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A Variational Theory of Convolution-Type Functionals
This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.
Mathematical Analysis of Continuum Mechanics and Industrial Applications II
As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.
Gamma-convergence for Beginners
The point of the technique is to describe the asymptotic behavior of families of minimum problems. This textbook was developed from a lectures series for doctoral students in applied functional analysis to describe all the main features of the convergence to an audience primarily interested in applications but not intending to enter the specialty. Annotation copyrighted by Book News, Inc., Portland, OR
Homogenization of Multiple Integrals
An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.
Nocturlabium
La scienza come non l’avete mai vista. Dalla collaborazione tra due fisici e un fumettista nasce un libro unico nel suo genere: una trattazione dall’indiscusso rigore scientifico, arricchita da fumetti, cronistorie, indizi nascosti, aneddoti e citazioni di film che vi farà vedere la fisica e la matematica attraverso un’ottica del tutto nuova e colorata. Come il notturlabio aiutava i marinai a orientarsi durante i loro viaggi, così questo volume vuole essere una guida per naviganti alla scoperta delle idee più affascinanti e significative della scienza moderna, dalla teoria classica della gravitazione alla teoria dei numeri, passando per la fisica dei buchi neri, la meccanica quantistica, l’evoluzione dell’Universo, la teoria del caos e molto altro.
Mathematical Reviews
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