Download or read book Nonlinear Hamiltonian Mechanics Applied to Molecular Dynamics written by Stavros C. Farantos and published by Springer. This book was released on 2014-09-22 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.
Download or read book Nonlinear Hamiltonian Mechanics Applied to Molecular Dynamics written by Stavros Farantos and published by Springer. This book was released on 2014-09-26 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.
Download or read book Structure preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics written by Peter Betsch and published by Springer. This book was released on 2016-05-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application of structure-preserving methods is illustrated by a number of examples dealing with, among others, nonlinear beams and shells, large deformation problems, long-term simulations and coupled thermo-mechanical multibody systems. In addition it links novel time integration methods to frequently used methods in industrial multibody system simulation.
Download or read book Simulating Hamiltonian Dynamics written by Benedict Leimkuhler and published by Cambridge University Press. This book was released on 2004 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
Download or read book Hamiltonian Dynamical Systems written by R.S MacKay and published by CRC Press. This book was released on 1987-01-01 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.
Download or read book Computational Molecular Dynamics Challenges Methods Ideas written by Peter Deuflhard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: On May 21-24, 1997 the Second International Symposium on Algorithms for Macromolecular Modelling was held at the Konrad Zuse Zentrum in Berlin. The event brought together computational scientists in fields like biochemistry, biophysics, physical chemistry, or statistical physics and numerical analysts as well as computer scientists working on the advancement of algorithms, for a total of over 120 participants from 19 countries. In the course of the symposium, the speakers agreed to produce a representative volume that combines survey articles and original papers (all refereed) to give an impression of the present state of the art of Molecular Dynamics. The 29 articles of the book reflect the main topics of the Berlin meeting which were i) Conformational Dynamics, ii) Thermodynamic Modelling, iii) Advanced Time-Stepping Algorithms, iv) Quantum-Classical Simulations and Fast Force Field and v) Fast Force Field Evaluation.
Download or read book Nonlinear Dynamics Volume 2 written by Gaetan Kerschen and published by Springer Science & Business Media. This book was released on 2014-03-28 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data
Download or read book State Estimation for Nonlinear Continuous Discrete Stochastic Systems written by Gennady Yu. Kulikov and published by Springer Nature. This book was released on with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Mechanics written by John Seimenis and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.
Download or read book Dynamics of Glassy Crystalline and Liquid Ionic Conductors written by Junko Habasaki and published by Springer. This book was released on 2016-10-19 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the physics of the dynamics of ions in various ionically conducting materials, and applications including electrical energy generation and storage. The experimental techniques for measurements and characterization, molecular dynamics simulations, the theories of ion dynamics, and applications are all addressed by the authors, who are experts in their fields. The experimental techniques of measurement and characterization of dynamics of ions in glassy, crystalline, and liquid ionic conductors are introduced with the dual purpose of introducing the reader to the experimental activities of the field, and preparing the reader to understand the physical quantities derived from experiments. These experimental techniques include calorimetry, conductivity relaxation, nuclear magnetic resonance, light scattering, neutron scattering, and others. Methods of molecular dynamics simulations are introduced to teach the reader to utilize the technique for practical applications to specific problems. The results elucidate the dynamics of ions on some issues that are not accessible by experiments. The properties of ion dynamics in glassy, crystalline and liquid ionic conductors brought forth by experiments and simulations are shown to be universal, i.e. independent of physical and chemical structure of the ionic conductor as long as ion-ion interaction is the dominant factor. Moreover these universal properties of ion dynamics are shown to be isomorphic to other complex interacting systems including the large class of glass-forming materials with or without ionic conductivity.By covering the basic concepts, theories/models, experimental techniques and data, molecular dynamics simulations, and relating them together, Dynamics of Glassy, Crystalline and Liquid Ionic Conductors will be of great interest to many in basic and applied research areas from the broad and diverse communities of condensed matter physicists, chemists, materials scientists and engineers. The book also provides the fundamentals for an introduction to the field and it is written in such a way that can be used for teaching courses either at the undergraduate or graduate level in academic institutions.
