E. O. Wilson’s autobiography is called Naturalist. I recently finished reading it and found it full of good ideas and also a useful source of advice on the scientific life. The more of Wilson’s ideas I read the better it all hangs together. Next up: The Origins of Creativity.
How the Universe Was Made
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How the Universe Was Made:
Before the Big Bang … and After
by Ken Roberts
24-July-2017
One day God was working on his latest project. He was making a perfect golden sphere. The sphere was so round, that there was nothing rounder. It was so smooth, that there was nothing smoother. And it was so pure, made of gold using only one type of atom, that there was nothing purer or more perfect.
You may be wondering why I am speaking of God as He. Well, it is a constraint of the English language that I am using to tell this story. God does not have a gender; God is He, She, It and everything else. God is plant, animal, rock, water and air. And time — God is past, present, and future, if those can be said to exist before the Universe. We will simply have to do the best we can in order to tell this story, using metaphors and frail vocabulary.
So … God had made a perfect sphere. It was almost done. Only a name was needed. The sphere was so perfect that only one bit of information would be needed to describe the sphere. God would call it 1. Or maybe 0. God hadn’t yet decided.
1 would be a good name, because it suggests One-ness, a Uni-Verse, a Poem that says everything. 0 would be a good name because it suggests the roundness of a perfect sphere, and the syllable Om. Either way, one bit would suffice for the sphere’s name.
While thinking about his decision, God took a coffee break. There was no rush … Infinite time, actually. After preparing his coffee, God returned to his workbench, where he had made the sphere. He set his coffee cup down on the workbench, and turned to examining the sphere, making sure it was perfectly smooth and pure.
Well, we’re here, so you know what happened. As God was concentrating on the sphere, his elbow nudged the coffee cup, which spilled coffee all over God’s workbench. God grabbed for the coffee cup, and the sphere, without his full attention, rolled to the edge of the workbench and fell onto the floor.
There was a Big Bang ! The perfect sphere was smashed into millions of bits. Coffee dripped off the workbench and mixed into the breakage, and created little bits of dark coffee and light cream. That became empty space and stary galaxies, and everything else in the Universe. “Oops!”, said God.
What happened after the Big Bang? Well, God is probably working on another sphere. Or, perhaps, She has a new project.
Pushkin Poem Arion Translation
Yesterday I tried translating a poem from Russian. Arion, by Alexander Pushkin, is a poem he published in 1827, when he was 27-28 years old. I’ve read three other translations, and all are good. However, each seems to miss some aspect of the original. So I tried my own translation. Remarks at end. Here is the translation.
Arion
Many men on board the bark.
Some strained the sturdy sail,
others set pace with powerful strokes,
oars drawing deep.
In calm control, our wise helmsman
lightly steered the laden ship.
And I – happy of heart,
careless of concern — sang sweetly.
Wild waves suddenly stopped our song …
All hands and helmsman were lost !
Only I, the singer, cast onto the beach.
I dance, chant songs of deliverance
and dry my garments in the sun.
Remarks:
1. Here are three other translations which I enjoy:
At https://russianlegacy.com/russian_culture/poetry/pushkin/arion.htm there are two translations, one by I. Zheleznova, “We many were who filled the boat…”, and the other by an unknown translator, “We sailed in numerous company…”. That site also has Pushkin’s poem in the original Russian.
A translation by Babette Deutsch, “We numbered many in the ship…”, appears on page 63 of “The Poems, Prose and Plays of Alexander Pushkin”. That volume was edited by Avrahm Yarmolinsky, and published by Random House, New York, 1936. It is part of the “Modern Library” collection.
2. Pushkin’s poem is 15 lines long, with a rhyme scheme of ABBA CDDDC EE FGGF. That is a variant of the sonnet form. All three translations also use 15 lines, with a similar rhyme scheme.
I try another approach. Instead of rhyme, I use alliteration to provide rhythmic structure in the poem. There is a tradition of alliterative verse in early English. Arion’s is an old tale and it is suitably respectful of that classic tale, of the poet Arion, and of Pushkin, to use an old form. Arion was the poet who established the dithyrambic poetic form, choral dance and song to be performed in honour of the wine god Dionysus. In telling Arion’s tale, one should not feel confined by the formalities of sonnet.
