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In this text the authors consider the Korteweg-de Vries (KdV) equation (u_t = - u_xxx + 6uu_x) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general.

Viewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are...

One major goal of the World Materials Research Institute Forum - WMRIF is to promote young scientists in the field of materials science and engineering. To enhance the international knowledge exchange between young postdoctoral scientists all over the world, WMRIF meanwhile regularly organizes joint workshops among the member institutes. These workshops also represent an increasingly appreciated platform to get known to each other and to build co-operations. For such workshops, various topics are selected, pointing to future perspectives and challenges in the field of Materials Science and...

In diesem Lehrbuch finden sich neben den Grundlagen und einer Formelsammlung 50 typische Aufgaben aus allen relevanten Fluid-Bereichen und den wichtigsten Ingenieurdisziplinen mit vollständig methodisch erarbeiteten Lösungen. In ergänzenden Videos zu spannenden Phänomenen und weiteren abrufbaren Kapiteln sind zusätzlich eine Fülle hilfreicher und langjährig erprobter Tipps und Anregungen für Studierende als auch Lehrende aufgeführt. Damit ist erstmals ein wirkliches Lehr- und Lernbuch entstanden, sowohl für die Erstellung fairer und für das sichere...

This work is based on experiences acquired by the authors regarding often asked questions and problems during manifold education of beginners in analytical transmission electron microscopy. These experiences are summarised illustratively in this textbook. Explanations based on simple models and hints for the practical work are the focal points.

This practically- oriented textbook represents a clear and comprehensible introduction for all persons who want to use a transmission electron microscope in practice but who are not specially qualified electron microscopists up to now.