Related papers: Mathematics and liquid crystals
The well-known fluid equation of cosmology is examined with a view to elucidating the precise conditions under which it is applicable.
Logical and mathematical aspects of the basic concepts of thermodynamics are considered.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant…
A general introduction to lattice QCD suitable for graduate students in experimental and theoretical particle physics. Aimed at those who want to know how lattice calculations are done, and what the pitfalls are, without having to do the…
Microscopic understanding of liquid properties is essential for advancing a wide range of applications from energy applications such as nuclear reactors and batteries to biomedical applications including drug delivery and microfluidics.…
Remarks on mathematical proof and the practice of mathematics.
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.
We humbly and briefly offer corrections and supplements to Mathematical Constants (2003) and Mathematical Constants II (2019), both published by Cambridge University Press. Comments are always welcome.
We develop the notion of crystal in the context of derived algebraic geometry, and to connect crystals to more classical objects such as D-modules.
This is an introductory article to the theory of multiple gaps.
This is an item in the "View and Perspective" category, which presents a brief overview of particular aspects of the topic of "quantum droplets". It is linked to a new theoretical paper, "Quantum droplets in two-dimensional optical…
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection…
This is a very basic introduction to some notions related to logic and complexity.
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
In this paper, we mainly study a hydrodynamic system modeling the flow of nematic liquid crystals. In three dimensions, we first establish local well-posedness of the initial-boundary value problem of the system. Then, we prove the…