3. The rhythm is regular at first, then becomes rough when the storm arises. I hope to capture that sea change. In the lines at the end, the structure returns somewhat as the poet offers Thanksgiving and rejoices at his rescue.
4. Pushkin was a young man, age 27-28 when this poem was published, and like many young men held passionate opinions about improvement of the social order.
The classical tale of Arion is that he was captured by pirates, and forced to choose between being killed on-board their ship, or being thrown into the sea – where he would drown. Arion sang while he made his choice, and dolphins gathered around the ship to admire his beautiful song. Arion was thrown into the sea, but was carried safely to shore on the back of a dolphin.
It is not unreasonable to suppose that Pushkin knew that his poem might be read with a political subtext. In Pushkin’s poem, Arion is not a captive, and his shipmates are companions not pirates. However, ships of state can encounter heavy weather. Ambiguity adds to the appeal of “Arion”.
5. Here are some links to articles about Pushkin, Arion, and dithyrambic poetry.
https://en.wikipedia.org/wiki/Alexander_Pushkin
https://en.wikipedia.org/wiki/Arion
https://en.wikipedia.org/wiki/Dithyramb
And a link to two readings of the original poem, in Russian. Click on either of the first two “Play” buttons to hear the reading.
6. And finally, to attach an image to this post, here is a painting of Alexander Pushkin.
Best wishes,
Ken Roberts
04-Sep-2016
Solar Cells and the Lambert W Function
Computations for the one-diode model for solar cells, if done using the exact formula with Lambert W function, are likely to produce arithmetic overflow or underflow. That is a constraint on the ability to implement such calculations in Fortran or C, or on microcontrollers. The solution: use a coordinate transformation of the computation problem. If the problem were being solved on graph paper, the coordinate transformation would be achieved by using log-log graph paper.
I gave a talk at a recent conference, “Celebrating 20 years of the Lambert W function”. Title: Solar Cells and the Lambert W function. Joint work with my colleague S. R. Valluri. The slides are available at Researchgate, at this URL:
https://www.researchgate.net/publication/305991463
Best wishes,
Ken R.
11-Aug-2016
Non-Harmonic Fourier Series
2016 is the 200th anniversary of the publication of Joseph Fourier’s ideas for the solution of heat conduction and radiation problems using trigonometric series expansions. What we now call Fourier series. His ideas appeared in book form in 1822, but they first appeared in 1816 in a paper Theorie de la Chaleur (Extrait) which describes the book’s contents. It is appropriate to return to Fourier’s work. And there are gems to be found.
Chapter 5 of his book, The Analytical Theory of Heat (in English translation by Alexander Freeman), discusses the conduction of heat in a solid sphere. Fourier obtains a sine series which solves the differential equation. However, his series is not a harmonic series of the form of a weighted sum of terms sin(k*x) where the k are positive integers. Rather, Fourier’s solution is what we now call a non-harmonic series. It is a weighted sum of terms sin(b*x) where the b values are positive reals, moving steadily out roughly as do the integers. What are those values of b ? They are the solutions to an equation of the form b*cotan(b) = B. Those basic modes can be summed in a linear combination to match other constraints of a particular problem.
We have seen the equation b*cotan(b) = B previously. It is the solution for the bound state energy levels in a quantum mechanics problem, the one-dimensional finite square well.
This looks like fun. Fourier’s solution is very clever. William Thomson (Kelvin) worked on this topic also — it is the subject of Thomson’s first published paper. There is plenty to explore.
Just a heads-up, for anyone else who may be interested in this topic.
Best wishes,
Ken Roberts
08-Aug-2016
ps. Fourier’s book was republished by Dover. It is also online via the archive.org website.
Finding Good Recommendations
There are many online services which attempt to recommend movies, books, webpages etc that someone will like. In some implementations, recommendations are based upon finding new items that are liked by other users: If you like A, and someone else likes A and B, then B is perhaps a good recommendation for you. The difficulty is that establishing your profile can be a tedious task, as you have to initially indicate several items that you like. On the order of twenty items, perhaps.
