Tangled In The Curves

Receiving a diagnosis of scoliosis - a condition where the spine bends and rotates for no known reason - can be an emotional time full of questions and concerns. You might feel like you have to navigate it all by yourself. But, know this: you are not alone. Tangled in the Curves is an honest firsthand account of real life with idiopathic scoliosis that fully captures the scoliosis journey through teenage diagnosis, bracing, surgery, and adulthood. It’s also a useful tool that provides easy access to an abundance of practical information: resources, options, research and expertise, tips and tricks, and personal stories from “scoliosis warriors” around the globe. All scoliosis warriors, no matter what stage they’re at in their physical and emotional journey, will find something that speaks to them in this book. New scoliosis patients and their families will obtain the information they need, in easy-to-understand language, to address their immediate worries and questions. Bracers will find tips and tricks to make life with a back brace easier. Those receiving surgical treatment will learn what to really expect during surgery day, hospital recovery, and home recovery. Adult warriors who feel alone will find a large and relatable scoli community sharing their challenges, solutions, and support. Tangled in the Curves will inspire you to find your inner strength, resilience, and determination. Scoliosis does not define you. You can handle this!

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.

Volume eight in this highly acclaimed series discusses the behavioral approaches to pattern recognition and concept formation in two sections: categories and concepts in birds, and shape and form. An ideal reference for students and professionals in experimental psychology and behavioral analysis.

How to Free Your Inner Mathematician delivers engaging mathematical content and provides reassurance that mathematical success has more to do with curiosity and drive than innate aptitude, offering readers more than 300 hand-drawn sketches alongside accessible descriptions of topics.

In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological complexity---including knotting---on the large scale. The work is highly visual, and illustrated with many beautiful diagrams revealing this unanticipated aspect of the physics of waves. Linear superpositions of waves create interference patterns, which means in some places they strengthen one another, while in others they completely cancel each other out. This latter phenomenon occurs on 'vortex lines' in three dimensions. In general wave superpositions modelling e.g. chaotic cavity modes, these vortex lines form dense tangles that have never been visualised on the large scale before, and cannot be analysed mathematically by any known techniques.