This book features a selection of articles based on the XXXV Bialowieza Workshop on Geometric Methods in Physics, 2016. The series of Bialowieza workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Bialowieza Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Interesting to anybody who wants to unearth the real sense and nature of solitary waves, and the relevant mathematical tools to use for effective investigation and analysis of these phenomena, the text focuses on numerical analysis of solitons. The integrability and multidimensionality of solitons is inextricably bound up with the approach of investigation and, as the more physical systems are not fully integrable, even in one dimension, numerical analysis is the main tool to investigate and understand the pertinent physical mechanisms.

Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

This book presents simple interdisciplinary stochastic models meant as a gentle introduction to the field of non-equilibrium statistical physics. It focuses on the analysis of two-state models with cooperative effects and explores a variety of mathematical techniques to solve the master equations that govern these models. The models discussed are at the confluence of nanophysics, biology, mathematics and the social science, and they provide a pedagogical path toward understanding the complex dynamics of particle self-assembly with the tools of statistical physics.

Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems.

Explore real-world applications of selected mathematical theory, concepts, and methods

Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems.

Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation for transitioning to more advanced subjects. The author utilizes MATLAB(R) to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include:

Linear algebra

Ranking web pages

Matrix factorizations

Least squares

Image compression

Ordinary differential equations

Dynamical systems

Mathematical models

Throughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB(R) code and additional resources.

A First Course in Applied Mathematics is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.

This volume emphasises studies related to
classical Stefan problems. The term "Stefan problem" is
generally used for heat transfer problems with
phase-changes such
as from the liquid to the solid. Stefan problems have some
characteristics that are typical of them, but certain problems
arising in fields such as mathematical physics and engineering
also exhibit characteristics similar to them. The term
classical" distinguishes the formulation of these problems from
their weak formulation, in which the solution need not possess
classical derivatives. Under suitable assumptions, a weak solution
could be as good as a classical solution. In hyperbolic Stefan
problems, the characteristic features of Stefan problems are
present but unlike in Stefan problems, discontinuous solutions are
allowed because of the hyperbolic nature of the heat equation. The
numerical solutions of inverse Stefan problems, and the analysis of
direct Stefan problems are so integrated that it is difficult to
discuss one without referring to the other. So no strict line of
demarcation can be identified between a classical Stefan problem
and other similar problems. On the other hand, including every
related problem in the domain of classical Stefan problem would
require several volumes for their description. A suitable
compromise has to be made.
The basic concepts, modelling, and analysis of the classical
Stefan problems have been extensively investigated and there seems
to be a need to report the results at one place. This book
attempts to answer that need. Within the framework of the
classical Stefan problem with the emphasis on the basic concepts,
modelling and analysis, it tries to include some weak
solutions and analytical and numerical solutions also. The main
considerations behind this are the continuity and the clarity of
exposition. For example, the description of some phase-field
models in Chapter 4 arose out of this need for a smooth transition
between topics. In the mathematical formulation of Stefan
problems, the curvature effects and the kinetic condition are
incorporated with the help of the modified Gibbs-Thomson relation.
On the basis of some thermodynamical and metallurgical
considerations, the modified Gibbs-Thomson relation can be
derived, as has been done in the text, but the rigorous
mathematical justification comes from the fact that this relation
can be obtained by taking appropriate limits of phase-field
models. Because of the unacceptability of some phase-field models
due their so-called thermodynamical inconsistency, some consistent
models have also been described. This completes the discussion of
phase-field models in the present context.
Making this volume self-contained would require reporting and
deriving several results from tensor analysis, differential
geometry, non-equilibrium thermodynamics, physics and functional
analysis. The text is enriched with appropriate
references so as not to enlarge the scope of the book. The proofs
of propositions and theorems are often lengthy and different from
one another. Presenting them in a condensed way may not be of much
help to the reader. Therefore only the main features of proofs
and a few results have been presented to suggest the essential
flavour of the theme of investigation. However at each place,
appropriate references have been cited so that inquisitive
readers can follow them on their own.
Each chapter begins with basic concepts, objectives and the
directions in which the subject matter has grown. This is followed
by reviews - in some cases quite detailed - of published works. In a
work of this type, the author has to make a suitable compromise
between length restrictions and understandability.

This thesis focuses on an unresolved problem in particle and nuclear physics: the relation between two important non-perturbative phenomena in quantum chromodynamics (QCD) - quark confinement and chiral symmetry breaking. The author develops a new analysis method in the lattice QCD, and derives a number of analytical formulae to express the order parameters for quark confinement, such as the Polyakov loop, its fluctuations, and the Wilson loop in terms of the Dirac eigenmodes closely related to chiral symmetry breaking. Based on the analytical formulae, the author analytically as well as numerically shows that at finite temperatures there is no direct one-to-one correspondence between them. The thesis describes this extraordinary achievement using the first-principle analysis, and proposes a possible new phase in which quarks are confined and chiral symmetry is restored.

