Explore further Citation: Fabricating 3D Photonic Crystals (2009, January 21) retrieved 18 August 2019 from https://phys.org/news/2009-01-fabricating-3d-photonic-crystals.html (PhysOrg.com) — “In photonic crystals, the ability to control the structure of a material in full three dimensional space, allows you to control the way that light flows through it,” John Rogers tells PhysOrg.com. “This approach to photonic materials can be useful in applications ranging from communications to lasers to optical waveguides.” Rogers, a scientist at the University of Illinois at Urbana-Champaign, and his colleagues at the University of Illinois and a team from Sandia National Laboratories in Albuquerque, New Mexico, have developed a simple technique that allows for the fabrication of silicon photonic crystals in 3-D. Their process is described in Applied Physics Letters: “Three dimensional silicon photonic crystals fabricated by two photon phase mask lithography.”“Theoretical studies of idealized structures of this general type suggest their promise for manipulating of the flow of light through devices,” Rogers continues, “but from a practical standpoint, the fabrication has been difficult. Often, these crystals are patterned in a two dimensional plane defined by a silicon wafer. If you want something three dimensional, you stack them up to form a thin structure that has some level of 3D character. Unfortunately, with this method, you have more steps, making it more involved and expensive.”The team from the University of Illinois and Sandia decided to use phase mask lithography to create a full three dimensional silicon photonic crystal from the outset. Silicon is used because it has a high index of refraction, making it ideal for applications that make use of light. “The technique we’ve achieved is the culmination of six years of work as we tried to figure out how to optimize this process.”In order to create 3-D photonic crystals, the team used rubber optical elements and a specially prepared polymer. Using a laser, it is possible to create a pattern out of the polymer to define the crystal geometry of the crystal – a mold. Next, Rogers said, the three dimensional structure mold was used as a template. “We grew silicon on the polymer template, similar to what is done in two dimensions in the microelectronics industry.” Finally, the polymer template is burned away, leaving the silicon photonic crystal behind.“One of the key aspects of this fabrication process is that it is scalable,” Rogers says. “Not only are we facilitating patterning up front, but we’re also talking about a process that we can do over large areas, such as a square meter. In addition, it has the advantage of being adaptable to technology that already exists.”The ability to create silicon photonic crystals that are larger, using a process that is less expensive and elaborate than what is normally used, offers some potential for applications dealing with light. Rogers points out that this fabrication process would be useful for reflective (or even anti-reflective) coatings, creating optical diodes and even accomplishing high speed data routing. He even sees potential to adapt the process to work on a micro level, integrating these types of techniques with electronics. “There are a number of applications that could benefit from this fabrication process, since it offers high quality, low-cost photonic crystals.”More information: Shir, D., et. al. “Three dimensional silicon photonic crystals fabricated by two photon phase mask lithography.” Applied Physics Letters (2009). Available online: link.aip.org/link/?APPLAB/94/011101/1 . Copyright 2007 PhysOrg.com. All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com. 2-D crystals conforming to 3-D curves create strain for engineering quantum devices This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.
