Related papers: Mathematics and liquid crystals
Liquid crystal is a typical kind of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the last four decades, which is of great importance on both…
These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
Liquid crystals are the prototype of the so-called soft condensed matter. In simple terms they are "structured liquids" that historically have received a lot of interest because they help to generate new concepts and knowledge in Physics,…
We outline the necessary background to understand the interaction of colloids in liquid crystals through boundary conditions and topology.
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
In this note I describe reliability standards for writing and reviewing mathematical papers; these standards are (in my opinion) vital for the progress of mathematics. I give examples of applying the described or other reliability…
Liquid crystals have attracted enormous interest because of the variety of their phases and richness of their application. The interplay of general physical symmetries and specific molecular features generates a myriad of different…
A brief review of some selected topics in p-adic mathematical physics is presented.
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.
Application of adeles in modern mathematical physics is briefly reviewed. In particular, some adelic products are presented.
The paper presents a teaching module about liquid crystals. Since liquid crystals are linked to everyday student experiences and are also a topic of a current scientific research, they are an excellent candidate of a modern topic to be…
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
We shall describe the one-to-one correspondence between the set of pictures and the set of Littlewood-Richardson crystals.
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
This is an expository introduction, for a general mathematics audience, to the modeling of the fluid/solid phase transition and in particular to complications created by the discovery of quasicrystals. One goal is to elucidate certain…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.