The continually growing plastics market consists of more than 250 million tons of product annually, making the recurring problem of polymer melt fracture an acute issue in the extrusion of these materials. Presenting a pictorial library of the different forms of melt fracture and real industrial extrusion melt fracture phenomena, Polymer Melt Fracture provides pragmatic identification and industrial extrusion defect remediation strategies based on detailed experimental and theoretical findings from the last 50 years.

Distinct microscopic photos

Each chapter in this comprehensive volume covers a different aspect of the science and technology relating to polymer melt fracture. The book begins with a collection of optical and scanning electron microscopy pictures. These photos show distorted capillary die extrudates for a number of commercially available polymers. The authors present a brief introduction to the basic science and technology of polymers. They explain what polymers are, how they are made, and how they can be characterized. They also discuss polymer rheology, review the principles of continuum mechanics, and define linear viscoelastic material functions.

Techniques for observing and measuring fracture

Next, the book explains how polymer melt fracture is actually experienced in the polymer processing industry. It explains the various ways polymer melt fracture may appear during polymer melt processing in different extrusion processes. The authors provide comprehensive reviews of the polymer melt fracture literature, with chapters on experimental findings and the techniques used to observe and measure polymer melt fracture, and the influence of polymer architecture and polymer processing conditions on the onset and types of polymer melt fracture. Posing a hypothesis about the phenomenon, the book presents the current understanding of polymer melt fracture.

Mathematical equations

Recognizing the importance of models for simulations that may indicate potential solutions, the book discusses aspects of non-linear constitutive equations and microscopic theory and develops a macroscopic model, explaining the capabilities and limitations of this approach. The book presents an overview of pragmatic tools and methods that have been used to prevent the appearance of polymer melt fracture and explains how to use them to suppress defects.

The continually growing plastics market consists of more than 250 million tons of product annually, making the recurring problem of polymer melt fracture an acute issue in the extrusion of these materials. Presenting a pictorial library of the different forms of melt fracture and real industrial extrusion melt fracture phenomena, Polymer Melt Fracture provides pragmatic identification and industrial extrusion defect remediation strategies based on detailed experimental and theoretical findings from the last 50 years. Distinct microscopic photos Each chapter in this comprehensive volume covers a different aspect of the science and technology relating to polymer melt fracture. The book begins with a collection of optical and scanning electron microscopy pictures. These photos show distorted capillary die extrudates for a number of commercially available polymers. The authors present a brief introduction to the basic science and technology of polymers. They explain what polymers are, how they are made, and how they can be characterized. They also discuss polymer rheology, review the principles of continuum mechanics, and define linear viscoelastic material functions. Techniques for observing and measuring fracture Next, the book explains how polymer melt fracture is actually experienced in the polymer processing industry. It explains the various ways polymer melt fracture may appear during polymer melt processing in different extrusion processes. The authors provide comprehensive reviews of the polymer melt fracture literature, with chapters on experimental findings and the techniques used to observe and measure polymer melt fracture, and the influence of polymer architecture and polymer processing conditions on the onset and types of polymer melt fracture. Posing a hypothesis about the phenomenon, the book presents the current understanding of polymer melt fracture. Mathematical equations Recognizing the importance of models for simulations that may indicate potential solutions, the book discusses aspects of non-linear constitutive equations and microscopic theory and develops a macroscopic model, explaining the capabilities and limitations of this approach. The book presents an overview of pragmatic tools and methods that have been used to prevent the appearance of polymer melt fracture and explains how to use them to suppress defects.

Mathematical modeling - the ability to apply mathematical concepts and techniques to real-life systems - has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts.Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to elaborated case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.

The focus of this work is on a single source of pollution, namely that by vessels from the perspective of the coastal state. This implies that exercises of jurisdiction with other objectives, for example security, are in general not dealt with even though these could also impede or entirely frustrate navigation. State practice is given a prominent place in this study. Relevant collective state practice exists in the form of bilateral or multilateral conventions or other international instruments, such as IMO Resolutions. Individual state practice can consist of unilateral declarations, legislation, and actual exercises of enforcement. The book gives insight into the way in which the LOSC legal regime of coastal state jurisdiction over vessel-source pollution operates in practice. Safeguards form an inseparable part of the jurisdictional balance in general, and that of enforcement jurisdiction in particular. The jurisdictional balance for vessel-source pollution in the LOSC is complemented by an innovative system of dispute settlement. The wide range of issues brought forward illustrates the extremely complex, but equally fascinating character of coastal state jurisdiction over vessel-source pollution.

In order to emphasize the relationships and cohesion between analytical and numerical techniques, this book presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained.