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Cardone Fabio: Energy Space Time:
Introducing Energy Metrics Of Interacti

Energy Space Time: Introducing Energy Metrics Of Interactions In Five Dimensions

Peking University Series in Mathematics

Principles of classical Hamiltonian mechanics say that the evolution of a dynamical system is determined by the Poisson bracket of observable functions with the given Hamiltonian function of the system. In Quantum Mechanics, these principles are modified so that the algebra of observable functions should be replaced by a noncommutative algebra of operators and the Poisson bracket by their commutator so that the canonical commutation relations hold. Thus, working with quantum systems, we must determine the 'quantisation' of our observables, i.e. to choose a noncommutative algebra whose elements would play the role of the observables. With some modifications, this question is the main content of the Deformation Quantisation problem formulated in 1978 by Flato and others.This book is based on the course that the author taught in the Fall semester of 2019 at Peking University. The main purpose of that course and of this book is to acquaint the reader with the vast scope of ideas related to the Deformation Quantisation of Poisson manifolds. The book begins with Quantum Mechanics and Moyal product formula and covers the three main constructions that solve the Deformation Quantisation problem: Lecomte and de Wilde deformation of symplectic manifolds, Fedosov's Quantisation theory and Kontsevich's formality theorem. In the appendices, the Tamarkin's proof of formality theorem is outlined.The book is written in a reader-friendly manner and is as self-contained as possible. It includes several sets of problems and exercises that will help the reader to master the material.

Lectures On Deformation Quantisation: From Moyal Product To Kontsevich's Formality Theorem

The Navier-Stokes equations - modeling the motion of viscous, incompressible Newtonian fluids - have been capturing the attention of an increasing number of mathematicians over the years and has now become one of the most intensely studied subjects in applied analysis. This project is dedicated to a complete and updated mathematical analysis of fundamental topics related to these equations. Every subject will be analyzed using different approaches. The main ideas behind them as well as their differences will also be emphasized and discussed. The book aims at being self-contained, however, it will also be supported by a vast bibliography for further reading.

Navier-Stokes Equations: A Mathematical Analysis

If there were no Coulomb interaction among electrons, it would be relatively straightforward to solve the many-electron Schrödinger equation. It is, however, precisely this interaction that is at the heart of numerous fascinating phenomena in condensed matter physics such as superconductivity, Kondo physics, magnetism, etc. Due to the large number of electrons in a material being of the order of Avogadro's number, it is at present - and perhaps in the foreseeable future - not feasible or even desirable to solve the Schrödinger equation to obtain the many-electron wavefunction. Fortunately, a large number of important physical properties can be calculated without explicit knowledge of the wavefunction.

Two of the most important formalisms for dealing with the many-electron problem which avoid a direct use of the many-electron wavefunction are the Green function and the density functional theory. Within the Kohn-Sham scheme the latter is used to calculate ground-state properties whereas the former for excitation spectra. The book presents the fundamentals of these two theories in detail with essential many-body tools, such as the occupation number representation and Grassmann algebra developed from scratch. Prior knowledge of many-body theory is not a prerequisite so that it is readable for final-year undergraduates and graduate students in physics and chemistry as well as researchers in the field of electronic structure and many-body theory. The book includes in the last chapter an exposition of a density-functional path for determining the Green function, a new formalism recently proposed by the author. The book should be a valuable companion for those embarking in the field of many-electron physics.

Elements Of Green Function And Density Functional Theory

De Gruyter Studies in Mathematical Physics

Mirror symmetry is one of the most exciting ideas in mathematics to emerge in the last two decades. It was introduced in physics as a duality between superconformal field theories. This book discusses this rapidly developing aspect of string theory.

Laurent Polynomials in Mirror Symmetry

Spin Fluids And Defect Dynamics: A Common Aspect Of Spinor Condensates And Polarization Optics

Series in Computational Biophysics

Multiscale methods are ideally suited to simulate the processes at work in many biomolecular systems, which often span a large range of time and length scales. Multiscale Methods in Molecular Biophysics highlights the advantages of these methods for integrating different levels of detail in a single simulation setting. It covers the practical methodology and successful applications in areas such as enzyme catalysis, protein folding, and ligand binding. The book is divided into three main sections: combination quantum and classical (atomistic) descriptions, approaches that combine atomistic and coarse-grained level of details, and multiscale methods where the resolution coupling is between global collective coordinates and local details.

