Mar 2, 2021 10:54 PM
(This post was last modified: Mar 2, 2021 11:00 PM by C C.)
Chemists boost boron’s utility
https://news.mit.edu/2021/chemists-boost...ility-0302
Meet the swirlon, a new kind of matter that bends the laws of physics
https://www.livescience.com/swirlonic-ma...havor.html
EXCERPTS: Fish school, insects swarm and birds fly in murmurations. Now, new research finds that on the most basic level, this kind of group behavior forms a new kind of active matter, called a swirlonic state.
[...] To explore active matter, Brilliantov and his colleagues used a computer to simulate particles that could self-propel. These particles weren't consciously interacting with the environment, Brilliantov told Live Science. Rather, they were more akin to simple bacteria or nanoparticles with internal sources of energy, but without information-processing abilities.
The first surprise was that this active matter behaves very differently than passive matter. Different states of passive matter can coexist, Brilliantov said. For example, a glass of liquid water can gradually evaporate into a gaseous state while still leaving liquid water behind. The active matter, by contrast, didn't coexist in different phases; it was all solid, all liquid or all gas.
The particles also grouped together as large conglomerates, or quasi-particles, which milled together in a circular pattern around a central void, kind of like a swirl of schooling sardines. The researchers dubbed these particle conglomerates "swirlons," and named the new state of matter they formed a "swirlonic state."
In this swirlonic state, the particles displayed bizarre behavior. For example, they violated Newton's second law: When a force was applied to them, they did not accelerate... (MORE - details)
Statistics postdoc tames decades-old geometry problem
https://www.quantamagazine.org/statistic...-20210301/
EXCERPTS: In the mid-1980s, the mathematician Jean Bourgain thought up a simple question about high-dimensional shapes. And then he remained stuck on it for the rest of his life. Bourgain, who died in 2018, was one of the preeminent mathematicians of the modern era. A winner of the Fields Medal, mathematics’ highest honor, he was known as a problem-solver extraordinaire — the kind of person you might talk to about a problem you’d been working on for months, only to have him solve it on the spot. Yet Bourgain could not answer his own question about high-dimensional shapes.
“I was told once by Jean that he had spent more time on this problem and had dedicated more efforts to it than to any other problem he had ever worked on,” wrote Vitali Milman of Tel Aviv University earlier this year.
In the years since Bourgain formulated his problem, it has become what Milman and Bo’az Klartag of the Weizmann Institute of Science in Israel called the “opening gate” to understanding a wide range of questions about high-dimensional convex shapes — shapes that always contain the entire line segment connecting any two of their points. High-dimensional convex shapes are a central object of study not just for pure mathematicians but also for statisticians, machine learning researchers and other computer scientists working with high-dimensional data sets.
[...] Bourgain’s problem boils down to the following simple question: Suppose a convex shape has volume 1 in your favorite choice of units. If you consider all the ways to slice through the shape using a flat plane one dimension lower, could these slices all have extremely low area, or must at least one be fairly substantial? Bourgain guessed that some of these lower-dimensional slices must have substantial area.
[...] Now, Bourgain’s guess has been vindicated: A paper posted online in November has proved, not quite Bourgain’s full conjecture, but a version so close that it puts a strict limit on high-dimensional weirdness, for all practical purposes. Bourgain, said Klartag, “would have dreamt” of achieving a result this strong.
The new paper, by Yuansi Chen — a postdoctoral researcher at the Swiss Federal Institute of Technology Zurich who is about to join the statistical science faculty at Duke University — gets at the Bourgain slicing problem via an even more far-reaching question about convex geometry called the KLS conjecture. This 25-year-old conjecture, which asks about the best way to slice a shape into two equal portions, implies Bourgain’s conjecture. What’s more, the KLS conjecture lies at the heart of many questions in statistics and computer science, such as how long it will take for heat to diffuse through a convex shape, or how many steps a random walker must take from a starting point before reaching a truly random location... (MORE - details)
https://news.mit.edu/2021/chemists-boost...ility-0302
Meet the swirlon, a new kind of matter that bends the laws of physics
https://www.livescience.com/swirlonic-ma...havor.html
EXCERPTS: Fish school, insects swarm and birds fly in murmurations. Now, new research finds that on the most basic level, this kind of group behavior forms a new kind of active matter, called a swirlonic state.
[...] To explore active matter, Brilliantov and his colleagues used a computer to simulate particles that could self-propel. These particles weren't consciously interacting with the environment, Brilliantov told Live Science. Rather, they were more akin to simple bacteria or nanoparticles with internal sources of energy, but without information-processing abilities.
The first surprise was that this active matter behaves very differently than passive matter. Different states of passive matter can coexist, Brilliantov said. For example, a glass of liquid water can gradually evaporate into a gaseous state while still leaving liquid water behind. The active matter, by contrast, didn't coexist in different phases; it was all solid, all liquid or all gas.
The particles also grouped together as large conglomerates, or quasi-particles, which milled together in a circular pattern around a central void, kind of like a swirl of schooling sardines. The researchers dubbed these particle conglomerates "swirlons," and named the new state of matter they formed a "swirlonic state."
In this swirlonic state, the particles displayed bizarre behavior. For example, they violated Newton's second law: When a force was applied to them, they did not accelerate... (MORE - details)
Statistics postdoc tames decades-old geometry problem
https://www.quantamagazine.org/statistic...-20210301/
EXCERPTS: In the mid-1980s, the mathematician Jean Bourgain thought up a simple question about high-dimensional shapes. And then he remained stuck on it for the rest of his life. Bourgain, who died in 2018, was one of the preeminent mathematicians of the modern era. A winner of the Fields Medal, mathematics’ highest honor, he was known as a problem-solver extraordinaire — the kind of person you might talk to about a problem you’d been working on for months, only to have him solve it on the spot. Yet Bourgain could not answer his own question about high-dimensional shapes.
“I was told once by Jean that he had spent more time on this problem and had dedicated more efforts to it than to any other problem he had ever worked on,” wrote Vitali Milman of Tel Aviv University earlier this year.
In the years since Bourgain formulated his problem, it has become what Milman and Bo’az Klartag of the Weizmann Institute of Science in Israel called the “opening gate” to understanding a wide range of questions about high-dimensional convex shapes — shapes that always contain the entire line segment connecting any two of their points. High-dimensional convex shapes are a central object of study not just for pure mathematicians but also for statisticians, machine learning researchers and other computer scientists working with high-dimensional data sets.
[...] Bourgain’s problem boils down to the following simple question: Suppose a convex shape has volume 1 in your favorite choice of units. If you consider all the ways to slice through the shape using a flat plane one dimension lower, could these slices all have extremely low area, or must at least one be fairly substantial? Bourgain guessed that some of these lower-dimensional slices must have substantial area.
[...] Now, Bourgain’s guess has been vindicated: A paper posted online in November has proved, not quite Bourgain’s full conjecture, but a version so close that it puts a strict limit on high-dimensional weirdness, for all practical purposes. Bourgain, said Klartag, “would have dreamt” of achieving a result this strong.
The new paper, by Yuansi Chen — a postdoctoral researcher at the Swiss Federal Institute of Technology Zurich who is about to join the statistical science faculty at Duke University — gets at the Bourgain slicing problem via an even more far-reaching question about convex geometry called the KLS conjecture. This 25-year-old conjecture, which asks about the best way to slice a shape into two equal portions, implies Bourgain’s conjecture. What’s more, the KLS conjecture lies at the heart of many questions in statistics and computer science, such as how long it will take for heat to diffuse through a convex shape, or how many steps a random walker must take from a starting point before reaching a truly random location... (MORE - details)