Artículos relacionados a Calculus of Variations on Thin Prestressed Films: Asymptotic...

Calculus of Variations on Thin Prestressed Films: Asymptotic Methods in Elasticity: 101 (Progress in Nonlinear Differential Equations and Their Applications, 101) - Tapa dura

Lewicka, Marta

 
9783031174940: Calculus of Variations on Thin Prestressed Films: Asymptotic Methods in Elasticity: 101 (Progress in Nonlinear Differential Equations and Their Applications, 101)
Tapa dura
ISBN 10: 3031174941 ISBN 13: 9783031174940
Editorial: Birkhäuser, 2023

Sinopsis

This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria.  It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry - that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations - that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate.

Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers.  While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book.

The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math.  It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Marta Lewicka is a mathematician specializing in the fields of Analysis and Partial Differential Equations. She has contributed results in the theory of hyperbolic systems of conservation laws, fluid dynamics, calculus of variations, nonlinear potential theory, and differential games. She is a Fellow of the American Mathematical Society and holds Professor’s scientific title awarded by the President of the Republic of Poland. She works at the University of Pittsburgh, USA.

De la contraportada

This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria.  It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry – that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations – that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate.


Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers.  While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book.

The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math.  It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
2023
Idioma
Inglés
ISBN 10 
3031174941
ISBN 13 
9783031174940
Encuadernación
Tapa dura
Número de páginas
460
Contacto del fabricante
no disponible
Persona responsable
ProductSafety@springernature.com
ProductSafety@springernature.com

Abraham-Lincoln-Straße 46
Wiesbaden
65189
Alemania