{"product_id":"9783319666723","title":"Modern Birkhäuser Classics","description":"\u003ch1\u003eModern Birkhäuser Classics\u003c\/h1\u003e \u003ch2\u003eBethuel, Fabrice; Brezis, Haïm; Hélein, Frédéric\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book is concerned with the study in two dimensions of stationary solutions of u\u003csub\u003eɛ\u003c\/sub\u003e of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small.  Thus, it is of great interest to study the asymptotics as ɛ tends to zero.\u003c\/p\u003e  \u003cp\u003eOne of the main results asserts that the limit u-star of minimizers u\u003csub\u003eɛ\u003c\/sub\u003e exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized.\u003c\/p\u003e  \u003cp\u003eThe material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis,partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2017-10-05\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319666723\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-66673-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 159\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45580697370764,"sku":"9783319666723","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319666723.jpg?v=1775754335","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319666723","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}