This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.

The volume collects several contributions to the INDAM workshop Mathematical Methods for Objects Reconstruction: from 3D Vision to 3D Printing held in Rome, February, 2021.  The goal of the workshop was to discuss new methods and conceptual structures for managing these challenging problems. The chapters reflect this goal and the authors are academic researchers and some experts from industry working in the areas of 3D modeling, computer vision, 3D printing and/or developing new mathematical methods for these problems. The contributions present methodologies and challenges raised by the emergence of large-scale 3D reconstruction applications and low-cost 3D printers. The volume collects complementary knowledges from different areas of mathematics, computer science and engineering on research topics related to 3D printing, which are, so far, widely unexplored.  Young researchers and future scientific leaders in the field of 3D data acquisition, 3D scene reconstruction, and 3D printing software development will find an excellent introduction to these problems and to the mathematical techniques necessary to solve them.

This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.

Vi siete mai chiesti cosa fa un matematico quando scrive freneticamente su un foglio di carta? Provate a chiederglielo. Vi sentirete rispondere qualcosa del tipo: "Sto cercando di dimostrare la natura iperbolica di questa equazione differenziale per poter applicare il metodo delle caratteristiche."

Non avete capito? Provate a chiedergli di spiegarvelo piA semplicemente. La risposta sarA: "Allora... Ecco... Come posso dire... Sto cercando di dimostrare che questo coso qui (indica un formulone) appartiene ad una certa categoria di equazioni in cui la soluzione si propaga da un certo dato iniziale lungo delle curve particolari."

Inutile insistere, non vi resta che andarvene. La matematica vi ha respinto un'altra volta.

Ma una soluzione esiste ed A] unica: leggere questo libro e lasciarvi guidare nella (TM)incantato mondo dell'alta matematica senza per questo fare alta matematica. Capirete finalmente cosa studiano i matematici, cosa pensano, cosa li appassiona ed in quale strano mondo n-dimensionale vivono. Dedicato a tutti coloro che vorrebbero studiare matematica ma che non lo hanno mai (o ancora) fatto, questo libro vi convincerA che la matematica A] il perfetto connubio tra scienza e arte, tra curiositA e fantasia, tra scoperta ed invenzione.