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.

Niels Bohr, the founding father of modern atomic physics and quantum theory, was as original a philosopher as he was a physicist. This study explores several dimensions of Bohr's vision: the formulation of quantum theory and the problems associated with its interpretation, the notions of complementarity and correspondence, the debates with Einstein about objectivity and realism, and his sense of the infinite harmony of nature. The author's chief attention is given to Bohr's epistemological lesson, the conviction that all our description of nature is dependent on the words we use and the ways we can unambiguously use them. Against those who would view Bohr as a vague positivist, the author argues here that Bohr is best understood as using transcendental arguments and shaping a kind of descriptive metaphysics in his defence of our abilities to offer a description of the world we live in.

Physicists are very smart people. Still, when it comes to moving their ideas from university to market, they often lack the basic set of know-hows that could help them succeed in the technology transfer process. To fill this gap, Entrepreneurship for Physicists: A Practical Guide to Move Ideas from University to Market offers a concise analysis of the key ingredients that enable entrepreneurs to bring added value to their customers. After a short discussion on why university physicists should pay more attention to this aspect of their professional life, the book dives into a set of theories, models, and tools that could help an academic scientist transform an idea into customer added value. The reader will be introduced to effectuation theory, internal resource analysis, external landscape analysis, value capture, lean startup method, business canvases, financial projections, and to a series of topics that, albeit often neglected, do play a fundamental role in technology transfer, such as trust, communication, and persuasion. In the last chapter, the book explains howmost of the concepts discussed actually find application in the career of scientists in a much broader sense.

Exam Board: OCR Level: A level Subject: Science / Physics First teaching: September 2015 First exams: June 2017 An ActiveBook is included with every Student Book, giving your students easy online access to the content in the Student Book. They can make it their own with notes, highlights and links to their wider reading. Perfect for supporting work and revision activities. Student Book 1 supports a standalone AS course and provides the first year of a two-year A level course; Student Books 1 and 2 together support the full A level course. A cumulative approach to learning constantly builds on what has previously been taught. The chapter openers highlight prior learning requirements and link to future learning. The required maths skills are highlighted at the start of each chapter providing opportunities for students to check understanding and remedy gaps. Bigger spreads require students to read real-life material that's relevant to the course and use knowledge in new contexts. Accompanying questions require students to analyse how scientists write, think critically and consider issues. Preparing for your exams sections highlight the key differences between preparing for an AS and full A level exam. Practice question spreads provide opportunities for students to regularly check their understanding using questions written in the style of the new exams from day one.

In the field of organic semiconductors researchers and manufacturers are faced with a wide range of potential molecules. This work presents concepts for simulation-based predictions of material characteristics starting from chemical stuctures. The focus lies on charge transport - be it in microscopic models of amorphous morphologies, lattice models or large-scale device models. An extensive introductory review, which also includes experimental techniques, makes this work interesting for a broad readership. Contents: Organic Semiconductor Devices Experimental Techniques Charge Dynamics at Dierent Scales Computational Methods Energetics and Dispersive Transport Correlated Energetic Landscapes Microscopic, Stochastic and Device Simulations Parametrization of Lattice Models Drift-Diusion with Microscopic Link

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 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.

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.

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.

In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.

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.

This book gathers selected, extended and revised papers presented at the 5th Iberian-Latin American Congress on Fire Safety, CILASCI 5, held on 15-17 July 2019, in Porto, Portugal. The respective chapters address experimental efforts and the computational and numerical modelling of materials (e.g. wood, concrete, and steel) and structures to assess their fire behavior and/or improve their fire resistance. In addition, they present simulation studies on fire events and findings from fire performance tests on walls. Given its scope, the book offers a valuable resource for researchers, graduate students, and practitioners whose work involves fire safety-related topics.

The aim of this book is to analyse historical problems related to the use of mathematics in physics as well as to the use of physics in mathematics and to investigate "Mathematical Physics" as precisely the new discipline which is concerned with this dialectical link itself. So the main question is: "When and why did the tension between mathematics and physics, explicitly practised at least since Galileo, evolve into such a new scientific theory? "

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The authors explain the various ways in which this science allowed an advanced mathematical modelling in physics on the one hand, and the invention of new mathematical ideas on the other hand. Of course this problem is related to the links between institutions, universities, schools for engineers, and industries, and so it has social implications as well.

The link by which physical ideas had influenced the world of mathematics was not new in the 19th century, but it came to a kind of maturity at that time. Recently, much historical research has been done into mathematics and physics and their relation in this period. The purpose of the Symposium and this book is to gather and re-evaluate the current thinking on this subject. It brings together contributions from leading experts in the field, and gives much-needed insight in the subject of mathematical physics from a historical point of view.

This book provides a selection of contributions to the DIPSI workshop 2019 (Droplet Impact Phenomena & Spray Investigations) as well as recent progress of the Int. Research Training Group "DROPIT".The DIPSI workshop, which is now at its thirteenth edition, represents an important opportunity to share recent knowledge on droplets and sprays in a variety of research fields and industrial applications. The research training group "DROPIT" is focused on droplet interaction technologies where microscopic effects influence strongly macroscopic behavior. This requires the inclusion of interface kinetics and/or a detailed analysis of surface microstructures. Normally, complicated technical processes cover the underlying basic mechanisms, and therefore, progress in the overall process modelling can hardly be gained. Therefore, DROPIT focuses on the underlying basic processes. This is done by investigating different spatial and/or temporal scales of the problems and by linking them through a multi-scale approach. In addition, multi-physics are required to understand e.g. problems for droplet-wall interactions, where porous structures are involved.

Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by leading experts in their corresponding fields, and features fully-refereed, high-quality papers exploring new results and trends in spectral theory, mathematical physics, geometric function theory, and partial differential equations. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. Another shared research interest of the contributors of this volume lies in the area of applied harmonic analysis, where a new notion called chromatic derivatives has recently been introduced in communication engineering. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6, 2014. During the event, participants honored the memory of Cora Sadosky-a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional mathematician and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.

This book offers a comprehensive and timely review of the fracture behavior of bimaterial composites consisting of periodically connected components, i.e. of bimaterial composites possessing periodical cracks along the interface. It first presents an overview of the literature, and then analyzes the isotropic, anisotropic and piezoelectric/dielectric properties of bimaterial components, gradually increasing the difficulty of the solutions discussed up to the coupled electromechanical problems. While in the case of isotropic and anisotropic materials it covers the problems generated by an arbitrary set of cracks, for the piezoelectric materials it focuses on studying the influence of the electric permittivity of the crack's filler, using not only a simple, fully electrically permeable model, but also a physically realistic, semi-permeable model. Throughout the analyses, the effects of the contact of the crack faces are taken into account so as to exclude the physically unrealistic interpenetration of the composite components that are typical of the classical open model. Further, the book derives and examines the mechanical and electromechanical fields, stress and electric intensity factors in detail. Providing extensive information on the fracture processes taking place in composite materials, the book helps readers become familiar with mathematical methods of complex function theory for obtaining exact analytical solutions.

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.

The second part of Bioenergy: Principles and Technologies continues the discussion of biomass energy technologies covering fuel ethanol production, pyrolysis, biomass-based hydrogen production and fuel synthesis, biodiesel, municipal solid water treatment and microbial fuel cells. With a combination of theories, experiments and case studies, it is an essential reference for bioenergy researchers, industrial chemists and chemical engineers.

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.

This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals.

In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step.

Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given.

Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.