A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold. Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of natural quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the field of crystallography. In crystallography the quasicrystals were predicted in 1981 by a five-fold symmetry study of Alan Lindsay Mackay,—that also brought in 1982, with the crystallographic Fourier transform of a Penrose tiling, the possibility of identifying quasiperiodic order in a material through diffraction. Quasicrystals had been investigated and observed earlier, but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter. In 2009, after a dedicated search, a mineralogical finding, icosahedrite, offered evidence for the existence of natural quasicrystals. Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions. Symmetrical diffraction patterns result from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six. In 1982 materials scientist Dan Shechtman observed that certain aluminium-manganese alloys produced the unusual diffractograms which today are seen as revelatory of quasicrystal structures. Due to fear of the scientific community's reaction, it took him two years to publish the results for which he was awarded the Nobel Prize in Chemistry in 2011.On 25 October 2018, Luca Bindi and Paul Steinhardt were awarded the Aspen Institute 2018 Prize for collaboration and scientific research between Italy and the United States, after they discovered icosahedrite, the first quasicrystal known to occur naturally. (Wikipedia).
Numerical mathematics of quasicrystals – Pingwen Zhang – ICM2018
Numerical Analysis and Scientific Computing Invited Lecture 15.8 Numerical mathematics of quasicrystals Pingwen Zhang Abstract: Quasicrystals are one kind of fascinating aperiodic structures, and give a strong impact on material science, solid state chemistry, condensed matter physics an
From playlist Numerical Analysis and Scientific Computing
Material Marvels with Ainissa Ramirez - Quasicrystals
The Nobel Prize in Chemistry went to quasicrystals. But what are they? Dr. Ainissa Ramirez guides us into the strange world where atoms arrange themselves in forbidden ways and create materials with weird properties.
From playlist Material Marvels
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Quasi-Fermi l
From playlist Electronics I: Semiconductor Physics and Devices
Why Do Physicists Believe In These Particles That DON'T Exist? Quasiparticles by Parth G
The answer: these "Quasiparticles" make physics much easier to study! In this video we'll be studying 3 quasiparticles (sometimes known as collective excitations). They don't actually exist, in that they are not fundamental particles themselves, but can be thought of as mathematical simpl
From playlist Quantum Physics by Parth G
Constructing group actions on quasi-trees – Koji Fujiwara – ICM2018
Topology Invited Lecture 6.12 Constructing group actions on quasi-trees Koji Fujiwara Abstract: A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary hype
From playlist Topology
AWESOME SUPERCONDUCTOR LEVITATION!!!
A quantum levitator it's a circular track of magnets above which a razor-thin disc magically levitates, seeming to defy the laws of physics. The key to the levitator is the disc, which is made of superconducting material sandwiched between layers of gold and sapphire crystal. A piece of fo
From playlist THERMODYNAMICS
Ancient Aliens: Mysterious Metals from Outer Space (Season 12) | History
Stay up to date on all of HISTORY's latest premieres at http://history.com/schedule Researching ancient cultures, archaeologists have found mysterious metals with no clear origin. Ancient astronaut theorists believe these mysterious alloys could be evidence of alien communication with man
From playlist Ancient Aliens: Official Series Playlist | New Episodes Fridays at 9/8c | History
The Search for Natural Quasicrystals - Paul Steinhardt
Paul Steinhardt Center for Theoretical Science, Princeton University March 7, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Schemes 17: Finite, quasifinite
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define finite morphisms, and attempt to sort out the three different definition of quasifinite morphisms in the literature.
From playlist Algebraic geometry II: Schemes
Cut-And-Project Quasicrystals: Patch Frequency and Moduli Spaces by Rene Rühr
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Intrinsic Diophantine approximation (Lecture 1) by Amos Nevo
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Schemes 27: Quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We show how to turn a module over a ring into a sheaf of modules over its spectrum. A quasicoherent sheaf of modules of one which looks locally like one constr
From playlist Algebraic geometry II: Schemes
An attempt at growing a quasicrystal
Like the simulation https://youtu.be/YjerTwsRUp0 this one shows the motion of particles coupled to a thermostat, and interacting with an anisotropic Lennard-Jones type potential. Only this time, the potential has a pentagonal symmetry instead of a square symmetry. Two isolated particles ha
From playlist Molecular dynamics
Not quite a quasicrystal (yet): Particles interacting with a potential based on the golden ratio
This new attempt at growing a quasicrystal uses a potential with rotation symmetry, which is similar to the Lennard-Jones potential, but has two stable equilibrium positions at distances whose ratio ls the golden mean Phi = 1.618.... This was suggested to me by Florian Theil. The result is
From playlist Molecular dynamics
Two types of particles interacting with Lennard-Jones-type potentials depending on the golden ratio
Like the simulation https://youtu.be/lnlZlq1owYQ this one shows the evolution of a mixture of two types of particles interacting with a radial potential. Here there are 1495 particles, 80% of which are of type I (indicated by small circles), and 20% of which are of type II (indicated by la
From playlist Molecular dynamics
The 2011 Nobel Prize in Chemistry - Periodic Table of Videos
Daniel Shechtman is awarded the Nobel Prize for his discovery of quasicrystals. Discussed here by Professor Martyn Poliakoff and Sixty Symbols' Professor Phil Moriarty. More chemistry at http://www.periodicvideos.com/ Follow us on Facebook at http://www.facebook.com/periodicvideos
From playlist Nobel Prize - Periodic Videos
How To Discover Weird New Particles | Emergent Quantum Quasiparticles
This video is about weird condensed matter systems, aka materials that have bizarre emergent particles in them that are unlike most other particles in the universe. Thanks to the Moore Foundation (http://www.moore.org) for supporting this video. More info about the physics of weird mate
From playlist MinutePhysics