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Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Calculus.

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This book contains well-written monographs within the broad spectrum of applied mathematics, offering an interesting reading of some of the current trends and problems in this fascinating and critically important field of science to a broad category of researchers and practitioners. Recent developments in high-performance computing are radically changing the way we do numerics. As the size of problems is expected to grow very large in the future, the gap between fast and slow algorithms is growing rapidly. Novel classes of numerical methods with reduced computational complexity are therefore needed to make the rigorous numerical solution of difficult problems arising in an industrial setting more affordable. The book is structured in four distinct parts, according to the purpose and approaches used in the development of the contributions, ranging from optimization techniques to graph-oriented approaches and approximation theory, providing a good mix of both theory and practice.

Mathematics. --- Math --- Science --- Physical Sciences --- Engineering and Technology --- Mathematics --- Applied Mathematics

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Fusion power may offer a long-term energy supply with an uninterrupted power delivery, a high power-generation density, and no greenhouse gas emissions, contributing to preventing the worst effects of climate change and making an enduring contribution to future energy supply. However, the intense conditions inside a fusion power plant (extreme temperatures and high magnetic fields necessary for nuclear fusion) call for addressing several potential problems. These include the development of new materials with extremely high heat tolerances and low enough vapor pressure and the design of mechanical structures that can withstand the electromagnetic force generated as well as feedback controllers to measure and counteract the unstable modes of evolution of the plasma, to name a few. The future of nuclear fusion as an efficient alternative energy source depends largely on techniques that enable us to control these instabilities. Mathematical modelling and physical experiments attempt to overcome some of the hindrances posed by these complexities. This book provides a comprehensive overview of the current state of the art in this fascinating and critically important field of pure and applied physics, mathematics, and engineering, presenting some of the most recent developments in theory, modelling, algorithms, experiments, and applications.

Nuclear fusion. --- Controlled fusion.