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October 20, 2008

Sic Transit

My previous article was the five hundredth entry on this blog, started on August 10, 2006. I've decided to cease publication of this blog. The computer scientist part of me wanted to hold out for a round number, like 512 (100000000 in base two) [1], but the pressures of my daily activities have become too severe. This blog has been an extracurricular activity, since there is no "blog project" and no corresponding project number to which I can charge my time. At my current billing rate, the five hundred articles on this blog qualify as a six-figure enterprise, so I must qualify for a gold star in pro bono activity.

The title of the article is derived from the Latin phrase, Sic transit gloria mundi. This is translated literally as, "Thus passes the glory of the world," but more descriptively as, "All worldly things are fleeting." I have several filing cabinets in my office full of research reports that were extremely important at the time, but they are now essentially worthless. It's said that only one of ten research projects is found to be worthwhile. In that case, my thirty years at Allied Chemical/Allied Corporation/Allied-Signal/Honeywell may have produced only three years of important work. Perhaps some of these five hundred articles were written in my composite Wonder Years.

As a substitute for this blog, I recommend Jennifer Ouellette's Cocktail Party Physics. Jennifer's articles are highly accessible to the non-specialist, and she writes about many of the same topics as this blog. I'm quite impressed by the length of her articles, and I must confess I'm somewhat envious of her blog; but she's a professional writer, and I'm a mere bench scientist. Another recommended physics-oriented blog with multiple contributors is Cosmic Variance.

*** Note added May, 2010 ***

Dev's Blog can be found now at Tikalon.com. Here's the new location.

1. A computer scientist is the type of scientist who transfers $32,768 from one bank account to another to see what happens.

October 17, 2008

Bring in 'Da Noise, Bring in 'Da Funky Circuits

Noise is the bane of physicists and electrical engineers. Our cell phones, satellite television and satellite radio are as much a consequence of improvements in the signal to noise ratio of high frequency amplifiers as they are a result of all those fancy analog and digital techniques. Perhaps I'm showing my age when I recall the time when 10 Mhz considered a high frequency for a transistor amplifier. White noise is the frequency-independent noise that plagues high frequency circuits. However, there is another type of noise that operates at low frequencies; in fact, it has an inverse frequency dependence, and is therefore called "1/f" noise. One-over-f noise is often called "flicker noise," possibly because it's an audio version of a flickering candle. A 1/f noise voltage is commonly seen across carbon composition resistors conducting large currents, and this is additional to the thermal noise seen across any resistor above absolute zero and covered in one of my previous articles.

An international team of scientists from Argonne National Laboratory (Argonne, Illinois USA), the University of Oslo (Norway), and the Russian Academy of Sciences (St. Petersburg, Russia) investigated 1/f noise in doped semiconductors [1]. They found that it originates in the random distribution of the dopant atoms and their interaction with adjacent electrons; specifically, by forcing the electrons to hop from one random location to another. This particular assemblage of randomly distributed and hopping electrons is called a "Coulomb glass." Computer simulations verified this Coulomb glass model of 1/f noise in semiconductors. Valerii Vinokour, the author of this paper from the Materials Science Division of Argonne National Laboratory, says that this is a general result that links all types of 1/f noise, not just the 1/f noise in semiconductors, with a random distribution of interacting agents. These 1/f noise sources are as diverse as information flow on the internet and traffic flow on highways [2].

Bring in 'Da Noise, Bring in 'Da Funk was a Broadway musical choreographed by Savion Glover. It's a retelling of black history through tap dancing, and it bested the popular "Rent" in several categories at the fiftieth annual Tony Awards, including Best Choreography. The show closed in 1999 after more than a thousand performances.

1. A. Glatz, V. M. Vinokur, and Y. M. Galperin, "Statistics of Deep Energy States in Coulomb Glasses," Phys. Rev. Lett., vol.98, 196401 (7 May 2007).
2. New '1/f noise' discovery promises to improve semiconductor-based sensors (Argonne National Laboratory Press Release, May 10, 2007).

October 16, 2008

They Travel in Pairs

We've all worked on teams. Even Einstein had his collaborators[1]. In Physics and Chemistry, some names are remembered in pairs.

Bose-Einstein: statistical distribution of energy for indistinguishable particles in thermal equilibrium.

Heitler-London: First quantum mechanical calculation in Chemistry (the hydrogen molecule, 1927).

Stern-Gerlach: Stern and Gerlach demonstrated that particles (in their experiment, electrons) obey quantum mechanics.

