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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
This is a handbook of Gamma-convergence, which is a theoretical tool to study problems in applied mathematics where varying parameters are present, with many applications that range from mechanics to computer vision.
Homogenization of Multiple Integrals
The object of homogenization theory is the description of the macroscopic properties of structures with fine microstructure, covering a wide range of applications that run from the study of properties of composites to optimal design. The structures under consideration may model cellular elastic materials, fibred materials, stratified or porous media, or materials with many holes or cracks. In mathematical terms, this study can be translated in the asymptotic analysis of fast-oscillating differential equations or integral functionals. The book presents an introduction to the mathematical theory of homogenization of nonlinear integral functionals, with particular regard to those general result...
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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