Related papers: Mathematics and liquid crystals
We use numerical simulation to examine the possibility of a reversible liquid-liquid transition in supercooled water and related systems. In particular, for two atomistic models of water, we have computed free energies as functions of…
The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
Ten years ago, the new era of time crystals began. Time crystals are systems that behave in the time dimension like ordinary space crystals do in space dimensions. We present a brief history of a decade of research on time crystals,…
In this paper we study the large time behavior of solutions to a nematic liquid crystals system in the whole space $\mathbb{R}^3$. The fluid under consideration has constant density and small initial data.
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.
I discuss various aspects of the concept of a quantity in physics and metrology and related consideration in reference documents of IUPAP, IUPAC, ISO, IEC, and JCGM.
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.
We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.
Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular field configurations, often markedly…
Some topics from recent progresses in lattice QCD are reviewed.
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.
We consider the practicalities of defining, simulating, and characterizing "Liquids" from a pedagogical standpoint based on atomistic computer simulations. For simplicity and clarity we study two-dimensional systems throughout. In addition…
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…