Davisson-Germer: In 1927, Davisson and Germer, working at Bell Labs, confirmed the de Broglie hypothesis that matter has wave properties.

Wiedemann-Franz: Wiedemann and Franz found that the ratio of thermal to electrical conductivity is proportional to temperature for metals.

Debye-Waller: Crystal lattice disorder.

Kronig-Penney: Quantum behavior of a particle in a one-dimensional periodic potential.

Kolmogorov-Smirnov: The Kolmogorov-Smirnov test is a statistical test for an hypothesis when only a small sample size is available.

Brunauer-Emmett-Teller: Three for the price of two! An isotherm used to determine surface area of solids by gas absorption.

Titius-Bode: The Titius-Bode Law relates the distance of planets from the sun to a numerical sequence.

Born-Oppenheimer: The Born-Oppenheimer approximation represents particle interactions using a scalar potential.

But, don't be fooled! Lennard-Jones, of the eponymous Lennard-Jones Potential, was an individual with a hyphenated name.

1. While I was at Syracuse University, I took a course in Mechanics from Peter G. Bergmann. Bergmann worked with Einstein in the late 1930's. For those of you who complain about your long commute, Bergmann lived in Manhattan and traveled to Syracuse for teaching.

October 15, 2008

What's Your Wavelength?

In a previous post (Photon Momentum, March 15, 2007), I wrote about the momentum of a photon. Since momentum for massive particles is defined as the product of mass and velocity, you would think that photons would have no momentum, since they have no mass. Well, life is strange in the quantum world, and photons do have momentum. A stranger case is that massive particles have a wavelength, and they can demonstrate the same properties as light under the right conditions. This was an hypothesis of physicist Louis de Broglie (1892-1987), who won the Nobel Prize for Physics in 1929.

Louis de Broglie (pronounced "de Broy") is a special case of a physicist in more than one respect. First, he was a member of the French nobility and was officially called Louis Victor, the Seventh duc de Broglie. This didn't dissuade his teaching theoretical physics at the Sorbonne, where he had obtained his Ph.D. under Paul Langevin. Second, he won the Nobel Prize based on the work for his Ph.D. thesis, the first person to have this distinction (Rudolf Ludwig Mössbauer is a later example). Among his many honors, he was Perpetual Secretary of the French Academy of Sciences, and he received the first Kalinga Prize from UNESCO for popularizing science.

De Broglie's hypothesis, the topic of his 1923 thesis, "Recherches sur la Théorie des Quanta," was that electrons could have a wave nature. This was a consequence of the principle of wave-particle duality that was introduced into Quantum Mechanics to explain the various properties of light. Light behave sometimes as a wave, sometimes as a particle, so physicists threw up their hands and decided that light was both a wave and a particle. De Broglie turned this reasoning around and conjectured that particles should act also as waves.

Of course, a crazy idea is only crazy enough for a Nobel Prize if it's proved by experiment. The experimental confirmation occurred in 1927 at Bell Labs, where Clinton Davisson and Lester Germer fired electrons at a crystal of nickel and showed that the pattern of the reflected electrons obeyed Bragg's Law. What is surprising to me, and to many physicists, is that Davisson and Germer did not share the Nobel Prize with de Broglie. Their experiment is considered by most to be pivotal in the acceptance of Quantum Mechanics.

Electrons are one thing, but what about "real" objects? According to de Broglie, the wavelength λ of an object is a function of Planck's constant (h, 6.626068 x 10-34 m2 kg / s) and its momentum p.

λ = h/p

I weigh about 88.5 kg, and a good walking pace is 1.5 meters/second, so my wavelength in meters while walking is

λ = h/p = 6.626068 x 10-34/(88.5 x 1.5) = 5 x 10-36 meters

What this means is that I have very little wave nature [1], so if you see me diffracting off the corridor walls as I walk, it must be because I'm distracted.

1. A famous Zen koan involves the question, "Does a dog have Buddha-nature?" Physicists consider instead whether a dog has wave nature.
2. Biography of Louis de Broglie at the Nobel Prize Web Site.

October 14, 2008

The Monty Hall Problem

Mathematical probability theory has its origins in the very human pastime of gambling. The mathematicians, Blaise Pascal and Pierre de Fermat, started the study of probabilities in an exchange of letters in 1654. The field was fairly well established in 1713 when Jacob Bernoulli's Ars Conjectandi was published, followed shortly thereafter by Abraham de Moivre's Doctrine of Chances (1718). After nearly three centuries of research in this field, you would think that there would be a consensus among mathematicians for every simple gaming problem expressed in about fifty words. This is not true for the Monty Hall problem, succinctly stated by the computer scientist, Brian Hayes, as follows [1]:

"You are shown three doors and told that exactly one of them has a prize behind it. After you choose a door, Monty Hall (who knows where the prize is) opens one of the two unchosen doors, showing that the prize is not there. You are then offered a choice: Stick with your original door or switch to the remaining unopened door."

The problem is this, do you increase your chance of winning if you change your choice from your selected door to the other available door? There's no question that your initial probability of success is 1/3, but after one door is opened, does your chance of success become 1/2? As it turns out, it's always best to switch your choice to the other door, and the reason resides in Bayes' theorem of posterior probabilities. Bayes's theorem allows a revised calculation of probability based on observation. The observation in the Monty Hall case being the fact that the game host was required to open a door, but it must be a door without the prize [2]. Those who change doors will win 2/3 of the time; those who don't will win only 1/3 of the time.

Bayes notwithstanding, much has been written about this problem in both the popular and academic press, so Hayes did what any computer scientist would do - he simulated the game. No supercomputer was required, and any computer-literate teenager could write such a program and get the same results. After 100,000 simulations, the door switchers won 66,841 times, and the steadfast players won 33,329 times [3]. The agreement between experiment and theory is quite superb.

1. Brian Hayes, "Monty Hall Redux," American Scientist, vol. 96, no. 5 (September-October, 2008), p. 434.
2. Monty Hall problem (Wikipedia).
3. Brian Hayes, "Programs and Probabilities," American Scientist, vol. 96, no. 4 (July-August, 2008), p. 334.

October 13, 2008


The title of this article may sound like a football cheer for GP University, but it expresses the progression of computer architectures.

CISC, or Complex Instruction Set Computer.

RISC, or Reduced Instruction Set Computer.

GPU, or Graphics Processing Unit

The first stored program computers were all CISC. These included the first commercial minicomputer, the DEC PDP-8, the Motorola 68000 (used in the Apple Macintosh), and the ubiquitous Intel X86 architecture. One look at the PDP-8 instruction set may make you wonder what about it is "complex," but the definition is more about the way data is stored and how it's moved in the CPU, rather than its complexity.

In one sense, the RISC architecture necessarily came after CISC, or there would have been nothing to "reduce." Famous RISC systems are the ARM, MIPS and SPARC. An easy way to identify a RISC architecture is by counting the number of data registers. RISC chips have a lot of registers. The MIPS chip has thirty-two general purpose registers, and the SPARC has 128.

Where do graphics chips figure into this progression of computer architectures? Most desktop computers have dedicated graphics chips for display, since the computing tasks of the typical graphical user interface (GUI) would steal too many cycles from the CPUs. Most display rendering tasks involve fast matrix and vector operations, and these are useful for many non-graphical calculations. A few years ago, computer scientists started to realize that GPU chips could be used for many applications requiring parallel computations, a computational regime previously reserved for supercomputers. An example calculation of this sort is genetic programming. Building computers containing many GPU chips allows some supercomputer-style processing to be implemented cheaply.

An article [1] in a recent issue of Electronic Design magazine describes how Nvidia Corp., a major supplier of GPU chips, has decided to simplify general processing on its chips. Nvidia has developed a variant of the C programming language that it calls Compute Unified Device Architecture (CUDA). CUDA allows programmers to write programs that take advantage of the multi-core parallel processors in GPU chips. To spur development in CUDA, Nvidia has created a CUDA Center of Excellence at the University of Illinois by donating half a million dollars. CUDA is being used by the University of Illinois Theoretical and Computational Biophysics Group for biophysics computations. Agilent is working with Nvidia on signal analysis, achieving more than an order of magnitude improvement in some applications.

Following the razor-and-blade marketing approach, Nvidia is hoping that CUDA will sell more of its GPU chips, so it's released CUDA free of charge at www.nvidia.com/cuda.

1. Joseph Desposito, "Is Your Personal Computer A CUDA-Enabled Speed Merchant?" Electronic Design, vol. 56, no. 19 (September 25, 2008), p. 15.

October 10, 2008

Madam I'm Adam

A palindrome is something that reads the same in either direction. As a convention, capitalization and punctuation are ignored, or else the invention of palindromes would be too hard, and the palindromes themselves wouldn't be interesting. Although the word palindrome wasn't devised until the 1600s by Ben Jonson, the English writer and a rival of Shakespeare, there are ancient examples of palindromes. A palindromic name for palindromes would have been apt, but I guess that Jonson couldn't devise one.

