It is a dinosaur scientist that she drew. A scientist who studies about dinosaurs; dinosaur poop in particular, I was explained.

Looking at the drawing, the first thing I observed is the scientist is a she. Good show my girl. And lo, she is wearing nerdy glasses, oh, oh, typecast I thought. I got rebuked later, but again, I am jumping ahead…

What follows in the video below is a six-minute discussion of her drawing. You need to believe me on this. The entire discussion is impromptu, right after she drew the picture. I got permission from her to video tape, but I am not showing my kid in the video. Science is above its practitioners, right?

I don’t know about you, but what amazed me is her sincerity of purpose in trying to explain the question at hand, without getting put off by my persistence at conveying to her she is not making sense. A trait hard to find – or lost in the growing up years – even among graduate students.

Biophysics usually studies biological (bio-chemical) processes by applying physical laws at a micro level – single molecule. Plants such as aquatic Chara (size in centimeters) – known to be around for about 500 million years it seems – have stems in millimeters containing cells (of 0.1 mm dia, few mm length) that are very big for micron sized molecules of biophysics. The plant is shown on the left in the picture below (source).

One of the major reason locomotion of anything is necessary in (and by) organisms is food. Nutrient sensing (called chemoreception, via chemoreceptor proteins) and transport in microorganisms can happen by diffusion. Macro-organisms have a hierarchical transport structure. In us, macro-organisms, things can travel by convection, faster than diffusion – necessary to traverse the body size within short duration. Of course, diffusion is also present but only at the cell level.

In plants of meso-size however, the cells are large enough and diffusion transport transfers nutrients quite slow while pure convection (physical movement of nutrient) is still strongly impeded by viscous damping (Reynolds numbers are quite low, << 1). So, they adopt a combination of diffusion and convection (or advection) strategy to transport nutrients.

One such mechanism is described by the research reported in the 2008 PRL paper (by Jan-Willem van de Meent et al., reference below) I am discussing in this note. The relevant question to ask, as posed in the Physics Viewpoint write-up of the paper by T. Squires, is: How can such a large, single cell drive the steady flows required for life, without the benefit of “macroscopic” moving parts like pumps or muscles?

The short answer is: cyclosis. The establishment of this type of motion and its effects are discussed in the PRL paper.

Cyclosis is a cell-level transport process within such plant cells. A video of cyclosis is here. Let me give a short explanation with the picture below (source).

The Actin filaments (in red) are charged and the myosin-like (motor proteins in large cells) particles (blue dots touching the red filaments) get dragged on the actin as wheels on railroads. They in turn drag the endoplasmic reticulum (ER) nodules attached to them and cause portions of cytoplasm close to the wall to move along (blue arrows in top picture). This movement along the cell wall is along two helical paths – co-axial, one up and one down – as shown in the center part of the first picture (of Chara plant). This movement of fluid inside cell is cyclosis. It is faster than diffusion.

As the authors point out, the advection-diffusion problem of Characean algae is a form of Stokes flow not previously examined. Because, interestingly, the speed U of the helical streaming discussed above can reach in a Chara plant cell of radius R as large as 0.5 mm. Even for smallest molecular species (nutrients etc.), with diffusion constant , the Peclet number . Peclet number, a dimensionless one, determines in a region of length scale R, whether diffusion or advection (convection) dominates. Thus, advection strongly dominates diffusion in the above helical steaming of Chara plant cell, even though the Reynolds number is small (if we assume cell fluid having kinematic viscosity as that of water, ).

In the top Chara plant picture, myosin are shown in green in center inset. They transport nutrients in the form of spherical vesicles (pink) along counter-winding, helical tracks of actin (yellow) that line the cell walls. The transport pulls the viscous liquid (Reynolds number << 1) at the interior of the cell along the walls (the velocity profile is indicated by the black arrows), which helps to mix the fluid perpendicular to the long axis of the plant (right) and move nutrients around the cell interior.

In the paper, the authors present solutions of the Stokes equation on a helical coordinate system they propose for the cyclosis flow, capturing the two counter streaming helical flow. The interesting outcome is, due to the vortical flow along the wall, the axial Taylor dispersion that is present in such diffusion-convection flows is reduced. This dispersion instead of carrying a chunk of chemical intact, stretches – disperses – it due to local convection. The Chara plant cell due to helical motion seem to have found a way to reduce dispersion of nutrients while transporting.

In summary, through their results, the authors show that the combination of helical forcing as presented in [Fig. 1(b)] just above, and high Peclet numbers as we saw earlier, leads to intriguing properties. Termed as “Nature’s microfluidic transporter,” by them, enables the Chara plant cell with:

(i) fast radial mass redistribution, (ii) enhanced mass flux across the boundary of the cell, and (iii) homogenization of longitudinal advection. These arise from the generation of transverse flows.

A lucid review of microfluidics by G. M. Whitesides (his quote) appeared recently in Nature. Micro-channel flows, falling within the purview of microfluidics, are typically viscous boundary layer flows. The cyclosis results discussed can be imitated to increase mass flow rates in such micro-channel flows encountered in microfluidic devices. One more biomimetic possibility for engineering to mimick nature – although I don’t know if it is the most efficient way.

*****

Paper Discussed in this note:

van de Meent JW, Tuval I, & Goldstein RE (2008). Nature’s microfluidic transporter: rotational cytoplasmic streaming at high Péclet numbers. Physical review letters, 101 (17) PMID: 18999789 | Download PDF (free)

Other References

• Physics Viewpoint with similar title as this one, discussing the paper – by T. Squires.
• The origins and the future of microfluidics by G. M. Whitesides Nature 442, 368-373 (27 July 2006) | doi:10.1038/nature05058
• Review of Microfluidics by T. M. Squires and S. R. Quake, Rev. Mod. Phys. 77, 977 (2005).

So what is NanoArt? Here is a sample.

The above piece is called “In Pieces” by the NanoArtist Cris Orfescu and it is one of his favorites. It is created by freezing a droplet of suspended graphite nanoparticles in Liquid Nitrogen at 196 degrees Celsius below zero. Scanning Electron Microscope is used to take the picture, which was further painted and manipulated digitally using a computer. The final image was printed on canvas with special inks to last for a long time.

So far so fine.

Cris Orfescu explains further that NanoArt is

[...] a new art discipline at the art-science-technology intersections. It features nanolandscapes (molecular and atomic landscapes which are natural structures of matter at molecular and atomic scales) and nanosculptures (structures created by scientists and artists by manipulating matter at molecular and atomic scales using chemical and physical processes). These structures are visualized with powerful research tools like scanning electron microscopes and atomic force microscopes and their scientific images are captured and further processed by using different artistic techniques to convert them into artworks showcased for large audiences.

This is also fine, although I am not sure why sophisticated instruments costing millions of dollars are to be invested in doing this. OK, artistic freedom and right to express one’s creative impulses and so on. Agreed.

Then he goes on to say this

[...] Artists should familiarize the general public with the nanouniverse, so people will focus on the positive effects and redirect the negative ones to benefit from them.

[...] Scientists are exploring the nanoworld hoping to find a better future and there is evidence that Nanotechnology might be the answer. At this time, an estimated 70 percent of the American public and a lot higher percentage of the international public are not aware of nanotechnology, although we are using nanotech products on a daily basis.

[...] NanoArt plays an important role here in educating the general public with attractive and interesting images to help a better understanding of the nanoworld. Artists and scientists should intensify their efforts to raise the awareness of the public at large.

This is where I wince. I am not convinced.

What ‘positive effects’ he is talking about? What negative effects the public should be re-directed from? All in a nanouniverse. Let art be expression of creativity and NanoArt be one form of it. But claiming such an art is necessary to educate the public about nanotechnology or nanoscience or nanouniverse or nanoworld is unsubstantiated.

I appreciate Cris’s art work. But I am not convinced public’s perception about nanotechnology could be improved by appreciating and getting to know about NanoArt.

An immediate example is Fractals. Pretty pictures. How many of us who have appreciated those pretty pictures have gone further to learn the science behind them? Check out the Mandelbulb for instance and the math behind it for a start.

Generating nice fractal images using computer programs is one thing; using such images as art in a gallery and hoping the viewing public would go home and get educated about complex numbers, higher math, programming, differential geometry and so on – actual math and science required to understand fractals as a scientific concept – is far fetched.

