Classical and stochastic Laplacian growth / Björn Gustafsson, Razvan Teodorescu, Alexander Vasil'ev.
| Author/creator | Gustafsson, Björn, 1947- |
| Other author | Teodorescu, Razvan. |
| Other author | Vasilʹev, Alexander, 1962- |
| Format | Electronic |
| Publication Info | Cham : Birkhauser, [2014] |
| Description | 317 pages : illustrations (some color) ; 24 cm |
| Supplemental Content | Full text available from Springer Books |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2014 English International |
| Supplemental Content | Full text available from eBooks on EBSCOhost |
| Subjects |
| Series | Advances in mathematical fluid mechanics Advances in mathematical fluid mechanics. |
| Contents | Introduction and Background -- Rational and Other Explicit Strong Solutions -- Weak Solutions and Related Topics -- Geometric Properties -- Capacities and Isoperimetric Inequalities -- Laplacian Growth and Random Matrix Theory -- Integrability and Moments -- Shape Evolution and Integrability -- Stochastic Löwner and Löwner-Kufarev Evolution -- References -- List of Symbols -- Index. |
| Abstract | This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics. |
| Bibliography note | Includes bibliographical references (pages 277-312) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2014955451 |
| ISBN | 3319082868 (cloth) |
| ISBN | 9783319082868 (cloth) |
| ISBN | (eBook) |
| ISBN | (eBook) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |