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Category: mathematics – Page 6

So-called Rayleigh–Bloch waves can release an enormous amount of energy that can damage technical systems under certain circumstances. They only exist below a precisely defined cut-off frequency; above this, they disappear abruptly. Strangely enough, however, there are isolated high frequencies at which they can also be detected.

Mathematicians from the Universities of Augsburg and Adelaide have recently proposed an explanation for this puzzling phenomenon. Together with researchers from the University of Exeter, they have now been able to prove experimentally that their theory is indeed correct. The study has just been published in the journal Communications Physics.

Suppose you had a gigantic barbecue grill that could easily accommodate several hundreds of sausages. Then, you could not only use it to invite your children’s entire school to a barbecue. The numerous stainless steel struts aligned parallel to each other are also ideal for generating Rayleigh–Bloch waves.

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The fundamental principles of thermodynamics have long been a cornerstone of our understanding of the physical world, with the second law of thermodynamics standing as a testament to the inexorable march towards disorder and entropy that governs all closed systems. However, the realm of quantum physics has traditionally appeared to defy this notion, with mathematical formulations suggesting that entropy remains constant in these systems.

Recent research has shed new light on this seeming paradox, revealing that the apparent contradiction between quantum mechanics and thermodynamics can be reconciled through a nuanced understanding of entropy itself. By adopting a definition of entropy that is compatible with the principles of quantum physics, specifically the concept of Shannon entropy, scientists have demonstrated that even isolated quantum systems will indeed evolve towards greater disorder over time, their entropy increasing as the uncertainty of measurement outcomes grows.

This breakthrough insight has far-reaching implications for our comprehension of the interplay between quantum theory and thermodynamics, and is poised to play a pivotal role in the development of novel quantum technologies that rely on the manipulation of complex many-particle systems.

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For decades, the realm of particle physics has been governed by two major categories: fermions and bosons. Fermions, like quarks and leptons, make up matter, while bosons, such as photons and gluons, act as force carriers. These classifications have long been thought to be the limits of particle behavior. However, a breakthrough has recently changed this understanding.

Researchers have mathematically proven the existence of paraparticles, a theoretical type of particle that doesn’t fit neatly into the traditional fermion or boson categories. These exotic particles were once deemed impossible, defying the conventional laws of physics. Now, thanks to advanced mathematical equations, scientists have demonstrated that paraparticles can exist without violating known physical constraints.

The implications of this discovery could be far-reaching, especially in areas like quantum computing. Paraparticles could offer new possibilities in how we understand the universe at its most fundamental level. While the discovery is still in its early stages, it provides a new tool for physicists to explore more complex systems, potentially unlocking new technologies in the future.

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The real magic of Fermi problems lies in their imperfection. They remind us that it’s okay to be wrong — as long as you’re thoughtfully wrong. “There are no wrong answers,” says Funk. “It’s about the process.”

No single formula exists. Yet each problem invites the same approach: break it down, make realistic (or at least consistent) assumptions, and trust your critical thinking. “No Wrong Answers” is a common Fermi problem refrain because even if your math arrives at a slightly off result, you’ve shown how you reason. And that, ultimately, is the real answer.

So, the next time you’re faced with a seemingly impossible question — whether it’s How many grains of sand are on all the world’s beaches? or How long would it take to drive to the moon? — grab a napkin and a pen. Start breaking it down. Make some guesses. Do some math. You might just surprise yourself with how close you can get.

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A new study in Nature Communications explores the dynamics of higher-order novelties, identifying fascinating patterns in how we combine existing elements to create novelty, potentially reshaping our understanding of human creativity and innovation.

Novelties—a common part of human life—refer to one of two things. The first is the discovery of a single item, like a place, song, or an artist. The second covers discoveries new to everyone, such as technological developments or drug discoveries.

The researchers in this study aimed to understand how both kinds of novelties emerge. The team was led by Prof. Vito Latora from the Queen Mary University of London, who spoke to Phys.org about the work.

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OpenAI, the company behind ChatGPT, says it has proof that the Chinese start-up DeepSeek used its technology to create a competing artificial intelligence model — fueling concerns about intellectual property theft in the fast-growing industry.

OpenAI believes DeepSeek, which was founded by math whiz Liang Wenfeng, used a process called “distillation,” which helps make smaller AI models perform better by learning from larger ones.

While this is common in AI development, OpenAI says DeepSeek may have broken its rules by using the technique to create its own AI system.

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While DeepSeek makes AI cheaper, seemingly without cutting corners on quality, a group is trying to figure out how to make tests for AI models that are hard enough. It’s ‘Humanity’s Last Exam’

If you’re looking for a new reason to be nervous about artificial intelligence, try this: Some of the smartest humans in the world are struggling to create tests that AI systems can’t pass.

For years, AI systems were measured by giving new models a variety of standardized benchmark tests. Many of these tests consisted of challenging, SAT-calibre problems in areas like math, science and logic. Comparing the models’ scores over time served as a rough measure of AI progress.

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Yale physicists have uncovered a sophisticated and previously unknown set of “modes” within the human ear, which impose crucial constraints on how the ear amplifies faint sounds, withstands loud noises, and distinguishes an astonishing range of sound frequencies.

By applying existing mathematical models to a generic mock-up of the cochlea—a spiral-shaped organ in the inner ear—the researchers revealed an additional layer of cochlear complexity. Their findings provide new insights into the remarkable capacity and precision of human hearing.

“We set out to understand how the ear can tune itself to detect faint sounds without becoming unstable and responding even in the absence of external sounds,” said Benjamin Machta, an assistant professor of physics in Yale’s Faculty of Arts and Science and co-senior author of a new study in the journal PRX Life. “But in getting to the bottom of this we stumbled onto a new set of low frequency mechanical modes that the cochlea likely supports.”

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