Discrete Variational Problems with Interfaces

Variational methods have been successful in transitioning from discrete to continuous models, especially for systems that depend on lattice energies. This book provides a systematic and unified presentation of research in the area over the last 20 years, covering topics such as compactness and representation, ferromagnetic energies, frustrated systems, and infinite-dimensional systems with diffuse interfaces. It is suitable as a graduate course text and an invaluable reference for researchers.

Format: Hardback
Length: 295 pages
Publication date: 21 December 2023
Publisher: Cambridge University Press

Numerous materials can be modeled as either discrete systems or as continua, depending on the scale. At intermediate scales, it is essential to understand the transition from discrete to continuous models, and variational methods have proven successful in this task, particularly for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs, and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.

Numerous materials can be modeled as either discrete systems or as continua, depending on the scale. At intermediate scales, it is essential to understand the transition from discrete to continuous models, and variational methods have proven successful in this task, particularly for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs, and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.

Weight: 552g
Dimension: 160 x 236 x 25 (mm)
ISBN-13: 9781009298780