A new algorithm, developed by Evgeny Frolov and Ivan Oseledets of the Skolkovo Institute, provides a much less time consuming, and likely more accurate, way of establishing your preferences. It uses information about items that you do not like, as well as about items that you like. Roughly stated, if you do not like item B, and those who like B also like C, then item C is perhaps not a good suggestion for you.
The details of their algorithm are subtle, and designed for efficient operation. It is not just graph searching. See Arxiv 1607.04228 for their paper — linked below — and a press release also linked below.
Best wishes,
Ken Roberts
01-Aug-2016
http://arxiv.org/abs/1607.04228
Evgeny Frolov and Ivan Oseledets — Fifty Shades of Ratings: How to Benefit from a Negative Feedback in Top-N Recommendations Tasks
Edmund Little — The Fantasts
Decades ago, I became an enthusiastic reader of J. R. R. Tolkien’s Hobbit tale and the Ring trilogy, and later other Tolkien works. Recently I encountered a small book, The Fantasts, by T. Edmund Little, which presents an excellent analysis of the idea of sub-creation and Fairie. Fairie was the subject of Tolkien’s famous 1938 lecture, On Fairy-Stories, which was published as the first half of Tree and Leaf — the second half being the story, Leaf by Niggle, one of my favourites.
Little’s book is worth one’s attention. Little explores Tolkien’s assertion that fantasy involves a process of what is called Sub-creation. Little considers five authors and their fantasy worlds: J. R. R. Tolkien’s Middle Earth, Lewis Carroll’s Wonderland, Mervyn Peake’s Gormenghast, Nicolai Gogol’s town NN depicted in Dead Souls, and Kenneth Grahame’s river bank world depicted in The Wind in the Willows. Little’s book The Fantasts is an extended essay, interesting and stimulating for anyone who has wondered about the process of sub-creation.
I will not attempt to summarize Little’s many insights and observations here. Suffice it that careful consideration of the details of sub-created worlds, as provided by Little in this essay, reveals many subtleties and amendments to the sketch provided by Tolkien in his essay on fairy story. For your enjoyment, and perhaps useful if you are engaged in creative (or sub-creative) writing …
T. Edmund Little died in 2013, and I provide links to two obituaries for your interest. The photo used to introduce this post from the second obit, and was perhaps taken in February 1997.
Best wishes,
Ken Roberts
31-July-2016
http://cathnews.co.nz/2013/06/10/fr-edmund-little-dies-in-takaka/
http://www.wn.catholic.org.nz/edmund-little-of-takaka-rip/
Bertoia Dandelion Sculpture
This metal dandelion sculpture is by Harry Bertoia, and is one of the most beautiful of his works. There are links below to a Wikipedia page about Bertoia, and to the Milwaukee Art Museum where this dandelion is on display. A visit to the Milwaukee museum is worthwhile, as the building’s entryway is fabulous, and the collection includes many excellent modern works, contributed by Mrs. Bradley who evidently had very good taste.
Best wishes,
Ken Roberts
23-July-2016
Wikipedia article about Harry Bertoia:
https://en.wikipedia.org/wiki/Harry_Bertoia
Milwaukee Art Museum links:
http://collection.mam.org/artist.php?id=632
Great Leopard Moth
This neat moth is called a Great Leopard Moth, or a Giant Leopard Moth, or an Eyed Tiger Moth. This is likely a male, because it is very large — about 7 cm in length. The Wikipedia article linked below says the mailes grow to 5 cm length, so this is an unusual specimen. Observed in Southwestern Ontario on 29 June 2016. This is a living specimen. It is standing vertically against a wood exterior wall, getting direct sunlight.
URLs with info:
http://www.butterfliesandmoths.org/species/Hypercompe-scribonia — from a good website devoted to butterflies and moths. Photos of caterpillar also. Note that the caterpillar has red bands, which I did not see on this adult moth.
https://en.wikipedia.org/wiki/Giant_leopard_moth — the Wikipedia article, some further info.
Best wishes,
Ken R.
30-June-2016
Raspberry Pi 3 Multi-Computer
It now makes sense to use Raspberry Pi 3 boards to build a multi-computer for serious scientific work. In a previous post on 25-Jan-2016 I described my tests using a Raspberry Pi 2 for density functional theory (DFT) calculations using the ELK software. The RP 2 operates at about 1-10th the speed of a Laptop purchased for scientific work, the laptop having an Intel i5-core processor and 4 GB of memory. Details in the previous post. Bottom line: RP version 2 is not economic for building a multi-computer for the ELK DFT tasks.