Many students complain about the useless of most of the mathematics they are forced to study. However, there is one mathematical concept that even mathematicians declare useless, palindrome primes. A prime number, of course, is a number that is only divisible without remainder by itself and one. Prime numbers have an important place in mathematics, in cryptography, and internet security. A palindrome prime is a prime number which is also a palindrome, a few examples are 181, 727, 929, and 11311. The sequence of palindrome primes (designated as integer sequence A002385) is thought to be endless, but this is an unproven conjecture. Of course, humans tend to think in base ten, but there are palindrome primes in all number bases. The hexadecimal (base 16) number BCB (decimal 3019) is a palindrome prime.

One of the best ways to learn a computer language is to write an actual application program in that language. Searching for palindrome primes is a good way to learn a new computer language. Among other things, you need to efficiently find prime numbers, convert numbers to character strings, test whether these strings are palindromes, and write your results to a graphical user interface or data file. In effect, you will be using most of the capabilities of the language. You also learn about the limits of a language; for example, how large a number you can stuff into an unsigned integer. I did this many years ago in Visual Basic (VB3). If you're interested, I could e-mail the program to you.

In 1987, Brian Westley wrote a C program, itself a palindrome, that generates the palindrome, "Able was I ere I saw Elba," for the The International Obfuscated C Code Contest. I tried the code on my gcc compiler [3], and it compiled and executed without error.

For those of you who are looking for "prime" real estate, people who live in Oakland CA, live in a palidrome prime zip code (94649), one of forty-five.

1. World!Of Palindromic Primes
2. Ivars Peterson, "Primes, Palindromes, and Pyramids" (Science News Online, August 25, 2005).
3. Command line for Linux fans: gcc westley.c -o palindr

October 09, 2008

2008 Nobel Prize in Chemistry

One day after the announcement of the winners of this year's Nobel Prize in Physics comes the announcement of the winners of the 2008 Nobel Prize in Chemistry. Osamu Shimomura of the Woods Hole Marine Biological Laboratory, Martin Chalfie of Columbia University and Roger Tsien of the University of California (San Diego) won for the discovery of what's known as green fluorescent protein (GFP) and its subsequent application as a genetic marker [1-5]. GFP, which emits a bright green light under ultraviolet excitation, was discovered by Shimomura in the jellyfish, Aequorea victoria, in 1962 off the coast of Washington state. Shimomura made regular visits there to harvest the jellyfish, sometimes gathering thousands in a single day, and his annual jellyfish harvest was typically two and a half tons.

After many years, Shimomura was able to isolate and purify GFP. A great leap in bioscientific research came about when Chalfie and others spliced the GFP gene into E. Coli and C. elegans to get them to express this protein as well. The GFP gene has served as a taggant for toxins and cancer cells, and it can monitor when other genes are turned on or off. Tsien improved GFP by making it more efficient, and he discovered similar proteins in coral that emitted other colors, so several biological processes can be traced simultaneously. Lest you think that winning a Nobel Prize is as easy as a fishing trip, the GFP protein on which Shimomura labored has a molecular weight of 26,900 Daltons, and it's composed of 238 amino acids. The major excitation band is centered at 395 nm and there's a minor excitation band at 475 nm. The peak emission is at 509 nm, which is a bluish-green [6].

GFP has become a cultural phenomenon, as well. A green-glowing bunny was commissioned by the artist, Eduardo Kac. Green-glowing pigs have been created, and these pigs pass along their green gene to their offspring. Some articles on the internet state that GFP has been used to create "fine art," but somehow bunnies and pigs don't seem to be in the same category as the Mona Lisa.

Osamu Shimomura is a Japanese citizen. He has a PhD in organic chemistry from Nagoya University. Martin Chalfie and Roger Y Tsien are both US citizens. Chalfie has a PhD in neurobiology from Harvard University, and Tsien has a PhD in physiology from Cambridge University. The three will share equally the $1.4 million cash award.

1. Niklas Pollard, "Green jellyfish protein scientists win Nobel" (Reuters, October 8, 2008).
2. Kenneth Chang, "Three Chemists Win Nobel Prize" (New York Times, October 8, 2008).
3. Matthew Herper, "Biotech's Glowing Breakthrough Wins Nobel Prize" (Forbes, October 8, 2008).
4. 'Glowing' jellyfish grabs Nobel (BBC, October 8, 2008).
5. James Randerson, "Nobel prize for chemistry illuminates disease" (Guardian (UK), October 8, 2008).
6. Green fluorescent protein (Wikipedia).