“The Dirac monopole is conceptually the simplest model for a magnetic point charge (i.e. a magnetic monopole) and this makes the Dirac monopole important,” Pietilä said. “Monopoles in general can be any point-like defects in a three-component vector field defined in three spatial dimensions, but they are not necessarily associated with a singular filament (the Dirac string).”Through modeling, Pietilä and Möttönen theoretically demonstrate that the Dirac string can be split into two parts by modifying the external magnetic field, which breaks the rotation symmetry of the system. In this case, state-of-the-art experimental methods that measure changes in particle density and spin density could be used to detect a signature of the monopole. In addition, in spin-1 BEC, the spin texture is topologically unstable, allowing it to be removed. Through simulations, the scientists show that removing the monopole could be done by turning off the external magnetic fields. The monopole “unwinds” itself along the Dirac string and leaves behind a closed vortex ring. The speed of the unwinding depends on how quickly or gradually the magnetic field is turned off.The existence of magnetic monopoles has far-reaching implications for many research areas, including the laws of quantum mechanics, theories of elementary particles, and cosmology. Experimentally confirming the existence of monopoles would provide long-sought evidence for some ideas, and possibly open up the doors to other new ones.“The existence of magnetic monopoles implies that the electric charge has to be quantized (that is, it can only appear as an integral multiple of the elementary charge),” Pietilä said. “Existence of magnetic monopoles has also certain cosmological implications. Since monopoles in general are related to the spontaneous symmetry breaking, they impact the unified theories describing the interactions between the elementary particles. In the context of condensed matter physics, monopoles typically arise as a manifestation of some exotic collective behavior of matter and can be used to explain the unusual characteristics of such systems.”More information: Ville Pietilä and Mikko Möttönen. “Creation of Dirac Monopoles in Spinor Bose-Einstein Condensates.” Physical Review Letters 103, 030401 (2009). link.aps.org/doi/10.1103/PhysRevLett.103.030401Copyright 2009 PhysOrg.com. All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com. This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. (PhysOrg.com) — For decades, scientists have been intrigued by the hypothetical existence of magnetic monopoles – particles with only a north or south magnetic pole, thus having a nonzero magnetic charge. But while modern theories predict their existence, monopoles have not yet been experimentally observed, despite numerous attempts. Recently, physicists have introduced a new method to create analogies to magnetic monopoles, and predict that they could be observed with current technology. Possible configurations for the spin texture of a Bose-Einstein condensate. These defects give rise to a vorticity field that is equivalent to the magnetic field of a magnetic monopole. Credit: Pietilä and Möttönen. Explore further Citation: Physicists Propose a Method to Observe Dirac Monopoles (2009, July 28) retrieved 18 August 2019 from https://phys.org/news/2009-07-physicists-method-dirac-monopoles.html Ville Pietilä and Mikko Möttönen, both of the Helsinki University of Technology in Finland and the University of New South Wales in Australia, have published their theoretical demonstration in a recent issue of Physical Review Letters. Here, they explain how applying an external magnetic field to a Bose-Einstein condensate (BEC) – a large group of cold atoms that exhibits coherent quantum properties – can create point-like topological defects on the spin texture of the BEC. These defects give rise to a vorticity field that is essentially equivalent to the magnetic field of a magnetic monopole.“Since all experimental attempts to find magnetic monopoles have proven to be futile, there is no experimental evidence supporting the existence of magnetic monopoles,” Pietilä told PhysOrg.com. “Other types of monopoles without the Dirac string have been realized in experiments already in the early ‘90s in liquid crystals. An analogy of the real space magnetic monopole was reported to occur in the crystal momentum space of a metallic ferromagnet, but the experimental evidence in this case is somewhat indirect. Dirac monopoles in the more general settings are predicted to occur in various systems such as superfluid Helium-3 and dilute spin-1 Bose-Einstein condensate but so far there are no (direct) experimental observations although they may have been present in some of the Helium-3 experiments. There is also a very recent suggestion on how to induce a magnetic monopole to a band insulator.“Since magnetic monopoles have never been observed, it is pertinent to ask whether there is something unphysical in the whole concept,” he continued. “Our work shows that at least the Dirac monopole can be realized experimentally, thus indicating that it is more than just a theoretical curiosity. However, it should be stressed that our work does not tell anything about the existence of magnetic monopoles in the electromagnetic field.”Pietilä and Möttönen predict that it should be possible to design an experiment to detect the monopole in this situation, if it does exist. As they explain, the magnetic field of the monopole is provided by a Dirac string, which is a line extending from the monopole to infinity. The Dirac string explains why the monopole charge comes in discrete quanta. Since the Dirac string carries two quanta of angular momentum, it is expected to be prone to splitting into two separate strings, each carrying a single quantum. Making magnetic monopoles, and other exotica, in the lab
