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Saturday, January 19, 2008

microchip-processing speeds

new chip

Copper's not coping: new chips call on light speed

The tiny copper wires that connect different areas of an integrated circuit may soon limit microchip-processing speeds. So European researchers have developed technologies to produce and combine semiconductor microlasers with silicon wave guides for novel, power-efficient optical connections.

We have all experienced the effect of Moore's Law: almost from the second you unpack a newly purchased computer it is already outdated. The next model - with faster processing power and more advanced features - is already in the shop.

Gordon E. Moore, co-founder of Intel, described the phenomenon of microchip miniaturisation in 1965 when he observed that the number of transistors you can fit into an integrated circuit appeared to double about every two years.

The microelectronics industry still follows this "law", but unless new fabrication or microprocessing technologies are quickly developed this relentless miniaturisation may peter out in less than a decade. Microchips based on silicon wafers are nearing their theoretical limits as physical properties of near nanoscale silicon integrated circuits begin to interfere with their performance.

The speed of data transfer within integrated circuits is one of the major bottlenecks. At present, to pass information from one part of a chip to another, the data packet is sent as electrons through copper wires, known as copper interconnects.

These wires may be just a few millimetres in length, but for the electrons it is like running between underground trains at rush hour. The electrons must all squeeze down narrow tunnels while a crowd backs up at the entrance.

Copper can't cope

"Copper-wire interconnects place serious limitations on the performance of silicon integrated circuits," says Dries Van Thourhout from Ghent University's Photonics Research Group and Belgium's micro- and nanoelectronics research centre IMEC. "It is hard to transmit data down these interconnects in a sufficiently fast, power-efficient way. It is a problem of bandwidth and copper will not be able to cope with the processing power of tomorrow's microchips."

Optical interconnects use light instead of electrons to represent information; they are a highly appealing alternative to copper interconnects, with the potential to be far more efficient, transmitting more data but using the same or even less power.

Instead of travelling along copper wires, photons travel the distance between source and detector along wave guides, like miniature optical fibres. At this scale, however, the wave guides are made out of silicon rather than glass.

"Lots of research has shown that you can etch wave guides for photons into silicon," says Van Thourhout. "This is great because you are using the same materials and fabrication technologies as you do to make integrated circuits. But there is one significant drawback: it is extremely hard to get light out of silicon."

Despite extensive research to exploit many of silicon's peculiar properties, it is highly unlikely that purely silicon-based lasers will reach an efficiency comparable to that of their semiconductor-based cousins for the foreseeable future.

Van Thourhout has coordinated a European consortium that has successfully combined the best of both worlds: silicon wave guides and microscale lasers made from a semiconductor call indium-phosphate. The PICMOS project was a partnership between several European research institutions, universities and two French companies STMicroelectronics and TRACIT Technologies, now owned by Soitec.

Mini-laser system

Part of the research involved the fabrication of a miniaturised laser system small enough to generate light for each interconnect. The PICMOS partners developed a method to etch indium-phosphate lasers with a diameter of just 7μm, sufficiently small to integrate several thousand onto a 2cm x 2cm silicon chip. This is the first time that such compact lasers have been produced in a very practical, cost-efficient way.

The tiny lasers could also have applications in miniature optical sensors, such as strain detectors, or be used to build incredibly cheap, but very powerful optical biosensors. But the biggest breakthrough in the project was the development of a bonding technology that joins the silicon and iridium-phosphate materials together.

"The bonding process, now transferred to TRACIT, effectively 'glues' the silicon and semiconducting indium-phosphate in layers. It is possible to etch out the microlasers and the silicon wave guides and produce an optical interconnecting layer," says Van Thourhout. "The bonding process and the refinement of the microlaser and the accompanying detectors have been major breakthroughs."

The production cost of the prototype optical interconnect layer is still too high for mass production, although the results from the demonstrator 'chip' have been extremely encouraging. A follow-up project, WADIMOS, will continue to drive the PICMOS platform towards commercialisation. In particular it will develop a pilot line that integrates the fabrication of the optical interconnect layer into the regular integrated circuit manufacturing process.

"We envisage a layer on an integrated circuit that sits on top of the classical etched copper electrical interconnect layer," says Van Thourhout. "This optical interconnect layer would be less sensitive to temperature, immune from electromagnetic noise, and have lower power consumption. Meanwhile, the bonding system could be adapted for many other electronics applications, for example to stack integrated circuits and in microfluidic technologies. The application of the PICMOS platform could be tremendous for tomorrow's chip technologies and wide-ranging in many other associated applications."

Intel unveils new chip technology

Intel has launched a new generation of chips that it hopes will boost its lead over rival Advanced Micro Devices heading into 2008.

The line of chips, code-named Penryn, uses a new manufacturing method that allows Intel (INTC) to make the chips both smaller and more efficient. Penryn chips should help companies like Hewlett-Packard (HPQ), Dell (DELL) and Apple (AAPL) to design more energy-efficient servers, more powerful of desktops and more portable laptops.

In the near term, Penryn's value to Intel could be more about reputation than the bottom line. Earlier in the decade, competitor AMD (AMD) took advantage of the chip giant's missteps and offered products that many in the industry judged to be technologically superior to Intel's. But now Intel is back with a vengeance, and has AMD on the ropes. And because the Penryn chips are based on an advanced 45-nanometer manufacturing process, they give the company valuable bragging rights.

The special ingredient in Intel's new 45-nanometer Penryn is hafnium, an element that allows it to shrink the size of its chips while improving their efficiency.

"Historically, silicon dioxide has been the main insulator and the base of these transistors," said Intel spokesman Bill Calder. "In 2003 we identified a new structure that was different, but we didn't say exactly what it was. So in January we announced that we had found a new material to replace silicon dioxide."

Despite the advantages from the new manufacturing process, Intel isn't likely to realize the full advantage from Penryn until the second half of 2008, when its chip-producing factories in Arizona, New Mexico and Israel will be able to churn them out at full tilt. At that point, Intel should be able to supply them to computer makers in the largest volumes at mass-market prices while, presumably, raking in major profits.

So far, Calder said, Penryn manufacturing at Intel's Oregon and Arizona facilities is going well.

"Yields are good, we are in volume manufacturing now, and we are ramping pretty much in accordance with all the previous processes," Calder said. "Moore's Law lives."

That still leaves AMD a window to answer Intel's challenge. In September, AMD announced a new chip for servers, code-named Barcelona, that sports an advanced design with four processing cores. AMD has also promised to offer a desktop version of the chip before the end of the year.

While AMD is touting Barcelona's design advantages, it's not a sure thing that it will translate into market success. Early versions of the Barcelona chip are slower than AMD had hoped, and it's not clear whether the company has been delivering large volumes of the chips to customers.

AMD's best chance of competing with Intel might lie in the graphics technology it acquired when it purchased graphics chipmaker ATI. AMD has said that the multimedia processing technology in graphics chips is now so important that it will become a core part of the way mainstream computer systems are designed. : , , , ,
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Solid gold nanoparticles have long been used to treat rheumatoid arthritis and treating various types of cancer.

Gold Nanoparticles Shine Brightly in Tumors
Solid gold nanoparticles have long been used to treat rheumatoid arthritis and more recently have shown promise in treating various types of cancer. Now, thanks to work by Shuming Nie, Ph.D., and his colleagues at the Emory-Georgia Tech Nanotechnology Center for Personalized and Predictive Oncology, these same nanoparticles could serve as a powerful tumor-homing beacon for detecting microscopic tumors or even individual malignant cells. The researchers report their findings in the journal Nature Biotechnology.

Starting with colloidal gold—a commercially available suspension of gold nanoparticles—the investigators attached one of several positively charged organic dye molecules to the particles’ surfaces. The chosen dye molecules absorb and emit light in the near-infrared region of the spectrum, a portion of the spectrum that passes unabsorbed through biological tissues.

The researchers then added a nanometer-thick layer of polyethylene glycol (PEG) to render the construct biocompatible. To their surprise, this coating also made the resulting optical probe incredibly stable under even harsh chemical conditions. More importantly, the optical properties of both the gold nanoparticles and the dye molecules remained constant even after application of the coating. These particles were also nontoxic to cells over periods as long as 6 days.

These initial experiments showed that the coated gold nanoparticles could serve as potent imaging agents for studies of cancer cells, but the real goal of this project was to develop targeted in vivo imaging agents for detecting cancer in humans.

To prepare a targeted nanoparticle, the researchers used a version of PEG to which they could chemically link an antibody that binds to epidermal growth factor receptor (EGFR), a molecule overexpressed on many types of tumors. Antibodies and small molecules that bind to EGFR have been approved to treat non-small cell lung cancer.

The investigators injected the targeted nanoparticles into mice with EGFR-positive human head and neck carcinomas and obtained SERS spectra 5 hours later. As control experiments, the researchers injected matching mice with the untargeted nanoparticle. The unique optical spectra of the nanoparticles were easily detected in both sets of animals, but only the targeted nanoparticles accumulated in tumors. In contrast, the untargeted nanoparticles accumulated largely in the liver.

This work, which was supported by the National Cancer Institute’s (NCI) Alliance for Nanotechnology in Cancer, is detailed in the paper “In vivo tumor targeting and spectroscopic detection with surface-enhanced Raman nanoparticle tags.” An abstract of this paper is available through PubMed.

Organizing Gold Nanoparticles with DNA

Tiny billionth-of-a-meter sized clusters of gold atoms — gold “nanoparticles” — are being widely studied by scientists. They have many useful potential applications, from carriers for cancer-treatment drugs to digital data storage. But many of these applications, particularly those in electronics, require that the nanoparticles form ordered arrays that can be hard to achieve. At Arizona State University (ASU), researchers have discovered that grids made of DNA strands are excellent templates for neatly organizing gold nanoparticles.
“The collective properties of nanoparticles are heavily dependent on how the particles are grouped. Achieving an even spacing between the particles is particularly important, but can be difficult,” said the study’s lead scientist, ASU chemist Hao Yan. “However, when deposited onto a DNA grid the particles fall neatly into patterns with little effort on our part.”
Yan and his research group used gold nanoparticles that were five nanometers in diameter. Rather than being bare, the particles were coated with a layer of DNA “pieces,” called “T15 sequences,” which radiated from the particles’ surfaces like arms. The scientists then deposited the particles onto lattices formed by two types of cross-shaped DNA “tiles”, “A” tiles and “B” tiles, that bind together in an alternating fashion to form the DNA grid.

At regular intervals, each A tile contained a short single strand (called an “A15” strand) that protruded out of the tile surface. These strands served as tethering points for the T15-coated nanoparticles, allowing the particles to stick to the DNA surface, a bit like DNA-nanoparticle “Velcro.”

This configuration caused the nanoparticles to “self assemble” into a square pattern — each particle sitting on one A tile — with a nearly constant particle-particle distance of about 38 nanometers. The group confirmed this using an atomic force microscope, a very powerful imaging device.

However, this result, while welcomed by the scientists, wasn’t exactly what they expected.

“We were pleased that the gold nanoparticles formed a very regular square pattern, but it wasn’t quite the pattern we thought we’d see,” said Yan. “If you picture nine DNA tiles forming a square, we predicted that five particles would be organized on the square — one on each corner and one in the middle. But the pattern we observed lacked that middle particle.”

The scientists guess that this is due to the T15 sequence layer, which effectively increases the diameter of each nanoparticle and, moreover, makes each particle highly negatively charged. As a result, the nanoparticles repel each other if they are too close together, which limits the minimum particle-particle distance. Therefore, a particle located at the center of the square would violate this limit.

In future research, Yan and may try to use this organization method to form more complex nanoparticle arrays, such as denser patterns or patterns of different shapes, by altering the particles’ DNA coating.

Two research groups in the Uk have been given permission to use hybrid human-animal embryos

The nuclear transfer technique would involve removing the nucleus of a cow egg - which contains most of its genetic information - and fusing the cow egg with the nucleus of a human cell such as a skin cell. The egg will then be encouraged to divide until it is a cluster of cells only a few days old called a blastocyst, or an early-stage cloned embryo.

Hybrid Human-Animal Embryo Research Approved In The UK

Two research groups in the United Kingdom have been given permission to use hybrid human-animal embryos in research which aims to lead to the development of new therapies for debilitating human conditions such as Parkinson's disease and stroke.

Newcastle University stem cell scientist Dr. Lyle Armstrong, who is based at the North East England Stem Cell Institute (NESCI) at the International Centre for Life in Newcastle, has received a licence from the Human Fertilisation and Embryology Authority (HFEA) to carry out research using human-animal cytoplasmic embryos. Another group -- the Stem Cell Biology Laboratory Wolfson Centre for Age-Related Diseases, at King's College London -- has also received a research license by HFEA to carry out research using hybrid embryos.

Dr. Armstrong says: "The award of the HFEA licence is great news. We initially applied for approval to use cow eggs as a means to understand the way they can convert skin cells into embryonic stem cells. Finding better ways to make human embryonic stem cells is the long term objective of our work and understanding reprogramming is central to this."

"Cow eggs seem to be every bit as good at doing this job as human eggs so it makes sense to use them since they are much more readily available but it is important to stress that we will only use them as a scientific tool and we need not worry about cells derived from them ever being used to treat human diseases," he said.

"Now that we have the licence we can start work as soon as possible. We have already done a lot of the work by transferring animal cells into cow eggs so we hope to make rapid progress."

Background information

Until now, work on the development of therapeutic cloning has used human eggs from consenting IVF patients but these are in short supply. Animal eggs are considered to be a viable alternative for research to understand more about how cells behave.

At first the NESCI team would be working with cow eggs. The nuclear transfer technique would involve removing the nucleus of a cow egg - which contains most of its genetic information - and fusing the cow egg with the nucleus of a human cell such as a skin cell. The egg will then be encouraged to divide until it is a cluster of cells only a few days old called a blastocyst, or an early-stage cloned embryo.

The scientists would attempt to extract stem cells from the blastocyst after six days. Stem cells are building blocks that can grow into any type of tissue such as liver, heart and muscle cells. The quality and the viability of stem cells would then be checked to see if nuclear transfer technique has worked. The scientists would also be observing the way that the cells are reprogrammed after fusion to see if there are useful processes they could replicate in the laboratory. The embryo would have to be destroyed at 14 days old in accordance with the licence.

The eventual aim is to develop a way of creating stem cells to grow new tissue that is genetically matched to individual patients. For example, scientists hope to take a cell from a patient and re-programme it so that stem cells can be extracted to grow new tissue for damaged body parts without fear of immune rejection.

There is no possibility of allowing any of the animal hybrid cells to be used to treat patients but this approach will protect precious resources of human eggs at this early development stage and complement existing NESCI research using human eggs.

The studies will be heavily regulated under the conditions of the HFEA licence.

Scientists Hope to Create Human-Animal Embryo

British regulators decided Wednesday to allow, at least in principle, the creation of hybrid human-animal embryos for research into degenerative diseases. The move came despite fierce opposition from some church and ethics groups.

Two teams of British scientists had applied to Britain's Human Fertilisation and Embryology Authority (HFEA) for permission to create what are known in Britain as cytoplastic hybrids, or cybrids, in order to overcome a shortage of donated human eggs.

The process involves injecting human DNA into an animal egg cell from which the nucleus has been removed.

Researchers hope to use the hybrid embryos, which must be destroyed after 14 days, which would create stem cells. The stem cells could be used to help find new medical treatments for diseases such as Alzheimer's, Lou Gehrig's, and Parkinson's.

The chief executive of HFEA, Angela McNabb, says the legal and ethical pros and cons were weighed very carefully.

"We've been able to weigh those up and take what's a very strong decision where we're saying we can move forward with cytoplasmic hybrid embryos and the creation of those in some research, so we can gain the potent benefits but only in the framework of very strong regulation," McNabb says.

Scientists have said they understand that the idea of the process - which would create a hybrid embryo that is 99.9 percent human and 0.1 percent animal - might be shocking to some people. But Dr. Stephen Minger of Kings College London says the public should not be alarmed.

"What we do when we take an animal egg, is we remove the nucleus from the egg. We remove not only the genetic identity but we remove the species identity. What makes a cow egg a cow is its nuclear DNA. And we take that out - it's no longer a cow," Minger says.

The regulators' consultation included an opinion poll of more than 2,000 British people. The survey found people supported the creation of the kind of hybrid embryos proposed by the two research teams - but only when they were given a reason for the experiments.

Some 61 percent of those asked gave their backing if the hybrids would help understand some diseases. That support fell to 35 percent if the hybrids were being created purely for nonspecific research.

But Dr. Helen Watt, a medical ethicist at the Catholic organization Linacre Centre for Healthcare Ethics, told the BBC the move is wrong and immoral.

"If we're looking at a model for studying disease, these embryos … will be highly abnormal," Watt says. "There's a limit to how much we're going to be able to learn from embryos containing animal material in this way. In any case, there are ways of doing science that respect both human life and human dignity. In these experiments, we not only risk creating a genuine human embryo who has no human parents and who has a nonhuman partial mother, but we also offend against human dignity by entering into animal reproduction."

HFEA deferred a decision on other types of human-animal embryos, such as what are known as "true hybrids" - created by the fusion of a human sperm and an animal egg - and so-called "human chimeras," where human cells are injected into animal embryos. The group said there was no evidence that British scientists are at present considering using such hybrids in research. : , , , , , ,
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Server maker's purchase of the open-source software maker expected to close in late 2008.

Sun Microsystems to buy MySQL for $1B
Sun Microsystems Inc. has agreed to buy open-source software maker MySQL AB for $1 billion, beefing up the server maker's database offerings with a company whose technology is used by some of the world's biggest Web sites.

Santa Clara-based Sun, in separate announcements before the market opened, said its second quarter revenue would narrowly exceed Wall Street estimates. It also said profit would fall at the high end of analysts' expectations. The company revealed its preliminary results ahead of schedule.

Sun is paying $800 million in cash and assuming $200 million in options to acquire MySQL. The Swedish company makes open-source database software used by companies such as online search leader Google Inc (GOOG, Fortune 500)., popular Internet hangout Facebook Inc. and Finnish phone maker Nokia Corp (NOK).

Sun said the deal will help spread MySQL's software to large corporations, which have been the biggest customers of Sun's servers and software, and boost its distribution through Sun's relationships with other server makers such as IBM Corp (IBM, Fortune 500). and Dell Inc. (DELL, Fortune 500)

The acquisition, expected to close in the third or fourth quarter, takes pressure off Sun to spend some of the cash it's been accumulating. It also bolsters its software offerings with a well-known name in Internet data retrieval.

Sun also said it expects net income of between $230 million to $265 million, or 28 cents to 32 cents per share. Analysts surveyed by Thomson Financial were expecting profit of between 22 and 38 cents.

Sun (JAVA, Fortune 500) said it expects to notch about $3.6 billion in sales during the second quarter. Analysts were expecting, on average, $3.58 billion in sales.

Sun Microsystems

Sun Microsystems, Inc. (NASDAQ: JAVA)[4] is an American vendor of computers, computer components, computer software, and information-technology services, founded on 24 February 1982.[5] The company is headquartered in Santa Clara, California (part of Silicon Valley), on the former west campus of the Agnews Developmental Center.

Sun is known as the developer of technologies such as the Java platform and NFS, and as a key promoter of open systems in general and UNIX in particular; it has recently emerged as one of the leading proponents and contributors of open source software.[6] Its products include computer servers and workstations based on its own SPARC processors as well as AMD's Opteron and Intel's Xeon processors; storage systems; and, a suite of software products including the Solaris Operating System, developer tools, Web infrastructure software, and identity management applications. Sun's manufacturing facilities are located in Hillsboro, Oregon and Linlithgow, Scotland.

NASA is wrestling with a potentially dangerous problem in a spacecraft

NASA Moon Rocket May Shake Too Much

NASA is wrestling with a potentially dangerous problem in a spacecraft, this time in a moon rocket that hasn't even been built yet.
Engineers are concerned that the new rocket meant to replace the space shuttle and send astronauts on their way to the moon could shake violently during the first few minutes of flight, possibly destroying the entire vehicle.
They know it's a real problem," said Carnegie Mellon University engineering professor Paul Fischbeck, who has consulted on risk issues with NASA in the past. "This thing is going to shake apart the whole structure, and they've got to solve it."

If not corrected, the shaking would arise from the powerful first stage of the Ares I rocket, which will lift the Orion crew capsule into orbit.

NASA officials hope to have a plan for fixing the design as early as March, and they do not expect it to delay the goal of returning astronauts to the moon by 2020.

"I hope no one was so ill-informed as to believe that we would be able to develop a system to replace the shuttle without facing any challenges in doing so," NASA administrator Michael Griffin said in a statement to The Associated Press. "NASA has an excellent track record of resolving technical challenges. We're confident we'll solve this one as well."

Professor Jorge Arenas of the Institute of Acoustics in Valdivia, Chile, acknowledged that the problem was serious but said: "NASA has developed one of the safest and risk-controlled space programs in engineering history."

The space agency has been working on a plan to return to the moon, at a cost of more than $100 billion, since 2005. It involves two different rockets: Ares I, which would carry the astronauts into space, and an unmanned heavy-lift cargo ship, Ares V.

The concern isn't the shaking on the first stage, but how it affects everything that sits on top: the Orion crew capsule, instrument unit, and a booster.

That first stage is composed of five segments derived from the solid rocket boosters that NASA uses to launch the shuttle and would be built by ATK Launch Systems of Brigham City, Utah.

The shaking problem, which is common to solid rocket boosters, involves pulses of added acceleration caused by gas vortices in the rocket similar to the wake that develops behind a fast-moving boat, said Arenas, who has researched vibration and space-launch issues.

Those vortices happen to match the natural vibrating frequencies of the motor's combustion chamber, and the combination causes the shaking.

Senior managers were told of the findings last fall, but NASA did not talk about them publicly until the AP filed a Freedom of Information Act request earlier this month and the watchdog Web site submitted detailed engineering-oriented questions.

The response to those questions, given to both Nasawatch and AP, were shared with outside experts, who judged it a serious problem.

NASA engineers characterized the shaking as being in what the agency considers the "red zone" of risk, ranking a five on a 1-to-5 scale of severity.

"It's highly likely to happen and if it does, it's a disaster," said Fischbeck, an expert in engineering risks.

The first launch of astronauts aboard Ares I and Orion is set for March 2015.
Severe vibration problem plagues moon rocket design.
Experts at NASA are wrestling with a propulsion system problem in the design of the new moonship that would create dangerously high vibrations for the spacecraft and its astronauts, the space agency said Friday.

Officials said in a statement that they expect to develop by March several options to address the problem with the Ares I rocket, which is in the early design phase.

NASA is counting on the Ares I rocket and the Orion crew capsule attached to it to replace the aging space shuttle, which is facing retirement in 2010.

At current funding levels, NASA hopes to begin launching astronauts to the international space station aboard the new moonship by March 2015.

Serious problem
The vibration problem was first disclosed on Friday by NASA Watch, an Web site focused on space agency issues.

NASA officials declined requests for interviews on Friday, but spokeswoman Beth Dickey provided a lengthy statement that identified the problem as "thrust oscillation," an issue that was discussed by the moonship's development team in October during a design review.

The statement characterized the problem, which was revealed in computer modeling, as a pulsing of the thrust late in the burn of the rocket's first stage.

"These longitudinal forces may increase the loads experienced by the Ares I during flight, and may exceed allowable loads on various portions of the vehicle and allowable forces on the astronaut crew," the statement said.

Program managers assigned the seriousness of the problem a "four" on a risk scale of five and have called on experts from outside of NASA as well as inside the agency for assistance.

Confident in solution

NASA Administrator Michael Griffin expressed confidence the issue will be resolved.

"This is a development project like Apollo. I hope no one was so ill-informed as to believe that we would be able to develop a system to replace the shuttle without facing any challenges in doing so," Griffin said in a separate statement. "NASA has an excellent track record of resolving technical challenges. We're confident we'll solve this one as well."

While NASA's Johnson Space Center manages the overall effort to develop the moonship, the propulsion work has been assigned to the Marshall Space Flight Center in Huntsville, Ala.

The Ares I first stage is a longer version of the shuttle's solid rocket booster. The upper stage is comprised of an upgrade of the Apollo-era rocket engine.

Normal design kinks

Thrust oscillation is a phenomenon found in all solid rocket motors, including the two used to power each launch of the space shuttle.

"It is a well and long understood phenomenon in the launch industry," said George Torres , a spokesman for ATK. "Many other launch vehicles at this stage of development have had to deal with this issue and have dealt with it as a normal part of the development process."

Four years ago, President Bush directed NASA's return to the moon with astronauts by 2020.

As part of the directive, Bush instructed the agency to retire the shuttle as it completes the assembly of the space station.

On Dec. 12, NASA awarded the last of the contracts for the development of the Ares I rocket and Orion capsule, a committment of $13.6 billion.

Three-dimensional snowflakes

Math Models Snowflakes In Extraordinary Detail
Three-dimensional snowflakes can now be grown in a computer using a program developed by mathematicians at UC Davis and the University of Wisconsin-Madison.

No two snowflakes are truly alike, but they can be very similar to each other, said Janko Gravner, a mathematics professor at UC Davis. Why they are not more different from each other is a mystery, Gravner said. Being able to model the process might answer some of these questions.

Intricate, incredibly variable and beautiful, snowflakes have been puzzling mathematicians since at least 1611, when Johannes Kepler predicted that the six-pointed structure would reflect an underlying crystal structure.

Snowflakes grow from water vapor around some kind of nucleus, such as a bit of dust. The surface of the growing crystal is a complex, semi-liquid layer where water molecules from the surrounding vapor can attach or detach. Water molecules are more likely to attach at concavities in the crystal shape.

The model built by Gravner and David Griffeath of the University of Wisconsin-Madison takes these factors, as well as temperature, atmospheric pressure and water vapor density, into account. By running the model under different conditions, the researchers were able to recreate a wide range of natural snowflake shapes.

Rather than trying to model every water molecule, it divides the space into three-dimensional chunks one micrometer across. The program takes about 24 hours to produce one "snowfake" on a modern desktop computer.

As in the real world, needles are the most common pattern of computer-generated snowflake. The classic six-pointed "dendritic" or feathery snowflake is relatively rare, both in the computer simulation and in nature.

Gravner and Griffeath also managed to generate some novel snowflakes, such as a "butterflake" that looks like three butterflies stuck together along the body. Gravner said there seemed to be no reason these shapes could not appear in nature, but they would be very fragile and unstable.

One surprise was that three-dimensional structure is often important, with complex structures often growing between two plates -- a feature that is difficult to see when observing actual snowflakes, but has been observed in careful studies of real snowflakes with electron microscopes.

Koch Snowflake
Snowflakes are amazing creations of nature. They seem to have intricate detail no matter how closely you look at them. One way to model a snowflake is to use a fractal which is any mathematical object showing "self-similarity" at all levels.

The Koch snowflake is constructed as follows. Start with a line segment. Divide it into 3 equal parts. Erase the middle part and substitute it by the top part of an equilateral triangle. Now, repeat this procedure for each of the 4 segments of this second stage. See Figure 1. If you continue repeating this procedure, the curve will never self-intersect, and in the limit you get a shape known as the Koch snowflake.

Amazingly, the Koch snowflake is a curve of infinite length!

And, if you start with an equilateral triangle and do this procedure to each side, you will get a snowflake, which has finite area, though infinite boundary!

Presentation Suggestions:
Draw pictures. If they like this Fun Fact, ask them: can you figure out how to construct a 3-dimensional example? [Hint: start with a regular tetrahedron. See Koch Tetrahedron for what happens.]

The Math Behind the Fact:
You can see that the boundary of the snowflake has infinite length by looking at the lengths at each stage of the process, which grows by 4/3 each time the process is repeated. On the other hand, the area inside the snowflake grows like an infinite series, which is geometric and converges to a finite area! You can learn about fractals in a course on dynamical systems.

The researchers' findings reveal a previously unknown mathematical relationship

"Ground states" are the lowest energy states of matter. They are created in real life by taking a liquid and slowly cooling it until you reach absolute zero temperature. The resulting arrangement of molecules or particles is a "ground state," which often is an ordered crystal structure. This image shows an ordered ground state (called the face-centered cubic lattice), which is the end result of the slow cooling process

Materials' Crystal Properties Illuminated By Mathematical 'Lighthouse'
A deeper fundamental understanding of complex materials may now be possible, thanks to a pair of Princeton scientists who have uncovered a new insight into how crystals form.
The researchers' findings reveal a previously unknown mathematical relationship between the different arrangements that interacting particles can take while freezing. The discovery could give scientists insight into the essential behaviors of materials such as polymers, which are the basis of plastics.

Molecules in a material cooled to absolute zero can take on a multitude of different configurations. Historically, scientists' difficulty with identifying crystallized molecules' spatial arrangements from this high number of possible configurations has blocked theoretical efforts to understand these materials' qualities, but the new findings could offer the tool that science needs.

"We believe our 'duality relations' will be a useful theoretical tool to understand how individual particles come together to form a crystal," said Salvatore Torquato, a professor of chemistry who co-wrote the paper with senior chemist Frank Stillinger. "If we can tune the interactions among particles that form a crystal, we might be able to create materials that respond to light or mechanical stress in novel ways."

A material that maintains its exact size and shape through extremes in temperature, for example, might be valuable in the manufacture of orbiting space telescopes, whose mirrors need to retain their shape as they pass from sunlight into the Earth's shadow.

A crystal is the state of matter that is easiest to analyze because its frozen molecules are motionless and often regularly organized. A crystal's properties -- its ability to bend light, for example -- generally reveal valuable information about how its constituent molecules will behave at higher temperatures, such as when they become a liquid.

The challenge is that many complex materials can crystallize into a multitude of different structures. When a substance is cooled to nearly absolute zero, and it can take on an enormously large number of possible "ground states" -- the term for the molecular arrangement with the lowest possible energy. Scientists seek to determine the true ground state because it provides a fundamental understanding of matter in the solid state and its possible uses. However, determining which molecular pattern is the true ground state requires mathematical proof that is hard to come by.

"We resort to approximations," said Christos Likos, a professor of theoretical physics at the University of Dusseldorf in Germany. "They help us produce meaningful results sometimes, but we need to have a lighthouse occasionally to show us we're on the right path. Such lighthouses are rare in this business, but Sal and Frank have found one."

Torquato and Stillinger's findings explore particles' behavior as they attract and repel each other over varying distances. By analyzing this behavior, the scientists were able to conceive a precise mathematical correspondence -- called duality relations -- between possible arrangements of particles. The work will enable the researchers to draw important conclusions about how particles at very low temperatures interact over great distances, a situation that is very difficult to treat theoretically.

"Once ground states can be determined and controlled with certainty, scientists might create materials with properties virtually unknown in nature," Torquato said.


Crystal quality and optical properties for Nd:GdVO4 single crystals by a floating zone method
Single crystals of neodymium-doped gadolinium orthovanadate (Nd:GdVO4) were successfully grown by the floating zone method (FZ) with an infrared convergence type heater. These crystal quality and optical properties are sufficient for application to a laser host. Distribution of (Nd/Nd + Gd) concentration by 50 mm in the growth direction was 0.20 ± 0.02 against a target concentration of 0.20. Distribution of extinction ratio at 633 nm by 50 mm in the growth direction was 51 ± 2 dB. Laser performance for these crystals with a-cut were measured. The maximum slope efficiency was 65% and the maximum output power was 3.4 W with continuous wave at 808 nm.

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