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Classical and Stochastic Laplacian Growth
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 equa...
Leading-edge Superconductivity Research Developments
This new book focuses on superconductivity which is the ability of certain materials to conduct electrical current with no resistance and extremely low losses. High temperature superconductors, such as La2-xSrxCuOx (Tc=40K) and YBa2Cu3O7-x (Tc=90K), were discovered in 1987 and have been actively studied since. In spite of an intense, worldwide, research effort during this time, a complete understanding of the copper oxide (cuprate) materials is still lacking.Many fundamental questions are unanswered, particularly the mechanism by which high-Tc superconductivity occurs. More broadly, the cuprates are in a class of solids with strong electron-electron interactions. An understanding of such 'strongly correlated' solids is perhaps the major unsolved problem of condensed matter physics with over ten thousand researchers working on this topic. High-Tc superconductors also have significant potential for applications in technologies ranging from electric power generation and transmission to digital electronics.
Opportunities in High Magnetic Field Science
High-field magnetsâ€"those that operate at the limits of the mechanical and/or electromagnetic properties of their structural materialsâ€"are used as research tools in a variety of scientific disciplines. The study of high magnetic fields themselves is also important in many areas such as astrophysics. Because of their importance in scientific research and the possibility of new breakthroughs, the National Science Foundation asked the National Research Council to assess the current state of and future prospects for high-field science and technology in the United States. This report presents the results of that assessment. It focuses on scientific and technological challenges and opportunities, and not on specific program activities. The report provides findings and recommendations about important research directions, the relative strength of U.S. efforts compared to other countries, and ways in which the program can operate more effectively.
Modern NMR Approaches to the Structure Elucidation of Natural Products
The first volume in a two-part set that discusses contemporary NMR approaches for the structure elucidation of natural products. It covers optimized hardware and experimental approaches.
Approximation Theory XVI
These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Advanced Research Instrumentation and Facilities
In recent years, the instrumentation needs of the nation's research communities have changed and expanded. The need for particular instruments has become broader, crossing scientific and engineering disciplines. The growth of interdisciplinary research that focuses on problems defined outside the boundaries of individual disciplines demands more instrumentation. Instruments that were once of interest only to specialists are now required by a wide array of scientists to solve critical research problems. The need for entirely new types of instrumentsâ€"such as distributed networks, cybertools, and sensor arraysâ€"is increasing. Researchers are increasingly dependent on advanced instrumen...
