This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed: 1. Lagrangian discretizations and wavefront tracking for synchronization models; 2. Astrophysics computations and post-Newtonian approximations; 3. Hyperbolic balance laws and corrugated isometric embeddings; 4. "Caseology" techniques for kinetic equations; 5. Tentative computations of compressible non-standard solutions; 6. Entropy dissipation, convergence rates and inverse design issues. Most of the articles are presented in a self-contained manner; some highlight new achievements, while others offer snapshots of the "state of the art" in certain fields. The book offers a unique resource, both for young researchers looking to quickly enter a given area of application, and for more experienced ones seeking comprehensive overviews and extensive bibliographic references.

This monograph tackles three challenges. First, show a mathematics-based meta-model that matches known elementary particles. Second, apply models, based on the meta-model, to match other known physics data. Third, predict future physics data. The math features solutions to isotropic pairs of isotropic quantum harmonic oscillators. This monograph matches some solutions to known elementary particles. Matched properties include spin, types of interactions in which the particles partake, and (for elementary bosons) approximate masses. Other solutions point to possible elementary particles. This monograph applies the models and the extended particle list. Results narrow gaps between physics data and theory. Results pertain to elementary particles, astrophysics, and cosmology. For example, this monograph predicts properties for beyond-the-Standard-Model elementary particles, proposes descriptions of dark matter and dark energy, provides new relationships between known physics constants (including masses of some elementary particles), includes theory that dovetails with the ratio of dark matter to ordinary matter, includes math that dovetails with the number of elementary-fermion generations, suggests forces that govern the rate of expansion of the universe, and suggests additions to and details for the cosmology timeline.

The non-Gaussianity in the primordial density fluctuations is a key feature to clarify the early Universe and it has been probed with the Cosmic Microwave Background (CMB) bispectrum. In recent years, we have treated the novel-type CMB bispectra, which originate from the vector- and tensor-mode perturbations and include the violation of the rotational or parity invariance. On the basis of our current works, this thesis provides the general formalism for the CMB bispectrum sourced by the non-Gaussianity in the scalar, vector and tensor-mode perturbations. Applying this formalism, we calculate the CMB bispectra from the two scalars and a graviton correlation and primordial magnetic fields, and then outline new constraints on these magnitudes. Furthermore, this formalism can be easily extended to the cases where the rotational or parity invariance is broken. We also compute the CMB bispectra from the scalar-mode non-Gaussianities with a preferred direction and the tensor-mode non-Gaussianities induced by the parity-violating Weyl cubic terms. Here, we show that these bispectra include unique signals, which any symmetry-invariant models can never produce.

The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems.

"Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications.

The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences.

Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.

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This work concerns the computational modelling of the dynamics of partially ionized gases, with emphasis on electrodischarge processes. Understanding gas discharges is fundamental for many processes in mechanics, manufacturing, materials science, and aerospace engineering. This second edition has been expanded to include the latest developments in the field, especially regarding the drift-diffusion model and rarefied hypersonic flow.

Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.

Network Science is the emerging field concerned with the study of large, realistic networks. This interdisciplinary endeavor, focusing on the patterns of interactions that arise between individual components of natural and engineered systems, has been applied to data sets from activities as diverse as high-throughput biological experiments, online trading information, smart-meter utility supplies, and pervasive telecommunications and surveillance technologies. This unique text/reference provides a fascinating insight into the state of the art in network science, highlighting the commonality across very different areas of application and the ways in which each area can be advanced by injecting ideas and techniques from another. The book includes contributions from an international selection of experts, providing viewpoints from a broad range of disciplines. It emphasizes networks that arise in nature-such as food webs, protein interactions, gene expression, and neural connections-and in technology-such as finance, airline transport, urban development and global trade. Topics and Features: begins with a clear overview chapter to introduce this interdisciplinary field; discusses the classic network science of fixed connectivity structures, including empirical studies, mathematical models and computational algorithms; examines time-dependent processes that take place over networks, covering topics such as synchronisation, and message passing algorithms; investigates time-evolving networks, such as the World Wide Web and shifts in topological properties (connectivity, spectrum, percolation); explores applications of complex networks in the physical and engineering sciences, looking ahead to new developments in the field. Researchers and professionals from disciplines as varied as computer science, mathematics, engineering, physics, chemistry, biology, ecology, neuroscience, epidemiology, and the social sciences will all benefit from this topical and broad overview of current activities and grand challenges in the unfolding field of network science.

Soon after she became involved in the didactics of physics, the author of this book realized that the transfer of new discoveries in physics into schools and to undergraduate programs is almost non-existent.

