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Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts (Lecture Notes in Mathematics #2353)
by Viorel Barbu Michael RöcknerThis book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions. The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.
Nonlinear Functional Analysis with Applications to Combustion Theory (Applied Mathematical Sciences #221)
by Kazuaki TairaExplore the fascinating intersection of mathematics and combustion theory in this comprehensive monograph, inspired by the pioneering work of N. N. Semenov and D. A. Frank-Kamenetskii. Delving into the nonlinear functional analytic approach, this book examines semilinear elliptic boundary value problems governed by the Arrhenius equation and Newton's law of heat exchange. Key topics include: Detailed analysis of boundary conditions, including isothermal (Dirichlet) and adiabatic (Neumann) cases. Critical insights into ignition and extinction phenomena in stable steady temperature profiles, linked to the Frank-Kamenetskii parameter. Sufficient conditions for multiple positive solutions, revealing the S-shaped bifurcation curves of these problems. Designed for researchers and advanced students, this monograph provides a deep understanding of nonlinear functional analysis and elliptic boundary value problems through their application to combustion and chemical reactor models. Featuring detailed illustrations, clearly labeled figures, and tables, this book ensures clarity and enhances comprehension of complex concepts. Whether you are exploring combustion theory, functional analysis, or applied mathematics, this text offers profound insights and a thorough mathematical foundation.
Nonlinear Hyperbolic Waves in Multidimensions (Monographs and Surveys in Pure and Applied Mathematics)
by Phoolan PrasadThe propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and pr
Nonlinear Internal Waves in Lakes
by Kolumban HutterInternal wave dynamics in lakes (and oceans) is an important physical component of geophysical fluid mechanics of 'quiescent' water bodies of the Globe. The formation of internal waves requires seasonal stratification of the water bodies and generation by (primarily) wind forces. Because they propagate in basins of variable depth, a generated wave field often experiences transformation from large basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson number sufficiently small (< ¼), the light epilimnion water mixes with the water of the hypolimnion, giving rise to vertical diffusion of substances into lower depths. This meromixis is chiefly responsible for the ventilation of the deeper waters and the homogenization of the water through the lake depth. These processes are mainly formed as a result of the physical conditions, but they play biologically an important role in the trophicational state of the lake.
Nonlinear Least Squares for Inverse Problems
by Guy ChaventThis book provides an introduction into the least squares resolution of nonlinear inverse problems. The first goal is to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, i.e. both wellposedness and optimizability. Using the results, the applicability of various regularization techniques can be checked. The second objective of the book is to present frequent practical issues when solving NLS problems. Application oriented readers will find a detailed analysis of problems on the reduction to finite dimensions, the algebraic determination of derivatives (sensitivity functions versus adjoint method), the determination of the number of retrievable parameters, the choice of parametrization (multiscale, adaptive) and the optimization step, and the general organization of the inversion code. Special attention is paid to parasitic local minima, which can stop the optimizer far from the global minimum: multiscale parametrization is shown to be an efficient remedy in many cases, and a new condition is given to check both wellposedness and the absence of parasitic local minima. For readers that are interested in projection on non-convex sets, Part II of this book presents the geometric theory of quasi-convex and strictly quasi-convex (s.q.c.) sets. S.q.c. sets can be recognized by their finite curvature and limited deflection and possess a neighborhood where the projection is well-behaved. Throughout the book, each chapter starts with an overview of the presented concepts and results.
Nonlinear Mathematical Physics and Natural Hazards
by Boyka Aneva Mihaela Kouteva-GuentchevaThis book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and create conditions to mitigate and reduce the negative consequences of natural and socio-economic disaster risk. This book summarizes the contributions of the International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, organized within the framework of the South East Europe Network in Mathematical and Theoretical Physics (SEENET MTP) and supported by UNESCO. It was held at the Bulgarian Academy of Sciences from November 28 to December 2, 2013. The contributions are divided into two major parts in keeping with the scientific program of the meeting. Among the topics covered in Part I (Nonlinear Mathematical Physics towards Critical Phenomena) are predictions and correlations in self organized criticality, space-time structure of extreme current and activity events in exclusion processes, quantum spin chains and integrability of many-body systems, applications of discriminantly separable polynomials, MKdV-type equations, and chaotic behavior in Yang-Mills theories. Part II (Seismic Hazard and Risk) is devoted to probabilistic seismic hazard assessment, seismic risk mapping, seismic monitoring, networking and data processing in Europe, mainly in South-East Europe. The book aims to promote collaboration at the regional and European level to better understand and model phenomena that can cause natural and socio-economic disasters, and to contribute to the joint efforts to mitigate the negative consequence of natural disasters. This collection of papers reflects contemporary efforts on capacity building through developing skills, exchanging knowledge and practicing mathematical methods for modeling nonlinear phenomena, disaster risk preparedness and natural hazards mitigation. The target audience includes students and researchers in mathematical and theoretical physics, earth physics, applied physics, geophysics, seismology and earthquake danger and risk mitigation.
