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Category: mathematics – Page 14

The search for quantum gravity has gone on for 100 years, but it is not the only unification challenge in physics. Many of us believe that one day there will be a unification theory—a theory that will reconcile many divergent physical theories.

Our new article published in Physica Scripta brings new hope that such a theory exists. It demonstrates that the use of a certain mathematical object called Alena Tensor reconciles various physical theories, including , electrodynamics, and continuum mechanics. Will this finally allow scientists to unify descriptions used in physics?

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A team of researchers from the University of Cologne, Hasselt University (Belgium) and the University of St Andrews (Scotland) has succeeded in using the quantum mechanical principle of strong light-matter coupling for an optical technology that overcomes the long-standing problem of angular dependence in optical systems.

The study, “Breaking the angular dispersion limit in thin film optics by ultra-strong light-matter coupling,” published in Nature Communications presents ultra-stable thin-film polariton filters that open new avenues in photonics, sensor technology, optical imaging and display technology.

The study at the University of Cologne was led by Professor Dr. Malte Gather, director of the Humboldt Center for Nano-and Biophotonics at the Department of Chemistry and Biochemistry of the Faculty of Mathematics and Natural Sciences.

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Science and Technology: Google said its quantum computer, based on a computer chip called Willow, needed less than five minutes to perform a mathematical calculation that one of the world’s most powerful supercomputers could not complete in 10 septillion years, a length of time that exceeds the age of the known universe.

Electronic skins (e-skins) are flexible sensing materials designed to mimic the human skin’s ability to pick up tactile information when touching objects and surfaces. Highly performing e-skins could be used to enhance the capabilities of robots, to create new haptic interfaces and to develop more advanced prosthetics.

In recent years, researchers and engineers have been trying to develop e-skins with individual tactile units (i.e., taxels) that can accurately sense both normal (i.e., perpendicular) and shear (i.e., lateral) forces. While some of these attempts were successful, most existing multi-axis sensors are based on intricate designs or require complex fabrication and calibration processes, which limits their widespread deployment.

Researchers at CNRS-University of Montpellier have introduced a new soft e-skin that leverages magnetic fields to independently detect forces on three axes. This e-skin, described in a paper published in Nature Machine Intelligence, has a simple design that could be easy to reproduce on a large scale.

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Summary: Human number cognition may be rooted in the putamen, a deep brain structure traditionally associated with movement rather than abstract thought. Neurosurgery patients demonstrated activity in this area while processing numbers as symbols, words, and concepts, suggesting that numerical understanding emerged early in evolution.

Researchers also observed activity in expected areas like the parietal lobe, highlighting how different brain regions collaborate in number processing. These findings could improve surgical outcomes by protecting areas crucial for number cognition and open pathways to enhancing math learning through targeted interventions.

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It was 1,229 CE in the monastery of St Sabas, near Jerusalem, and a monk named Johannes Myronas was in need of some parchment. He had evidently been tasked with creating a copy of the Euchologion – an important book of prayer and worship directions for Eastern Orthodox and Byzantine Catholic churches.

The problem was, parchment was expensive and hard to come by. Recycling was the name of the game, and Johannes had just the thing: a 200-year-old manuscript filled with old math notes that nobody was all that interested in anymore. Compared with the Holy Word, there was no contest: he pulled it apart, scraped the old text off, and used the pages for the new book – a technique known as palimpsesting.

You probably know where this is going. In creating his Euchologion, Johannes had – presumably unwittingly – destroyed one of the most valuable relics of Archimedes’s work. Not just some notebook or single treatise, even: the manuscript now known as “Codex C” contained multiple works from the ancient polymath, some of which now exist nowhere else in the world.

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Mathematician Stephen Wolfram has attempted to develop a theory of everything using hypergraphs, which are essentially sets of graphs that can describe space-time. Recently, another mathematician named Jonathan Gorard has used hypergraphs to describe what happens if a black hole accretes matter. He claims that evidence for hypergraphs should be observable in the energy that is emitted during the accretion. Big if true, as they say. Let’s take a look.

Paper: https://arxiv.org/abs/2402.

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Vorticity, a measure of the local rotation or swirling motion in a fluid, has long been studied by physicists and mathematicians. The dynamics of vorticity is governed by the famed Navier-Stokes equations, which tell us that vorticity is produced by the passage of fluid past walls. Moreover, due to their internal resistance to being sheared, viscous fluids will diffuse the vorticity within them and so any persistent swirling motions will require a constant resupply of vorticity.

Physicists at the University of Chicago and applied mathematicians at the Flatiron Institute recently carried out a study exploring the behavior of viscous fluids in which tiny rotating particles were suspended, acting as local, mobile sources of vorticity. Their paper, published in Nature Physics, outlines fluid behaviors that were never observed before, characterized by self-propulsion, flocking and the emergence of chiral active phases.

“This experiment was a confluence of three curiosities,” William T.M. Irvine, a corresponding author of the paper, told Phys.org. “We had been studying and engineering parity-breaking meta-fluids with fundamentally new properties in 2D and were interested to see how a three-dimensional analog would behave.

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