Explore further Citation: Intel’s Atom CE 4100 SoC Will Transform Internet TV (w/ Video) (2009, September 25) retrieved 18 August 2019 from https://phys.org/news/2009-09-intel-atom-ce-soc-internet.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. Dell Talking About 80-Core Chip Processor The new Atom processor is part of Intel’s new family of media processors. Formerly codenamed “Sodaville,” the new chip is the first 45nm-based System-on-Chip to be designed on Intel’s architecture.The CE4100 replaces Intel’s former CE 3100 processor which is an older Pentium core processor. Intel’s newest Atom processor core is expected to reach speeds of about 1.2GHz and offer support for a range of industry standards. Intel is also teaming up with Adobe to provide support for the Adobe Flash Player 10 on Intel’s family of CE media processors. The new CE4100 SoC also provides MPEG-4 support, 3D graphics capability, high-end audio and can also capture uncompressed 1080p video. (PhysOrg.com) — At the IDF event, in Santa Clara, California, Intel announced the debut of their newest System-on-Chip (SoC), the Intel Atom processor CE4100. The CE4100 SoC is designed exclusively to facilitate Internet content and other services to digital TVs, Blu-ray players and other entertainment devices. At the IDF event, in Santa Clara, California, Intel’s Eric Kim (Sr. VP of Intel Corporation’s Digital Home Group) commented: “The architecture of Intel media processors provides a powerful and innovative platform to showcase Flash-based applications in a vivid way. Flash Player 10 combined with the performance of the Intel media processor and its support for standards such as OpenGL ES 2.0 offers a compelling environment for Flash-based games, videos and other rich Web content and applications.”The chip also features an integrated NAND controller, along with support for DDR2 and DDR3 memory, which will provide a choice to developers of digital TVs and set-top boxes. It is not certain when the Atom CE4100-based devices will reach the market, however Intel has promised some hardware demos from its partners.© 2009 PhysOrg.com
Explore further More information: Patent: appft1.uspto.gov/netacgi/nph-P … 45&RS=DN/20120188245AbstractThere are provided apparatuses and methods for increasing the pixel density of a digital display through mechanical actuation. In some embodiments, a display device is described having a processor configured to provide an image for display and a memory coupled to the processor. The memory stores the image and is configured to map the image to a pixel matrix. A display controller is coupled to the memory and configured to sample portions of the image and to store the portions of the image into planes. Each sampled portion comprises a different set of pixels of the pixel matrix. A display is coupled to the display controller and is configured to display the contents of the sampled planes. In particular, the display controller is configured to sequentially provide the sampled planes to the display for sequential display. At least one actuator is coupled to the display to displace the display for the displaying of the sampled planes, so that pixels of each plane are displayed in a unique location from the pixels of other planes.via: www.patentlyapple.com/patently … e-video-glasses.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. © 2012 Phys.org Citation: Apple bowl-headed patent shows wearable computing plans (2012, July 29) retrieved 18 August 2019 from https://phys.org/news/2012-07-apple-bowl-headed-patent-wearable.html (Phys.org) — Like Google, Apple has plans to win recognition as wearable computing leaders. Patently Apple reports on a patent that was filed by Apple in January last year but made known earlier this week. The patent application is causing a stir over what Apple has in mind to compete with Google over the latter’s highly anticipated Project Glass heads-up display. The Apple patent in question, titled “Display resolution increase with mechanical actuation,” speaks of multiple “embodiments,” but the concept appears to relate to raising the quality of a display placed over a wearer’s eye. The patent drawings show a very odd-looking bowl over a person’s head extending out to eyewear over just one eye. The implication beyond the obtuse patent text is clear that Apple is fixed on competing with Google for the coming generation of heads-up display wearers, and, in competing, is to use its key ammunition, its own brand