This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.

This book presents the theory of electromagnetic pulses in a simple and physical way. All pulses discussed are exact solutions of the Maxwell equations, and have finite energy, momentum and angular momentum. The subject matter is restricted to free-space classical electrodynamics, but contact is made with quantum theory in proofs that causal pulses are equivalent to superpositions of photons.

In any linear system the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in space-time, the corresponding output is called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. This book provides a survey of the state-of-the-art knowledge of infinite-space dyadic Green functions.

The portable Raspberry Pi computing platform with the power of Linux yields an exciting exploratory tool for beginning scientific computing. Science and Computing with Raspberry Pi takes the reader through explorations in a variety of computing exercises with the physical sciences. The book guides the user through: configuring your Raspberry Pi and Linux operating system; understanding the software requirements while using the Pi for scientific computing; computing exercises in physics, astronomy, chaos theory, and machine learning.

Lissajous figures are produced by combining two oscillations at right angles to each other. The figures, drawn by mechanical devices called harmonographs, have scientific uses, but are also enjoyed for their own beauty. The author has been working with harmonographs since his undergraduate days, building several of them, lecturing on them and has written articles about them. This book is intended for people who enjoy physics or art or both.

The book contains a detailed account of numerical solutions of differential equations of a number of elementary problems of physics using Euler and second order Runge-Kutta methods using Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.

Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations.

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ? N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein's special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

A Deep Dive into NoSQL Databases: The Use Cases and Applications, Volume 109, the latest release in the Advances in Computers series first published in 1960, presents detailed coverage of innovations in computer hardware, software, theory, design and applications. In addition, it provides contributors with a medium in which they can explore their subjects in greater depth and breadth. This update includes sections on NoSQL and NewSQL databases for big data analytics and distributed computing, NewSQL databases and scalable in-memory analytics, NoSQL web crawler application, NoSQL Security, a Comparative Study of different In-Memory (No/New)SQL Databases, NoSQL Hands On-4 NoSQLs, the Hadoop Ecosystem, and more.

This book develops two exciting areas of particle physics research. It applies the recent new insights about the usefulness of helicity amplitudes in understanding gauge theory to the long-standing effort to understand theories with both electric and magnetic charges. It is known that for some supersymmetric theories there is an exact duality that relates two descriptions of the physics, one where the electric charges are weakly coupled and another where the electric charges are strongly coupled. The calculations in this thesis suggest that this duality can also hold in the low-energy limit of nonsupersymmetric gauge theories. The idea of addressing the hierarchy problem of the standard model Higgs mechanism using conformal symmetry is also explored. Analogously to "Little Higgs" models, where divergences are cancelled only at one-loop order, models are studied that have infrared conformal fixed points which related gauge and Yukawa couplings, allowing for a cancellation between seemingly unrelated quantum loop diagrams.

Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics-the heat equation, the wave equation and Laplace's equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green's functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

In any linear system, the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in spacetime, the corresponding output is called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. This book provides a survey of the state-of-the-art knowledge of infinite space dyadic Green functions.

The work presented in this book is based on the proton-proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector in 2015 and 2016. The research program of the ATLAS experiment includes the precise measurement of the parameters of the Standard Model, and the search for signals of physics beyond the SM. Both these approaches are pursued in this thesis, which presents two different analyses: the measurement of the Higgs boson mass in the di-photon decay channel, and the search for production of supersymmetric particles (gluinos, squarks or winos) in a final state containing two photons and missing transverse momentum. Finally, ATLAS detector performance studies, which are key ingredients for the two analyses outlined before, are also carried out and described.

This work introduces heavy ion beam probe diagnostics and presents an overview of its applications. The heavy ion beam probe is a unique tool for the measurement of potential in the plasma core in order to understand the role of the electric field in plasma confinement, including the mechanism of transition from low to high confinement regimes (L-H transition). This allows measurement of the steady-state profile of the plasma potential, and its use has been extended to include the measurement of quasi-monochromatic and broadband oscillating components, the turbulent-particle flux and oscillations of the electron density and poloidal magnetic field. Special emphasis is placed on the study of Geodesic Acoustic Modes and Alfven Eigenmodes excited by energetic particles with experimental data sets. These experimental studies help to understand the link between broadband turbulent physics and quasi-coherent oscillations in devices with a rather different magnetic configuration. The book also compares spontaneous and biased transitions from low to high confinement regimes on both classes of closed magnetic traps (tokamak and stellarator) and highlights the common features in the behavior of electric potential and turbulence of magnetized plasmas. A valuable resource for physicists, postgraduates and students specializing in plasma physics and controlled fusion.

This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

This book is the second volume of the proceedings of the joint conference X. International Symposium "Quantum Theory and Symmetries" (QTS-X) and XII. International Workshop "Lie Theory and Its Applications in Physics" (LT-XII), 19-25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.