This book presents a new approach to the analysis of networks, which emphasizes how one can compress a network while preserving all information relative to the network's spectrum. Besides these compression techniques, the authors introduce a number of other isospectral transformations and demonstrate how, together, these methods can be applied to gain new results in a number of areas. This includes the stability of time-delayed and non time-delayed dynamical networks, eigenvalue estimation, pseudospectra analysis and the estimation of survival probabilities in open dynamical systems. The theory of isospectral transformations, developed in this text, can be readily applied in any area that involves the analysis of multidimensional systems and is especially applicable to the analysis of network dynamics. This book will be of interest to Mathematicians, Physicists, Biologists, Engineers and to anyone who has an interest in the dynamics of networks.

This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes.
Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

For those who have always wanted to discover the joy of physics, this is the book that they've been waiting for.
Many people remember their struggles with physics in high school and have wished for the right opportunity to gain an appreciation of this significant area of knowledge. Now is their chance not only to understand physics, but to do physics. The author provides the general reader with a fun-filled, entertaining, and truly educational tour of this all-important science.
What makes the study of physics so worthwhile? The author says that, despite its reputation for difficulty, physics has an enormously ambitious goal, which appeals to people's innate curiosity: to understand the workings of the entire universe, from the smallest quarks to the largest galaxies. Learning and comprehending as much as we can about the inner and outer workings of the universe is what evokes the joy of physics. Taking a hands-on approach, he invites the reader to share the joy. Easy, practical experiments pepper the book and connect the ideas of physics with the reality of the universe. The yo-yo, flying disc, shake flashlight, laser pointer, LED, and even a microwave experiment with an edible result add to the fun.
Complete with lively, memorable cartoons by Sidney Harris--America's premier science cartoonist--this book reveals the inherent fun, intellectual pleasure, and supreme importance of a subject that we can now finally tackle and enjoy.

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

This book is the eighth in a series of Proceedings for the S eminaire Poincar e, which is directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up to date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed "Bourbaphy", this Poincar e SeminarisheldattheInstitutHenriPoincar einParis,withcontributionsprepared inadvance.Particularcareisdevotedtothepedagogicalnatureofthepresentation so as to ful?ll the goal of being readable by a large audience of scientists. This new volume of the Poincar e Seminar series "The Spin" corresponds to the eleventh such Seminar, held on December 8, 2007. It describes how this once mysterious quantum reality called spin has become ubiquitous in modern physics from the most theoretical aspects down to the most practical applications of miniaturizing electronic and computer devices or helping medical diagnosis.

After more than four decades and scores of books, documentaries, and films on the subject, what more can be said about the assassination of President John F. Kennedy? A great deal, according to this physicist and ballistics expert. This provocative, rigorously researched book presents evidence and compelling arguments that will make you rethink the sequence of terrible events on that traumatic day in Dallas. Drawing on his fifteen years experience as an experimental physicist for the US Navy, the author demonstrates that the commonly accepted view of the assassination is fundamentally flawed from a scientific perspective. The physics behind lone-gunmen theories is not only wrong, but frankly impossible. He devotes separate chapters to the Warren Commission, challenges to the single-bullet theory, the witnesses, how science arrives at the truth, the medical and acoustic evidence, the Zapruder film, and convincing evidence for at least a second rifleman in Dealey Plaza.
This is the first book to:
- identify the second murder weapon;
- prove the locations of the assassins;
- demonstrate multiple shooters with scientific certainty.
The author concludes with a persuasive chapter on why this horrible event, now almost half a century old, should still matter to us today. For anyone seeking a fresh understanding of the JFK assassination, this is an indispensable book.

When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and KP equations are treated extensively, with material on NLS and AKNS systems, and in following the tau function theme one is led to conformal field theory, strings, and other topics in physics. The extensive list of references contains about 1000 entries.

Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012.

The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability, partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems, its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory and to stimulate discussions and possibly new collaborations among researchers with different backgrounds.

The book contains lecture notes written by Francois Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navier-Stokes) from the Boltzmann equation, and several short papers written by some of the participants in the conference. Among the topics covered by the short papers are hydrodynamic limits; fluctuations; phase transitions; motions of shocks and anti shocks in exclusion processes; large number asymptotics for systems with self-consistent coupling; quasi-variational inequalities; unique continuation properties for PDEs and others.

The book will benefit probabilists, analysts and mathematicians who are interested in statistical physics, stochastic processes, partial differential equations and kinetics theory, along with physicists."

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology.

The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008.

The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.