recognition that Apple provides high quality visuals whether on its desktop, tablet, phone or, now possibly, on video glasses. The inventor is listed on the patent application as Edward Craig Hyatt.Those bloggers watching Apple and writing about the patent news agree that the text is obtuse, ambitiously general, and hard to pin down, as a patent application for ideas that could take any form of multiple “embodiments.” Nonetheless, it can be said that the goal of Apple seems to be to improve the resolution of images seen through a head-mounted display.According to the patent application, “There are provided apparatuses and methods for increasing the pixel density of a digital display through mechanical actuation. In some embodiments, a display device is described having a processor configured to provide an image for display and a memory coupled to the processor. The memory stores the image and is configured to map the image to a pixel matrix. A display controller is coupled to the memory and configured to sample portions of the image and to store the portions of the image into planes. Each sampled portion comprises a different set of pixels of the pixel matrix. A display is coupled to the display controller and is configured to display the contents of the sampled planes. In particular, the display controller is configured to sequentially provide the sampled planes to the display for sequential display. At least one actuator is coupled to the display to displace the display for the displaying of the sampled planes, so that pixels of each plane are displayed in a unique location from the pixels of other planes.” Google patent sends ring signals to Project Glass
Explore further More information: The gravity tunnel in a non-uniform Earth, Am. J. Phys. 83, 231 (2015); dx.doi.org/10.1119/1.4898780 . On Arxiv: arxiv.org/abs/1308.1342AbstractThis paper examines the gravity tunnel using the internal structure of Earth as ascertained from seismic data. Numerically, it is found that the time taken to fall along the diameter is 38 min, compared to 42 min for a planet with uniform density. The time taken to fall along a straight line between any two points is no longer independent of distance but interpolates between 42 min for short trips and 38 min for long trips. The brachistochrone path (minimizing the time between any two points) is similar in shape to the uniform-density solution but tends to reach a greater maximum depth and takes less time to traverse. Although the assumption of uniform density works well in many cases, the simpler assumption of a constant gravitational field serves as a better approximation to the true results. Are astronauts really weightless? A composite image of the Western hemisphere of the Earth. Credit: NASA (Phys.org)—Alexander Klotz a student at McGill University in Canada has calculated a new answer to the commonly asked physics question, how long would it take a person to fall all the way through the Earth? Instead of the commonly accepted 42 minutes, he claims it is 38. He has published his reasoning, math and conclusions in a paper published in The American Journal of Physics. © 2015 Phys.org Journal information: American Journal of Physics If someone were to drill a hole all the way through the planet, and then somehow manage to fall into it, how long would it take them to arrive on the other side? That is a physics question put to students every year, and those who give it expect the answer to be 42 minutes. But is that answer correct? Klotz says no and has the math to prove it, Science reported.The accepted answer of 42 minutes takes into account the constantly changing impact that gravity will have (and ignoring drag due to the presence of air) on the person falling, becoming less and less of a factor as the center of the Earth is approached then growing stronger and stronger as the person heads “up” against gravity on the other side. It is accepted that the speed attained during the descent on the first half of the journey would be significant enough to cause the person to continue moving against gravity on the other side of the planet, right up until the surface is reached.But Klotz argues that it is time to start taking the different densities of the Earth’s layers into consideration—after all, a lot of research has shown that our planet is a lot denser at the center than at the crust for example—and that of course would have an impact on the person falling through. He has used seismic data to calculate the different densities at different depths and has used that data to give a more accurate answer to the falling man question, stating that it would in fact, take just 38 minutes (and 11 seconds) to fall all the way through, not 42 and (12 seconds).Interestingly, Klotz also notes that if gravity were to be assumed to be at a surface level constant throughout the duration of the trip, the math shows it would take just 38 minutes as well. , Science , arXiv Citation: New way to calculate how long it would take to fall through a hole in the Earth (2015, March 26) retrieved 18 August 2019 from https://phys.org/news/2015-03-fall-hole-earth.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.