October 08, 2008

2008 Nobel Prize in Physics

This year's Nobel Prize in Physics was awarded to three theoretical physicists who applied the idea of spontaneous symmetry breaking to the behavior of elementary particles [1-5]. Yoichiro Nambu of the University of Chicago's Enrico Fermi Institute was awarded half this year's prize of $1.4 million for being the first to apply the mathematical formalism of spontaneous broken symmetry to the forces that exist in the subatomic regime. Makoto Kobayashi of the Tsukuba High Energy Accelerator Research Organization and Toshihide Maskawa of Kyoto University's Yukawa Institute for Theoretical Physics will share equally the other half of the prize. Kobayashi and Maskawa showed that the violation of a combined type of symmetry involving charge conjugation (replacing a particle with its antiparticle) and parity (replacing a system with its mirror-image) could be explained if there were three families of quarks. The combined work of these physicists led to a major advance in the standard model of particle physics. In an unusual display of prescience, I discussed quarks in a recent article (Three Quarks for Muster Mark, September 16, 2008). I gave an example of symmetry breaking in a previous article (Symmetry Breaking, April 16, 2007).

The Universe would be a far different place if everything were symmetrical. On a most fundamental level, perfect symmetry would require an equal number of matter and antimatter particles to have existed in the early days (actually, pico-yactoseconds) of the universe. These would have annihilated each other, leaving nothing but photons, and we wouldn't exist. An exceedingly small breaking of the particle-antiparticle symmetry allowed an extra particle of matter for every ten billion antimatter particles, thus allowing the universe to exist as we know it. Of course, science is founded on experimental confirmation of theory. Charge conjugation - parity violation (CP Violation) was confirmed by James Cronin and Val Fitch in 1964, and they shared the Nobel Physics Prize in 1980. Nambu first discovered spontaneous symmetry breaking in superconductivity, a collective behavior of electrons far removed from the subatomic regime. With this experience, Nambu was able to discern symmetry breaking in elementary particle interactions and express this as a scalar field theory that could be manipulated mathematically to give novel results.

Elementary particles have been well represented in Nobel Prizes since the 1980 award to Cronin and Fitch [6].

• 1980 - James Cronin and Val Fitch (Discovery of CP Violation in K-meson decay).

• 1984 - Carlo Rubbia and Simon van der Meer (Elucidation of the weak interaction).

• 1988 - Leon M. Lederman, Melvin Schwartz and Jack Steinberger (Lepton physics).

• 1990 - Jerome I. Friedman, Henry W. Kendall and Richard E. Taylor (Refined quark model).

• 1992 - Georges Charpak (Advanced particle detectors).

• 1995 - Martin L. Perl and Frederick Reines (Lepton physics).

• 1999 - Gerardus 't Hooft and Martinus J.G. Veltman (Electroweak interaction).

• 2004 - David J. Gross, H. David Politzer and Frank Wilczeck (Discovery of the strong nuclear force and quarks).

Nambu, who is 87, is a naturalized US citizen born in Japan. He became a U.S. citizen in 1970. Kobayashi is 64, and Maskawa is 68. They are both Japanese The Nobel Prizes are awarded formally on December tenth in Stockholm, Sweden.

1. Ron Cowen, "Nobel Prize in physics shared for work that unifies forces of nature" (Science News Online, October 7, 2008).
2. Dennis Overbye, "1 American, 2 Japanese Share Nobel Physics Prize" (New York Times, October 8, 2008).
3. Matt Moore and Karl Ritter, "2 Japanese, 1 American share Nobel physics prize" (Associated Press, October 7, 2008).
4. Ian Sample, "Nobel prize for physics goes to work on fundamental laws of nature" (Guardian (UK), October 7, 2008).
5. Particle physics celebrates Nobel (BBC News, October 7, 2008).
6. Recent winners of the Nobel Prize in physics (Associated Press, October 7, 2008).

October 07, 2008

Mathematics, Astronomy and the Happy Face Crater

The link between mathematics and astronomy was first established by Johannes Kepler, who is known for his Laws of Planetary Motion. These are

• The movement of every planet traces an ellipse with the sun at one of the foci.

• The line drawn between a planet and the sun sweeps out equal areas in equal time intervals as it obits the sun.

• The time it takes a planet to circle the sun T is related to the semi-major axis of its elliptical orbit b by the expression T2 = k b3, where k is a constant with a value of about 3 x 10-19 sec2/m3.

