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Archive for the ‘mathematics’ category: Page 9

Sep 2, 2019

Introduction to Supersymmetry

Posted by in categories: information science, mathematics, particle physics, quantum physics

20th century physics has seen two major paradigm shifts in the way we understand Mother Nature. One is quantum mechanics, and the other is relativity. The marriage between the two, called quantum field theory, conceived an enfant terrible, namely anti-matter. As a result, the number of elementary particles doubled. We believe that 21st century physics is aimed at yet another level of marriage, this time between quantum mechanics and general relativity, Einstein’s theory of gravity. The couple has not been getting along very well, resulting in mathematical inconsistencies, meaningless infinities, and negative probabilities. The key to success may be in supersymmetry, which doubles the number of particles once more.

Why was anti-matter needed? One reason was to solve a crisis in the 19th century physics of classical electromagnetism. An electron is, to the best of our knowledge, a point particle. Namely, it has no size, yet an electric charge. A charged particle inevitably produces an electric potential around it, and it also feels the potential created by itself. This leads to an infinite “self-energy” of the electron. In other words, it takes substantial energy to “pack” all the charge of an electron into small size.

On the other hand, Einstein’s famous equation says that mass of a particle determines the energy of the particle at rest. For an electron, its rest energy is known to be 0.511 MeV. For this given amount of energy, it cannot afford to “pack” itself into a size smaller than the size of a nucleus. Classical theory of electromagnetism is not a consistent theory below this distance. However, it is known that the electron is at least ten thousand times smaller than that.

Sep 2, 2019

Theory: M-theory is a theory in physics that unifies all consistent versions of superstring theory

Posted by in categories: mathematics, quantum physics

M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at a string theory conference at the University of Southern California in the Spring of 1995. Witten’s announcement initiated a flurry of research activity known as the second superstring revolution.

Prior to Witten’s announcement, string theorists had identified five versions of superstring theory. Although these theories appeared, at first, to be very different, work by several physicists showed that the theories were related in intricate and nontrivial ways. In particular, physicists found that apparently distinct theories could be unified by mathematical transformations called S–duality and T–duality. Witten’s conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity.

Although a complete formulation of M-theory is not known, the theory should describe two- and five-dimensional objects called branes and should be approximated by eleven-dimensional supergravity at low energies. Modern attempts to formulate M-theory are typically based on matrix theory or the AdS/CFT correspondence.

Aug 30, 2019

Science Mystery: Amazing Facts About The Golden Ratio You Have To Know

Posted by in categories: mathematics, science, space

The famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the Universe. Science amazing science cool stuff science weird science cool nature science cool stuff.

We’ve talked about the Fibonacci series and the Golden ratio before, but it’s worth a quick review. The Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on forever. Each number is the sum of the two numbers that precede it. It’s a simple pattern, but it appears to be a kind of built-in numbering system to the cosmos. Here are 15 astounding examples of phi in nature. Science amazing science cool stuff science weird science cool nature science cool stuff.

science golden ratio

Aug 23, 2019

New Technique Streamlines Design of Intricate Fusion Devices

Posted by in categories: habitats, mathematics, nuclear energy, space

O.o.


Stellarators, twisty machines that house fusion reactions, rely on complex magnetic coils that are challenging to design and build. Now, a physicist at the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory ( PPPL ) has developed a mathematical technique to help simplify the design of the coils, making stellarators a potentially more cost-effective facility for producing fusion energy.

“Our main result is that we came up with a new method of identifying the irregular magnetic fields produced by stellarator coils,” said physicist Caoxiang Zhu, lead author of a paper reporting the results in Nuclear Fusion. “This technique can let you know in advance which coil shapes and placements could harm the plasma ’s magnetic confinement, promising a shorter construction time and reduced costs.”

Continue reading “New Technique Streamlines Design of Intricate Fusion Devices” »

Aug 23, 2019

Gene editing turns cells into minicomputers that can record data

Posted by in categories: bioengineering, biotech/medical, computing, mathematics

Gene editing can turn living cells into minicomputers that can read, write and perform complex calculations. The technology could track what happens inside the body over time.

DNA computers have been around since the 1990s, when researchers created DNA molecules able to perform basic mathematical functions. Instead of storing information as 0s and 1s like digital computers do, these computers store information in the molecules A, C, G and T that make up DNA.

Aug 23, 2019

Smaller, cheaper, sharper lenses should be possible as Mexican scientist solves aberration problem

Posted by in categories: information science, mathematics

One of the oldest problems in optics has been solved. Rafael Gonzalez from Mexico’s Tecnologico de Monterrey has come up with an almost comically dense equation that can be used to almost completely eliminate spherical aberration in optical lenses, and the effects could be widespread.

Camera lenses are insanely complex and extraordinarily precise devices, and one of the reasons for this is spherical aberration. This is distinct from chromatic aberration, or color fringing, which you get when a lens is unable to focus light from all parts of the visual color spectrum together. Spherical aberration is what causes some lenses to be sharp in the middle, but blurrier toward the outside edges.

Lens manufacturers have for years been building aspherical lenses to try to counteract this effect, modifying the sphere shape slightly to try to sharpen up the whole image. By and large, many have done a great job, as evidenced by the general optical sharpness of today’s lenses. But rather than working to a precise mathematical formula that works to correct all spherical lens aberration, lens companies have had to work on each lens as a separate problem, finding solutions that worked, more or less, but forcing them to start over each time.

Aug 22, 2019

Giving Mars a Magnetosphere

Posted by in categories: biological, engineering, environmental, mathematics, space, sustainability

Any future colonization efforts directed at the Mars all share one problem in common; their reliance on a non-existent magnetic field. Mars’ magnetosphere went dark about 4 billion years ago when it’s core solidified due to its inability to retain heat because of its small mass. We now know that Mars was quite Earth-like in its history. Deep oceans once filled the now arid Martian valleys and a thick atmosphere once retained gasses which may have allowed for the development of simple life. This was all shielded by Mars’ prehistoric magnetic field.

When Mars’ magnetic line of defense fell, much of its atmosphere was ripped away into space, its oceans froze deep into the red regolith, and any chance for life to thrive there was suffocated. The reduction of greenhouse gasses caused Mars’ temperature to plummet, freezing any remaining atmosphere to the poles. Today, Mars is all but dead. Without a magnetic field, a lethal array of charged particles from the Sun bombards Mars’ surface every day threatening the potential of hosting electronic systems as well as biological life. The lack of a magnetic field also makes it impossible for Mars to retain an atmosphere or an ozone layer, which are detrimental in filtering out UV and high energy light. This would seem to make the basic principles behind terraforming the planet completely obsolete.

I’ve read a lot of articles about the potential of supplying Mars with an artificial magnetic field. By placing a satellite equipped with technology to produce a powerful magnetic field at Mars L1 (a far orbit around Mars where gravity from the Sun balances gravity from Mars, so that the satellite always remains between Mars and the Sun), we could encompass Mars in the resulting magnetic sheath. However, even though the idea is well understood and written about, I couldn’t find a solid mathematical proof of the concept to study for actual feasibility. So I made one!

Aug 21, 2019

New technique could streamline design of intricate fusion device

Posted by in categories: habitats, mathematics, nuclear energy, space

Stellarators, twisty machines that house fusion reactions, rely on complex magnetic coils that are challenging to design and build. Now, a physicist at the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory (PPPL) has developed a mathematical technique to help simplify the design of the coils, making stellarators a potentially more cost-effective facility for producing fusion energy.

“Our main result is that we came up with a new method of identifying the irregular magnetic fields produced by coils,” said physicist Caoxiang Zhu, lead author of a paper reporting the results in Nuclear Fusion. “This technique can let you know in advance which coil shapes and placements could harm the plasma’s magnetic confinement, promising a shorter construction time and reduced costs.”

Fusion, the power that drives the sun and stars, is the fusing of light elements in the form of plasma—the hot, charged state of matter composed of free electrons and atomic nuclei—that generates massive amounts of energy. Twisty, cruller-shaped stellarators are an alternative to doughnut-shaped tokamaks that are more commonly used by scientists seeking to replicate on Earth for a virtually inexhaustible supply of power to generate electricity.

Aug 21, 2019

Mathematical framework turns any sheet of material into any shape using kirigami cuts

Posted by in categories: biological, information science, mathematics, physics, transportation

This could lead to self-healing cars.


Researchers from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have developed a mathematical framework that can turn any sheet of material into any prescribed shape, inspired by the paper craft termed kirigami (from the Japanese, kiri, meaning to cut and kami, meaning paper).

Unlike its better-known cousin origami, which uses folds to shape , kirigami relies on a pattern of cuts in a flat paper sheet to change its flexibility and allow it to morph into 3D shapes. Artists have long used this artform to create everything from pop-up cards to castles and dragons.

Continue reading “Mathematical framework turns any sheet of material into any shape using kirigami cuts” »

Aug 17, 2019

Physicists solve 2,000-year-old optical problem

Posted by in categories: mathematics, physics, robotics/AI

A trio of physicists from the National Autonomous University of Mexico and Tec de Monterrey has solved a 2,000-year-old optical problem—the Wasserman-Wolf problem. In their paper published in the journal Applied Optics, Rafael González-Acuña, Héctor Chaparro-Romo, and Julio Gutiérrez-Vega outline the math involved in solving the puzzle, give some examples of possible applications, and describe the efficiency of the results when tested.

Over 2,000 years ago, Greek scientist Diocles recognized a problem with —when looking through devices equipped with them, the edges appeared fuzzier than the center. In his writings, he proposed that the effect occurs because the lenses were spherical—light striking at an angle could not be focused because of differences in refraction. Isaac Newton was reportedly stumped in his efforts to solve the problem (which became known as ), as was Gottfried Leibniz.

In 1949, Wasserman and Wolf devised an analytical means for describing the problem, and gave it an official name—the Wasserman-Wolf problem. They suggested that the to solving the problem would be to use two aspheric adjacent surfaces to correct aberrations. Since that time, researchers and engineers have come up with a variety of ways to fix the problem in specific applications—most particularly cameras and telescopes. Most such efforts have involved creating aspherical lenses to counteract refraction problems. And while they have resulted in improvement, the solutions have generally been expensive and inadequate for some applications.

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