This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. Citation: Best of Last Week –A radiationless revolution, progress towards a fusion reactor and neuroticism’s link to over-thinking (2015, August 31) retrieved 18 August 2019 from https://phys.org/news/2015-08-week-radiationless-revolution-fusion-reactor.html © 2015 Phys.org Explore further Tri Alpha Energy reportedly makes important breakthrough in developing fusion reactor (Phys.org)—It has been another good week for physics as a team working at the CERN complex found evidence that suggests subatomic particles could defy the standard model—they found tau leptons and muons decaying at different rates. Also, another team at the Australian National University announced a new theory that could lead to a radiationless revolution—it describes a way to confine electromagnetic energy without leakage. And Matthew Fisher with the University of California proposed the idea of quantum cognition based on synaptic nuclear spins, i.e. neural qubits. His idea is that quantum processing with nuclear spins might be happening in the brain. Also, a company called Tri Alpha Energy reportedly made an important breakthrough in developing a fusion reactor—they found a way to hold a ball of superheated hydrogen plasma for five milliseconds. The news from space was good as well, as NASA announced that the New Horizons mission exceeded expectations—sending back images of Pluto and its moons along with a host of other valuable scientific data. Also, another team of astrophysicists found supermassive black holes in the quasar nearest Earth—within Galaxy Markarian 231, they discovered has two black holes spinning around each other.In other news, researchers working at Los Alamos National Laboratory announced that they had created quantum dot solar windows that go non-toxic and colorless, all with record efficiency—the windows capture some of the light that passes through the glass and divert it to solar cells at the edges. And a team of researchers at the University of Toronto announced that they had developed a new “tissue Velcro” that could help repair damaged hearts—it is a scaffolding upon which new heart muscle can grow. Also, another team working at MIT created a new printer called “Multifab” that 3D-prints a record 10 materials at once with no assembly required. It has a resolution of 40 microns and is the first 3D printer to use 3D scanning techniques from machine vision.And finally, if you have ever been accused of being neurotic, a small team of psychologists with King’s College in London and Columbia University in the U.S. asked the question: Is neuroticism fueled by overthinking? And they think they have found why creativity and neurosis-related unhappiness and go hand-in-hand—the same parts of the brain appear to be involved in both. In this event display from the LHCb experiment at CERN’s Large Hadron Collider, proton-proton collisions at the interaction point (far left) result in a shower of leptons and other charged particles. The yellow and green lines are computer-generated reconstructions of the particles’ trajectories through the layers of the LHCb detector. Credit: CERN/LHCb Collaboration
Explore further More information: A comprehensive phylogeny of birds (Aves) using targeted next-generation DNA sequencing, Nature (2015) DOI: 10.1038/nature15697AbstractAlthough reconstruction of the phylogeny of living birds has progressed tremendously in the last decade, the evolutionary history of Neoaves—a clade that encompasses nearly all living bird species—remains the greatest unresolved challenge in dinosaur systematics. Here we investigate avian phylogeny with an unprecedented scale of data: >390,000 bases of genomic sequence data from each of 198 species of living birds, representing all major avian lineages, and two crocodilian outgroups. Sequence data were collected using anchored hybrid enrichment, yielding 259 nuclear loci with an average length of 1,523 bases for a total data set of over 7.8 × 107 bases. Bayesian and maximum likelihood analyses yielded highly supported and nearly identical phylogenetic trees for all major avian lineages. Five major clades form successive sister groups to the rest of Neoaves: (1) a clade including nightjars, other caprimulgiforms, swifts, and hummingbirds; (2) a clade uniting cuckoos, bustards, and turacos with pigeons, mesites, and sandgrouse; (3) cranes and their relatives; (4) a comprehensive waterbird clade, including all diving, wading, and shorebirds; and (5) a comprehensive landbird clade with the enigmatic hoatzin (Opisthocomus hoazin) as the sister group to the rest. Neither of the two main, recently proposed Neoavian clades—Columbea and Passerea1—were supported as monophyletic. The results of our divergence time analyses are congruent with the palaeontological record, supporting a major radiation of crown birds in the wake of the Cretaceous–Palaeogene (K–Pg) mass extinction. Citation: Group builds most comprehensive family tree of birds to date (2015, October 8) retrieved 18 August 2019 from https://phys.org/news/2015-10-group-comprehensive-family-tree-birds.html Building a family tree for modern birds has been difficult for scientists because of the dearth of fossil evidence going past 66 million years—the time before the mass extinction that wiped out the other dinosaurs. After the extinction, bird species evolved so rapidly that it has been difficult to use traditional genomic techniques to follow the paths of the evolution of new species, which in turn has made it almost impossible to create an accurate tree. To overcome such problems the researchers with this latest effort used a different type of genomic sequencing technique—it is called anchored hybrid enrichment and allows for sampling parts of the genome that evolved both slowly and more quickly in the flanking regions.In all the team collected and tested samples from 198 bird species (which included 390,000 bases of genomic sequence data) that together represented approximately 90 percent of all known birds—a group known collectively as Neoaves. In looking at the data they retrieved, the team found that virtually all birds (excluding flightless and some chickens and ducks) could be grouped into five sub-groups, i.e. major clads. They also found evidence that suggested that all modern birds likely evolved from a single ancestor, one that lived approximately 75 million years ago, or ten million years before all the other dinosaurs went extinct—birds in general are believed to have evolved from the dinosaur family, developing feathers approximately 150 million years ago.In addition, the researchers claim their results show (and agree with paleontology records) that there was a major radiation event following the mass extinction. Dinosaur family tree gives fresh insight into rapid rise of birds (Phys.org)—A team of researchers from several institutions in the U.S. has created the most comprehensive family tree of birds to date. In their paper published in the journal Nature the team describes the genomic sequencing technique they used and the structure of the tree they created. Gavin Thomas with the University of Sheffield, in the U.K. offers a News & Views piece on the work done by the team in the same issue, highlighting differences in phylogeny between this newer work and that conducted by another team last year. House finchnigel. Credit: Wikimedia Commons © 2015 Phys.org Journal information: Nature This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.
