This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
“A history of “secular,” or non-supernatural, or entertainment magic as an important but neglected constituent of modern culture” (Nicholas Daly). Magic, Simon During suggests, has helped shape modern culture. Devoted to this deceptively simple proposition, During’s superlative work, written over the course of a decade, gets at the aesthetic questions at the very heart of the study of culture. How can the most ordinary arts—and by “magic,” During means not the supernatural, but the special effects and conjurings of magic shows—affect people? Modern Enchantments takes us deeply into the history and workings of modern secular magic, from the legerdemain of Isaac Fawkes in 1720, to the return of real magic in nineteenth-century spiritualism, to the role of magic in the emergence of the cinema. Through the course of this history, During shows how magic performances have drawn together heterogeneous audiences, contributed to the molding of cultural hierarchies, and extended cultural technologies and media at key moments, sometimes introducing spectators into rationality and helping to disseminate skepticism and publicize scientific innovation. In a more revealing argument still, Modern Enchantments shows that magic entertainments have increased the sway of fictions in our culture and helped define modern society’s image of itself. Praise for ModernEnchantment “During documents the extent to which magic and magical thinking have pervaded, and continue to pervade, secular life . . . the author examines 19th- and 20th-century theatrical magic and “commercial conjuring” with great sensitivity to the social and cultural context in the Western world. Equally fascinating is the analysis of magic and early film.” —R. Sugarman, Choice “A richly informed, warmly argued addition to the growing number of books in which writers worry at the pervasive blurring of distinctions between act and appearance, organic consciousness and artificial intelligence, imagination and empirical experience, illusion and thought, reality TV and real life, dreams and money.” —Marina Warner, Financial Times “During moves confidently across three centuries of magic (and covers aspects of a few more besides). The sheer wealth of historical detail he provides is impressive, but no less impressive is the subtlety of his argumentation, and the suggestiveness of his claims . . . This extremely significant piece of work will appeal to literary critics, historians, and not least, devotees of magic.” —Nicholas Daly, author of Modernism, Romance, and the Fin de Siècle: Popular Fiction and British Culture, 1880–1914
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
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