Kepler discovered these laws in 1605 using data from detailed observations by his mentor, Tycho Brahe. It wasn't until 1687 when the physical basis of these laws, universal gravitation, was discovered by Newton.

Of course, these laws express the movement of isolated planets under the gravitational influence of the sun alone, and it soon became apparent that other gravitational forces were influencing the orbit of the seventh planet, Uranus. In the mid-1800s there were several calculations done for the orbit of an eighth planet which would cause the observed deviation in Uranus' orbit. Using the calculations of Urbain Le Verrier, Johann Gottfried Galle discovered the eighth planet, now called Neptune, on September 23, 1846, very close to where Le Verrier had predicted it to be. Needless to say, the mathematical approach to astronomy was vindicated. It's interesting to note that Galileo had observed Neptune more than two hundred years earlier, but he thought it was a star. This is probably all for the best, since you can imagine the trouble this would have caused him.

There is a crater on Mars named after Johann Gottfried Galle. This crater is known also as the "Happy Face" crater for its resemblance to the pop icon [1]. There's another Galle crater on the Moon, and a ring of Neptune is named after Galle. The Galle Ring of Neptune has an orbital radius of 41,900 km and a width of 2000 km.

1. Photograph of the Galle Crater on Mars.

October 06, 2008

Going with the Flow

When I was a child, I loved reading comic books. At that age, they were the only good reason for learning how to read. In those days, there were very few supermarkets; instead, there were small corner grocery stores. The grocery store across the street from my parents' apartment sold used comic books at quite a discount over the cover price. Their comic book enterprise was fueled by the proximity of the local high school. The high school students were the key to this used book market, since they were the only ones with enough money to buy new comics. The selection of used books mirrored the interests of these high school students, so many of the comics were of the science fiction-amazing stories variety. One story I remember is about a man with incredible luck. He would wager on the outcome of everyday events, such as which raindrop would slide down a pane of window glass faster than another. As it turned out, he made his own luck, because he prepared objects to give him the edge he needed. In the raindrop example, he had prepared the window pane with a thin track of oil on one side so water droplets would move faster on that track. This made me wonder about two things. How could he possibly do all this successfully, and why do water droplets move faster on an oily surface. I decided that the answer to the first question was just artistic license. Years later, I discovered that the answer to the second question was surface energy, in this case, hydrophobicity.

Beyond the case of a single rain drop is the steadier water flow in a rivulet. Rivulets running down a partially wet surface exhibit a dynamic meandering pattern. Factors that will affect the rivulet flow include surface tension and the fine-grained hydrophillicity of the surface, which contributes to contact angle changes. The resultant problem is so nonlinear that physicists have avoided its analysis until a non-meandering flow regime was discovered to occur when flow rate was constant [1-2]. This discovery suggested that meandering may be caused by flow rate fluctuations.

A recent paper [3] in Physical Review Letters examined the meandering of water rivulets on a hard inclined surface, in this case, a 2.4 meter surface that could be inclined up to sixty degrees. As in the previous work, a straight stream was obtained when flow rate disturbances were absent. The meandering was induced in the steady rivulet by changing the flow rate of the water through use of a modulated valve that interrupted the water flow for a tenth of a second every second. The meandering was influenced also by the water left on the surface by previous rivulets. These experiments demonstrated a power-law distribution of water flow from a center line, which rules out the idea that there's a preferred wavelength associated with meandering.

As could be expected, stream splitting occurs usually at points of high curvature in the rivulet stream. The research team, which involved a mechanical engineer from the University of New Mexico and mathematicians from the University of California (Santa Barbara) and Colorado State University (Fort Collins), derived a model for meandering from first principles that agrees with the experimental observations. Their interpretation of the meander mechanism is that flow variations allow perturbations to propagate upstream.

1. K. Mertens, V. Putkaradze, and P. Vorobieff, "Braiding patterns on an inclined plane," Nature, vol. 430, no. 6996 (July 8, 2004), pp. 165ff.
2. K. Mertens, V. Putkaradze, and P. Vorobieff, "Morphology of a stream flowing down an inclined plane. Part 1. Braiding," J. Fluid Mech., vol. 531 (May, 2005), pp. 49-58.
3. Björn Birnir, Keith Mertens, Vakhtang Putkaradze, and Peter Vorobieff, "Meandering Fluid Streams in the Presence of Flow-Rate Fluctuations," Phys. Rev. Lett., vol. 101 (September 12, 2008), 114501.

