Fields In Motion

Fields in Motion: Ethnography in the Worlds of Dance examines the deeper meanings and resonances of artistic dance in contemporary culture. The book comprises four sections: methods and methodologies, autoethnography, pedagogies and creative processes, and choreographies as cultural and spiritual representations. The contributors bring an insiders insight to their accounts of the nature and function of these artistic practices, giving voice to dancers, dance teachers, creators, programmers, spectators, students, and scholars. International and intergenerational, this collection of groundbreaking scholarly research points to a new direction for both dance studies and dance anthropology. Traditionally the exclusive domain of aesthetic philosophers, the art of dance is here reframed as cultural practice, and its significance is revealed through a chorus of voices from practitioners and insider ethnographers.

Dynamic Neural Field Theory for Motion Perception provides a new theoretical framework that permits a systematic analysis of the dynamic properties of motion perception. This framework uses dynamic neural fields as a key mathematical concept. The author demonstrates how neural fields can be applied for the analysis of perceptual phenomena and its underlying neural processes. Also, similar principles form a basis for the design of computer vision systems as well as the design of artificially behaving systems. The book discusses in detail the application of this theoretical approach to motion perception and will be of great interest to researchers in vision science, psychophysics, and biological visual systems.

This volume reviews the most recent progress on new exact solutions of the Yang-Mills SU(2) gauge field equations. In order to have a better understanding of the physical meaning of the Yang-Mills fields, the motion of a particle in these fields, first in general and then, in particular fields were discussed. Contents:IntroductionThe Yang-Mills Field Equations and the Null-Tetrad MethodClassification of the Yang-Mills FieldsStatic Solutions of the Sourceless Yang-Mills Field EquationsClassification of Gauge Fields — ApplicationExact Solutions of the Yang-Mills Field EquationsThe Motion of a Test Particle in Classical Yang-Mills FieldsSummary and Concluding Remarks Readership: High energy physicists, mathematical physicists and mathematicians. Keywords:Yang-Mills Fields;Yang-Mills Field Equations;Eigenspinor-Eigenvalue Method;Electromagnetic Field ;Carmeli Field;Morris Field;Gauge Fields;Null Tetrads;Lorentz Invariance;Gauge Invariance

Using a designed vector field to guide robots to follow a given geometric desired path has found a range of practical applications, such as underwater pipeline inspection, warehouse navigation, and highway traffic monitoring. It is thus in great need to build a rigorous theory to guide practical implementations with formal guarantees. It is even so when multiple robots are required to follow predefined desired paths or maneuver on surfaces and coordinate their motions to efficiently accomplish repetitive and laborious tasks. The book introduces guiding vector fields on Euclidean spaces and Riemannian manifolds for single-robot and multi-robot path-following and motion coordination, provides rigorous theoretical guarantees of vector field guided motion control of robotic systems, and elaborates on the practical implementation of the proposed algorithms on mobile wheeled robots and fixed-wing aircraft. It provides guidelines for the robust, reliable, and safe practical implementations for robotic tasks, including path-following navigation, obstacle-avoidance, and multi-robot motion coordination. In particular, the book reveals fundamental theoretic underpinnings of guiding vector fields and applies to addressing various robot motion control problems. Notably, it answers many crucial and challenging questions such as: · How to generate a general guiding vector field on any n-dimensional Riemannian manifold for robot motion control tasks? · Do singular points always exist in a general guiding vector field? · How to generate a guiding vector field that is free of singular points? · How to design control algorithms based on guiding vector fields for different robot motion control tasks including path-following, obstacle-avoidance, and multi-robot distributed motion coordination? Answering these questions has led to the discovery of fundamental assumptions, a “topological surgery” to create a singularity-free guiding vector field, a robot navigation algorithm with the global convergence property, a provably safe collision-avoidance algorithm and an effective distributed motion control algorithm, etc

What is Motion Field In computer vision, the motion field is an ideal representation of motion in three-dimensional space (3D) as it is projected onto a camera image. Given a simplified camera model, each point in the image is the projection of some point in the 3D scene but the position of the projection of a fixed point in space can vary with time. The motion field can formally be defined as the time derivative of the image position of all image points given that they correspond to fixed 3D points. This means that the motion field can be represented as a function which maps image coordinates to a 2-dimensional vector. The motion field is an ideal description of the projected 3D motion in the sense that it can be formally defined but in practice it is normally only possible to determine an approximation of the motion field from the image data. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Motion Field Chapter 2: Chain Rule Chapter 3: Curl (Mathematics) Chapter 4: Polar Coordinate System Chapter 5: Green's Theorem Chapter 6: Line Element Chapter 7: Camera Matrix Chapter 8: Pinhole Camera Model Chapter 9: Derivation of the Navier-Stokes Equations Chapter 10: Relativistic Lagrangian Mechanics (II) Answering the public top questions about motion field. (III) Real world examples for the usage of motion field in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Motion Field.

Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.