Related papers: Frieze patterns
We report frozen patterns for the water droplets impacting on a cold substrate through fast-speed images. These patterns can be manipulated by several physical parameters (the droplet size, falling height, and substrate temperature), and…
We survey the close relationship between sound and light rays and geometry. In the case where the medium is at rest, the geometry is the classical geometry of Riemann. In the case where the medium is moving, the more general geometry known…
The term "surface polarization" is introduced to describe the in-plane polarization existing at the surface of an insulating crystal when the in-plane surface inversion symmetry is broken. Here, the surface polarization is formulated in…
We study the joint variability of structural information in a hard sphere fluid biased to avoid crystallisation and form fivefold symmetric geometric motifs. We show that the structural covariance matrix approach, originally proposed for…
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form…
Water adopts many different crystal structures in its solid form. These provide insight into potential structures of water even in its liquid phase, and they can be used to calibrate pair potentials used for simulation of water. In crowded…
This work presents the tessellations and polytopes from the perspective of both n-dimensional geometry and abstract symmetry groups. It starts with a brief introduction to the terminology and a short motivation. In the first part, it…
We study numerically the crystallization of a hard-sphere mixture with 8\% polydispersity. Although often used as a model glass former, for small system sizes we observe crystallization in molecular dynamics simulations. This opens the…
Frieze patterns (in the sense of Conway and Coxeter) are in close connection to triangulations of polygons. Broline, Crowe and Isaacs have assigned a symmetric matrix to each polygon triangulation and computed the determinant. In this paper…
Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…
The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.
This lecture presents a short review of the main features of diffractive processes and QCD inspired models. It includes the following topics: (1) Quantum mechanics of diffraction: general properties; (2) Color dipole description of…
Comparisons and analogies are drawn between materials ferroic glasses and conventional spin glasses, in terms of both experiment and theoretical modelling, with inter-system conceptual transfers leading to suggestions of further issues to…
A simple framework is presented for unified applications in various fields of colloidal research, with minimal additional concepts & definitions. Several case studies concerning glass transition & crystallization are provided under the…
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
The dynamics of fluids is a long standing challenge that remained as an unsolved problem for centuries. Understanding its main features, chaos and turbulence, is likely to provide an understanding of the principles and non-linear dynamics…
The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional…
We introduce a 3D porous photonic crystal whose inner surfaces are chemically functionalized in arbitrary spatial patterns with micro-scale resolution. We use this platform to demonstrate pattern-formation.
The differential geometric aspects of Geometric Phases are reviewed.
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…