More information: Dhagash Mehta et al. “Kinetic Transition Networks for the Thomson Problem and Smale’s Seventh Problem.” Physical Review Letters. DOI: 10.1103/PhysRevLett.117.028301 , Also at arXiv:1605.08459 [cond-mat.soft] This puzzle is the essence of Thomson’s problem, which asks how to arrange equal charges (such as electrons) on the surface of a sphere in a way that minimizes their electrostatic potential energy—the energy caused by all of the electrons repelling each other. According to Coulomb’s law, the total energy is inversely related to the sum of the distances between all possible pairs of charges, so the goal is to spread the charges as far apart as possible.This task is more difficult than it sounds—Thomson’s problem has been rigorously solved only for numbers of 2, 3, 4, 6, and 12 charges. In 1998, mathematician Steven Smale identified the problem of how to choose starting points close to the lowest-energy state (which makes it easier to solve Thomson’s problem) as the seventh problem on his list of 18 unsolved problems for the 21st century. Part of the reason why Thomson’s problem is so important is because its applications are so far-reaching. In 1904, J.J. Thomson originally proposed the model of charges on a sphere to describe the structure of an atom. Even though experiments disproved this “plum pudding model” long ago, the Thomson problem still has notable applications in chemistry (for understanding how electrons fill electron shells in atoms), biology (for determining the arrangements of proteins on the shells of spherical viruses), as well as in physics, computer science, and such practical applications as determining the optimal placement of communication satellites around the Earth. Spheres on treesNow in a new paper published in Physical Review Letters, a team of mathematicians, engineers, and scientists from the US, the UK, and Australia has taken a new approach to Thomson’s problem that makes it much easier to determine the lowest-energy configuration. For seven numbers of charges (every third number from 132 to 150), they have constructed tree-shaped disconnectivity graphs, where the vertical axis or “trunk” corresponds to the energy of a particular charge arrangement. Each “branch” terminates at a local minimum, which are the states that have lower energies than all of their neighboring states, and so they are candidates for the ultimate lowest energy state, the global minimum. By visualizing the problem in this way, the researchers noticed that these particular graphs don’t have lots of branches extending from lots of other branches. Instead, every branch connects to only a few other branches and then to the trunk at regularly spaced energy thresholds, so that the graph resembles a palm tree or single funnel structure.The researchers found that this “funneled potential energy landscape” is characteristic of a highly ordered structure and displays characteristics of a small-world network. As a result, it provides an important clue for finding the global minimum. It tells the researchers to start their optimization algorithms using the local minima because, in these networks, it turns out that every local minimum is always within 5-7 steps (branches) of the global minimum. This is true even for local minima that have much higher energies than the global minimum, and even when the total number of local minima is very large. (Phys.org)—How do you arrange a group of points on the surface of a sphere so that all the points are as far apart from each other as possible? With two points, the answer is easy: place them on opposite sides of the sphere, as if they are endpoints of the diameter. With three points, make them the vertices of an equilateral triangle, and so on. But as the number of points increases, so does the difficulty of the problem. By visualizing the problem from a new perspective, the researchers found that lower-energy configurations have more connections than higher-energy configurations do. Credit: Mehta et al. ©2016 American Physical Society Journal information: Physical Review Letters This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only. Spin glass physics with trapped ions © 2016 Phys.org The disconnectivity graph for 147 charges on a sphere has a structure-seeking “palm tree” organization. The five lowest minimum energy configurations are shown. Credit: Mehta et al. ©2016 American Physical Society Citation: Researchers chip away at Smale’s 7th unsolved problem in mathematics (2016, July 15) retrieved 18 August 2019 from https://phys.org/news/2016-07-chip-smale-7th-unsolved-problem.html