Nonlinear Modeling of Solar Radiation and Wind Speed Time Series
by Luigi Fortuna Giuseppe Nunnari Silvia NunnariThis brief is a clear, concise description of the main techniques of time series analysis --stationary, autocorrelation, mutual information, fractal and multifractal analysis, chaos analysis, etc. -- as they are applied to the influence of wind speed and solar radiation on the production of electrical energy from these renewable sources. The problem of implementing prediction models is addressed by using the embedding-phase-space approach: a powerful technique for the modeling of complex systems. Readers are also guided in applying the main machine learning techniques for classification of the patterns hidden in their time series and so will be able to perform statistical analyses that are not possible by using conventional techniques. The conceptual exposition avoids unnecessary mathematical details and focuses on concrete examples in order to ensure a better understanding of the proposed techniques. Results are well-illustrated by figures and tables.
Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems (Monographs And Surveys In Pure And Applied Math #76)
by Songmu ZhengThis monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators.The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown.Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set.A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the firstchapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.
Nonlinear Partial Differential Equations
by Kenneth H. Karlsen Helge HoldenThe topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.
Nonlinear Partial Differential Equations for Future Applications: Sendai, Japan, July 10–28 and October 2–6, 2017 (Springer Proceedings in Mathematics & Statistics #346)
by Shigeru Sakaguchi Hideo Kozono Shigeaki Koike Takayoshi OgawaThis volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier–Stokes equations, new estimates for a compressible Gross–Pitaevskii–Navier–Stokes system, singular limits for the Keller–Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.
Nonlinear Partial Differential Equations for Scientists and Engineers
by Lokenath DebnathThe revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.
Nonlinear Physics of Ecosystems
by Ehud MeronNonlinear Physics of Ecosystems introduces the concepts and tools of pattern formation theory and demonstrates their utility in ecological research using problems from spatial ecology. Written in language understandable to both physicists and ecologists in most parts, the book reveals the mechanisms of pattern formation and pattern dynamics. It als
Nonlinear Resonances
by Shanmuganathan Rajasekar Miguel A.F. SanjuanThis introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.
Nonlinear Theory of Electroelastic and Magnetoelastic Interactions
by Luis Dorfmann Ray W. OgdenThis book provides a unified theory on nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classic theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell's equations. They summarize relevant theories of continuum mechanics, required to account for the deformability of material and present a constitutive framework for the nonlinear magneto-and electroelastic interactions in a highly deformable material. The equations contained in the book formulate and solve a variety of representative boundary-value problems for both nonlinear magnetoelasticity and electroelasticity.
Nonlinear Wave Equations (Chapman And Hall/crc Pure And Applied Mathematics Ser. #194)
by Satyanad KichenassamyThis work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Nonlinear Waves and Pattern Dynamics
by Efim Pelinovsky Nizar Abcha Innocent MutabaziThis book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.
Nonlinear Waves and Solitons on Contours and Closed Surfaces
by Andrei LuduThis volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.
Nonlinear Waves: From Dissipative Solitons to Magnetic Solitons
by Emmanuel Kengne WuMing LiuThis book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
Nonlinear and Modern Mathematical Physics: NMMP-2022, Tallahassee, Florida, USA (Virtual), June 17–19 (Springer Proceedings in Mathematics & Statistics #459)
by Solomon Manukure Wen-Xiu MaThis book gathers peer-reviewed, selected contributions from participants of the 6th International Workshop on Nonlinear and Modern Mathematical Physics (NMMP-2022), hosted virtually from June 17–19, 2022. Works contained in this volume cover topics like nonlinear differential equations, integrable systems, Hamiltonian systems, inverse scattering transform, Painleve's analysis, nonlinear wave phenomena and applications, numerical methods of nonlinear wave equations, quantum integrable systems, and more. In this book, researchers and graduate students in mathematics and related areas will find new methods and tools that only recently have been developed to solve nonlinear problems. The sixth edition of the NMMP workshop was organized by Florida A&M University in Tallahassee, Florida, USA, with support from the University of South Florida, Florida State University, Embry-Riddle Aeronautical University, Savannah State University, Prairie View A&M University, and Beijing Jiaotong University. The aim was to bring together researchers from around the world to present their findings and foster collaboration for future research.
Nonlinear, Nonlocal and Fractional Turbulence: Alternative Recipes for the Modeling of Turbulence
by Kolumban Hutter Peter William EgolfExperts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-β, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new ‘law of the wall’ and a generalization of Kraichnan’s energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.
Nonnative Oysters In The Chesapeake Bay
by National Research Council of the National AcademiesNonnative Oysters in the Chesapeake Bay discusses the proposed plan to offset the dramatic decline in the bay’s native oysters by introducing disease-resistant reproductive Suminoe oysters from Asia. It suggests this move should be delayed until more is known about the environmental risks, even though carefully regulated cultivation of sterile Asian oysters in contained areas could help the local industry and researchers. It is also noted that even though these oysters eat the excess algae caused by pollution, it could take decades before there are enough of them to improve water quality.
