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Laplacian Growth on Branched Riemann Surfaces
This book studies solutions of the Polubarinova–Galin and Löwner–Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved. When the mapping function is no longer locally univalent interesting phase transitions take place, leading to structural changes in the data of the solution, for example new zeros and poles in the case of rational maps. This topic intersects with several areas, including mathematical physics, potential theory and complex analysis. The text will be valuable to researchers and doctoral students interested in fluid dynamics, integrable systems, and conformal field theory.
Why the Boundary of a Round Drop Becomes a Curve of Order Four
This monograph concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution. This curve is the image of an ellipse under a reflection with respect to a circle. Since the 1940s, work on this problem has led to generalizations of the reflection property and methods for constructing explicit solutions. More recently, the results have been extended to multiply connected domains. This text discusses this topic and other recent work in the theory of fluid flows with a moving boundary. Problems are included at the end of each chapter, and there is a list of open questions at the end of the book.
Fisheries Review
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Formal Methods and Software Engineering
This book constitutes the refereed proceedings of the 18th International Conference on Formal Engineering Methods, ICFEM 2016, held in Tokyo, Japan, in November 2016. The 27 revised full papers presented together with three invited talks were carefully reviewed and selected from 64 submissions. The conference focuses in all areas related to formal engineering meth-ods, such as verification and validation, software engineering, formal specification and modeling, software security, and software reliability.
Spectroscopy of Biological Molecules: New Directions
Investigation of the structure and function of biological molecules through spectroscopic methods is a field rich in revealing, clever techniques and demanding experiments. It is most gratifying to see that the basic concepts are applied to more and more complex systems, making feasible the study of the behaviour of whole systems in relation to molecular disturbances. The analytical potential of spectroscopy and spectroscopic imaging enables species identification of bacteria and tissue recognition. Clear opportunities for in vivo applications become apparent in the medical field. The methods developed in biophysics start to generate spin-off in the direction of biotechnology, where in previ...
