Image may be NSFW.
Clik here to view.
From The California Institute of Technology
5.28.24
Materials scientists and engineers would like to know precisely how electrons interact and move in new materials and how the devices made with them will behave. Will the electrical current flow easily within the material? Is there a temperature at which the material will become superconducting, enabling current to flow without a power source? How long will the quantum state of an electron spin be preserved in new electronic and quantum devices? A community of materials physicists attempt to address such questions by understanding what takes place inside materials, calculating their behavior down to the level of individual electron interactions and atomic motions.
Now a Caltech team has made a key discovery that helps simplify such calculations, speeding them up by a factor of 50 or more while maintaining accuracy. As a result, it is possible to compute electron interactions in more complex materials and devices as well as to develop new calculations that were previously thought impossible.
Image may be NSFW.
Clik here to view.
To understand the SVD method the Caltech team used, suppose you wanted to compress an image of Albert Einstein. This well-known photograph could be represented as a matrix. At each x and y coordinate, you could assign a value—that is, a number—that describes the gray scale of that pixel, perhaps 1 for white, 5 for medium gray, and 10 for black. SVD compresses the matrix by then providing singular values that describe both the color value and how important each pixel is with relation to certain features. In this case, perhaps it would give more importance or weight to pixels related to the outline of the face, hair, eyes, nose, and shoulders, for example. When the program keeps only 10 percent of those singular values from the original image, you can still make out that this is the well-known photo of Feynman. Even when only 1 percent of the singular values are kept, there is still a resemblance to the original image. Surprisingly, such a 1 percent level of compression is sufficient to reconstruct electron interactions in materials with high accuracy.
Image may be NSFW.
Clik here to view.
The SVD method gives researchers a “physical intuition” about electron interactions in a material, something that has been missing from the first principles calculations in the past. For example, in a calculation involving silicon, it became clear that the dominant singular value was associated with the stretching and squeezing of a particular bond.
In a new paper published in the journal Physical Review X, Caltech’s Yao Luo, a graduate student in applied physics; his advisor Marco Bernardi, professor of applied physics, physics and materials science; and colleagues describe a new data-driven method that has enabled these advances.
Image may be NSFW.
Clik here to view.
Credit: Physical Review X (2024)
See the science paper for further instructive material with images.
Their approach simplifies the dense computational matrices used to represent the interactions that take place in a material between electrons and atomic vibrations (or phonons, which can be thought of as individual units of vibrational energy). Luo and Bernardi say that the new method allows them to use only 1 to 2 percent of the data typically used to solve such problems, greatly accelerating calculations and, in the process, revealing the most important interactions that dictate the properties of materials.
“This was very surprising,” says Bernardi. “The electron–phonon interactions computed with the compressed matrices are nearly as accurate as the full calculation. This reduces the computing time and memory usage tremendously, by about two orders of magnitude in most cases. It’s also an elegant example of Occam’s razor, the idea of favoring simple physical models with minimal numbers of parameters.”
Finding a New Middle Ground for the Field
Researchers in this field generally follow one of two approaches to understand materials on this most fundamental level. One approach emphasizes building minimal models, reducing the complexity of the system, so that researchers can tweak a handful of parameters in pen-and-paper calculations to get a qualitative understanding of materials. The other begins with nothing more than the structure of a material and uses so-called “first principles” methods—quantum mechanical calculations requiring large computers— to study materials properties with quantitative accuracy.
This latter set of methods, which Bernardi’s group focuses on, use extremely large matrices featuring billions of entries to compute electron interactions that control a wide range of physical properties. That translates to thousands of hours of computing time for each calculation. The new work suggests a kind of middle ground between the two approaches, Bernardi says. “With our new method you can truncate the size of these matrices, extract the key information, and generate minimal models of the interactions in materials.”
Rooting Out the Most Important Singular Values
His group’s approach is based on applying a method called singular value decomposition (SVD) to the electron–phonon interactions in a material. The SVD technique is widely used in fields like image compression and quantum information science. Here, it allows the authors to separate, or disentangle, the electronic and vibrational components in a matrix of thousands or millions of electron–phonon interactions and to assign each fundamental interaction a number. These real positive numbers are called singular values and rank the fundamental interactions in order of importance. Then the program can eliminate all but a few percent of the interactions in each matrix, leaving only the leading singular values, a process that makes the determination cheaper by a factor proportional to the amount of compression. So, for example, if the program keeps only 1 percent of the singular values, the calculation becomes faster by a factor of 100. The researchers have found that keeping only a small fraction of singular values, typically 1 to 2 percent, the approximate result retains nearly the same accuracy as the full calculation.
“By using SVD, you can cut the number of singular values and capture only the main features of the matrices representing electronic interactions in a given material,” says Luo, lead author on the paper who is in his third year in Bernardi’s group. “This truncates the original matrix, thus speeding up the algorithm, and has the added benefit of revealing which interactions in the material are dominant.”
Bernardi notes that this latter benefit of the SVD method gives the researchers a “physical intuition” about electron interactions in a material, something that has been missing from the first principles calculations in the past. For example, in a calculation involving silicon, it became clear that the dominant singular value was associated with the stretching and squeezing of a particular bond. “It’s something simple, but before doing the calculation, we didn’t know that was the strongest interaction,” explains Bernardi.
