Presents the hydrodynamic theory of flocking - the collective motion of organisms - for readers in physics, mathematics, and biology.

In creatures ranging from birds to fish to wildebeest, we observe the collective and coherent motion of large numbers of organisms, known as 'flocking.' John Toner, one of the founders of the field of active matter, uses the hydrodynamic theory of flocking to explain why a crowd of people can all walk, but not point, in the same direction. Assuming a basic undergraduate-level understanding of statistical mechanics, the text introduces readers to dry active matter and describes the current status of this rapidly developing field. Through the application of powerful techniques from theoretical condensed matter physics, such as hydrodynamic theories, the gradient expansion, and the renormalization group, readers are given the knowledge and tools to explore and understand this exciting field of research. This book will be valuable to graduate students and researchers in physics, mathematics, and biology with an interest in the hydrodynamic theory of flocking.

Written for the novice AI programmer, this text introduces the reader to techniques such as finite state machines, fuzzy logic, neural networks and many others in an easy-to-understand language, supported with code samples throughout the text.

This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.

From molecular motors to bacteria, from crawling cells to large animals, active entities are found at all scales in the biological world. Active matter encompasses systems whose individual constituents irreversibly dissipate energy to exert self-propelling forces on their environment. Over the past twenty years, scientists have managed to engineer synthetic active particles in the lab, paving the way towards smart active materials. This book gathers a pedagogical set of lecture notes that cover topics in nonequilibrium statistical mechanics and active matter. These lecture notes stem from the first summer school on Active Matter delivered at the Les Houches school of Physics. The lectures covered four main research directions: collective behaviours in active-matter systems, passive and active colloidal systems, biophysics and active matter, and nonequilibrium statistical physics—from passive to active.

Driven by demand from the entertainment industry for better and more realistic animation, technology continues to evolve and improve. The algorithms and techniques behind this technology are the foundation of this comprehensive book, which is written to teach you the fundamentals of animation programming. In this third edition, the most current techniques are covered along with the theory and high-level computation that have earned the book a reputation as the best technically-oriented animation resource. Key topics such as fluids, hair, and crowd animation have been expanded, and extensive new coverage of clothes and cloth has been added. New material on simulation provides a more diverse look at this important area and more example animations and chapter projects and exercises are included. Additionally, spline coverage has been expanded and new video compression and formats (e.g., iTunes) are covered. - Includes companion site with contemporary animation examples drawn from research and entertainment, sample animations, and example code - Describes the key mathematical and algorithmic foundations of animation that provide you with a deep understanding and control of technique - Expanded and new coverage of key topics including: fluids and clouds, cloth and clothes, hair, and crowd animation - Explains the algorithms used for path following, hierarchical kinematic modelling, rigid body dynamics, flocking behaviour, particle systems, collision detection, and more

Powerful analytical tools from statistical physics, guided by field observations are applied to spread of epidemics and movement ecology.