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Category: mathematics – Page 139

For decades, physicists, engineers and mathematicians have failed to explain a remarkable phenomenon in fluid mechanics: the natural tendency of turbulence in fluids to move from disordered chaos to perfectly parallel patterns of oblique turbulent bands. This transition from a state of chaotic turbulence to a highly structured pattern was observed by many scientists, but never understood.

At EPFL’s Emerging Complexity in Physical Systems Laboratory, Tobias Schneider and his team have identified the mechanism that explains this phenomenon. Their findings have been published in Nature Communications.

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A growing body of research suggests that exposure to air pollution in the earliest stages of life is associated with negative effects on cognitive abilities. A new study led by the Barcelona Institute for Global Health (ISGlobal), a centre supported by “la Caixa”, has provided new data: exposure to particulate matter with a diameter of less than 2.5 μm (PM2.5) during pregnancy and the first years of life is associated with a reduction in fundamental cognitive abilities, such as working memory and executive attention.

The study, carried out as part of the BREATHE project, has been published in Environmental Health Perspectives. The objective was to build on the knowledge generated by earlier studies carried out by the same team, which found lower levels of cognitive development in children attending schools with higher levels of traffic-related air pollution.

The study included 2,221 children between 7 and 10 years of age attending schools in the city of Barcelona. The children’s cognitive abilities were assessed using various computerized tests. Exposure to air pollution at home during pregnancy and throughout childhood was estimated with a mathematical model using real measurements.

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Many ways to approach the Riemann Hypothesis have been proposed during the past 150 years, but none of them have led to conquering the most famous open problem in mathematics. A new paper in the Proceedings of the National Academy of Sciences (PNAS) suggests that one of these old approaches is more practical than previously realized.

“In a surprisingly short proof, we’ve shown that an old, abandoned approach to the Riemann Hypothesis should not have been forgotten,” says Ken Ono, a theorist at Emory University and co-author of the paper. “By simply formulating a proper framework for an old approach we’ve proven some new theorems, including a large chunk of a criterion which implies the Riemann Hypothesis. And our general framework also opens approaches to other basic unanswered questions.”

The paper builds on the work of Johan Jensen and George Pólya, two of the most important mathematicians of the 20th century. It reveals a method to calculate the Jensen-Pólya polynomials—a formulation of the Riemann Hypothesis—not one at a time, but all at once.

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A mathematician from the University of Bristol has found a solution to part of a 64-year old mathematical problem – expressing the number 33 as the sum of three cubes.

Since the 1950s, mathematicians have wondered if all could be expressed as the sum of three cubes; whether the equation k = x³+ y³+ z³ always has a .

The puzzle is a Diophantine equation in the field of , and forms part of one of the most mysterious and wickedly hard in . We still don’t know the answer.

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A prime number theory equation by mathematics professor emeritus Carl Pomerance turned up on The Big Bang Theory, where it was scrawled on a white board in the background of the hit sitcom about a group of friends and roommates who are scientists, many of them physicists at the California Institute of Technology.

In a recent paper, “Proof of the Sheldon Conjecture,” Pomerance, the John G. Kemeny Parents Professor of Mathematics Emeritus, does the math on a claim by fictional quantum physicist Sheldon Cooper that 73 is “the best ” because of several . Pomerance’s proof shows that 73 is indeed unique.

The Big Bang Theory is known for dressing the set with “Easter eggs” to delight the self-avowed science nerds in the audience. When UCLA physics professor David Saltzberg, technical consultant for The Big Bang Theory, heard about the Sheldon proof, he contacted Pomerance to ask if they could use it in the show, which was broadcast April 18.

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Given that everything at its base atom is moving maybe our interpretation of reality may be different than its actuality. From shooting photons bouncing off surfaces the world is a cacophony of all sorts of things happening at once.

A provocative new column in Scientific American floats the idea that what’s fundamentally real in the universe — its actual, base reality — isn’t the quarks, fields, and quantum phenomena that seem to comprise it.

Instead, according to scientist and philosopher Bernardo Kastrup, some are starting to suspect that matter itself is an illusion — and that the only real thing is information.

Information Space

Continue reading “Physicists Are Starting to Suspect Physical Reality Is an Illusion” | >

A team of researchers from the University of Central Florida and Michigan Technological University has developed a laser system concept built on the principles of supersymmetry. In their paper published in the journal Science, the group reports that their system is meant to solve the problem of producing more light with a compact laser system. Tsampikos Kottos with Wesleyan University has written a Perspective piece on the work done by the team in the same journal issue.

Kottos points out that there are a lot of physics applications that require use of a compact laser system that also has high-output power requirements. To fulfill this need, many physicists have taken to combining multiple lasers into an array. Unfortunately, this approach suffers from the production of a lesser-quality beam. Kottos notes that one way to overcome this problem is to use selective amplification of a single mode—but doing so has its own drawbacks. In this new effort, the researchers have come up with a different approach—one based on the principles of .

Supersymmetry is a math-based theory that describes the relationship between bosons and —it suggests that for every known elementary particle, there has to be a much heavier “super partner.” To build a new kind of laser system, the researchers used this idea to create a stable array of semiconductor lasers that together offer the power needed for prospective applications. More specifically, they designed a system that emphasizes the fundamental mode by suppressing higher-order modes. They did this by pairing them with low-quality modes—their lossy super-partners. The idea was for the to support them such that they were phase-matched with the higher order modes.

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