This book presents a numerical scheme for the solution of field problems governed by partial differential equations: the cell method. The technique lends itself naturally to the solution of multiphysics problems with several interacting phenomena. The Cell Method, based on a space-time tessellation, is intimately related to the work of Tonti and to his ideas of classification diagrams or, as they are nowadays called, Tonti diagrams: a graphical representation of the problem's equations made possible by a suitable selection of a space-time framework relating physical variables to each other. The main features of the cell method are presented and links with many other discrete numerical methods (finite integration techniques, finite difference time domain, finite volumes, mimetic finite differences, etc.) are discussed. After outlining the theoretical basis of the method, a set of physical problems which have been solved with the cell method is described. These single and multiphysics problems stem from the authors' research experience in the fields of electromagnetism, elasticity, thermo-elasticity and others. Finally, the implementation of the numerical technique is described in all its main components: space-time discretization, problem formulation, solution and representation of the resulting physical fields.

The Cell Method (CM) is a computational tool that maintains critical multidimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This book highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modeling heterogeneous materials. Professional engineers and scientists, as well as graduate students, are offered: • A general overview of physics and its mathematical descriptions; • Guidance on how to build direct, discrete formulations; • Coverage of the governing equations of the CM, including nonlocality; • Explanations of the use of Tonti diagrams; and • References for further reading.

The previous edition of this book marked the shift in technology from video to digital camera use with microscope use in biological science. This new edition presents some of the optical fundamentals needed to provide a quality image to the digital camera. Specifically, it covers the fundamental geometric optics of finite- and infinity-corrected microscopes, develops the concepts of physical optics and Abbe's theory of image formation, presents the principles of Kohler illumination, and finally reviews the fundamentals of fluorescence and fluorescence microscopy. The second group of chapters deals with digital and video fundamentals: how digital and video cameras work, how to coordinate cameras with microscopes, how to deal with digital data, the fundamentals of image processing, and low light level cameras. The third group of chapters address some specialized areas of microscopy that allow sophisticated measurements of events in living cells that are below the optical limits of resolution. - Expands coverage to include discussion of confocal microscopy not found in the previous edition - Includes "traps and pitfalls" as well as laboratory exercises to help illustrate methods

Looking for the real state of play in computational many-particle physics? Look no further. This book presents an overview of state-of-the-art numerical methods for studying interacting classical and quantum many-particle systems. A broad range of techniques and algorithms are covered, and emphasis is placed on their implementation on modern high-performance computers. This excellent book comes complete with online files and updates allowing readers to stay right up to date.

Expansion Microscopy for Cell Biology, Volume 161 in the Methods in Cell Biology series, compiles recent developments in expansion microscopy techniques (Pro-ExM, U-ExM, Ex-STED, X10, Ex-dSTORM, etc.) and their applications in cell biology, ranging from mitosis, centrioles or nuclear pore complex to plant cell, bacteria, Drosophila or neurons. Chapters in this new release include Protein-retention Expansion Microscopy: Improved Sub-cellular Imaging Resolution through Physical Specimen Expansion, Ultrastructure Expansion Microscopy (U-ExM), Expansion STED microscopy (ExSTED), Simple multi-color super-resolution by X10 microscopy, Expansion microscopy imaging of various neuronal structures, Mapping the neuronal cytoskeleton using expansion microscopy, Mechanical expansion microscopy, and much more. - Provides the authority and expertise of leading contributors from an international board of authors - Represents the latest release in the Methods in Cell Biology series - Includes the latest information on Expansion Microscopy for Cell Biology

Summary: A Generalized Multiscale Analysis Approach brings together comprehensive background information on the multiscale nature of the composite, constituent material behaviour, damage models and key techniques for multiscale modelling, as well as presenting the findings and methods, developed over a lifetime's research, of three leading experts in the field. The unified approach presented in the book for conducting multiscale analysis and design of conventional and smart composite materials is also applicable for structures with complete linear and nonlinear material behavior, with numerous applications provided to illustrate use. Modeling composite behaviour is a key challenge in research and industry; when done efficiently and reliably it can save money, decrease time to market with new innovations and prevent component failure.