Drawing miniatures on rice grains and displaying it to the public doesn’t maker them ask questions about the quality of rice, whether it is genetically modified, world human starvation index and so on. Public simply appreciate the rice-art and perhaps go on to wonder how it is made. The technique.

In NanoArt, there is a technique that public may get interested in. But as we can see the technique is not simple – manipulating matter at molecular and atomic scales using chemical and physical processes and capturing them with scanning electron microscopes is not an easy task. I doubt members of the public would want to go through years of college, learn all the nanotechnology techniques with sophisticated instruments, only to generate computer modified patterns of modern-art.

That is a world where we study theoretical physics only to get a job as a video game programmer.

I am not going to discuss here whether Hawking is right or wrong or how much of it is right. Many around the web and in the blogosphere have done it. Read here, here, here, here and here for a start. But read Brin if you need to pick one.

A lively discussion about aliens eventually gets us to Drake Equation, SETI, METI, Fermi Paradox, radio silence, and even Eerie Silence, a new book by Paul Davies. There now is even a SETI@home where our idle PCs computing power can be used in sifting radio signals for locating one that matters, if it exists.

But I refrain to elaborate these lofty ideals and actions. What I am going to mention is something trivial. A mere technicality.

At least one of the intelligent folks present in such discussions would throw up the argument in the title of this note, to dismiss with contempt whatever plans we propose in the future to prevent, preempt or promote alien encounter.

The argument goes like, since the rerun of I Love Lucy sixty years back, and thenceforth, we have transmitted all our cultural ‘garbage’ out to space as radio waves. The aliens could have picked up any of these signals by now. What is the point of doing something about it now… right?

Wrong.

Well, at least if such an argument is promulgated without the caveats…

Our radio or TV program signals don’t matter very much. At least highly unlikely that they would be picked. Reason?

David Brin, who assessed all the existing alien theories in a classic peer-reviewed Great Silence review paper (which I haven’t read, but have read some follow-up popular accounts by him – here is one), has provided a neat example for this I Love Lucy versus Arecibo type signals (see table below for difference) and their detection:

go to a lake with a rock and a laser pointer. Now drop the rock into the pond, making ripples. Then aim the laser pointer at the other shore. Which wave front will be detected on the opposite side? That is “I love Lucy” vs a high-power, collimated, coherent transmission from Arecibo.  Sure, in theory, advanced scientists on the other shore, who are passionately eager and who know where to look, might detect the rock-ripples. But Jesus, have some scale and some sense, before you blithely declare that everybody on all shores will always detect all ripples!

In which case, How far away could we detect radio transmissions? For instance,

a TV picture having 5 MHz of bandwidth and 5 MWatts of power could not be detected beyond the solar system even with a radio telescope with 100 times the sensitivity of the 305 meter diameter Arecibo telescope.

That is for broadband signals, which includes most of our AM/FM radio and UHF TV signals (see the table below). For narrow band, it is more promising and that is what Arecibo – at 305m, it is the largest we have – is designed to detect as one of its exercises. Arecibo radio telescope could detect narrow band signals coming from thousands of light-years away from us. A small amateur radio telescope could of course detect narrow-band signals from within 100 light years, provided the transmitting power at the source is in terra-watts. The detailed calculation for all of this is in the SET@home FAQ. The formula comes down to

where R is the signal detection range in Light Years (if Rl is in LY). Some of the other terms are: EIRP is the effective power at the source, is the effective area of the receiver (radio telescope), snr is the signal to noise ratio.

The take home point is for maximum detection range R, the transmitting power, the area of the receiving antenna and the time bandwidth product (twp) should be high. The snr, the receiver bandwidth (Br), and thus transmit signal bandwidth (Bt), and the receiver system temperature (Tsys) to be as small as possible.

Here is the data by doing such a calculation for some of our radio sources. The receiver is assumed to be as big as the Arecibo (305 m dia, efficiency 50%); snr = 25, twp = Br * Tr = 1.

The orange circled numbers are what we are capable of by our radio and TV shows. For reference, 1 AU is the distance between us and our Sun, 5 AU is about the distance from Sun to Jupiter and the next nearest star is about 4.2 light years away.

In short, we don’t need to think we have irreversibly sinned by blaring our radio into space. It is highly unlikely it will be heard beyond our galaxy, is at all.

