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Numerical Methods For Polymeric Systems
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Author :Stuart G. Whittington Publisher :Springer Science & Business Media ISBN 13 :1461217040 Total Pages :225 pages Book Rating :4.4/5 (612 download)
Book Synopsis Numerical Methods for Polymeric Systems by : Stuart G. Whittington
Download or read book Numerical Methods for Polymeric Systems written by Stuart G. Whittington and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymers occur in many different states and their physical properties are strongly correlated with their conformations. The theoretical investigation of the conformational properties of polymers is a difficult task and numerical methods play an important role in this field. This book contains contributions from a workshop on numerical methods for polymeric systems, held at the IMA in May 1996, which brought together chemists, physicists, mathematicians, computer scientists and statisticians with a common interest in numerical methods. The two major approaches used in the field are molecular dynamics and Monte Carlo methods, and the book includes reviews of both approaches as well as applications to particular polymeric systems. The molecular dynamics approach solves the Newtonian equations of motion of the polymer, giving direct information about the polymer dynamics as well as about static properties. The Monte Carlo approaches discussed in this book all involve sampling along a Markov chain defined on the configuration space of the system. An important feature of the book is the treatment of Monte Carlo methods, including umbrella sampling and multiple Markov chain methods, which are useful for strongly interacting systems such as polymers at low temperatures and in compact phases. The book is of interest to workers in polymer statistical mechanics and also to a wider audience interested in numerical methods and their application in polymeric systems.
Book Synopsis Diffusion in Polymer-solvent Systems by : Raymond Franklin Riek
Download or read book Diffusion in Polymer-solvent Systems written by Raymond Franklin Riek and published by . This book was released on 1967 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Numerical Methods in the Solution of Problems in Statistical Mechanics of Polymer Systems by : Robert Frank Hoffman
Download or read book Applications of Numerical Methods in the Solution of Problems in Statistical Mechanics of Polymer Systems written by Robert Frank Hoffman and published by . This book was released on 1967 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Layered Polymeric Systems by : Patrick James Harris
Download or read book Layered Polymeric Systems written by Patrick James Harris and published by . This book was released on 2015 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents novel mechanical designs and advances in both polymer layer multiplication and extensional rheology. In Part I, advances in polymer layer multiplication include the investigation of typical thermoplastic layer multiplication extrusion dies and the redesign of such by means of experimental and computational investigation. Results show a decrease in flow instabilities including viscous encapsulation and elastic instabilities. Similarly, an innovative layer multiplication system for highly filled and elastic rubber compounds is presented. Both of these novel systems for thermoplastic and thermosetting polymer systems are validated and understood by numerical methods using ANSYS Polyflow and CFD-Post. These advances in multilayer coextrusion allow for layering of new families of rheologically complex and as well mismatched materials, thus widening the processing capabilities at the Center for Layered Polymeric Systems. In Part II, advances in extensional rheology include a newly developed extensional rheometer for achieving high Henkystrains. The Meissner Extensional Rheometer Accessory or MERA is limited in strain only by sample rupture. Experimental validation is performed using two materials, a styrene-butadiene rubber (SBR) and a linear polystyrene (PS); the results are compared with those obtained using the well-known SER. Due to its design, it was possible to achieve homogeneous extensional flow up to unprecedented real Hencky strains in excess of 8. The second half of Part II covers a rheological understanding behind the mechanism of sharkskin, a melt fracture instability during extrusion. Solution-styrene-butadiene-styrene blended with various polybutadienes is studied. Experimental extrusion results show a behavior difference depending on the molecular architecture of the latter, polybutadiene. Extensional rheological techniques are used to investigate the behavior. Results show a higher sensitivity to stress relaxation after a step-strain rather than typical stress growth coefficients in extension.
