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This book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
This book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
Polymer and cell dynamics play an important role in processes like tumor growth, metastasis, embryogenesis, immune reactions and regeneration. Based on an international workshop on numerical simulations of polymer and cell dynamics in Bad Honnef (Germany) in 2000, this volume provides an overview of the relevant mathematical and numerical methods, their applications and limits. Polymer and Cell Dynamics will be of interest to scientists and advanced undergraduates.
"This book compiles real-world case studies on discovering, understanding and engineering emergent behaviors in a computational environment across multiple application domains such as wargaming, biology, IoT, disaster management and space architecting. All the application domains are described through an undercurrent of System of Systems (SoS) engineering in conjunction with theoretical foundations required for engineering a Modeling and Simulation SoS capable of displaying valid emergent behavior. An excellent read and state-of-the-art in M&S of emergent behavior in complex systems!" --Dr. Saurabh Mittal, Department Chief Scientist, The MITRE Corporation This book is the of its kind to address real-world applications of the phenomenon of emergent behavior in real-world system of systems. It launches from the foundation of theory and basic understanding of the subject of emergent behavior as found in system of systems applications. It includes real-world examples where emergent behavior is manifested. Each chapter addresses the following major points, which are exploratory in nature: the physical results of the presence of emergent behavior; the implications for the existence of emergent behavior; the manifestation of emergent behavior; and methods to either control emergent behavior assuming its effects are negative in nature, or capitalize on emergent behavior given its effects are positive in nature.
This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.
This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. In light of the recent COVID-19 pandemic, special consideration is given to applications of crowd dynamics to the prevention of the spreading of contagious diseases. Some of the specific topics covered in this volume include: - Impact of physical distancing on the evacuation of crowds- Generalized solutions of opinion dynamics models- Crowd dynamics coupled with models for infectious disease spreading- Optimized strategies for leaders in controlling the dynamics of a crowd Crowd Dynamics, Volume 3 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.
This volume critically evaluates more than a century of empirical research on the effectiveness of small, task-performing groups, and offers a fresh look at the costs and benefits of collaborative work arrangements. The central question taken up by this book is whether -- and under what conditions -- interaction among group members leads to better performance than would otherwise be achieved simply by combining the separate efforts of an equal number of people who work independently. This question is considered with respect to a range of tasks (idea-generation, problem solving, judgment, and decision-making) and from several different process perspectives (learning and memory, motivation, and member diversity). As a framework for assessing the empirical literature, the book introduces the concept of 'synergy.' Synergy refers to an objective gain in performance that is attributable to group interaction. Further, it distinguishes between weak and strong synergy, which are performance gains of different magnitude. The book highlights the currently available empirical evidence for both weak and strong synergy, identifies the conditions that seem necessary to produce each, and suggests where the search for synergy might best be directed in the future. The book is at once a high-level introduction to the field, a review of the field's history, and a scholarly critique of the current state-of-the-art. As such, it is essential reading for graduate students, advanced undergraduate students, and researchers interested in group dynamics generally -- and small group performance in particular.
Dispersal of plants and animals is one of the most fascinating subjects in ecology. It has long been recognized as an important factor affecting ecosystem dynamics. Dispersal is apparently a phenomenon of biological origin; however, because of its complexity, it cannot be studied comprehensively by biological methods alone. Deeper insights into dispersal properties and implications require interdisciplinary approaches involving biologists, ecologists and mathematicians. The purpose of this book is to provide a forum for researches with different backgrounds and expertise and to ensure further advances in the study of dispersal and spatial ecology. This book is unique in its attempt to give an overview of dispersal studies across different spatial scales, such as the scale of individual movement, the population scale and the scale of communities and ecosystems. It is written by top-level experts in the field of dispersal modeling and covers a wide range of problems ranging from the identification of Levy walks in animal movement to the implications of dispersal on an evolutionary timescale.