A radio telescope as big as the Arecibo should be at least 0.3 light years within us to detect our radio ga ga.

That is, if by sheer Providence (I presume an event with such infinitesimal likelihood of occurrence could require such an un-human impetus) a radio telescope is in the right place and is turned in the right direction at the right time (remember, our radio programs are intermittent).

It goes without saying, that radio telescope would be christened John McClane.

One such Dec 2009 concert was by Vedavalli at Raaga Sudha Hall.

Yes, one can magnify certain slips due to her age but one can do that always. As ever, she acquitted herself well in most of the facets of the music. Elegance and intelligence always implicitly entwine with classicism and creativity in Vedavalli’s music.

Here is a video snippet of Vedavalli’s thOdi rAgam Alapanai.

The remarkable ease with which she can do an exposition of a raaga scale, the magical note that she only knows for gliding from one rAgA to another in the AlApanais during virutham singing makes one wonder; Ah! Carnatic music, it is easy to listen and easy to deliver…

Like looks, listening can be deceiving.

Instead of elaborating more on each song of the concert, let me present an audio of her rendition of gnana mosaga rAdhA, a kirthana of tyAgarAjA. It is usually sung in pUrvikalyAni rAgam, but Vedavalli gave a rendition in sadvidhamArgini the 46th rAgam in the 72 sampUrna mEla rAga scheme of vEnkatamakhi.

sadvidhamArgini is pronounced shut-vidha-maa-r-gini where the gini is like guinea (and not as in bikini or genie). sampUrna means the rAgam scale has all the 7 notes within an octave of sa to SA and the mEla rAgam indicates the ArOhanam and avarOhanam are of the same notes.

Here is the audio

As Vedavalli requested at the end of that rendition, I am spreading the message. She states the original of this kIrthana was set in sadvidhamArgini. She has learnt this sadvidhamArgini rendition from Madurai Srirangam Iyengar and says until as recently as in the 1960s musicians were singing this version in concerts. She backs her claim with an aesthetic reason too. The lyrics of the kIrthanA goes

gnana mosaga rAdhA, garuda gamana vAdhA,

nI nAmamuchE nA mathi nirmala mainathi

means (my translation)

give refined intelligence, one who use Garuda as career

your name’s glory purified my mind

Vedavalli doubts whether such a yearning appeal would be set in pUrvikalyAni rAgam with a majestic tempo almost ‘demanding gnanam for the trade of a few slaps on the cheek’ (listen to her saying this at the end in the above audio).

On the other hand, it is not clear to me on what basis sadvidhamArgini should be chosen for such lyrics, if we should believe lyric-music aesthetics would have played a role in tyAgarAja’s rAgA choice. TyagarAjA himself has proven that the same rAga could be deftly used to bring out ethos or pathos or contrasting moods. A case in point is the atAnA rAgam handled by him.

If is not merely a matter of choice, why choose sadvidhamArgini for this kIrthanA. Does this mean over the years we have also lost certain aspects, lakshanas, of sadvidhamargini rAgam; on how it should be sung evoking certain moods (that could fit the meaning of the above lyrics)?

The way Vedavalli sang the song, it did evoke a soothing, yearning, bordering pathos mood. But I couldn’t relate this way to her AlApanai of the rAgam before the rendition. That could be because I have not listened to this rAgam now in concerts for several years (the only other elaborate rendition of this rAga I have as a recording is by Tanjore S. Kalyanaraman, the much underrated genius of our times). There is no immediate reference to seek a pattern for the mind to switch on the relevant emotions.

I checked Prof. Janakiraman’s volumes on rAga lakshanas in Tamil and English but couldn’t find this rAgam. From the book rAgalakshanasangraha a comprehensive compilation of rAga descriptions by Hema Ramanathan, I could learn sadvidhamArgini (or gani) has been mentioned in sangraha chUdAmani of gOvindhAchAryA with a curious ending sentence of the rAga lakshna that goes “…granting the fulfillment of penance, SadvidhamArgini is named the fortysixth (adhikara/mela)” (translation from sanskrit is by the author. Let me leave it at that for now.

Here are some more videos of snippets of Vedavalli’s concert in the later half.

Ahiri rAgam

and a khamAs jAvali

The accompanying vocalist is Sumitra Vasudev, student of Vedavalli and an upcoming performer. R. K. Sriramkumar is enjoying the violin.