In the paper, the researchers show that the compression of matrices related to electron–phonon interactions using the SVD method provides accurate results for various properties of materials researchers might want to calculate, including charge transport, spin relaxation times, and the transition temperature of superconductors.
Bernardi and his team are extending the SVD-based calculations to a wider range of interactions in materials and developing advanced calculations that were previously thought impossible. The team is also working to add the new SVD method into its open source Perturbo code, a software package that helps researchers calculate how electrons interact and move in materials. Bernardi says that this will enable users in the scientific community to predict material properties associated with electron–phonon interactions significantly faster.
See the full article here .
Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct.
Image may be NSFW.
Clik here to view.
five-ways-keep-your-child-safe-school-shootings
Image may be NSFW.
Clik here to view.
Please help promote STEM in your local schools.
Clik here to view.
The California Institute of Technology is a private research university in Pasadena, California. The university is known for its strength in science and engineering, and is one among a small group of institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences.
The California Institute of Technology was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began attracting influential scientists such as George Ellery Hale, Arthur Amos Noyes, and Robert Andrews Millikan in the early 20th century. The vocational and preparatory schools were disbanded and spun off in 1910 and the college assumed its present name in 1920. In 1934, The California Institute of Technology was elected to the Association of American Universities, and the antecedents of National Aeronautics and Space Administration ‘s Jet Propulsion Laboratory, which The California Institute of Technology continues to manage and operate, were established between 1936 and 1943 under Theodore von Kármán.
The California Institute of Technology has six academic divisions with strong emphasis on science and engineering. Its 124-acre (50 ha) primary campus is located approximately 11 mi (18 km) northeast of downtown Los Angeles. First-year students are required to live on campus, and 95% of undergraduates remain in the on-campus House System at The California Institute of Technology. Although The California Institute of Technology has a strong tradition of practical jokes and pranks, student life is governed by an honor code which allows faculty to assign take-home examinations. The The California Institute of Technology Beavers compete in 13 intercollegiate sports in the NCAA Division III’s Southern California Intercollegiate Athletic Conference (SCIAC).
There are many Nobel laureates who have been affiliated with The California Institute of Technology, including alumni and faculty members (Linus Pauling being the only individual in history to win two unshared prizes). In addition, Fields Medalists and Turing Award winners have been affiliated with The California Institute of Technology. Crafoord Laureates and non-emeritus faculty members (as well as many emeritus faculty members) who have been elected to one of the United States National Academies. There are or have been Chief Scientists of the U.S. Air Force and numerous United States National Medal of Science or Technology winners. Many faculty members are associated with the Howard Hughes Medical Institute as well as National Aeronautics and Space Administration. According to a Pomona College study, The California Institute of Technology ranked very highly in the U.S. for the percentage of its graduates who go on to earn a PhD.
Research
The California Institute of Technology is classified among “R1: Doctoral Universities – Very High Research Activity”. Caltech was elected to The Association of American Universities in 1934 and remains a research university with “very high” research activity, primarily in STEM fields. The largest federal agencies contributing to research are National Aeronautics and Space Administration; National Science Foundation; Department of Health and Human Services; Department of Defense, and Department of Energy.
The California Institute of Technology has over 739,000 square feet (68,700 m^2) dedicated to research: 330,000 square feet (30,700 m^2) to physical sciences, 163,000 square feet (15,100 m^2) to engineering, and 160,000 square feet (14,900 m^2) to biological sciences.
In addition to managing NASA-JPL/Caltech , The California Institute of Technology also operates the Caltech Palomar Observatory; The Owens Valley Radio Observatory along with the New Jersey Institute of Technology; the Caltech Submillimeter Observatory; the W. M. Keck Observatory at the Maunakea Observatory along with the University of California; the Laser Interferometer Gravitational-Wave Observatory at Livingston, Louisiana and Hanford, Washington along with the Massachusetts Institute of Technology; and Kerckhoff Marine Laboratory in Corona del Mar, California. The Institute launched the Kavli Nanoscience Institute at The California Institute of Technology in 2006; the Keck Institute for Space Studies in 2008; and is also the current home for the Einstein Papers Project. The Spitzer Science Center, part of the Infrared Processing and Analysis Center located on The California Institute of Technology campus, is the data analysis and community support center for NASA’s Spitzer Infrared Space Telescope [no longer in service] .
Clik here to view.
Clik here to view.
Clik here to view.
Clik here to view.
Clik here to view.
Clik here to view.
Image may be NSFW.
Clik here to view.
Caltech /MIT Advanced aLigo. Credit: Caltech.
Clik here to view.
Clik here to view.
The California Institute of Technology partnered with University of California-Los Angeles to establish a Joint Center for Translational Medicine (UCLA-Caltech JCTM), which conducts experimental research into clinical applications, including the diagnosis and treatment of diseases such as cancer.
The California Institute of Technology operates several Total Carbon Column Observing Network stations as part of an international collaborative effort of measuring greenhouse gases globally. One station is on campus.