Book Synopsis Analysis and Implementation of Numerical Methods for Simulating Dilute Polymeric Fluids by : David Knezevic
Download or read book Analysis and Implementation of Numerical Methods for Simulating Dilute Polymeric Fluids written by David Knezevic and published by . This book was released on 2008 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Viscoelasticity of Polymers by : Kwang Soo Cho
Download or read book Viscoelasticity of Polymers written by Kwang Soo Cho and published by Springer. This book was released on 2016-05-30 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to polymer rheology with a focus on the viscoelastic characterization of polymeric materials. It contains various numerical algorithms for the processing of viscoelastic data, from basic principles to advanced examples which are hard to find in the existing literature. The book takes a multidisciplinary approach to the study of the viscoelasticity of polymers, and is self-contained, including the essential mathematics, continuum mechanics, polymer science and statistical mechanics needed to understand the theories of polymer viscoelasticity. It covers recent achievements in polymer rheology, such as theoretical and experimental aspects of large amplitude oscillatory shear (LAOS), and numerical methods for linear viscoelasticity, as well as new insights into the interpretation of experimental data. Although the book is balanced between the theoretical and experimental aspects of polymer rheology, the author’s particular interest in the theoretical side will not remain hidden. Aimed at readers familiar with the mathematics and physics of engineering at an undergraduate level, the multidisciplinary approach employed enables researchers with various scientific backgrounds to expand their knowledge of polymer rheology in a systematic way.
Book Synopsis The Equilibrium Theory of Inhomogeneous Polymers by : Glenn Fredrickson
Download or read book The Equilibrium Theory of Inhomogeneous Polymers written by Glenn Fredrickson and published by Oxford University Press on Demand. This book was released on 2006 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a pedagogical introduction to the theoretical and computer simulation techniques that are useful in the design of polymer formulations including personal care products, multiphase plastic materials, processed foods, and colloidal and nanoparticle dispersions. The book serves to unify previous work in a common language and provides a balanced treatment of analytical theory and numerical techniques, including an introduction to the exciting new field offield-theoretic polymer simulations - the direct numerical simulation of field theory models of meso-structured polymer melts, solutions, and dispersions.
Book Synopsis Simulation Methods for Polymers by : Michael Kotelyanskii
Download or read book Simulation Methods for Polymers written by Michael Kotelyanskii and published by CRC Press. This book was released on 2004-03-01 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems by : Eusebius Doedel
Download or read book Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems written by Eusebius Doedel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.
Book Synopsis Random Polymer Models by : Giambattista Giacomin
Download or read book Random Polymer Models written by Giambattista Giacomin and published by Imperial College Press. This book was released on 2007 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials. This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models.
Book Synopsis Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ by : Jorge Alberto Calvo
Download or read book Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ written by Jorge Alberto Calvo and published by American Mathematical Soc.. This book was released on 2002 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.
Book Synopsis Field-Theoretic Simulations in Soft Matter and Quantum Fluids by : Glenn H. Fredrickson
Download or read book Field-Theoretic Simulations in Soft Matter and Quantum Fluids written by Glenn H. Fredrickson and published by Oxford University Press. This book was released on 2023-02-28 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to field-theoretic simulations in classical soft matter and Bose quantum fluids. The method represents a new class of molecular computer simulation in which continuous fields, rather than particle coordinates, are sampled and evolved. Field-theoretic simulations are capable of analysing the properties of systems that are challenging for traditional simulation techniques, including dense phases of high molecular weight polymers, self-assembling fluids, and quantum fluids at finite temperature. The monograph details analytical methods for converting classical and quantum many-body problems to equilibrium field theory models with a molecular basis. Numerical methods are described that enable efficient, accurate, and scalable simulations of such models on modern computer hardware, including graphics processing units (GPUs). Extensions to non-equilibrium systems are discussed, along with an introduction to advanced field-theoretic simulation techniques including free energy estimation, alternative ensembles, coarse-graining, and variable cell methods.