Multiscale Methods in Molecular Biophysics

Cambridge Monographs on Mathematical Physics

An Introduction to Fundamental Structures, Methods and Applications

Causal Fermion Systems

Metrical Fixed Point Theory, originating from the 1922 Banach Fixed Point Theorem, is one of the most dynamic areas within Operator Equations Theory. This book aims to discuss the foundational aspects of this theory, focusing on questions of existence, uniqueness, and approximation in operator equations - whether explicit or implicit, anticipative or non-anticipative - across standard, ordered, and relational metric spaces. Key themes include implicit methods for analyzing metrical contractions, factorial techniques for reducing coincidence point problems to standard fixed point ones, homotopical fixed point results in gauge spaces with ordered metric space parameters, and constant class reduction of PPF-dependent fixed point results.

The book is structured into four chapters. Chapter 1 provides an overview of essential preliminary concepts. Chapter 2 delves into various contraction classes within bi-relational, local Branciari, and ordered metric spaces. Chapter 3 applies maximal techniques to address the discussed questions, and Chapter 4 explores additional topics, including contractive-type conditions derived from self and non-self maps. Through this structure, the book offers a comprehensive view of the core aspects and applications of Metrical Fixed Point Theory.

Modern Topics In Metrical Fixed Point Theory

This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications.&nbsp;Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
&nbsp;

With Applications to Oil and Gas Development

Introduction to Continuum Mechanics

Origami Engineering: Combining Science, Art, And Industry

Handbook of Electronic Structure Theory provides a much-needed learning resource that collects and demonstrates the various key methods involved in electronic structure theory, the feasibility and reliability of electronic structure calculations and their applications using computational chemistry, with a particular focus on the most modern and recent problems which are poorly covered in existing, largely outdated book literature. This handbook is designed with early career researcher learning in mind by aiming to provide a careful, structured, coherent, measured, and incremental presentation of the subject matter as well as appropriate problems and worked tutorial examples. Elements like summary boxes, worked examples, and downloadable data sets make this a holistic guide to the topic for learners from different backgrounds who require a deeper understanding of electronic structure theory. Part I one of the book focuses on the critical core theories, before Part II moves on to some of the most important recent developments and their potential future directions, including key topics such as the electronic excited states and the harnessing of machine learning. Finally, Part III then collects a range of key case study examples of applications such as for biomolecules, in spectroscopy, or for use in catalysis amongst others. Handbook of Electronic Structure Theory is written primarily for masters, PhD, and postdoctoral students in theoretical and computational chemistry as well as experimental researchers wishing to apply quantum chemical methods in a critical way. The book will also have significant relevance to those studying and teaching in the adjacent fields of computational physics, materials science, and astrochemistry, who are making use of electronic structure methods. It is also likely to be of interest to chemists working on designing new materials and compounds targeting industrial and environmental applications such as catalysis, energy harvesting or green chemistry.

Methods and Applications

Handbook of Electronic Structure Theory

The monograph focuses on the analytical challenges of describing incompressible fluid flows using Lagrangian variables. The Lagrangian method is presented as a complementary approach to the Eulerian method for studying fluid motion. The fundamental nature of fluid dynamics is linked to tracing the trajectories of individual fluid particles, which is precisely what the Lagrangian method facilitates.

The purpose of this publication is to reflect as fully as possible the achievements of analytical fluid dynamics in Lagrangian variables. A significant part of it consists of original articles by the author. Considerable attention is paid to the subtleties of the Lagrangian description and its popularization among experts in fluid dynamics, students, postgraduates, and anyone interested in problems of fluid mechanics.

The book can be considered, among other things, as a tutorial on Lagrangian fluid dynamics. The book covers issues of the general description of the movement of incompressible fluid, problems of classical hydrodynamics and geophysical hydrodynamics. Fundamental topics include free-boundary motion, vortices in fluids, and water waves. The book includes a number of problems that take into account the stratification and viscosity of fluids, as well as the rotation of the Earth.

Analytical Fluid Dynamics In Lagrangian Variables

Energy Space Time: Introducing Energy Metrics Of Interactions In Five Dimensions

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