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Category: mathematics – Page 49

Carlos Bravo-Prieto1,2,3, Ryan LaRose4, M. Cerezo1,5, Yigit Subasi6, Lukasz Cincio1, and Patrick J. Coles1

1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87,545, USA. 2 Barcelona Supercomputing Center, Barcelona, Spain. 3 Institut de Ciències del Cosmos, Universitat de Barcelona, Barcelona, Spain. 4 Department of Computational Mathematics, Science, and Engineering & Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48,823, USA. 5 Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA 6 Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87,545, USA

Get full text pdfRead on arXiv Vanity.

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Open-source supercomputer algorithm predicts patterning and dynamics of living materials and enables studying their behavior in space and time.

Biological materials are made of individual components, including tiny motors that convert fuel into motion. This creates patterns of movement, and the material shapes itself with coherent flows by constant consumption of energy. Such continuously driven materials are called “active matter.” The mechanics of cells and tissues can be described by active matter theory, a scientific framework to understand shape, flows, and form of living materials. The active matter theory consists of many challenging mathematical equations.

Scientists from the Max Planck Institute of Molecular Cell.

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An open-source advanced supercomputer algorithm predicts the patterning and dynamics of living materials, allowing for the exploration of their behaviors across space and time.

Biological materials consist of individual components, including tiny motors that transform fuel into motion. This process creates patterns of movement, leading the material to shape itself through coherent flows driven by constant energy consumption. These perpetually driven materials are called “active matter.”

The mechanics of cells and tissues can be described by active matter theory, a scientific framework to understand the shape, flows, and form of living materials. The active matter theory consists of many challenging mathematical equations.

Read more | >

Hopfions, magnetic spin structures predicted decades ago, have become a hot and challenging research topic in recent years. In a study published in Nature, the first experimental evidence is presented by a Swedish-German-Chinese research collaboration.

“Our results are important from both a fundamental and applied point of view, as a new bridge has emerged between and abstract , potentially leading to hopfions finding an application in spintronics,” says Philipp Rybakov, researcher at the Department of Physics and Astronomy at Uppsala University, Sweden.

A deeper understanding of how different components of materials function is important for the development of innovative materials and future technology. The research field of spintronics, for example, which studies the spin of electrons, has opened up promising possibilities to combine the electrons’ electricity and magnetism for applications such as new electronics.

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Biological materials are made of individual components, including tiny motors that convert fuel into motion. This creates patterns of movement, and the material shapes itself with coherent flows by constant consumption of energy. Such continuously driven materials are called active matter.

The mechanics of cells and tissues can be described by active matter theory, a scientific framework to understand the shape, flow, and form of living materials. The active matter theory consists of many challenging mathematical equations.

Scientists from the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG) in Dresden, the Center for Systems Biology Dresden (CSBD), and the TU Dresden have now developed an algorithm, implemented in an open-source supercomputer code, that can for the first time solve the equations of active matter theory in realistic scenarios.

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While physics tells us that information can neither be created nor destroyed (if information could be created or destroyed, then the entire raison d’etre of physics, that is to predict future events or identify the causes of existing situations, would be impossible), it does not demand that the information be accessible. For decades physicists assumed that the information that fell into a black hole is still there, still existing, just locked away from view.

This was fine, until the 1970s when Stephen Hawking discovered the secret complexities of the event horizon. It turns out that these dark beasts were not as simple as we had been led to believe, and that the event horizons of are one of the few places in the entire cosmos where meets quantum mechanics in a manifest way.

The quest to unify quantum mechanics and gravity stretches back over a century, soon after the development of those two great domains of physics. What prevented their unification was a proliferation of infinities in the mathematics. Anytime gravity became strong at small scales, our equations diverged to infinity and gave useless non-results. But here we are at the boundaries of black holes, which by definition are places of strong gravity. And because the event horizons are mathematical constructs, not actual surfaces with finite extent, to truly understand them we must examine them microscopically, which plants them firmly in the realm of the quantum.

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One of the most startling scientific discoveries of recent decades is that physics appears to be fine-tuned for life. This means that for life to be possible, certain numbers in physics had to fall within a certain, very narrow range.

One of the examples of fine-tuning which has most baffled physicists is the strength of dark energy, the force that powers the accelerating expansion of the universe.

If that force had been just a little stronger, matter couldn’t clump together. No two particles would have ever combined, meaning no stars, planets, or any kind of structural complexity, and therefore no life.

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Undeterred after three decades of looking, and with some assistance from a supercomputer, mathematicians have finally discovered a new example of a special integer called a Dedekind number.

Only the ninth of its kind, or D, it is calculated to equal 286 386 577 668 298 411 128 469 151 667 598 498 812 366, if you’re updating your own records. This 42 digit monster follows the 23-digit D discovered in 1991.

Grasping the concept of a Dedekind number is difficult for non-mathematicians, let alone working it out. In fact, the calculations involved are so complex and involve such huge numbers, it wasn’t certain that D would ever be discovered.

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Cavities at the sides of a water channel can cause waves to be completely absorbed, suggesting new techniques for protecting coastlines.

If waves of water, light, or sound were to impinge upon a hypothetical object called a perfect absorber, they would be neither reflected nor transmitted; they would simply vanish. Researchers have now demonstrated perfect absorption using ordinary water waves traveling down a narrow channel [1]. The waves are canceled out by their own reflections from cavities built into the side of the channel. With further development, the researchers believe that the effect could be used to reduce erosion or protect sensitive structures by using an array of elements deployed near coastlines.

“We were motivated by the need to control or absorb waves in rivers or to protect coastlines,” says mathematical physicist Agnes Maurel of ESPCI Paris. “Completely absorbing wave energy is even better than redirecting it, and you can also imagine perhaps harvesting such energy.”

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