October 03, 2008

The Actress, the Composer, and the Patent

One way to send a secure message through the mails without encryption is the following. Send each word in a separate letter. If several of the letters are intercepted, there would be little chance that the message could be discerned. This is an analogy of a communications technique known as frequency-hopping spread spectrum. Instead of sending each word in a separate envelope, you transmit it on a separate frequency. This communications technique was patented during World War II by the actress, Hedy Lamarr, and the avant-garde composer, George Antheil.

Hedy Lamarr (1913-2000), also known as Hedwig Eva Maria Kiesler Markey, was a film actress. She had attended a meeting with a former husband, Friedrich Mandl, an Austrian munitions manufacturer, at which the problems of secure communications were discussed. Eventually, she and George Antheil co-invented the concept of a frequency-hopping radio. The influence of musician George Antheil is evident in the embodiment. They proposed using a player-piano roll to move between eighty-eight frequencies according to a code punched in the roll. Their patent, US Patent no. 2,292,387, "Secret Communications System", had long expired before the first commercial implementation, when it was used by ships of the US Navy in 1962 during the Cuban Missile Crisis. Although Lamarr made no money from her patent, she received an award in 1997 from the Electronic Frontier Foundation, a foundation dedicated to privacy, free speech, and fair use rights in the electronic age [1]. Today, spread-spectrum communications are used in many home communications devices, such as cordless telephones and Wi-Fi networks.

George Carl Johann Antheil (1900-1959) was an avant-garde composer in the most extreme sense. His most famous work, Ballet Mécanique (1924), uses an airplane propeller as a sound-making device. This was too much to take for many an audience, so he was not accepted as a serious composer. He eventually earned the title, "bad boy of music," and it wasn't until the time of John Cage that such shenanigans were acceptable. Antheil wrote the theme for the CBS television show, "The 20th Century," narrated by Walter Cronkite from 1957-1970 [2]. This is likely his most heard composition. I watched The 20th Century studiously when I was a child, and I still remember the theme song.

1. I've been a member of the Electronic Frontier Foundation for many years. You can view the web site here.
2. Walter Cronkite's The 20th Century on the Internet Movie Database.

October 02, 2008

The Ulam Spiral

Prime numbers have fascinated mathematicians long before they had utility in securing internet transactions. A number is prime if it can't be expressed as the product of other numbers, a process called factoring or factorization. I mentioned tests for prime numbers in a previous article (Independence Day, July 4, 2007). Cryptographically secure communications are based on the idea that it's easy to multiply large prime numbers, but difficult to find the prime factors of numbers [1]. One interesting property of prime numbers is that large prime numbers occur less frequently than small prime numbers. One way to explain this is that large numbers have many predecessors which may be their factors (at least up to their square root). What's most unusual, however, is the fact that the distribution of prime numbers can be expressed as an equation. On the average, the probability p that a randomly selected number N will be prime is given as

p = 1/ln(N)

Where ln(N) is the natural logarithm of N. This approximation is good for large numbers, but not that good for smaller numbers. For example, there are no primes between 31398 and 31468, but the equation predicts six.

One person associated with the unusual properties of prime numbers is Stanislaw Ulam (1909-1984), a prolific mathematician who worked on many fundamental physics problems. Ulam participated in the Manhattan Project, and he was co-inventor, with Edward Teller, of the hydrogen bomb. When he was invited by his friend and fellow mathematician, John von Neumann, to join this secret government project in New Mexico, he did what any scientist would do - he went to the university library to research New Mexico. When he saw that a popular book on New Mexico had been checked-out by quite a few talented faculty members who hadn't been seen on campus for a while, he decided to accept von Neumann's invitation. Ulam was one of the first scientists to use computers to perform what he called "mathematical experiments," which are now called computer simulations. One of Ulam's most important contributions in this area was a simulation of a non-linear system called the Fermi-Pasta-Ulam problem.

As happens to most of us, Ulam's mind started to wander during a scientific meeting, and he started to doodle, writing an array of numbers on a grid. He put 1 in the center, and he continued the number sequence on the grid, spiraling around the central number. He found that prime numbers were concentrated along diagonals in the plane [2]. Not all primes were on diagonals on the Ulam Spiral, but a significant fraction were. Extensive computer studies have shown that this diagonal effect is present when the central number is any number, and it is true for very large numbers. What this means is that the formula

f(n) = 4n2 + kn + c

generates a sequence of numbers that has a high proportion of prime numbers for any constants k and c. A more dramatic version of the Ulam spiral was created by Robert Sacks.

Ulam was the first to voice the concept of a technological singularity, a time after which technological progress would proceed so quickly that human culture would crumble. I think this singularity is near, because it seems that I spend more time working for my computer than my computer works for me.