However, I have now had an opportunity to test the Raspberry Pi version 3, released earlier this year. It is faster, and completed the ELK calculations in 43 minutes elapsed time, vs 79 minutes on the RP version 2, and vs 8 minutes on the i5-core laptop. That means it takes 5.5 RP3 boards to equal the capability of the laptop. Since each RP3 (board only) costs $35 Cdn from a typical supplier (or $45 if one includes a power adaptor, or $75 if one wants a case, cables, etc as well), one can set up a config of about 6 RP3 boards for something like $250. The laptop costs $300 as a refurb system.
There are of course complexities. One has to mount the RP3 boards somewhere — a bit of lumber should suffice for home brew. And six power supplies can probably be replaced by a single supply of larger amperage capacity. Ethernet cables are needed, and a switch, but most tinkerers have that sort of stuff around. Still, all considered, one can probably build a very nice multi-computer out of RP3 boards at about three-quarters the cost of an equivalent multi-computer based upon i5-core refurb laptops.
I’m not planning to actually build this multi-computer. I already have what I need for my calculational tasks. But it’s nice to see the Raspberry Pi become suitable for this serious calculation.
Best wishes,
Ken Roberts
05-May-2016
Bernays on Propaganda
Propaganda is the title of a book by Edward Bernays published in 1928. A less provocative title might be Public Relations. Bernays was the pioneer of public relations.
The premise of Bernays’ book is that “in almost every act of our daily lives, whether in the sphere of politics or business, in our social conduct or our ethical thinking, we are dominated by the relatively small number of persons … who understand the mental proceses and social patterns of the masses.” [pp 9-10]. Is that bad? I suppose it depends upon one’s position in society. It is not egalitarian.
Regardless of one’s take on the ethics of propaganda, there is certainly a great deal of realism in Bernays’ view of the world. Anyone who hopes to improve the world should be aware of the ideas and methods described by Bernays.
I wish I had read Bernays’ book many decades ago when I was engaged in social justice and political endeavours. I was no great activist, but did fight many minor skirmishes. Perhaps, using Bernays’ ideas, some situations might have been handled better.
So … a word to the wise — which means you, dear reader! — Bernays’ book is worth one’s attention. It’s a fast read, and decently written. The examples are a bit antique in some ways — 88 years ago — but the book is up to date in essentials.
Best wishes,
Ken Roberts
02-May-2016
Links:
Wikipedia article about the book:
https://en.wikipedia.org/wiki/Propaganda_%28book%29
Wikipedia articla about Edward Berneys:
https://en.wikipedia.org/wiki/Edward_Bernays
Online text of Propaganda, book by Bernays:
http://www.historyisaweapon.com/defcon1/bernprop.html
Scan of first edition of the book, open source:
https://archive.org/details/Propaganda1928ByEdwardL.Bernays
Interference Inkjet Printing
Interference Inkjet Printing refers to the production of a color image using colorless ink and an inkjet printer. The color comes from the interference of reflected light, which has passed through thin layers of the ink deposited on the paper.
A recent paper (Jan-2016) by four authors at ITMO University, Saint Petersburg, Russia, describes their technique. Details at links below. Their innovations include the use of an inexpensive office inkjet printer, and an ink formulation which does not require high temperature or other special processing.
It’s impressive work. If this topic interests you, I think there are many opportunities for follow up studies.
Best wishes,
Ken Roberts
18-Feb-2016
Paper:
Aleksandr V. Yakovlev, Valentin A. Milichko, Vladirm V. Vinogradov, and Alexandr V. Vinogradov.
Inkjet Color Printing by Interference Nanostructures.