Download or read book Carbon Nanotube Reinforced Polymers written by Roham Rafiee and published by Elsevier. This book was released on 2017-10-06 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carbon Nanotube-Reinforced Polymers: From Nanoscale to Macroscale addresses the advances in nanotechnology that have led to the development of a new class of composite materials known as CNT-reinforced polymers. The low density and high aspect ratio, together with their exceptional mechanical, electrical and thermal properties, render carbon nanotubes as a good reinforcing agent for composites. In addition, these simulation and modeling techniques play a significant role in characterizing their properties and understanding their mechanical behavior, and are thus discussed and demonstrated in this comprehensive book that presents the state-of-the-art research in the field of modeling, characterization and processing. The book separates the theoretical studies on the mechanical properties of CNTs and their composites into atomistic modeling and continuum mechanics-based approaches, including both analytical and numerical ones, along with multi-scale modeling techniques. Different efforts have been done in this field to address the mechanical behavior of isolated CNTs and their composites by numerous researchers, signaling that this area of study is ongoing. - Explains modeling approaches to carbon nanotubes, together with their application, strengths and limitations - Outlines the properties of different carbon nanotube-based composites, exploring how they are used in the mechanical and structural components - Analyzes the behavior of carbon nanotube-based composites in different conditions
Download or read book Nonequilibrium Molecular Dynamics written by Billy D. Todd and published by Cambridge University Press. This book was released on 2017-03-10 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent collection of theory, algorithms, and illustrative results presents the field of nonequilibrium molecular dynamics in detail.
Download or read book NBS Special Publication written by and published by . This book was released on 1968 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Integrators for Differential Equations with Highly Oscillatory Solutions written by Xinyuan Wu and published by Springer Nature. This book was released on 2021-09-28 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions.
Download or read book Molecular Quantum Dynamics written by Fabien Gatti and published by Springer Science & Business Media. This book was released on 2014-04-09 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on current applications of molecular quantum dynamics. Examples from all main subjects in the field, presented by the internationally renowned experts, illustrate the importance of the domain. Recent success in helping to understand experimental observations in fields like heterogeneous catalysis, photochemistry, reactive scattering, optical spectroscopy, or femto- and attosecond chemistry and spectroscopy underline that nuclear quantum mechanical effects affect many areas of chemical and physical research. In contrast to standard quantum chemistry calculations, where the nuclei are treated classically, molecular quantum dynamics can cover quantum mechanical effects in their motion. Many examples, ranging from fundamental to applied problems, are known today that are impacted by nuclear quantum mechanical effects, including phenomena like tunneling, zero point energy effects, or non-adiabatic transitions. Being important to correctly understand many observations in chemical, organic and biological systems, or for the understanding of molecular spectroscopy, the range of applications covered in this book comprises broad areas of science: from astrophysics and the physics and chemistry of the atmosphere, over elementary processes in chemistry, to biological processes (such as the first steps of photosynthesis or vision). Nevertheless, many researchers refrain from entering this domain. The book "Molecular Quantum Dynamics" offers them an accessible introduction. Although the calculation of large systems still presents a challenge - despite the considerable power of modern computers - new strategies have been developed to extend the studies to systems of increasing size. Such strategies are presented after a brief overview of the historical background. Strong emphasis is put on an educational presentation of the fundamental concepts, so that the reader can inform himself about the most important concepts, like eigenstates, wave packets, quantum mechanical resonances, entanglement, etc. The chosen examples highlight that high-level experiments and theory need to work closely together. This book thus is a must-read both for researchers working experimentally or theoretically in the concerned fields, and generally for anyone interested in the exciting world of molecular quantum dynamics.
Download or read book Publications of the National Institute of Standards and Technology Catalog written by National Institute of Standards and Technology (U.S.) and published by . This book was released on 1983 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Developments in Structure Preserving Algorithms for Oscillatory Differential Equations written by Xinyuan Wu and published by Springer. This book was released on 2018-04-19 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.