1. D. M. Gualtieri, "Keeping Secrets," Phi Kappa Phi Forum, vol. 83, no. 2. pp. 6-7 (Spring 2003). Copy available via e-mail request.
2. Image of an Ulam Spiral (Wikipedia).

October 01, 2008

Noctilucent Clouds

Since weather radar is ubiquitous, appearing on the internet as well as on television, everyone is familiar with the idea that water precipitation can be detected by radar. Not many people have thought to question why rain can be seen by radar, but not the clouds from whence it comes. The important factor here is the size of the radar-reflecting water particles. Typical weather radar operates at a wavelength of a few centimeters, so the ratio of the radar wavelength to the water particle size is large. This is the condition known to optical physicists as Rayleigh scattering. Rayleigh scattering is distinguished from Mie reflection, in which the particle diameter is about the same as the wavelength. It's the particle size that determines the radar reflectivity. In fact, the reflectivity for Rayleigh scattering is proportional to the sixth power of the particle size. It's no wonder that clouds, which are composed of small ice crystals, are invisible to radar.

There are some mysterious clouds known as noctilucent clouds in Earth's upper atmosphere at the edge of space [1-4]. These clouds get their name from their glow-in-the-dark property. These clouds occur at about 85 kilometers in altitude, where the air is rare and the sky is as black as space. In fact, 99.999% of the Earth's atmosphere resides below that altitude, and the density of water is many orders of magnitude smaller than that in the air above a desert. Astronauts on the International Space Station have seen these clouds, but their apparition is not reserved for astronauts only. Noctilucent clouds were first noted after the eruption of the volcano, Krakatoa, in 1883. This eruption, equivalent to 200 megatons of TNT, put enough volcanic dust into the atmosphere to cause spectacular sunsets for many years thereafter. Robert Leslie of Southampton, England, published the first observation of noctilucent clouds, noted as wispy blue filaments, in the journal Nature. He observed the clouds in July, 1885.

Since our ancestors, who were keen observers of the night sky, had not seen such clouds, it was assumed that they were another side-effect of the Krakatoa explosion. Noctilucent clouds, however, have been observed continually since Leslie's observation. Observations were typically reserved at high latitudes, but observations have begun to be reported in the continental United States, below 49-degrees north latitude. There's the hypothesis that the existence of these clouds may be a consequence of industrialization or global warming, and geophysicists and meteorologists are interested enough to have secured the launch of the Aeronomy of Ice in the Mesosphere (AIM) satellite to study these clouds.

There's another unusual feature of noctilucent clouds. Their radar reflectivity is large, much larger than can be expected from ice crystals in a cloud. This was discovered about twenty-five years ago at the Poker Flat Research Range, a research rocket range operated by the University of Alaska (Fairbanks, Alaska). Paul Bellan, a physicist at the California Institute of Technology (Pasadena, California) has recently published an article in the Journal of Geophysical Research-Atmospheres that explains this anomalous radar reflectivity as caused by a thin coating of the metals, iron and sodium, on the surface of the ice crystals [5-6]. The sodium and iron comes from micrometeors that vaporize in the same region of the atmosphere that hosts noctilucent clouds. Measurements indicate that eighty percent of the available sodium is scavenged by these clouds since they are extremely cold (more than a hundred degrees below zero Celsius). It's not just the enhanced radar reflectivity of the individual grains that's responsible; rather, ripples in the clouds cause a phase-reinforcement of the radar signal that enhances the reflectivity, much like the diffraction of xrays from a crystal.

1. Strange Clouds at the Edge of Space (NASA Science Web Site, August 25, 2008).
2. Jeremy Hsu, "Strange Clouds Spotted at the Edge of Space" (Space.com, September 1, 2008).
3. Dwayne Brown, Tabatha Thompson, Cynthia O'Carroll and Nina Stickles, "NASA Sims to Clear Up Mystery of Elusive Clouds at Edge of Space" (NASA Press Release No. 07-84, April 11, 2007).
4. Maggie McKee, "Satellite to study source of night shining clouds" (New Scientist Online, April 11, 2007).
5. Kathy Svitil, "Caltech Scientist Proposes Explanation for Puzzling Property of Night-Shining Clouds at the Edge of Space" (Cal Tech Press Release, April 25, 2008).
6. P. M. Bellan, "Ice iron/sodium film as cause for high noctilucent cloud radar reflectivity," Jour. Geophysical Research, vol. 113 (August, 2008), D16215, doi:10.1029/2008JD009927.