Category: Mathematics
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Mathematics. World. Randomness.
Brownian motion describes the random movement of particles in fluids, however, this revolutionary model only works when a fluid is static, or at equilibrium. In real-life environments, fluids often contain particles that move by themselves, such as tiny swimming microorganisms. These self-propelled swimmers can cause movement or stirring in the fluid, which drives it away…
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Classical physics. QM. Intuitionism.
In classical physics, it is accepted that everything has already been determined since the Big Bang. To explore the future of our cosmos, physicists employ the language of classical mathematics and represent the universe’s initial conditions conditions by real numbers. “These numbers are characterized by an infinite number of decimals that follow the dot,” says…
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Why doesn’t any animal have three legs?
If ‘Why?’ is the first question in science, ‘Why not?’ must be a close second. Sometimes it’s worth thinking about why something does not exist. Such as a truly three-legged animal. At least one researcher has been pondering the non-existence of tripeds. “Almost all animals are bilateral,” he said. The code for having two sides…
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Chaos. Numbers. Simulations.
Digital computers use numbers based on flawed representations of real numbers, which may lead to inaccuracies when simulating the motion of molecules, weather systems and fluids, find scientists. The study, published today in Advanced Theory and Simulations, shows that digital computers cannot reliably reproduce the behaviour of ‘chaotic systems’ which are widespread. This fundamental limitation…
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Old mathematics… Broken cosmos… Blurry image…
By combining cutting-edge machine learning with 19th-century mathematics, a Worcester Polytechnic Institute (WPI) mathematician worked to make NASA spacecraft lighter and more damage tolerant by developing methods to detect imperfections in carbon nanomaterials used to make composite rocket fuel tanks and other spacecraft structures. Using machine learning, neural networks, and an old mathematical equation, Randy…
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