Nonperturbative Topological Phenomena in QCD and Related Theories (Lecture Notes in Physics #977)
by Edward ShuryakThis book introduces a variety of aspects in nonperturbative Quantum Chromodynamics (QCD), focusing on the topological objects present in gauge theories. These objects, like magnetic monopoles, instantons, instanto-dysons, sphalerons, QCD flux tubes, etc, are first introduced individually and, later, treated collectively. As ensembles, they produce various phenomena that can be modeled numerically in lattice gauge theories and such collective effects, produced on the lattice, are extensively discussed in some chapters. In turn, the notion of duality, which is crucial in modern field/string theories, is elucidated by taking into consideration the electric-magnetic duality, the Poisson duality, and the AdS/CFT duality. This monograph is based on various lectures given by Edward Shuryak at Stony Brook during the last three decades and it is meant for advanced graduate students and young researchers in theoretical and mathematical physics who are willing to consolidate their knowledge in the topological phenomena encountered in fundamental QCD research.
Nord Stream 2 - Das Beharren auf widerlegten Argumenten (RaumFragen: Stadt – Region – Landschaft)
by Gerhard HalderDas Buch analysiert umfangreiche Literatur zum Konflikt um die Erdgaspipeline Nord Stream 2 und zeigt auf, dass praktisch alle geführten Argumente innerhalb weniger Jahre nach Baubeginn obsolet wurden. Das Festhalten an den Argumenten auch nach Entfall ihrer Gültigkeit zeigt, dass eher die erhoffte Wirkung (pro oder contra) als die Argumente selbst für die Akteure ausschlaggebend sind. Nach einem Überblick über die Rahmenbedingungen werden die Argumente pro und contra Nord Stream 2 besprochen, gegliedert nach den Dimensionen des erweiterten Zieldreiecks der Energiepolitik, also Bezahlbarkeit im Wechselspiel von Angebot und Nachfrage, Umweltschutz, Versorgungssicherheit sowie neu einer außenpolitischen Dimension. Als extrem schwierig zeigt sich die Abschätzung von Angebot und Nachfrage, angesichts der Schiefergas-Revolution, dem drastischen Rückgang der eigenen Förderung und der laufenden Dekarbonisierung der EU. Den eigentlichen „Game-Changer“ bildet indes die Einrichtung des EU-Binnenmarktes für Erdgas sowie die Wirksamkeit der damit verbundenen Maßnahmen, was die einseitige Abhängigkeit drastisch verringert. Die umweltpolitische Diskussion übersieht vielfach den Vorteil von Erdgas wegen der schadstoffärmeren Verbrennung, v.a. aber die Gefahren durch Leckagen (80-fach höhere Klimawirksamkeit gegenüber CO2). Die submarine Nord Stream 2 ist hier unbedenklich, anders als viele russischen Zuläufe, dem maroden ukrainischen Korridor, und dem Flüssiggas aus unkonventionellen Förderungen der USA. Das Buch schließt mit einer Diskussion der Faktoren und von geostrategischen Aspekten.
Nordic Approaches to Climate-Related Human Mobility (Routledge Studies in Environmental Migration, Displacement and Resettlement)
by Matthew Scott Miriam CullenAcademic discussion of climate‑related human mobility has understandably focused on the places where people are especially vulnerable to climate‑related harm: the Global South. Yet, the unique biophysical, legal and socio‑political characteristics of the Nordic region, as well as its roles as both ‘home’ and ‘host’ to climate‑related mobilities, justify its independent attention. Filling this lacuna, this collection is the first to address climate‑related human mobility in the Nordic region. It is a timely and much needed collection, which brings together leading and emerging voices from both academia and practice in a single volume, spanning policy and geographical breadth. Its chapters cover both regional approaches to the global phenomenon of climate mobility, such as the traditional role of the Nordic states as norm entrepreneurs and their representation in multilateral fora, and on‑the‑ground climate impacts unique to this region and their localised responses. Case studies include judicial decision‑making as it relates to climate‑related migration, insights into the local communication of climate risk, changes to Nordic development and climate policy, as well as climate‑related mobilities of Nordic Indigenous Peoples.This volume will be of great interest to students and scholars of disaster and climate studies, as well as climate‑related mobility, migration and displacement.The Open Access version of this book, available at http://www.taylorfrancis.com, has been made available under a Creative Commons [Attribution-Non Commercial-No Derivatives (CC-BY-NC-ND)] 4.0 license.
Nordic Case Collection on Sustainability and Transition to a Circular Economy (Springer Business Cases)
by Gitte HaarCompanies play a pivotal role in the green transition. They must transform business models, develop purpose-driven strategies, and innovate products to meet customer and regulatory demands. This book of case studies offers strategic insights and best-practice examples from the Nordic region, showcasing leading companies in sustainability. It evaluates businesses based on the Climate Nexus framework, covering Energy Transition, Sustainable Transport, Sustainable Agriculture, Healthy Diet, and Circular Economy. Featured cases from outside the Nordic region are also included, including cases on the Municipality of Amsterdam and Stanford Sustainability Utilities & Infrastructure. Drawing on a network within the Nordic Circular Hotspot, this collection provides actionable strategies and supports the growing knowledge of the transition to a green and circular economy. Whether you’re an executive seeking to transform your business or a student exploring green transition opportunities, this book is an essential guide to achieving a sustainable future.