Book Synopsis Eco-friendly and Smart Polymer Systems by : Hamid Mirzadeh
Download or read book Eco-friendly and Smart Polymer Systems written by Hamid Mirzadeh and published by Springer Nature. This book was released on 2020-05-29 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings book presents the main findings of the 13th International Seminar on Polymer Science and Technology ( ISPST 2018), which was held at Amirkabir University of Technology, Tehran, on November 10–22, 2018. This forum was the culmination of more than three decades of academic and industrial activities of Iranian scholars and professionals, and the participation of many notable international scientists, in covering various important polymer-related subjects of concern to Iran and the world at large, including polymer synthesis, processing and properties, as well as issues concerning polymer degradation, stability, and environmental aspects. For the past half a century, the growing concern for advancing human health, quality of life, and – especially in the last few decades – avoiding and combating environmental pollution have shaped and driven scientific activities geared toward the creation of smart materials that are compatible with the human body, and have prompted scientists and technologists to pursue research using natural and sustainable sources. This book highlights efforts to responsibly address the problems caused by, and which can potentially be solved by, polymers and plastics.
Book Synopsis Mathematical Modeling of Mixtures and Numerical Solution with Applications to Polymer Physics by : John Timothy Cummings
Download or read book Mathematical Modeling of Mixtures and Numerical Solution with Applications to Polymer Physics written by John Timothy Cummings and published by . This book was released on 2017 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider in this dissertation the mathematical modeling and simulation of a general diffuse interface mixture model based on the principles of energy dissipation. The model developed allows for a thermodynamically consistent description of systems with an arbitrary number of different components, each of which having perhaps differing densities. We also provide a mathematical description of processes which may allow components to source or sink into other components in a mass conserving, energy dissipating way, with the motivation of applying this model to phase transformation. Also included in the modeling is a unique set of thermodynamically consistent boundary conditions which allows flow across the boundary of a select number of components. The result of this modeling is a unique Cahn-Hilliard, Allen-Cahn-like system of equations. For numerical solution of this model, we use cell-centered finite difference methods for discretization and Full Approximation Storage (FAS) multigrid methods to solve the resulting system of equations via use of the BSAM (Block- Structured Adaptive Multigrid) libraries. Upon development of the mathematical model, we consider two applications. The primary application of this mathematical modeling is the time evolution of a quaternary mixture consisting of a volatile solvent in the liquid phase, solvent in the vapor phase, and two polymers. This modeling is motivated by the need to better understand the active layer in Organic Photovoltaics (OPVs). In this mixture, the volatile solvent is evaporating into the its vapor phase, and upon fully evaporating the polymer mixture which results is the active layer of the OPV device. Simulations are provided which demonstrate the solvent evaporation phenomenon and the resulting microstructure of the active layer. As a future application, we consider a mixture of a charged polymer and its counterion. We provide a description of the system based on the dissipation of the electrochemical free energy which allows for the permittivity to be dependent on the volume fractions. Simulations are provided which vary the gradient energies and polymer chain length and demonstrate the different steady-state microstructures which can result.
Book Synopsis Computer Simulations in Condensed Matter: From Materials to Chemical Biology. Volume 2 by : Mauro Ferrario
Download or read book Computer Simulations in Condensed Matter: From Materials to Chemical Biology. Volume 2 written by Mauro Ferrario and published by Springer. This book was released on 2007-04-16 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extensive and comprehensive collection of lectures by world-leading experts in the field introduces and reviews all relevant computer simulation methods and their applications in condensed matter systems. Volume 2 offers surveys on numerical experiments carried out for a great number of systems, ranging from materials sciences to chemical biology, including supercooled liquids, spin glasses, colloids, polymers, liquid crystals, biological membranes and folding proteins.
Book Synopsis Parallel Solution of Partial Differential Equations by : Petter Bjorstad
Download or read book Parallel Solution of Partial Differential Equations written by Petter Bjorstad and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computers offer the promise of greatly increased perfor mance and the routine calculation of previously intractable problems. The papers in this volume were presented at the IMA workshop on the Paral lel Solution of PDE held during June 9-13, 1997. The workshop brought together leading numerical analysts, computer scientists, and engineers to assess the state-of-the-art and to consider future directions.
Book Synopsis Lectures on Monte Carlo Methods by : Neal Noah Madras
Download or read book Lectures on Monte Carlo Methods written by Neal Noah Madras and published by American Mathematical Soc.. This book was released on 2002 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the ``curse of dimensionality'', which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability. The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.
