mind, the presentation of the book is self-contained and detailed, with an abundance of figures and examples.

Rigidity and Symmetry

Rigidity and Symmetry
Author: Robert Connelly
Publisher: Springer
Total Pages: 378
Release: 2014-06-11
Genre: Mathematics
ISBN: 1493907816
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This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Handbook of Discrete and Computational Geometry

Handbook of Discrete and Computational Geometry
Author: Csaba D. Toth
Publisher: CRC Press
Total Pages: 2354
Release: 2017-11-22
Genre: Computers
ISBN: 1351645919
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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems

Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems
Author: Alphose Zingoni
Publisher: CRC Press
Total Pages: 4438
Release: 2022-09-02
Genre: Technology & Engineering
ISBN: 1000824365
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Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems comprises 330 papers that were presented at the Eighth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2022, Cape Town, South Africa, 5-7 September 2022). The topics featured may be clustered into six broad categories that span the themes of mechanics, modelling and engineering design: (i) mechanics of materials (elasticity, plasticity, porous media, fracture, fatigue, damage, delamination, viscosity, creep, shrinkage, etc); (ii) mechanics of structures (dynamics, vibration, seismic response, soil-structure interaction, fluid-structure interaction, response to blast and impact, response to fire, structural stability, buckling, collapse behaviour); (iii) numerical modelling and experimental testing (numerical methods, simulation techniques, multi-scale modelling, computational modelling, laboratory testing, field testing, experimental measurements); (iv) design in traditional engineering materials (steel, concrete, steel-concrete composite, aluminium, masonry, timber); (v) innovative concepts, sustainable engineering and special structures (nanostructures, adaptive structures, smart structures, composite structures, glass structures, bio-inspired structures, shells, membranes, space structures, lightweight structures, etc); (vi) the engineering process and life-cycle considerations (conceptualisation, planning, analysis, design, optimization, construction, assembly, manufacture, maintenance, monitoring, assessment, repair, strengthening, retrofitting, decommissioning). Two versions of the papers are available: full papers of length 6 pages are included in the e-book, while short papers of length 2 pages, intended to be concise but self-contained summaries of the full papers, are in the printed book. This work will be of interest to civil, structural, mechanical, marine and aerospace engineers, as well as planners and architects.

Habitability of the Universe before Earth

Habitability of the Universe before Earth
Author:
Publisher: Academic Press
Total Pages: 578
Release: 2017-12-11
Genre: Science
ISBN: 0128119411
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Habitability of the Universe before Earth: Astrobiology: Exploring Life on Earth and Beyond (series) examines the times and places—before life existed on Earth—that might have provided suitable environments for life to occur, addressing the question: Is life on Earth de novo, or derived from previous life? The universe changed considerably during the vast epoch between the Big Bang 13.8 billion years ago and the first evidence of life on Earth 4.3 billion years ago, providing significant time and space to contemplate where, when and under what circumstances life might have arisen. No other book covers this cosmic time period from the point of view of its potential for life. The series covers a broad range of topics encompassing laboratory and field research into the origins and evolution of life on Earth, life in extreme environments and the search for habitable environments in our solar system and beyond, including exoplanets, exomoons and astronomical biosignatures. Provides multiple hypotheses on the origin of life and distribution of living organisms in space Explores the diversity of physical environments that may support the origin and evolution of life Integrates contemporary views in biology and cosmology, and provides reasons that life is far more mobile in space than most people expect Includes access to a companion web site featuring supplementary information such as animated computer simulations

Origin of Life via Archaea

Origin of Life via Archaea
Author: Richard Gordon
Publisher: John Wiley & Sons
Total Pages: 1268
Release: 2024-10-01
Genre: Science
ISBN: 1119901022
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This book surveys the models for the origin of life and presents a new model starting with shaped droplets and ending with life as polygonal Archaea; it collects the most published micrographs of Archaea (discovered only in 1977), which support this conclusion, and thus provides the first visual survey of Archaea. Origin of Life via Archaea’s purpose is to add a new hypothesis on what are called “shaped droplets”, as the starting point, for flat, polygonal Archaea, supporting the Vesicles First hypothesis. The book contains over 6000 distinct references and micrographs of 440 extant species of Archaea, 41% of which exhibit polygonal phenotypes. It surveys the intellectual battleground of the many ideas of the origin of life on earth, chemical equilibrium, autocatalysis, and biotic polymers. This book contains 17 chapters, some coauthored, on a wide range of topics on the origin of life, including Archaea’s origin, patterns, and species. It shows how various aspects of the origin of life may have occurred at chemical equilibrium, not requiring an energy source, contrary to the general assumption. For the reader’s value, its compendium of Archaea micrographs might also serve many other interesting questions about Archaea. One chapter presents a theory for the shape of flat, polygonal Archaea in terms of the energetics at the surface, edges and corners of the S-layer. Another shows how membrane peptides may have originated. The book also includes a large table of most extant Archaea, that is searchable in the electronic version. It ends with a chapter on problems needing further research. Audience This book will be used by astrobiologists, origin of life biologists, physicists of small systems, geologists, biochemists, theoretical and vesicle chemists.

Cooperative Coordination and Formation Control for Multi-agent Systems

Cooperative Coordination and Formation Control for Multi-agent Systems
Author: Zhiyong Sun
Publisher: Springer
Total Pages: 189
Release: 2018-02-23
Genre: Technology & Engineering
ISBN: 3319742655
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The thesis presents new results on multi-agent formation control, focusing on the distributed stabilization control of rigid formation shapes. It analyzes a range of current research problems such as problems concerning the equilibrium and stability of formation control systems, or the problem of cooperative coordination control when agents have general dynamical models, and discusses practical considerations arising during the implementation of established formation control algorithms. In addition, the thesis presents models of increasing complexity, from single integrator models, to double integrator models, to agents modeled by nonlinear kinematic and dynamic equations, including the familiar unicycle model and nonlinear system equations with drift terms. Presenting the fruits of a close collaboration between several top control groups at leading universities including Yale University, Groningen University, Purdue University and Gwangju Institute of Science and Technology (GIST), the thesis spans various research areas, including robustness issues in formations, quantization-based coordination, exponential stability in formation systems, and cooperative coordination of networked heterogeneous systems.

The Shape of a Life

The Shape of a Life
Author: Shing-Tung Yau
Publisher: Yale University Press
Total Pages: 327
Release: 2019-01-01
Genre: Biography & Autobiography
ISBN: 0300235909
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A Fields medalist recounts his lifelong transnational effort to uncover the geometric shape--the Calabi-Yau manifold--that may store the hidden dimensions of our universe. Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world's most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal-winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

Polytopes and Graphs

Polytopes and Graphs
Author: Guillermo Pineda Villavicencio
Publisher: Cambridge University Press
Total Pages: 482
Release: 2024-02-29
Genre: Mathematics
ISBN: 1009257781
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This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.