The disconnectivity graph reveals other information, such as that lower-energy local minima have more connections to other states than do higher-energy local minima. The researchers also discovered that the global minimum is always the most highly connected node in the entire network, making it the network’s central node. Implications for Thomson’s and Smale’s problemsUsing this insight from the network’s single-funneled, small-world structure, finding the global minimum for Thomson’s problem becomes much easier than before.”Our work looks at Smale’s seventh problem from a completely different perspective and sheds novel light on it,” coauthor Dhagash Mehta, at the University of Notre Dame and the University of Adelaide, told Phys.org. “In this work, methods developed by the theoretical chemistry community have helped understand a deep mathematical problem. Often it is the other way around.”As the researchers explain, it’s easier to solve Thomson’s problem in these particular cases than it is to solve Smale’s problem (of choosing good starting points). So although the results will likely be useful, they do not go very far toward solving Smale’s seventh problem.”I think ‘chip away’ is about right,” said coauthor David Wales at University Chemical Laboratories in Cambridge, UK. “There is no rigorous mathematical progress on the problem from an analytic point of view.”In the future, the researchers plan to extend this approach to larger numbers of charges. From earlier work, they expect that landscapes with more than 400 charges will start to display multiple funnels, so the small-world structure may disappear. “While we have only shown data for seven numbers, we have strong reasons to believe that the single funnel is a feature for numbers less than 150,” said coauthor Halim Kusumaatmaja at Durham University in Durham, UK. “For larger numbers, there will likely be multiple funnels. Nonetheless, the network analysis could still be exploited to help us quickly identify candidates for the global minimum.”Other lines of work include exploiting the small-world properties discovered here to improve other optimization algorithms and develop novel algorithms, as well as to incorporate weight and direction into these networks, which may provide additional insight into the Thomson problem.”The social network analogy for networks of minima of the Thomson problem will go further when we analyze other network properties of these networks of minima,” Mehta said. “Our results will also help in constructing novel algorithms to find the global minimum more efficiently by exploiting these network properties.” Explore further
Upgraded to an international crafts fair, the Surajkund Crafts Mela will be inaugurated by President Pranab Mukherjee on Saturday in Haryana’s Faridabad district in the National Capital Region. Surajkund has, since its inception, been quite a favourite with Delhiites. Assam will be the flavour of the fair this year. Nearly 20 countries, including SAARC (South Asian Association for Regional Cooperation) members, have confirmed their participation in the 27th edition of the fair, a state government spokesman said. Also Read – ‘Playing Jojo was emotionally exhausting’As many as 300 crafts persons, weavers, artisans, folk musicians and dancers would participate from the theme state of Karnataka, he pointed out. ‘Keeping in view the record participation of 12 countries in the last year’s mela, it has now been upgraded as International Crafts Mela. This year also, the countries that have confirmed their participation are Rwanda, Guinea, Tunisia, South Africa, Namibia, Zambia, Ethiopia, Congo and Egypt from the African continent. Also Read – Leslie doing new comedy special with Netflix‘Eurasian countries namely Turkmenistan, Kyrgyzstan and Tajikistan and SAARC nations Sri Lanka, Afghanistan, Bhutan, Bangladesh, Nepal and Pakistan would participate. Thailand and Peru would also participate,’ he added.Surajkund Mela Authority will provide 50 per cent rebate in the entry tickets to the disabled, senior citizens, serving soldiers and ex-servicemen. Freedom fighters will have free entry to the fair.The fortnight-long fair showcases traditional crafts from all over India and leading artisans.Surajkund derives its name from the ancient amphitheatre sun pool constructed here in the 10th century AD by Raja Suraj Pal, one of the Tomar chieftains, in the Aravalli mountain range.DETAILAt: Surajkund Mela Grounds, Faridabad When: 1-15 FebruaryTimings: 9.30 am to 7.30 pm
She has crooned soft numbers in the