Mathematical physics

After a century of successes, physicists still feel the need to probe the limits of the validity of theories based on special relativity.

At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems.

The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time.

Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems.

A mathematically consistent formulation of relativistic quantum electrodynamics (QED) has still to be found.

Since the late 1980s, Toeplitz operators and matrices have remained a ?

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems.

Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors.

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The present third edition of The Statistical Mechanics of Financial Markets is published only four years after the ?

This volume gathers selected papers presented at the ICMSQUARE 2023 - 12th International Conference on Mathematical Modeling in Physical Sciences held in Belgrade, Serbia from August 28-31, 2023.

This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics.

This book comprehensively describes recent developments in the research of renormalizable quantum gravity, focusing on its application to physics beyond the Planck scale, particularly in inflationary cosmology.

The aim of this text is to provide an account of the fundamentals of thermodynamics which is accessible at graduate level to physicists, mathematicians and philosophers of physics.

Navigating the realm where physics intersects with programming, this book serves as an indispensable guide for students embarking on their journey with Julia.

This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs).

Part of my lecturing work in the School of Mathematics at the University of Leeds involved teaching quantum mechanics and statistical mechanics to mathematics undergraduates, and also mathematical methods to undergraduate students in the School of Electronic and Electrical Engineering at the University.

Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate.

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Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations.

This book provides an introduction to the ideas and methods of linear fu- tional analysis at a level appropriate to the ?

This book presents peer-reviewed articles from the 1st International Conference on Sustainability and Emerging Technologies for Smart Manufacturing (SETSM 2024) held on 27-28 April at Hanoi in Vietnam.

The Fortran 2003 Handbook is a definitive and comprehensive guide to Fortran 2003 and its use.

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right.

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity.

Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2.

Mobile robotics has until now focused on issues like design of controllers and robot hardware.

Since the last century, the postulational method and an abstract point of view have played a vital role in the development of modern mathematics.

Stochastic geometry is a relatively new branch of mathematics.

Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques.

Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications.

Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer.

This book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks.

This monograph presents the existence and properties of both weak and strong solutions to the problems of the flow of a compressible fluid in a domain whose motion is prescribed.

Maths is everywhere, in everything.

Even the most enthusiastic of maths students probably at one time wondered when exactly it would all prove useful in ';real life'.

Is anything truly random?

This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves.

This book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements.

This book introduces readers to the fascinating world of quantum chromodynamics (QCD) and quarks and gluons, the elementary constituents of protons, neutrons, and all hadrons.

This book presents a detailed exploration of advanced computational modeling techniques in the design, testing, and applications of rigid polyurethane foams (RPUFs).

This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry.

This book provides an in-depth, comprehensive, and comprehensible description of the theoretical background and numerical methodologies corresponding to advanced particle methods formulated in classical Newtonian mechanics for simulation of fluids, structures, and their interactions.

This book provides an in-depth analysis of the hydrodynamics of two-dimensional (2D) electronic systems, with a particular focus on graphene and other Dirac materials.

Spectral properties for Schrodinger operators are a major concern in quantum mechanics both in physics and in mathematics.

This book highlights the presentation of methods for studying oscillations under external periodic influence and random changes in parameters in dynamic systems with nonlinearities that have discontinuities and kinks.