ACS Nano
http://pubs.acs.org/doi/abs/10.1021/acsnano.5b06074
Paper is unfortunately behind a paywall, but at least abstract has some detail, and the supplementary file with more tech detail is not paywalled:
http://pubs.acs.org/doi/suppl/10.1021/acsnano.5b06074
Paper info at Researchgate, including links to profiles of the four authors:
https://www.researchgate.net/publication/291815114
Press release about the technique:
http://tass.ru/en/science/857145
[end]
Clarity, Delusion, and Focus
Clear and focused thinking is important for progress when working on a task, such as understanding a situation. One brings to bear whatever one has deduced from previous encounters with a similar situation, as well as whatever one has learned from study of books — history or worked problems, as appropriate. Yet clear and focused thinking is also very closely related to delusional thinking. Clarity and focus can also prevent one from including important information that might bear upon the matter. Another person, observing one’s reasoning, might categorize such a problem formulation or investigative framework as delusional.
For instance, Freeman Dyson, recalling his work in the Operational Research Section of the British RAF Bomber Command during the second world war, tells how his and colleagues’ inability to go beyond operational dogma was a contributing factor to their failure to deduce the existance of a German fighter anti-bomber weapon system: “Schräge Musik”. This weapon involved guns pointing upward from the fighter at an angle of about 60 degrees from the horizontal. The fighter could fly underneath the bomber, observe its outline against the night sky, and shoot up at it; without the bomber crew being aware of an impending attack.
Dyson’s words: “I later applied the same method of analysis to the question of whether experience helped crews to survive. Bomber Command told the crews that their chances of survival would increase with experience, and the crews believed it. They were told, After you have got through the first few operations, things will get better. This idea was important for morale at a time when the fraction of crews surviving to the end of a 30-operation tour was only about 25 percent. I subdivided the experienced and inexperienced crews on each operation and did the analysis, and again, the result was clear. Experience did not reduce loss rates. The cause of losses, whatever it was, killed novice and expert crews impartially. This result contradicted the official dogma, and the Command never accepted it. I blame the ORS, and I blame myself in particular, for not taking this result seriously enough. The evidence showed that the main cause of losses was an attack that gave experienced crews no chance either to escape or to defend themselves. If we had taken the evidence more seriously, we might have discovered Schräge Musik in time to respond with effective countermeasures.
Source URL: https://www.technologyreview.com/s/406789/a-failure-of-intelligence/ (Dyson, 2006)
Another illustration, which is similar in nature, is inherent in some post-war comments by the German general Siegfried Westphal:
“Propaganda must be flexible, although it must not be forgotten that the tune cannot be changed from day to day. Under certain circumstances it can be a very dangerous poison since it may influence or frustrate the decisions of its propagators against their will. Examples of this can be found on both the German and Allied sides during the war and also after it.” (S. Westphal, “The German Army in the West”, Cassell & Co, 1951, page 16).
We can observe numerous illustrations of such delusional behaviour, believing one’s own propaganda, nowadays.
The risks of clarity and focus are not restricted to military or political situations. Scientific investigation, and organizational structure, are also worth considering in the context of the clarity – delusion – focus model.
Best wishes,
Ken Roberts
10-Feb-2016
Microcephaly, Zika Virus, and Radiation
There are many news stories currently about the Zika virus, including a possible link with infant microcephaly. The news coverage is sometimes too decided on such possibilities, and it may be worthwhile to stand back a bit from decisions. Microcephaly can have several causes. I’m not a medical practitioner, but even a non-specialist can get a bit of calm perspective from reviewing some of the info sources.
The WHO (world Health Organization) website has some Q&A about the Zika virus, and includes this text:
“Should pregnant women be concerned about Zika?
“Health authorities are currently investigating a potential link between Zika virus in pregnant women and microcephaly in their babies. Until more is known, women who are pregnant or planning to become pregnant should take extra care to protect themselves from mosquito bites.
“If you are pregnant and suspect that you may have Zika virus disease, consult your doctor for close monitoring during your pregnancy.
“What is microcephaly?
“Microcephaly is a rare condition where a baby has an abnormally small head. This is due to abnormal brain development of the baby in the womb or during infancy. Babies and children with microcephaly often have challenges with their brain development as they grow older.
“Microcephaly can be caused by a variety of environmental and genetic factors such as Downs syndrome; exposure to drugs, alcohol or other toxins in the womb; and rubella infection during pregnancy.”
