Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.

Mountain pass theorem. --- Critical point theory (Mathematical analysis) --- Hamiltonian systems. --- Variational principles. --- Variational inequalities (Mathematics) --- Maxima and minima. --- Nonsmooth optimization. --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Minima --- Mathematics --- Extremum principles --- Minimal principles --- Variation principles --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Differential topology --- Global analysis (Mathematics) --- MPT (Mathematical analysis) --- Mountain pass theorem --- Hamiltonian systems --- Variational principles --- Variational inequalities --- Maxima and minima --- Nonsmooth optimization

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume contains the proceedings of the international workshop Variational Problems in Materials Science, which was jointly organized by the International School for Advanced Studies (SISSA) of Trieste and by the Dipartimento di Matematica ``Francesco Brioschi'' of the Politecnico di Milano. The conference took place at SISSA from September 6 to 10, 2004. The study of variational problems in materials science has a long history, and it has contributed a lot in shaping our understanding on how materials work and perform. There is, however, a recent renewed interest in this subject as a consequence of the fruitful interaction between mathematical analysis and the modelling of new, technologically advanced materials. On one hand, a sizable group of analysts has found in materials science a valuable source of inspiration for new variational theories and interesting problems. On the other hand, workers in the fields of theoretical, applied, and computational mechanics are increasingly using innovative variational techniques. The workshop intended to review some of the recent advances stemming from the successful interaction between the two communities, and to identify promising areas for further cooperation. Talks were devoted to a wide spectrum of analytical techniques and of physical systems and phenomena. They included the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, variational techniques for the study of crystal plasticity, of dislocations, and of concentrations in Ginzburg-Landau functionals, concentrated contact interactions, and phase transitions in biaxial liquid crystals. This volume collects contributions authored or co-authored by 11 of the 20 speakers invited to deliver lectures at the workshop. They all contain original results in fields which are at the forefront of current research, and in rapid evolution. .

Materials science --- Variational principles --- Mathematics --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- Material science --- Physical sciences --- Materials. --- Differential equations, partial. --- Mathematical optimization. --- Computer science --- Computer science. --- Materials Science, general. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Mathematical Modeling and Industrial Mathematics. --- Mathematics. --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Partial differential equations --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Materials --- Materials science. --- Partial differential equations. --- Calculus of variations. --- Computer mathematics. --- Mathematical models. --- Models, Mathematical --- Isoperimetrical problems --- Variations, Calculus of

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical understanding rather than on rigorous mathematical derivations, the content is accessible to graduate students and researchers in the broad areas of materials science and engineering, chemistry, chemical and biomolecular engineering, applied mathematics, condensed-matter physics, without specific training in theoretical physics or calculus of variations.

Chemoinformatics. --- Simulation and Modeling. --- Mathematical and Computational Biology. --- Models. --- Molecular models --- Engineering. --- Computer simulation. --- Biomathematics. --- Statistics. --- Continuum mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Computer Applications in Chemistry. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Molecules --- Chemical models --- Mechanics. --- Mechanics, Applied. --- Chemistry. --- Solid Mechanics. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Physical sciences --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Variational principles. --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- Statistics . --- Biology --- Chemical informatics --- Chemiinformatics --- Chemoinformatics --- Chemistry informatics --- Chemistry --- Information science --- Computational chemistry --- Data processing

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Key Features: - Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view - Bridges the gap between regularization theory in image analysis and in inverse problems - Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography - Discusses link between non-convex calculus of variations, morphological analysis, and level set methods - Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations - Uses numerical examples to enhance the theory This book is geared towards graduate students and researchers in applied mathematics. It can serve as a main text for graduate courses in image processing and inverse problems or as a supplemental text for courses on regularization. Researchers and computer scientists in the area of imaging science will also find this book useful.

Imaging systems. --- Variational principles. --- Extremum principles --- Minimal principles --- Variation principles --- Mathematics. --- Radiology. --- Image processing. --- Numerical analysis. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Numerical Analysis. --- Imaging / Radiology. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Mathematical analysis --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Radiological physics --- Physics --- Radiation --- Math --- Science --- Calculus of variations --- Radar --- Remote sensing --- Television --- Scanning systems --- Equipment and supplies --- Mathematical optimization. --- Computer vision. --- Radiology, Medical. --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Variational principles --- Optical data processing. --- Signal processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment