DISCOVERING HOW ROMULAN CLOAKING TECHNOLOGY WORKS THROUGH MATH

FROM:  THE NATIONAL SCIENCE FOUNDATION
Hidden from view
Mathematicians formulate equations, bend light and figure out how to hide things

The idea of cloaking and rendering something invisible hit the small screen in 1966 when a Romulan Bird of Prey made an unseen, surprise attack on the Starship Enterprise on Star Trek. Not only did it make for a good storyline, it likely inspired budding scientists, offering a window of technology's potential.

Today, between illusionists who make the Statue of Liberty disappear to Harry Potter's invisibility cloak that not only hides him from view but also protects him from spells, pop culture has embraced the idea of hiding behind force fields and magical materials. And not too surprisingly, National Science Foundation (NSF)-funded mathematicians, scientists and engineers are equally fascinated and looking at how and if they can transform science fiction into, well, just science.

"Cloaking is about detection and rendering something--and the cloak itself--not detectable or seen," said Michael Weinstein, an NSF-funded mathematician at Columbia University. "An object is seen when waves are bounced off it and observed by a detector."

In recent years, researchers have developed new ways in which light can move around and even through a physical object, making it invisible to parts of the electromagnetic spectrum and undetectable by sensors. Additionally, mathematicians, theoretical physicists and engineers are exploring how and whether it's feasible to cloak against other waves besides light waves. In fact, they are investigating sound waves, sea waves, seismic waves and electromagnetic waves including microwaves, infrared light, radio and television signals.

Successful outcomes have far-reaching results--like protecting deep-water oil rigs from earthquakes and vulnerable beaches from tsunamis.

Uncloaking cloaking's math and science history

Partial differential equations, coordinate invariance, wave equations--when you start talking to researchers about cloaking, it soon starts sounding a lot like math. And that's because at the very heart of this scientific question lies a mathematical one.

"There are very nice mathematical problems associated with this, and some of the ideas are mathematically very, very simple," said Michael Vogelius, NSF's division director for mathematical sciences and whose own research at Rutgers University has contributed significantly to this field. "But that doesn't mean they are simple to implement. In transformation cloaking the materials with the desired cloaking properties are found by singular or nearly singular change of variables in the energy expression--these material coefficients are sometimes referred to as the push-forward (or pull-back) of the original background. Basically, mathematicians ask, 'what do the equations have to look like to get this effect?' The thing that will be very hard--and is very hard--is to build these materials. They are singular in all kinds of ways."

That is why throughout cloaking research history, mathematicians, theoretical physicists and engineers have looked at the problem together.

According to Graeme Milton, an NSF-funded mathematician at the University of Utah, cloaking's start is rooted in math.

"Mathematicians and theoretical physicists basically had the idea independently for transformation-based cloaking," he said, adding that other mathematicians along the way--including himself--have taken the same wave equations and developed them further.

Milton and his collaborators created superlens cloaking, where cloaking occurs near lenses with capabilities far greater than traditional ones, and active exterior cloaking, where cloaking is created by active devices, and the cloak does not completely surround the object.

While cloaking has made considerable theoretical strides, its triumphs have been fairly limited for those awaiting real-world applications.

"Essentially, all the cloaking that has been done successfully in experiment involves a fixed frequency or small band of frequencies," Weinstein said. "So, it's a bit like--suppose you detect things by shining a light on them, and we all agree you're only allowed to shine blue light. I can construct a cloak that will conceal it under blue light, but if you vary the color--that is the wavelength--of the probing light, it will then be detectable. So far, we are unable to cloak something that is invisible to all colors. And because white light is composed of a broad spectrum of colors, no one has come near to making things truly undetectable."

Even with those limitations, there have been distinct milestones in cloaking research.

One of the best examples is actually widely available but probably not commonly thought of as cloaking technology, yet it applies the same sort of math. It involves sounds waves.

"Noise-cancelling headphones are basically cloaking the sounds from outside so they don't reach your ears," Milton said. "Active cloaking is very much along these same lines."

In 2006, as Milton published a key paper that expanded on the superlens cloaking he developed more than a decade earlier, a group of Duke University physicists created the first-ever microwave invisibility cloak using specially engineered "metamaterials," which can manipulate wavelengths, such as light, in a way that naturally occurring materials cannot do alone. However, it only cloaked microwaves and only in two dimensions.

And in 2014, a group in France actually did some experiments with a company to drill 5-meter-deep holes in strategic locations that would modify the earth's density and then measure effectiveness in cloaking. The experiments man-made vibrations that were at a given frequency, not earthquakes. They were able to deflect the seismic waves, showing some possibility to develop this application further.

"Science needs to figure out how to cloak against multiple frequencies before there can be any 'real' cloaking, however," Milton said. "Earthquakes and tsunamis involve a mixture of frequencies, so they are particularly challenging problems."

Passive and active approaches to cloaking research

To understand cloaking, one must first understand where the idea comes from.

When light encounters an object, it is either reflected, refracted or absorbed. Reflection means light waves bounce off an object, like a mirror. Refraction bends light waves, much like looking at a straw in a glass of water seems to break the straw into two pieces. When waves are absorbed, they are stopped, neither bouncing back nor transmitting through the object--although perhaps heating it. Objects which absorb light appear opaque or dark. These interactions between light and objects are what allow us to see those objects.

For cloaking to occur, light must be tricked into doing unusual things that reduce our ability to "see" or detect the object. Mathematicians look for how to control the flow of waves, using wave equations to characterize their behavior. Wave equations are an example of partial differential equation (PDE); PDEs are the language of the fundamental laws of physics. (Just this year, John Nash and Louis Nirenberg received the prestigious Abel Prize for their work in partial differential equations. Their contributions have had a major impact on how mathematicians analyze the PDEs used to understand phenomena such as cloaking.)

"All wave phenomena are predictable from these wave equations--at least in principle," Weinstein said. "That is, light waves, sound waves, elastic waves, quantum waves, gravitational waves. But the problem is that these equations are not so easily solved, so one tries to come up with guiding principles, useful approximations and rules of thumb. Coming to the question of cloaking, there's a mathematical property of wave equations, governing, for example, light, called coordinate invariance. That's basically a way of saying that you can change coordinates and perspectives of viewing the object, and the equations themselves don't change their essential form. By exploiting this idea of coordinate invariance, scientists have come up with prescriptions for optical properties that can cloak arbitrary objects."

In 2009, Milton and colleagues first introduced exterior active cloaking. Scientists in this field describe their research as involving either active or passive cloaking. Active cloaking uses devices that actively generate electromagnetic fields that distort waves. Passive cloaking employs metamaterials that passively shield objects from electromagnetic waves rather than intervening.

"The term 'metamaterial' is a bit deceptive," Weinstein noted. "Metamaterials are roughly composite materials. You take a bunch of building blocks, made from naturally occurring materials, and put them together in interesting ways to create some emergent property--some collective property of this novel arrangement not in naturally occurring materials. That new collective material is a metamaterial. But it's more like a device that actually interacts actively with waves moving through it."

With new metamaterial designs come new cloaking capabilities. NSF-funded engineer Andrea Alù won NSF's Waterman award in 2015 for creating metamaterials that can cloak a three-dimensional object. He and his team developed two methods--plasmonic cloaking and mantle cloaking--that take advantage of different light-scattering effects to hide an object.

Weinstein is exploring, through his research on the partial differential equations governing light, electromagnetism, sound, etc.--different ways of controlling the flow of energy, cloaking being one example, by using novel media such as metamaterials. Vogelius is known for bringing credibility to the transformation optics that serve as a backbone to cloaking broadly.

Where's my invisibility cloak?

But most fans of stealthful space ships, submarines and cloaks will still wonder: how close are we to really having any of this technology?

"I think that from the perspective of lay people, the most misunderstood thing is thinking this technology is right around the corner," Milton said. "Realistic Harry Potter cloaks are still a long way off."

Unfortunately, addressing multi-frequency cloaking will take time.

"What I do see is a merging of mathematical, physical and engineering principles to more effectively enable isolation of objects from harmful environments--there will be movement in that direction," Weinstein said. "Also, there will be important experimental advances resulting from attempts to achieve what is only theoretically possible at this time."

In the meantime, these mathematicians often look at other issues--sometimes similar ones that offer the potential to rethink their approaches.

"Right now, we're working on the opposite sort of problem--on the limitations to cloaking," Milton said. "Cloaking is just one of the many avenues I work on. Honestly, it's always stimulating to explore the limitations of what's possible and what's impossible."

-- Ivy F. Kupec
Investigators
Andrea Alu
Graeme Milton
Michael Vogelius
Michael Weinstein
Related Institutions/Organizations
Rutgers University
University of Utah
Columbia University
University of Texas at Austin

THEORETICAL PHYSICIST LISA RANDALL

FROM:  NATIONAL SCIENCE FOUNDATION
After the lecture: Extra dimensions, interacting dark matter, and the power of uncertainty
A conversation with theoretical physicist Lisa Randall

In her most recent book, physicist Lisa Randall--Harvard professor, libretto composer, Lego figurine, star in the world of theoretical physics--writes that the universe repeatedly reveals itself to be cleverer than we are. This is not a submission to the mysteries of the universe; rather, it's a recognition that the more we discover about the fundamental nuts and bolts of this world, the more questions we have.

Randall works to uncover those fundamental nuts and bolts. She studies theoretical particle physics and cosmology, and her research has advanced our understanding of supersymmetry, models of extra dimensions, dark matter and more. She's made a career out of sharing these discoveries--what they are, how we know them and why they matter--with the public.

Randall is the author of three books and has appeared in dozens of media outlets--from Charlie Rose and The New York Times to The Colbert Report and Vogue. We sat down with Randall after her lecture "New ideas about dark matter" as part of the National Science Foundation's Distinguished Lecture Series in Math and Physical Sciences.

I liked doing math. And I liked understanding how things work. I took a physics class in high school, and I didn't really know for sure that I would be doing it [long term], but I kept going. I enjoyed it. I like that you got answers. I kind of liked that it was challenging.

I think it's important to explain these theories are evolving and what it means for the world. Uncertainty in science isn't actually a bad thing. It actually drives you forward. You can have a lot of certainty even with uncertainty at the edges.

Sometimes it's a question not just of saying 'I'm going to figure this out,' but just with being smart enough to recognize something interesting when it happens. When we found this warped geometry we hadn't been looking for it, it just was a solution. Then we realized what kind of implications it could have. Both in terms of solving the hierarchy problem and explaining particle masses, but also in terms of having an infinite extra dimension.

There's usually a moment when you realize it. Then there are a lot of moments when you think you're wrong and you go back.

I think there's just a lot of ideas about creativity that people don't fully appreciate for scientists. I think there's a lot of ideas about right and wrong that people don't fully appreciate, and how science advances.

I'd just written a book where you try so hard to do everything in a liner order. I'd just written Warped Passages and it was kind of nice the idea of just introducing ideas without having to explain them. And just have different voices. You sort of realize the richness of operas and just expressing ideas and just getting people familiar with something. You have music, you have art, you have words. It's very exciting.

I don't think anyone should just set themselves up to be a role model. I think every person is different, and certainly there's a few enough women that we're all different. But it is true that one of the small advantages you have as a woman is that you are doing something important beyond your work, which is just establishing that women can be out there doing these things. And it is definitely true that when I wrote my book I thought it's good to have someone out there in the public eye, so that people know there are women physicists. And in terms of the response, I can say that--both negative and positive--people do not realize there are women out there sometimes. So it was really important. But it also means you have to put up with a lot of distracting comments and questions sometimes that you wouldn't otherwise.

-- Jessica Arriens,
Investigators
Lisa Randall
Related Institutions/Organizations
Harvard University
Massachusetts Institute of Technology

MATHEMATICIAN SEEKS TO UNDERSTAND MUDSLIDES

FROM:  NATIONAL SCIENCE FOUNDATION

The uphill challenge

Understanding mudslides and other debris flows through mathematics

Mudslides. Landslides. Volcanic debris flows. Avalanches. Falling rocks...

They can come along so suddenly that people, homes, roads and even towns are buried or destroyed without much warning. Recently, we've had dramatic reminders of this, such as the mudslide in Oso, Wash., where 41 people died; an avalanche on Mt. Everest that killed 13 experienced Sherpas and another landslide event in Jackson, Wyo. And as much as ancient Pompeii serves as the most dramatic, historic reminder of the incredible element of surprise these events can wield, what seems extraordinarily incalculable is becoming...well, calculable.

Maybe that doesn't seem so surprising on the surface as one reminisces about math story problems of long ago, such as, "if an avalanche flow is moving at a rate of 50 meters per second, how long will it take to swallow up a village located 30 kilometers away?" Unfortunately, for geologists and others involved in these issues, the particulars make the solution far from simple algebra.

Earthen, volcanic and snowy materials--all of which can move quickly downhill--do so at varying rates depending on their composition, the composition of the geological features over which they flow, and the weather. The benefit to building forecasting models--showing how the earthen materials are prone to move and where they might go post-volcano or during a particularly wet spring--is that they can assist policymaking, urban planning, insurance risk assessment and, most importantly, public safety risk reduction.

One National Science Foundation (NSF)-funded mathematician, E. Bruce Pitman from the University of Buffalo, has been modeling the dynamics of flowing granular materials since 2001 when engineering and geology colleagues came together to start estimating volcanic flow.

"You see these wonderful volcanic eruptions with the plumes, but gravity currents are going down the mountain even as all this stuff is going up into the air," Pitman said. "It can be very deadly. And depending on the mountain--if there's snow on the mountain--then you have this muddy sort of muck, so it can go even faster downhill."

Volcanic flows and mudslides are examples of what geoscientists call "gravity currents."

According to the Centers for Disease Control and Prevention, "landslides and debris flows result in 25 to 50 deaths each year" in the United States. The U.S. Geological Survey (USGS) reports that "all 50 states and the U.S. territories experience landslides and other ground-failure problems," including 36 states with "moderate to highly severe landslide hazards," which include the Appalachian and Rocky Mountains, Pacific Coast regions and Puerto Rico.

USGS notes that areas denuded because of wildfires or overdevelopment are particularly vulnerable to the whims of what's termed generally as "ground failures."

Pitman has spent the past 13 years studying the flows of the Soufrière Hills volcano on Montserrat, the Colima volcano west of Mexico City and the Ruapehu volcano in New Zealand, among other sites. Working with an engineer whose expertise is in high performance computing, statisticians and several geologists, Pitman studies geophysical mass flows, specifically volcanic avalanches and pyroclastic (hot gas and rock) flows, which are "dry" flows.

"We started modeling volcanic flows as dry volcanic flows, so the equation described the material as each particle frictionally sliding over the next particle," Pitman said. "However, we knew it wasn't only solid particles. There could be air or water too, so we developed another model. This naturally makes the analysis harder. In mudslides, you have to factor in mud, which is a viscoplastic fluid--partly like a fluid but also able to deform like a plastic material and never rebound. In wet or dry materials, you can make some reasonable predictions because flow is more or less the same. It is much harder to do that with mud."

Pitman explained the way a mathematician works to develop a predictive model of a landslide.

"There are three questions," he said. "First, is something going to happen? That is notoriously difficult--what's going on under the ground? Where's the water table? How much moisture is in the soil? What's the structure of the soil? Since we can't look under the ground, we have to make all kinds of assumptions about the ground, which poses difficulties.

"Secondly, if a slide were to occur, what areas are at risk? That's something that with a math model you can hope to explain. OK, is the east, west, north or south slope going to slip? How large a flow? Which areas downstream are at risk?

"Lastly, you have to ask what part of the model do you most care about. This helps you to simplify the modeling. Then you run the what-if scenarios to determine the greatest risk. Is it an area at risk and do mudslides happen regularly?"

According to Michael Steuerwalt, an NSF Division of Mathematical Sciences program director, many would be inclined to think that lava flows are far more complicated to model because of the issues of heat and explosive force. However, a mix of dramatically different particle sizes and shapes--which range from dirt grains to people, cars, houses, boulders and trees--can considerably complicate a slide model.

"If you're trying to deduce, for example, where under this mudslide is the house that used to be way up there (along with its inhabitants), then the model is very complicated indeed," Steuerwalt said. "Math won't solve this problem alone, either. But with topographic data, soil data and predictions of precipitation, one could make assessments of where not to build and estimates of risk. This really is an opportunity for mathematicians coupled not only with statisticians, but also with geographers, geoscientists and engineers."

Ultimately, the process needs good data. But it is also about understanding where the model has simplified the equation and created "errors."

"This may sound odd, but it's not about developing the perfect model," Pitman said. "All models have errors in them because we make simplifications to wrap our brains around the physical processes at work. The key is quantifying those errors."

So, essentially the mathematician has to know where to simplify the equation, and that too comes with his collaborative approach and working with other experts, such as volcanologists, and then interfacing with public safety officials.

For a guy who "hated" math in the fifth grade and majored in physics initially in college, this work has turned into something he loves, but also something where he feels he makes a difference.

"I love how this work stretches me and my ability to understand other fields," he said. "I get to explore what interests them and what just might be the little hook that allows me to pry apart a problem."

-- Ivy F. Kupec,
Investigators
Abani Patra
Eliza Calder
Marcus Bursik
Puneet Singla
Tarunraj Singh
E. Bruce Pitman
Related Institutions/Organizations
SUNY at Buffalo

EDUCATION AWARDS $14 MILLION IN GRANTS TO 31 NATIVE AMERICAN AND ALASKA NATIVE ENTITIES

FROM:  U.S. DEPARTMENT OF EDUCATION 
U.S. Department of Education Awards $14 Million in Grants to 31 Native American and Alaska Native Entities
SEPTEMBER 25, 2013

The U.S. Department of Education today announced the award of about $14 million in grants to 31 Indian tribes, tribal organizations, and Alaska Native entities to help them improve career and technical education programs.

Under the 2013 Native American Career and Technical Education Program (NACTEP) competition, the Department encouraged applicants to propose projects that included promoting science, technology, engineering and mathematics (STEM), and the use of technology within career and technical education programs. Career and technical education in the STEM fields is important to providing students with education that can lead to employment in high growth, in-demand industry sectors.

"In today's global and knowledge-based economy, it's critical that we prepare all students for jobs that lead to a success career," said U.S. Secretary of Education Arne Duncan. "These grants will help underrepresented groups attain the necessary resources to earn an industry certification and postsecondary certificate or degree, while also strengthening our country’s global competitiveness."

The NACTEP requires the Secretary to ensure that activities will improve career and technical education for Native American and Alaska Native students. Additionally, NACTEP grants are aligned with other programs under the Carl D. Perkins Career & Technical Education Act of 2006 that require recipients to provide coherent and rigorous content aligned with challenging academic standards. NACTEP projects also include preparing students for the high-skill, high-wage, or high-demand occupations in emerging or established professions.

Below is a list of the 2013 NACTEP Grantees:

Cook Inlet Tribal Council, Inc. (Alaska) $417,543

Council of Athabascan Tribal Governments (Alaska) $470,022

Pascua Yaqui Tribe (Ariz.) $411,460

Hoopa Valley Tribe (Calif.) $470,130

Coeur d’ Alene Tribe (Idaho) $469,362

Keweenaw Bay Ojibwa Community College (Mich.) $341,938

Little Traverse Bay Bands of Odawa Indians (Mich.) $452,804

Mississippi Band of Choctaw Indians (Miss.) $470,689

Aaniiih Nakota College (Mont.) $467,256

Blackfeet Community College (Mont.) $386,966

Blackfeet Tribal Employment Rights Office (Mont.) $464,890

Fort Peck Community College (Mont.) $469,785

Salish Kootenai College (Mont.) $471,559

Stone Child College (Mont.) $473,556

Winnebago Tribe of Nebraska (Neb.) $469,345

Cankdeska Cikana Community College (N.D.) $450,564

Fort Berthold Community College (N.D.) $452,874

Sitting Bull College (N.D.) $415,660

Turtle Mountain Community College (N.D.) $471,466

Alamo Navajo School Board, Inc. (N.M.) $471,937

Coyote Canyon Rehabilitation Center, Inc. (N.M.) $473,912

Cherokee Nation (Okla.) $470,425

Choctaw Nation of Oklahoma (Okla.) $468,923

Shawnee Tribe (Okla.) $434,613

Pawnee Nation College (Okla.) $470,956

Oglala Lakota College (S.D.) $467,835

Sinte Gleska University (S.D.) $466,900

Muckleshoot Indian Tribe (Wash.) $437,674

Northwest Indian College (Wash.) $416,097

The Tulalip Tribes of Washington (Wash.) $451,113

College of Menominee Nation (Wis.) $472,994