Uniqueness Of Fat Tailed Self Similar Profiles To Smoluchowski S Coagulation Equation For A Perturbation Of The Constant Kernel

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Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models. Initially, an in-depth survey of coagulation-fragmentation processes is presented, together with an account of relevant early results obtained on the associated model equations. These provide motivation for the subsequent detailed treatment of more up-to-date investigations which have led to significant theoretical developments on topics such as solvability and the long-term behaviour of solutions. To make the account as self-contained as possible, the mathematical tools that feature prominently in these modern treatments are introduced at appropriate places. The main theme of Volume I is the analysis of linear fragmentation models, with Volume II devoted to processes that involve the nonlinear contribution of coagulation. Features of Volume II: A primer on weak compactness in L 1 and dynamical systems A comprehensive theory of solvability of the coagulation-fragmentation equation by both the semigroup and weak compactness methods, including a thorough analysis of the gelation and shattering phenomena A detailed analysis of the long-term dynamics of the coagulation-fragmentation equations with a state-of-the-art discussion on self-similar solutions

This book is the first authoritative text on the role that physicists play in solving the inherently multidisciplinary science and technology challenges in food manufacturing. Topics range from designing safe, nutritious and great-tasting foods to the process technology and manufacturing know-how needed to deliver compelling product innovation. The book provides a foundational resource for the transformation of engineering and materials characterisation in the food and pharmaceuticals industries. It is an essential reference for interdisciplinary physical scientists, food/nutrition scientists and engineers working in academic research, government labs and industry, and it is also a valuable resource for R&D staff and product engineers working for suppliers of specialist instrumentation and equipment to the food processing industry. The book is augmented by complementary presentations from the Fourth IOP Physics in Food Manufacturing Conference 2020, held in Leeds, UK. Key Features The first authoritative account of the diverse role that physics and physicists play in the food processing industry. A go-to reference source for anyone wishing to become involved in food processing - science, technology, engineering. Expert accounts by leading academics and industrial scientists.

Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0

This book provides a rigorous treatment of the coupling of chemical reactions and fluid flow. Combustion-specific topics of chemistry and fluid mechanics are considered and tools described for the simulation of combustion processes. This edition is completely restructured. Mathematical Formulae and derivations as well as the space-consuming reaction mechanisms have been replaced from the text to appendix. A new chapter discusses the impact of combustion processes on the atmosphere, the chapter on auto-ignition is extended to combustion in Otto- and Diesel-engines, and the chapters on heterogeneous combustion and on soot formation are heavily revised.

The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.

Academic and industrial research around polymer-based colloids is huge, driven both by the development of mature technologies, e.g. latexes for coatings, as well as the advancement of new materials and applications, such as building blocks for 2D/3D structures and medicine. Edited by two world-renowned leaders in polymer science and engineering, this is a fundamental text for the field. Based on a specialised course by the editors, this book provides the reader with an invaluable single source of reference. The first section describes formation, explaining basic properties of emulsions and dispersion polymerization, microfluidic approaches to produce polymer-based colloids and formation via directed self-assembly. The next section details characterisation methodologies from microscopy and small angle scattering, to surface science and simulations. The final chapters close with applications, including Pickering emulsions and molecular engineering for materials development. A comprehensive guide to polymer colloids, with contributions by leaders in their respective areas, this book is a must-have for researchers and practitioners working across polymers, soft matter and chemical and molecular engineering.

Until now colloid science books have either been theoretical, or focused on specific types of dispersion, or on specific applications. This then is the first book to provide an integrated introduction to the nature, formation and occurrence, stability, propagation, and uses of the most common types of colloidal dispersion in the process-related industries. The primary focus is on the applications of the principles, paying attention to practical processes and problems. This is done both as part of the treatment of the fundamentals, where appropriate, and also in the separate sections devoted to specific kinds of industries. Throughout, the treatment is integrated, with the principles of colloid and interface science common to each dispersion type presented for each major physical property class, followed by separate treatments of features unique to emulsions, foams, or suspensions. The first half of the book introduces the fundamental principles, introducing readers to suspension formation and stability, characterization, and flow properties, emphasizing practical aspects throughout. The following chapters discuss a wide range of industrial applications and examples, serving to emphasize the different methodologies that have been successfully applied. Overall, the book shows how to approach making emulsions, foams, and suspensions with different useful properties, how to propagate them, and how to prevent their formation or destabilize them if necessary. The author assumes no prior knowledge of colloid chemistry and, with its glossary of key terms, complete cross-referencing and indexing, this is a must-have for graduate and professional scientists and engineers who may encounter or use emulsions, foams, or suspensions, or combinations thereof, whether in process design, industrial production, or in related R&D fields.