506 research outputs found
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Matrix recursion for positive characteristic diagrammatic Soergel bimodules for affine Weyl groups
Let be an affine Weyl group, and let be a field of characteristic . The diagrammatic Hecke category for over is a categorification of the Hecke algebra for with rich connections to modular representation theory. We explicitly construct a functor from to a matrix category which categorifies a recursive representation , where is the rank of the underlying finite root system. This functor gives a method for understanding diagrammatic Soergel bimodules in terms of other diagrammatic Soergel bimodules which are "smaller" by a factor of . It also explains the presence of self-similarity in the -canonical basis, which has been observed in small examples. By decategorifying we obtain a new lower bound on the -canonical basis, which corresponds to new lower bounds on the characters of the indecomposable tilting modules by the recent -canonical tilting character formula due to Achar-Makisumi-Riche-Williamson
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Screening Cargo Containers to Remove a Terrorist Threat
Each year some 48 million cargo containers move between the world's ports. More than 6 million of these enter the U.S., but only about 2 percent are opened and inspected when they arrive at U.S. seaports. The West Coast ports of Los Angeles-Long Beach, Oakland, and Seattle alone process 11,000 containers per day, or about 8 containers per minute. Because of this high traffic volume, U.S. seaports are especially vulnerable to a terrorist attack. Illicit radioactive materials could be hidden in any one of the cargo-filled containers that arrive at U.S. ports. Yet, searching every shipment would be bring legitimate commercial activities to a halt. Improving security at U.S. ports is thus one of the nation's most difficult technical and practical challenges because the systems developed for screening cargo must operate in concert with ongoing seaport activities. Working at this intersection of commerce and national security, Lawrence Livermore researchers are applying their expertise in radiation science and detection to develop improved technologies for detecting hidden radioactive materials. One new technology being designed and tested at the Laboratory is a neutron interrogation system for cargo containers. This system will quickly screen incoming shipments to ensure that nuclear materials such as plutonium and highly enriched uranium (HEU) are not smuggled into the U.S
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Indecomposable tilting modules for the blob algebra
The blob algebra is a finite-dimensional quotient of the Hecke algebra of type which is almost always quasi-hereditary. We construct the indecomposable tilting modules for the blob algebra over a field of characteristic in the doubly critical case. Every indecomposable tilting module of maximal highest weight is either a projective module or an extension of a simple module by a projective module. Moreover, every indecomposable tilting module is a submodule of an indecomposable tilting module of maximal highest weight. We conclude that the graded Weyl multiplicities of the indecomposable tilting modules in this case are given by inverse Kazhdan-Lusztig polynomials of type
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Testing the Physics of Nuclear Isomers
For much of the past century, physicists have searched for methods to control the release of energy stored in an atom's nucleus. Nuclear fission reactors have been one successful approach, but finding other methods to capitalize on this potential energy source have been elusive. One possible source being explored is nuclear isomers. An isomer is a long-lived excited state of an atom's nucleus--a state in which decay back to the nuclear ground state is inhibited. The nucleus of an isomer thus holds an enormous amount of energy. If scientists could develop a method to release that energy instantaneously in a gamma-ray burst, rather than slowly over time, they could use it in a nuclear battery. Research in the late 1990s indicated that scientists were closer to developing such a method--using x rays to trigger the release of energy from the nuclear isomer hafnium-178m ({sup 178m}Hf). To further investigate these claims, the Department of Energy (DOE) funded a collaborative project involving Lawrence Livermore, Los Alamos, and Argonne national laboratories that was designed to reproduce those earlier results
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New Gas Gun Helping Scientists Better Understand Plutonium Behavior
One of the most daunting scientific and engineering challenges today is ensuring the safety and reliability of the nation's nuclear arsenal. To effectively meet that challenge, scientists need better data showing how plutonium, a key component of nuclear warheads, behaves under extreme pressures and temperatures. On July 8, 2003, Lawrence Livermore researchers performed the inaugural experiment of a 30-meter-long, two-stage gas gun designed to obtain those data. The results from a continuing stream of successful experiments on the gas gun are strengthening scientists' ability to ensure that the nation's nuclear stockpile is safe and reliable. The JASPER (Joint Actinide Shock Physics Experimental Research) Facility at the Department of Energy's (DOE's) Nevada Test Site (NTS) is home to the two-stage gas gun. In the gun's first test, an unqualified success, Livermore scientists fired a projectile weighing 28.6 grams and traveling about 5.21 kilometers per second when it impacted an extremely small (about 30-gram) plutonium target. This experiment marked the culmination of years of effort in facility construction, gun installation, system integration, design reviews, and federal authorizations required to bring the experimental facility online. Ongoing experiments have drawn enthusiastic praise from throughout DOE, the National Nuclear Security Administration (NNSA), and the scientific community. NNSA Administrator Linton Brooks said, ''Our national laboratories now have at their disposal a valuable asset that enhances our due diligence to certify the nuclear weapons stockpile in the absence of underground nuclear weapons testing.'
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Seeing the Universe in a Grain of Dust
Imagine traveling halfway to Jupiter--3.2 billion kilometers--for a small handful of comet dust. That's the mission for the National Aeronautics and Space Administration's (NASA's) Stardust spacecraft launched on February 7, 1999. This past January, Stardust flew by Comet Wild 2's nucleus and through a halo of gases and dust at the comet's head, collecting cometary dust particles released from the surface just hours before. In 2006, the spacecraft will deliver the less than 1 milligram of particles to Earth. A Lawrence Livermore team is perfecting ways to extract and analyze the tiny particles using its new focused-ion-beam instrument and SuperSTEM, a scanning transmission electron microscope. Stardust is the first NASA space mission dedicated solely to collecting comet dust and will be the first to return material from a comet to Earth. Comets are the oldest and most primitive bodies in the solar system. They are formed from frozen gas, water, and interstellar dust and may have brought water to Earth, making life possible. Wild 2--pronounced ''Vilt 2'' after the name of its Swiss discoverer--was formed with the Sun and the rest of the solar system 4.5 billion years ago. For billions of years, it has circled the Sun in the Kuiper Belt, a region beyond the orbit of Neptune. Scientists think comets from this region have escaped the warming, vaporization, and collisions that have altered matter in the inner solar system. Unlike Halley's Comet, which has been altered as a result of orbiting the Sun for a long time, Wild 2's pristine composition is expected to offer a rich source of information about the solar system's potential building blocks. As the 5-meter-long Stardust spacecraft traveled through Wild 2's dust and gas cloud, to within about 100 kilometers of the comet's nucleus, particles were captured in the spacecraft's collector grid. The 1,000-square-centimeter grid is filled with the silica-based material aerogel, whose lightness minimizes damage to the grains as they encounter the spacecraft at a speed of about 21,000 kilometers per hour--or six times faster than a bullet. In the late 1980s, Livermore scientists developed an aerogel made up of 99 percent air, making it ideal for NASA projects. Mission planners expect to have collected more than 1,000 grains between 2 to 5 nanometers in diameter. Most of the grains will be heterogeneous aggregates of carbonaceous matter, glass, and crystals
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Probing the Universe with Mirrors That Trick Light
For astrophysicists, stargazing may be different than for most people, who are content to admire a star's beauty or possibly make a wish. More than a few astrophysicists wish they could be closer to the stars--or to at least have more sophisticated probing instruments--to understand more about the universe. Astrophysicists study x-rays originating from our Sun, stars, and supernova remnants to understand the extreme physical processes occurring there. In recent years, Livermore researchers have developed optics for astrophysical applications that can focus hard x-rays (that is, x-rays with energy levels above 20 kiloelectronvolts) emanating from celestial objects, such as supernovae. In addition to astrophysics, hard x-ray optics have a variety of possible applications, including medical imaging, laser target characterization, and radiation detection. Livermore researchers have long contributed to advancements in supernova astrophysics because studying thermonuclear processes is a central part of the Laboratory's national security mission, and the physical processes involved in a nuclear weapon and an exploding star are similar. Livermore physicists Bill Craig, who is involved in several projects using x-ray optics, says, ''We can do a better job of detecting illicit radioactive sources because of what we have learned from our developments in astrophysics. Whether the radiation source is from a black hole in space or nuclear material in a dirty bomb, detecting the source involves the same challenge, which is to pick up faint signals (high-energy photons) amidst background radiation.'
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Identifying Airborne Pathogens in Time to Respond
Among the possible terrorist activities that might threaten national security is the release of an airborne pathogen such as anthrax. Because the potential damage to human health could be severe, experts consider 1 minute to be an operationally useful time limit for identifying the pathogen and taking action. Many commercial systems can identify airborne pathogenic microbes, but they take days or, at best, hours to produce results. The Department of Homeland Security (DHS) and other U.S. government agencies are interested in finding a faster approach. To answer this national need, a Livermore team, led by scientist Eric Gard, has developed the bioaerosol mass spectrometry (BAMS) system--the only instrument that can detect and identify spores at low concentrations in less than 1 minute. BAMS can successfully distinguish between two related but different spore species. It can also sort out a single spore from thousands of other particles--biological and nonbiological--with no false positives. The BAMS team won a 2005 R&D 100 Award for developing the system. Livermore's Laboratory Directed Research and Development (LDRD) Program funded the biomedical aspects of the BAMS project, and the Department of Defense's Technical Support Working Group and Defense Advanced Research Project Agency funded the biodefense efforts. Developing a detection system that can analyze small samples so quickly has been challenging. Livermore engineer Vincent Riot, who worked on the BAMS project, explains, ''A typical spore weighs approximately one-trillionth of a gram and is dispersed in the atmosphere, which contains naturally occurring particles that could be present at concentrations thousands of times higher. Previous systems also had difficulty separating benign organisms from those that are pathogenic but very similar, which has resulted in false alarms''
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Radiation Detection Center on the Front Lines
Many of today's radiation detection tools were developed in the 1960s. For years, the Laboratory's expertise in radiation detection resided mostly within its nuclear test program. When nuclear testing was halted in the 1990s, many of Livermore's radiation detection experts were dispersed to other parts of the Laboratory, including the directorates of Chemistry and Materials Science (CMS); Physics and Advanced Technologies (PAT); Defense and Nuclear Technologies (DNT); and Nonproliferation, Arms Control, and International Security (NAI). The RDC was formed to maximize the benefit of radiation detection technologies being developed in 15 to 20 research and development (R&D) programs. These efforts involve more than 200 Laboratory employees across eight directorates, in areas that range from electronics to computer simulations. The RDC's primary focus is the detection, identification, and analysis of nuclear materials and weapons. A newly formed outreach program within the RDC is responsible for conducting radiation detection workshops and seminars across the country and for coordinating university student internships. Simon Labov, director of the RDC, says, ''Virtually all of the Laboratory's programs use radiation detection devices in some way. For example, DNT uses radiation detection to create radiographs for their work in stockpile stewardship and in diagnosing explosives; CMS uses it to develop technology for advancing the detection, diagnosis, and treatment of cancer; and the Energy and Environment Directorate uses radiation detection in the Marshall Islands to monitor the aftermath of nuclear testing in the Pacific. In the future, the National Ignition Facility will use radiation detection to probe laser targets and study shock dynamics.'
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Improved Algorithms Speed It Up for Codes
Huge computers, huge codes, complex problems to solve. The longer it takes to run a code, the more it costs. One way to speed things up and save time and money is through hardware improvements--faster processors, different system designs, bigger computers. But another side of supercomputing can reap savings in time and speed: software improvements to make codes--particularly the mathematical algorithms that form them--run faster and more efficiently. Speed up math? Is that really possible? According to Livermore physicist Eugene Brooks, the answer is a resounding yes. ''Sure, you get great speed-ups by improving hardware,'' says Brooks, the deputy leader for Computational Physics in N Division, which is part of Livermore's Physics and Advanced Technologies (PAT) Directorate. ''But the real bonus comes on the software side, where improvements in software can lead to orders of magnitude improvement in run times.'' Brooks knows whereof he speaks. Working with Laboratory physicist Abraham Szoeke and others, he has been instrumental in devising ways to shrink the running time of what has, historically, been a tough computational nut to crack: radiation transport codes based on the statistical or Monte Carlo method of calculation. And Brooks is not the only one. Others around the Laboratory, including physicists Andrew Williamson, Randolph Hood, and Jeff Grossman, have come up with innovative ways to speed up Monte Carlo calculations using pure mathematics
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