Related papers: Topics on mathematical crystallography
The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we…
Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one…
The exquisite precision delivered by interferometric techniques is rapidly being applied to more and more branches of optical astronomy. One particularly successful strategy to obtain structures at the scale of the diffraction limit is…
Diffraction is the most common method to solve for unknown or partially known crystal structures. However, it remains a challenge to determine the crystal structure of a new material that may have nanoscale size or heterogeneities. Here we…
Liquids crystallize as they cool; however, when crystallization is avoided in some way, they supercool, maintaining their liquidity, and freezing into glass at low temperatures, as ubiquitously observed. These metastable states crystallize…
Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on…
Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials…
Critical points and singularities are encountered in the study of critical phenomena in probability and physics. We present recent results concerning the values of such critical points and the nature of the singularities for two prominent…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
Understanding material composition-structure-function relationships is of critical importance for the design and discovery of novel functional materials. While most such studies focus on individual materials, we conducted a global mapping…
This article is written in memory of Pierre Hohenberg with appreciation for his deep commitment to the basic principles of theoretical physics. I summarize recent developments in the theory of dislocation-enabled deformation of crystalline…
Transmission electron diffraction is a powerful and versatile structural probe for the characterization of a broad range of materials, from nanocrystalline thin films to single crystals. With recent developments in fast electron detectors…
The cosmic crystallography method of Lehoucq et al. [1] produces sharp peaks in the distribution of distances between the images of cosmic sources. But the method cannot be applied to universes with compact spatial sections of negative…
We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension.…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…
Optical methods are most convenient to analyze spatially periodic patterns with wavevector $\bm q$ in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a 'short' wavelength $\lambda…
Linus Pauling contributions span structural biology, chemistry in its broadest definition, quantum mechanical theory, valence bond theory, and even nuclear physics. A principal tool developed and used by Pauling is Xray, and electron,…
We propose a new systematic method of studying correlations between parameters that describe an astronomical (or any) physical system. We recall that behind Dimensionless scaling laws in complex, self-interacting physical objects lies a…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…