Recently one academic asked me what is the difference between a blog and a twitter. Oh, that is easy, blog is both a noun and a verb; twitter is neither. OK seriously, if you are a maverick academic, unlike in a blog, in twitter you cannot rant for more than 125 characters per tweet; the 15 remaining characters are reserved for the default hash tags #f*** #s*** #damn.

So you also think this note is frivolous. That is what maverick academic bloggers who practice irreverence by ranting are typecast to do.

Because, I should practice irreverence to excel as a scientist if not an academic. But there are academics who question the impending necessity for even that attitude. The danger in such critique, nay, blog rant by a maverick academic is, the irony of being irreverent by questioning the need for irreverence will be missed by many academics who practice reverence.

They would argue how one should agree with authority, if it says you should practice irreverence. After all, authority is defined by a copyright and pay-wall protected Science magazine editorial, which is supremacist to a local Current Science editorial disagreeing with it (pdf) by allowing only free pdf auto-downloads that freezes your US made web browser, if not your 220 volt driven laptop.

Even when someone does proper research about ground realities and pulls a fast one on you (pdf), you should stay irreverent and ignore such hard data. Statistics are damn lies.

The particular lie, er, statistics the above figure depicts is between  proportion of researchers (defined as FTER, Full Time Equivalent Researcher) in the population and (b) proportion of GDP spent on Research and Development.

To erase the effects of the above lie and reach the leagues of countries like USA, it seems India not only must increase its investment by 30 – 50 times but also its number of R&D workers by 30 – 80 times. As a sick joke, statistics like this compete with the Science editorial exhortation to practice irreverence.

As such, India graduates about 650 Ph. D.s per year. The number of Indians obtaining Ph.D.s per year in the US alone is higher than this. That is because the IIXs and NITs train their flagship UGly content to excel only outside India.

We have some established IIXs that specialize in such exodus. It provides us with a masochistic pleasure as perk. Our mission is to send forth men and women of the highest professional competence with a breath of learning and a character to deal constructively with issues, and problems anticipated in the next decade relevant to the programmes of development of our country. Mind you, we don’t say which country.

That the country needs human resource is a MHRD mandate. We are starting many more IIX by the minute. All Indians have a right to get branded in an IIX and do a foreign PhD. We should not let education intrude.

Vie for starting an IIX, if you can prove your part of India remains uneducated after independence and (so?) can satisfy the prerequisite of not finding enough qualified people to educate. Most of those who pass the World’s toughest entrance exam and get herded into IIXs usually don’t like to be taught anything after that in their Indian life. They shall stay irreverent so that when they are out of India, they can practice adventurism and creativity as the Western typecast expects them to.

While we are talking about irreverence we should keep in mind that Indian classical music remains uncreative because it upholds reverence. The lack of creativity is clear from its lack of harmony – although it claims only melody and not harmony as its structural trait. How many new raagas are sung as standard fare in regular concerts? That elements such as neraval, manodharma and kalpana swara prastharas exist as core proves beyond doubt that Indian Classical music revels in a systematic suppression of the student’s creativity. We should stop listening to the melody driven Indian classical music, if we were to become creative scientists or passable academics.

The day Indian classical music turns irreverent, like Indian scientists, Indian classical musicians will become fair-skinned, World Class creators. While the former can write research articles, rather than editorials in Science, the latter can harmonize successfully a thOdi raagam with all its gamakams in a creative swoop, without having to worry about the uncreative un-thOdi like atonal overlaps in such harmony audible only to the untrained Indian ears.

BTW, for those prospective academics at IIXs who discuss respectfully albeit anonymously at this pinned post for prospective faculty to IITs/IISc about their prospective employers, here is a tip. You may have practiced reverence where you did your PhDs but leave such typecast qualities in the West. Practice irreverence. Else you would be relegated to comment with a OpenID at the maverick academic blog nanopolitan, which doesn’t allow respectful anonymous comments anymore – as a rebellious protest to practice reverence.

Further, practicing irreverence is the only way to be a top-notch scientist in India.

Here is another tip. Don’t expect to get good PhD students to do the research for you. All good studs have left India like you, to do PhDs elsewhere. We only have a few million others remaining – give or take fewer millions. But no sweat. As the Science editorial on practicing irreverence suggests, be like Feynman. He has gone on record stating, to win his Nobel, he has guided successfully many PhD students hailing from karunthattangudi and other Google-maps-invisible places of India.

I shall stop with this one last tip for the prospective IIX recruits. You can get your ten foot pole I mention at the start for free at the time of appointment, if you can conclusively prove to the attender who verifies your UG certificates that you are not a maverick academic blogger but only a conservative anonymous commentator. After you complete your probation period, you can use the ten foot pole on the attender and also touch with it, academics who blog. Just to get them to rant on

Or rant off.

*****

Links to articles referred in this note

1. Irreverence and Indian Science, Mashelkar, R. A., Science, 2010, 328, 547 [Link]
2. How much should a nation spend on academic research? Gangan Prathap, Current Science, 98(9), p.1182, 2010 [Link to pdf]
3. Irreverence and Advancement, Editorial by Prof. Balaram, in Current Science, 98(9), 2010 [Link to pdf]

— George M. Whitesides

…in his Writing a Paper (2004) Advanced Materials 16: 1375. doi:10.1002/adma.200400767 [free pdf - Writing a Paper]

(as of Aug 2009, GMW is the living chemist with the highest H-index – 155)

CFD stands for Computational Fluid Dynamics. It is one of the branches of fluid mechanics that uses numerical methods to algebraize partial and ordinary differential equations (that represent fluid flow) and use algorithms to perform iterative operations seeking solutions to those algebraic equations. In general, it is a way to solve equations that describe fluid flow through iterative schemes that are amenable to be programmed and solved using computers. At times, CFD can be a cheap substitute for expensive experiments. On occasions, it is the only way to understand fluid flow. Like this example of computationally simulated fluid flow around a Protoceratops

CFD animation Picture Credit: http://www2.icfd.co.jp/examples/protoc/pr2.htm

Here is one more pretty picture using CFD – which, for this reason, is also expanded as Colorful Fluid Dynamics.

The above (click on the picture for accessing a higher resolution version) is a computer simulation of Taylor-Rayleigh fluid instability, happening at the interface between two fluids of different densities, with the lighter fluid pushing the heavier fluid.

Picture Credit: LCSE Multimedia Gallery, Scientific Visualization. Explore that site for many pretty fluid mechanics picture for your computer wall papers.

We briefed earlier on what is a Schlieren image, when we discussed how human cough was captured using that technique. Schlieren is German for streaks; in this case it refers to regions of different densities in a gas or a liquid, which can be photographed as shadows. We don’t get to see directly with our eye, shock waves arising in air or shimmers of hot air. Or invisible gas leak, or coughing or air flow around a dog sniff. For the shimmer to be visible, we need that region of air to be contrast with something in the background. In the case of a shock wave in air (which is basically a compression wave front sustaining a large pressure discontinuity across it), we need to look at its shadow. Here is a Schlieren of the firing of an AK-47 and the bullet trajectory with the gas puffs and associated shock wave.

Photo Credit: Gary Settles/Penn State. Here is the NY Times article with many such unusual pictures taken by Prof. Settles using Schlieren.

And now for something completely different. Cerebrospinal fluid, visualized in a laser light by fluorescent particles.

Picture Credit: Institute of Environmental Engineering, ETH and source is via Alex Liberzon, a fluid mechanics experimentalist.

Shall close this note with a video. We have been using the conventional table fan with three or four blades housed inside a metal grid and rotated with a motor. Here is a video of a new invention by James Dyson, the bladeless fan.

YouTube Video Link

More information is available from the New Scientist. It looks like a contrived Coanda effect is what we see in this invention. I am not sure how noise, size, tipping etc. will be handled. Anyway, nice home application of fluid mechanics principles.

But here is a simple and elegant real-life fluid mechanics experiment that is reversible. Take two concentric cylindrical containers made of transparent glass or perspex. The cylinders are of different diameters and placed one inside the other. The inner cylinder is fixed to a motor from the top and it can be made to rotate at fixed speeds. A small gap separates the bottom surface of the inner cylinder from that of the outer cylinder. The annular space is filled with a highly viscous fluid. Say honey or Golden Syrup. Put a blob of ink or colouring agent using an ink filler somewhere inside the fluid, away from all of the cylinder walls. This configuration is shown as the first diagram in the accompanying schematic.

