Related papers: Mathematics and liquid crystals
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…
We review the features of Dark Matter as a particle, presenting some old and new instructive models, and looking for their physical implications in the early universe and in the process of structure formation. We also present a schematic of…
This paper presents certains aspects of the mathematics of Aryabhata that are of interest to the cryptography community.
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
This is a short review on the applications of Lieb-Robinson bounds for a general readership of mathematical physicists.
The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
We present a brief introduction to analytic capacity, with an emphasis on its numerical computation. We also discuss several related open problems.
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Highlights of Quark Matter 95 are discussed.
Traditionally, mathematical knowledge is published in printed media such as books or journals. With the advent of the Internet, a new method of publication became available. To date, however, most online mathematical publications do not…
This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.
This article gives a brief survey of the theory and applications of anomalies.
Current problems in particle physics are reviewed from the viewpoint of theories possessing extra spatial dimensions.