Related papers: Mathematics and liquid crystals

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…

This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…

We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…

The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.

The last decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result an integrated view of cell biology is evolving, where genetic and molecular features…

The study of hydrodynamics of liquid crystal leads to many fasci- nating mathematical problems, which has prompted various interesting works recently. This article reviews the static Oseen-Frank theory and surveys some recent progress on…

We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…

A liquid can be used to represent signals, actuate mechanical computing devices and to modify signals via chemical reactions. We give a brief overview of liquid based computing devices developed over hundreds of years. These include…

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.

A review of the superstatistics concept is provided, including various recent applications to complex systems.

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

This paper gives an introduction to some of the statistical physics problems which appear in the study of structural glasses. It is a shortened and updated version of a more detailed review paper which has appeared in cond-mat/0005173.

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

We introduce the concept of protometric and present some properties of protometrics.

We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…

Physics of dielectric mixtures are presented to stimulate discussion and to provide information on the recent advances in this topic.

In this article, we review the mathematical modeling for the vascular system.

This entry is aimed at describing cloud physics with an emphasis on fluid dynamics. As is inevitable for a review of an enormously complicated problem, it is highly selective and reflects of the authors' focus. The range of scales involved,…

One of the variants for systematizing the activities of the historian of mathematics is proposed, as well as a scheme for organizing research and search work in the preparation of scientific articles and reports on the history of science.

This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…