Rotate the inner cylinder slowly. The blob shears and spreads as shown in the second diagram. After a few turns, the blob is stretched and thinned all around the annulus as shown in the third diagram. A snapshot taken at this stage would not have evidence about which cylinder was rotated and its initial direction of rotation.

Interestingly, if we now rotate the inner cylinder in the reverse, the ink-strip begins to rewind. If the sequence is rewound with care, rotating the inner cylinder slowly as before, the strip would gain back its concentration and eventually becomes the blob. Well, almost exactly, the same blob.

A live experiment where the blob remembers its shape history in time like a movie event.

Here is an excellent video of this experiment filmed at the University of New Mexico Physics Department.

[YouTube Video Link]

Let us explore the technical explanation. What is observed is surprising to us because, it is a low Reynolds number phenomenon. Most of our daily life fluid mechanics – like water running from a tap or river flow – are high Reynolds number phenomena. What is Reynolds number? For most circumstances, it can be understood as a ratio of the acceleration terms (forces) and viscous terms (forces) in the momentum conservation statement that is believed to hold true for any fluid flow.

Reynolds number, named after Osborne Reynolds a pioneer in fluid mechanics understanding, is a way to quantify what forces dominate in a flow. Read my Pipe Turbulence for more on this number and its significance in fluid flow. If it is a large number (say, 1000 or 10000 when compared to 1), the acceleration terms dominate over the viscous terms (the brakes). Stirring your tea vigorously with a spoon and the air flow over a jet plane wing respectively generate Reynolds numbers of order 1000 and 10000. But the wading of our hands through rice patter or wheat dough generates only a low Reynolds number flow. Like the one observed in the above experiment.

Low Reynolds number flows are almost reversible.

But why? For this we need to appreciate how the momentum conservation reads for such flows.

The momentum conservation statement for fluid flows is the Navier-Stokes equations, which for incompressible flows in Cartesian coordinates can be written in the form

The first equation is for momentum conservation and the second one is for mass conservation and in tandem they represent the equations of motion for any fluid flow. Here p denotes the pressure in the fluid and V with an arrowhead represents the velocity vector for the fluid flow. ? and µ are the density and viscosity of the fluid. In the first equation, the left most terms are the acceleration terms while the rightmost are the viscous terms.

Reynolds number is the ratio of the acceleration and viscous terms and after simplification can be written as

In our reversibility experiment the slow rotation that shears and stretches the blob is a low Re flow. This means the LHS of equation (1) can be dropped in comparison to the viscous terms in the RHS. The resulting equations in 2 dimension (a good approximation for our experiment) can be written as

Observe in the above equations there is no term changing in time (no time derivative). Perhaps enough to convince us the phenomenon explained by any solution of this equation is reversible. More rigour can also be mustered. Assuming the rotation is slow, the blob stretches into a thin annular strip eventually. In other words, this final state is a steady state solution of the above equation. So, there should be finite values for u, v and p at this state that satisfy the above equations. Let them be u₁, v₁ and p₁, satisfying also the boundary conditions at the cylinder walls, where the fluid has to move with the velocity of the wall, say, u₁ = u_W and v₁ = v_W .

This solution is valid at state (1) or (3) in the diagram above.

If we now reverse the experiment, the boundary condition at the wall is reversed. That is, u₁ = -u_W and v₁ = -v_W . Likewise, if we now replace all u, v and p in the above equations with -u, -v and -p respectively, each term would have changed sign. Hence, the solution remains the same (as before).

That is the explanation for the almost 100 percent reversibility of highly viscous flows or low Re flows.

To round off, if we try to pull the same trick with the original Navier-Stokes equation in (1) above, it won’t work. the acceleration terms on the LHS (being quadratic in u and v) won’t change sign as they are product terms.

We kept saying almost reversible. There is a reason. Diffusion. The blob is made of a separate constituent from the base fluid. The blob medium diffuses in time in the fluid and lose its concentration. This works even if the cylinders remain stationary. So it works even when the cylinder is rotated. Hence, when we rewind, the blob doesn’t exactly regroup into the same volume, as some of it continually is diffusing. This phenomenon (governed separately by a Fickian diffusion term) is not captured in the Navier-Stoeks equation. It should not be confused with the viscous diffusion that is present in the RHS of equations (1) and (3). Viscous diffusion diffuses momentum not concentration.

