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Primeur weekly 2016-08-29

Exascale supercomputing

World's biggest telescope meets world's second fastest supercomputer ...

NSF awards $110 million for advanced cyberinfrastructure to nation's scientists and engineers ...

Neuromorphic computing market worth $6,480.1 million by 2024 according to Grand View Research Inc. ...

University of Texas at Arlington physicists to upgrade Titan supercomputer software for extreme scale applications ...

Quantum computing

Artificial atom created in graphene ...

Focus on Europe

Next steps in understanding brain function ...

New approach to computing boosts energy efficiency ...

Silicon nanoparticles trained to juggle light ...

Middleware

Avere Systems and Cycle Computing provide one-click Cloud compute scalability ...

Hardware

SCinet Inventory: High performance storage - untangling 89 miles of fiber ...

New microchip demonstrates efficiency and scalable design ...

Programmable routers could enable more resilient networks ...

Chaos could provide the key to enhanced wireless communications ...

Secure networks for the Internet of the future ...

Mellanox expands Asia-Pacific presence, new Singapore headquarters and state-of-the-art Solutions Centre to strengthen footprint in Asia ...

IDT and IBM develop high-performance computing solution for telecom edge computing networks ...

Applications

IBM Research opens in South Africa; Cognitive computing and the IoT help track diseases and forecast air quality ...

ACM Gordon Bell Prize recognizes top accomplishments in running science apps on HPC ...

Insights into the dawn of the universe ...

Reef castaways: Can coral make it across Darwin's impassable barrier? ...

RAND and Lawrence Livermore National Lab combine computing & public policy analysis ...

Problems in mechanics open the door to the orderly world of chaos ...

New approach to determining how atoms are arranged in materials ...

Post-disaster optimization technique capable of analyzing entire cities ...

Where does AlphaGo go? ...

PPPL and Princeton help lead centre for study of runaway electrons ...

NSF funds new integrative approaches to study the brain ...

Streamlining accelerated computing for industry ...

Finalists compete for prestigious ACM Gordon Bell Prize in High Performance Computing ...

University of Texas at Austin and Technical University of Dresden PhD students to receive International High Performance Computing Fellowships ...

The Cloud

IBM expands all-flash storage offerings for Cloud and cognitive computing ...

Bodhi Healthcare Group brings Cloud-based health care solution to Chinese hospital with IBM LinuxONE ...

Problems in mechanics open the door to the orderly world of chaos


Cover for Lectures in Nonlinear Mechanics and Chaos Theory. Credit: World Scientific.
22 Aug 2016 Singapore - The word "chaos" has two meanings that are almost exact opposites. In general usage, it means "wild unpredictable confusion". In physics and mathematics it often refers to the behaviour of systems for which the tools of traditional mathematics fail and one is forced to think in a rigorous new semi-quantitative way.

The first person to realize this was the French mathematician Henri Poincaré. In the late 19th century he was challenged to prove that the solar system is stable, but instead raised the possibility that it might not be. If one ignores the gravitational attraction between the planets one is left with a solvable problem that appears in all undergraduate mechanics texts. Including these small perturbations leads to a problem that can be described with partial differential equations, but these equations have no proper solutions except possibly in terms of infinite series.

These equations can be solved numerically of course, but the results show an odd combination of order and unpredictability. Henri Poincaré went on to lay the foundation for the study of such systems. He identified criteria that make a system inescapably chaotic and showed how a kind of order can emerge from the chaos. In this century, the Russian mathematician Kolomogrov developed what has come to be called the KAM theorem; one of the crowning works of modern mathematics. He showed that there is an odd fractal-like landscape of infinite series solutions in otherwise unsolvable problems.

"Lectures in Nonlinear Mechanics and Chaos Theory" begins by reviewing the tools of traditional classical mechanics - the Hamiltonian formulation, abstract transformation theory, and perturbation theory - and shows how they ultimately fail. It then moves on to the landmarks of chaos theory, the Poincaré-Hopf or "hairy ball" theorem, followed by the Poincaré-Birkoff theorem for rational winding numbers, and finally, the KAM theorem. These are discussed in terms of rigorous mathematics and illustrated with numerous examples of computer-drawn solutions. It finishes with a discussion of the relevance of the KAM theorem and measure theory to the ergodic hypothesis.

This book is based on a one-quarter course in graduate mechanics that has been given in the Physics Department of Oregon State University. It is intended to be used as a textbook to review conventional mechanics and introduce students to more recent developments in chaos theory.

This book retails for US$35 / GBP29 (paperback) and US$70 / GBP58 (hardback), and is also available on Amazon, Barnes and Noble, and other major online booksellers. To know more about the book or to purchase a copy, you can visit the World Scientific website.

Source: World Scientific

Back to Table of contents

Primeur weekly 2016-08-29

Exascale supercomputing

World's biggest telescope meets world's second fastest supercomputer ...

NSF awards $110 million for advanced cyberinfrastructure to nation's scientists and engineers ...

Neuromorphic computing market worth $6,480.1 million by 2024 according to Grand View Research Inc. ...

University of Texas at Arlington physicists to upgrade Titan supercomputer software for extreme scale applications ...

Quantum computing

Artificial atom created in graphene ...

Focus on Europe

Next steps in understanding brain function ...

New approach to computing boosts energy efficiency ...

Silicon nanoparticles trained to juggle light ...

Middleware

Avere Systems and Cycle Computing provide one-click Cloud compute scalability ...

Hardware

SCinet Inventory: High performance storage - untangling 89 miles of fiber ...

New microchip demonstrates efficiency and scalable design ...

Programmable routers could enable more resilient networks ...

Chaos could provide the key to enhanced wireless communications ...

Secure networks for the Internet of the future ...

Mellanox expands Asia-Pacific presence, new Singapore headquarters and state-of-the-art Solutions Centre to strengthen footprint in Asia ...

IDT and IBM develop high-performance computing solution for telecom edge computing networks ...

Applications

IBM Research opens in South Africa; Cognitive computing and the IoT help track diseases and forecast air quality ...

ACM Gordon Bell Prize recognizes top accomplishments in running science apps on HPC ...

Insights into the dawn of the universe ...

Reef castaways: Can coral make it across Darwin's impassable barrier? ...

RAND and Lawrence Livermore National Lab combine computing & public policy analysis ...

Problems in mechanics open the door to the orderly world of chaos ...

New approach to determining how atoms are arranged in materials ...

Post-disaster optimization technique capable of analyzing entire cities ...

Where does AlphaGo go? ...

PPPL and Princeton help lead centre for study of runaway electrons ...

NSF funds new integrative approaches to study the brain ...

Streamlining accelerated computing for industry ...

Finalists compete for prestigious ACM Gordon Bell Prize in High Performance Computing ...

University of Texas at Austin and Technical University of Dresden PhD students to receive International High Performance Computing Fellowships ...

The Cloud

IBM expands all-flash storage offerings for Cloud and cognitive computing ...

Bodhi Healthcare Group brings Cloud-based health care solution to Chinese hospital with IBM LinuxONE ...