The famous sunspots on the surface of the Earth's star result from the dynamics of strong magnetic fields, and their numbers are an important indicator of the state of activity on the Sun. Researchers have been conducting multifractal analysis into the changes in the numbers of sunspots. The resulting graphs were surprisingly asymmetrical in shape, suggesting that sunspots may be involved in hitherto unknown physical processes.
Researchers from the University of Liverpool have used mathematical equations to shed new light...
Quantum particles behave in strange ways and are often difficult to study experimentally. Using...
Researchers from North Carolina State Univ. and the Univ. of Colorado, Boulder, have developed a statistical model that allows them to tell where a dust sample came from within the continental U.S. based on the DNA of fungi found in the sample.
Washington State Univ. mathematicians have designed an encryption code capable of fending off the phenomenal hacking power of a quantum computer. Using high-level number theory and cryptography, the researchers reworked an infamous old cipher called the knapsack code to create an online security system better prepared for future demands.
To humor mathematicians, picture a pile of sand grains in one square of a vast sheet of graph paper. If four or more grains occupy a single square, that square topples by sending one grain to each of its four neighboring squares. Keep zooming out so the squares become very small, and something strange happens: The sand still “remembers” that it used to live on a square lattice, and a distinctive pattern emerges.
When it comes to boiling water, is there anything left for today’s scientists to study? The surprising answer is, yes, quite a bit. How the bubbles form at a surface, how they rise up and join together, what are the surface properties, what happens if the temperature increases slowly versus quickly. While these components might be understood experimentally, the mathematical models for the process of boiling are incomplete.
A team of scientists has identified the complex process by which materials are shaped and ultimately dissolved by surrounding water currents. The study, conducted by researchers at New York Univ. (NYU)’s Courant Institute of Mathematical Sciences and Florida State Univ., appears in the Journal of Fluid Mechanics.
As a grape slowly dries and shrivels, its surface creases, ultimately taking on the wrinkled form of a raisin. Similar patterns can be found on the surfaces of other dried materials, as well as in human fingerprints. While these patterns have long been observed in nature, and more recently in experiments, scientists have not been able to come up with a way to predict how such patterns arise in curved systems, such as microlenses.
Optimization algorithms are everywhere in engineering. Among other things, they’re used to evaluate design tradeoffs, to assess control systems and to find patterns in data. One way to solve a difficult optimization problem is to first reduce it to a related but much simpler problem, then gradually add complexity back in, solving each new problem in turn and using its solution as a guide to solving the next one.
Massachusetts Institute of Technology researchers have discovered a new mathematical relationship—between material thickness, temperature and electrical resistance—that appears to hold in all superconductors. The result could shed light on the nature of superconductivity and could also lead to better-engineered superconducting circuits for applications like quantum computing and ultra-low-power computing.
Researchers have begun to describe theoretical limits on the degree of imprecision that communicating computers can tolerate, with very real implications for the design of communication protocols.
Researchers from the Queen Mary Univ. of London gave a computer program the outline of how a magic jigsaw puzzle and a mind-reading card trick work, as well the results of experiments into how humans understand magic tricks, and the system created completely new variants on those tricks which can be delivered by a magician.
From a mechanical perspective, granular materials are stuck between a rock and a fluid place, with behavior resembling neither a solid nor a liquid. Think of sand through an hourglass: As grains funnel through, they appear to flow like water, but once deposited, they form a relatively stable mound, much like a solid.
Scientists at Oak Ridge National Laboratory have made the first direct observations of a 1-D boundary separating two different, atom-thin materials, enabling studies of long-theorized phenomena at these interfaces. Theorists have predicted the existence of intriguing properties at 1-D boundaries between two crystalline components, but experimental verification has eluded researchers.
Most modern cryptographic schemes rely on computational complexity for their security. In principle, they can be cracked, but that would take a prohibitively long time, even with enormous computational resources. There is, however, another notion of security—information-theoretic security—which means that even an adversary with unbounded computational power could extract no useful information from an encrypted message.
A team led by Virginia Tech researchers studied cells found in breast and other types of connective tissue and discovered new information about cell transitions that take place during wound healing and cancer. They developed mathematical models to predict the dynamics of cell transitions, and by comparison gained new understanding of how a substance known as transforming growth factor triggers cell transformations.
What could the natural diversity and beauty of plant leaves have in common with the violin? Much more than you might imagine. Dan Chitwood of the Donald Danforth Plant Science Center in St. Louis is applying “morphometrics”, which statistically tests hypotheses about factors that affect shape, to changes in the shape of violins over time. His work revealed a strong degree of design transmission and imitation.
Metabolic networks are mathematical models of every possible sequence of chemical reactions available to an organ or organism, and they’re used to design microbes for manufacturing processes or to study disease. Based on both genetic analysis and empirical study, they can take years to assemble. Unfortunately, a new analytic tool suggests that many of those models may be wrong.
An improved theoretical model of photoabsorption of nitrous oxide, developed by scientists in Malaysia, could shed light on the atmospheric chemistry of ozone depletion. The new theoretical work unveils, through improvements in established calculation approaches, the actual dynamic of stratospheric catalytic ozone destruction.
Mathematicians from Brown Univ. have introduced a new element of uncertainty into an equation used to describe the behavior of fluid flows. Ironically, allowing uncertainty into a mathematical equation that models fluid flows makes the equation much more capable of correctly reflecting the natural world, including the formation, strength, and position of air masses and fronts in the atmosphere.
Univ. of California, Santa Barbara’s Paul Atzberger, a professor in the Department of Mathematics and in mechanical engineering, often works in areas where mathematics plays an ever more important role in the discovery and development of new ideas. Most recently he has developed new mathematical approaches to gain insights into how proteins move around within lipid bilayer membranes.
Mathematics might be able to reduce the need for invasive biopsies in patients suffering kidney damage related to the autoimmune disease lupus. In a new study, researchers developed a math model that can predict the progression from nephritis, or kidney inflammation, to interstitial fibrosis, scarring in the kidney that current treatments cannot reverse. A kidney biopsy is the only existing way to reach a definitive diagnosis.
Calculating the pros and cons of a potential decision is a way of decision-making. But repeated engagement with numbers-focused calculations, especially those involving money, can have unintended negative consequences, including social and moral transgressions, says new study. Several experiments supported these findings and pointed to a “calculative mindset” that can take precedence in reaching conclusions.
The central mystery of quantum mechanics is that small chunks of matter sometimes seem to behave like particles, sometimes like waves. The traditional view holds that a single particle really is a wave that collapses only when observed. But John Bush, of the Massachusetts Institute of Technology, believes that another explanation, the pilot-wave theory, deserves a second look.
Dr. John Carr, a scientist at the U.S. Naval Research Laboratory, is part of an international team that has found what they believe is evidence of a planet forming around a star about 335 light years from Earth. They made the chance discovery while studying the protoplanetary disk of gas around a distant forming star using a technique called spectro-astrometry, which allows astronomers to detect small changes in the position of moving gas.
Proofs are the key method of mathematics. Until now, it has mainly been humans who have verified whether proofs are correct. This could change, says Russian mathematician Vladimir Voevodsky, who points to evidence that, in the near future, computers rather than humans could reliably verify whether a mathematical proof is correct.
Researchers at the Univ. of Rochester have cleared up an apparent violation of quantum mechanics’ wave-particle duality that was announced in 2012 by a team of scientists in Germany. They replicated the experiment, which simultaneously determined a photon’s path and observed high contrast interference fringes created by the interaction of waves. But they also found an undiscovered source of bias sampling that explained the strange results.
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