This book presents generalized heat-conduction laws which, from a mesoscopic perspective, are relevant to new applications (especially in nanoscale heat transfer, nanoscale thermoelectric phenomena, and in diffusive-to-ballistic regime) and at the same time keep up with the pace of current microscopic research. The equations presented in the book are compatible with generalized formulations of nonequilibrium thermodynamics, going beyond the local-equilibrium. The book includes six main cha...

**A master physicist and a self-taught scientist present the ultimate introduction to classical mechanics for people who are serious about learning physicsA New York Times BestsellerA Wall Street Journal Best Book of the Year“Beautifully clear explanations of famously ‘difficult’ things.” ―Wall Street Journal**If you ever regretted not taking physics in college – or simply want to know how to think like a physicist – this is the boo...

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area, pres...

Density functional theory (DFT) has become the standard workhorse for quantum mechanical simulations as it offers a good compromise between accuracy and computational cost.However, there are many important systems for which DFT performs very poorly, most notably strongly-correlated materials, resulting in a significant recent growth in interest in 'beyond DFT' methods. The widely used DFT+U technique, in particular, involves the addition of explicit Coulomb repulsion terms to reprod...

The main features of high-temperature superconductors (HTSC) that define their properties are intrinsic brittleness of oxide cuprates, the layered anisotropic structure and the supershort coherence length. Taking into account these features, this treatise presents research into HTSC microstructure and properties, and also explores the possibilities of optimization of the preparation techniques and superconducting compositions. The "composition-technique-experiment-theory-model," employed h...

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation.The practical importance of a work about the theory of elasticity, whi...

After an insightful introductory part on recent developments in the thermodynamics of small systems, the author presents his contribution to a long-standing problem, namely the connection between irreversibility and dissipation. He develops a method based on recent results on fluctuation theorems that is able to estimate dissipation using only information acquired in a single, sufficiently long, trajectory of a stationary nonequilibrium process. This part ends with a remarkable application...

This thesis is concerned with establishing a rigorous, modern theory of the stochastic and dissipative forces on crystal defects, which remain poorly understood despite their importance in any temperature dependent micro-structural process such as the ductile to brittle transition or irradiation damage.The author first uses novel molecular dynamics simulations to parameterise an efficient, stochastic and discrete dislocation model that allows access to experimental time and length ...

Classical mechanics is a chief example of the scientific method organizing a "complex" collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling. This textbook covers standard topics of a mechanics course, namely, the mechanics of rigid bodies, Lagrangian and Hamiltonian formalism, stability and small oscillations, an introduction to celestial mechanics, and Hamilton–Jacobi theory, but a...

This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invaria...

This book discusses the physics of the dynamics of ions in various ionically conducting materials, and applications including electrical energy generation and storage. The experimental techniques for measurements and characterization, molecular dynamics simulations, the theories of ion dynamics, and applications are all addressed by the authors, who are experts in their fields. The experimental techniques of measurement and characterization of dynamics of ions in glassy, crystalline, and l...

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators.The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible.The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one...