We kept saying very high viscous flows and low Reynolds number flows in the same breadth as if one implies the other. Not necessarily. For instance, if we rotate the cylinders very fast, the acceleration terms (and forces) cannot be neglected in our experiment even though the fluid is highly viscous and its flow can be identified as highly viscous flow. The correct way to classify our phenomenon is as a low Reynolds number phenomenon.

Reference

1. From Calculus to Chaos, An Introduction to Dynamics by David Acheson, Oxford Uty. Press, 1987. [Amazon Link] [Google Books]

We are aware of the original Mandelbrot set and its famous two dimensional image. It is generated using a complex number polynomial ploy where the way we choose c, defines the plausibility and complexity of the Mandelbrot set. Two dimension and complex numbers are fine, what is it for three dimension. Quaternions perhaps. And so on. For the past twenty odd years, Rudy Rucker, first imagined the concept behind the potential three dimensional Mandelbrot set, called the Mandelbulb and has ever since attempted to create various improved versions. Here is a low resolution 8th power 3D Mandelbrot, rendered by Paul Nylander

The 3D version requires billions of calculations. Detailed explanation is provided here. A high quality (7500 by 7500 pixel) version is available here. Go ahead, I dare you to click it, you with those low resolution browsers. Here is a video that delves infinitely into the Mandelbulb.

More details on the Mandlebulb, background and is it worthwhile to pursue such quest.

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We have seen snow flakes. Don’t look. How many sides? Can you spot one as a snow flake or a snow fake? What about the two below.

So, how many sides a natural snow flake have: Six or eight? Your answer could congregate you into the artist or scientist side of the divide. Greeting cards and other such new year advertisements carry artist version of the snow flake with non-hexagonal shapes. When one such eight-sided snow flake appeared on Nature website advertisement captioned “… for anyone who loves science.” Professor Thomas Koop, who specialises in ice crystal formation at the University of Bielefled in Germany, got enough of it. He wrote a strong rejoinder to Nature [Read news item 1 and news item 2] debunking such snow-fakes and explaining why natural snow flakes cannot have anything other than 3, 6 or 12 sided structure (half or twice of, or the hexagonal shape). In short, the molecular building blocks of snow flakes are obviously water molecules and there is only a certain way they can fit together. This fitment is always in a six-cornered shape, even at the tiniest molecular scale. So, both the above picture show naturally grown (in the lab) snow flakes.

Johannes Kepler seems to be the earliest scientist who has done a systematic study of the snow flakes and have reported his findings in an essay titled The Six cornered Snow Flake. Farmer Wilson A. Bentley’s pictures of snow flakes, taken as early as 1925, have won several accolades. Read more about the snow flakes at the Snow Crystals website for beautiful images with scientific explanations.

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A trio of prismatic drops (left to right: water, ethylene glycol and ethanol) balances on a new ultra-repellent surface invented by scientists at the University of Wisconsin–Madison. The surface, made up of silicon spikes just 400 nanometers wide, physically repels a wide variety of liquids, including water, oil, solvents and detergents. Previously, scientists relied on chemical modification to make surfaces repel liquids, a time-consuming process. In the end, each coating worked to repel only certain liquids, and oil-repellent surfaces simply weren’t possible to manufacture. The new surface blocks almost all liquids.

Read my note Lotus Leaves, Hydrophobic and Omniphobic Surfaces for more relevant details on such surfaces.

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The above is a close-up of a ferro-fluid in action – i.e. the iron/magnet is being attracted in a direction by the applied magnetic field. It is more than a home mixture of iron filings in an aqueous medium. In short, ferro-fluids are tiny magnets suspended in oil using surfactants. For further details read How To Make Ferrofluids.

Here is a video briefing applications of Ferro-fluids

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And to sign off, here is a Periodic Table

Fred on twitter clarified the location of the table: Across the parking lot from him! In Wake Forest University, just outside Salem Hall (Chemistry building), in Winston-Salem, NC (Fred is in Olin Physics Lab). Thanks Fred (follow him here).