[end of quote from WHO] Source URL: http://www.who.int/features/qa/zika/en/
Another possible cause of microcephaly is exposure of the fetus to radiation. Here is a text from the “Mother to Baby” website supported by the the state of Illinois, USA:
“CNS [Central Nervous System] defects and Growth Retardation
“Manifestations of in utero irradiation in humans are microcephaly, mental retardation and other CNS defects, and growth retardation (Mole 1991). Microcephaly is the most common malformation reported after exposure to a high dose of radiation during pregnancy. In one study, 25% of children exposed to more than 100 rads of radiation during gestation were microcephalic or hydrocephalic (Goldstein and Murphy 1929, 1930). Almost all microcephalic children irradiated in utero were mentally retarded and had short stature as well. The incidence of microcephaly rose with increasing exposure (Brent et al. 1993).”
[end of quote from “Mother to Baby” website] Source: http://fetal-exposure.org/radiation-and-pregnancy/
Another, non-medical, resource on the relationship between radiation exposure and microcephaly is found in Susan Southard’s book “Nagasaki: Life After Nuclear War” (2015): “Microcephaly — a condition defined by a significantly smaller-than-average head size in proportion to a child’s body, reduced life expectancy, and decreased brain function — occurred in approximately 15 percent of children exposed to radiation in utero up to 1.25 miles from the hypocenter [of the atomic bomb explosion], a rate almost four times higher than for those not exposed.” [page 177]. Also, on page 190,. a study is cited that exposure during weeks 8-15 after conception was much riskier than exposure in later weeks of pregnancy.
Bottom line for a cautious non-specialist reader: There can be a variety of causes of the observed high incidence of microcephalic infants. A possible connection with the Zika virus is worth investigation, but also it is advisable to investigate possible presence of other causative factors. WHO is doing those investigations. We should not rush to decision and action about a possible mosquitoes and Zika virus causation, if that would result in other avenues of inquiry being abandoned. It is worthwhile to reduce mosquito populations in general, because of other diseases they can transmit (Dengue fever, for instance). But, regarding Zika, don’t let media frenzy divert investigative focus.
Best wishes,
Ken Roberts
03-Feb-2016
How to Find Papers
A site named “ResearchGate” has become one of my tools for locating papers. The site is a bit annoying at times. Sort of like Facebook, for scholarly work. There is a continual stream of “helpful” emails, and popups asking one to consider a job posting, or add a publication, etc etc. Rather like a hyperactive and gossipy personal assistant. Also, there is a lack of confidentiality — if one “follows” a particular paper, to be apprised of future citations of it, all of one’s contacts are advised that one is following that paper. So if one wants to work under the radar, then ResearchGate is not the tool for you. Be advised!
However, on the plus side: ResearchGate is excellent as a way of finding out what a person has published, who has cited it, what that person has published, and so on. I recently was looking at a paper by Neil Turok, “On quantum tunneling in real time”, and wanted to find out if anyone had cited it. Web of Science / Knowledge said not. But Google Scholar reported some related papers, and one of them led me to a paper by Carl Bender and Daniel Hook which cites the Turok paper. And that, in turn, via Hook’s ResearchGate publications list, led me to the very interesting and stimulating paper by Bender and Hook, Arxiv 1011.0121, “Quantum tunneling as a classical anomaly”.
That enables me to return to a subject I’ve been interested in for some time, whether the complex plane tangencies of the Lambert W lines with the strength contours of a quantum well, represent sensitivities which have a physical implication — for example, whether one can devise a sensor which uses that tangency. The QWIP, quantum well infrared photodetector, which is found in night vision apparatus, is an example of such a sensor. In general, a sensor can be made by conditioning a quantum well device at or near a context which changes the number of bound states or a tunneling probability, and then allowing the environment to stress the sensor — changing the energy, changing a dimension, changing temperature, and so on. Finding the Bender and Hook papers, and a couple of Turok papers, offers the possibility of a new look at that topic.
Best wishes,
Ken Roberts
31-Jan-2016
ELK Software and Raspberry Pi
ELK is a software package for density functional theory calculations. Raspberry Pi is an inexpensive computer. I was interested in whether the RasPi might be useful for ELK calculations. This post reports on some timing tests.
ELK is open source software, written in Fortran, available via the SourceForge link given below. ELK runs its calcs on multiple parallel processors. My typical config for using ELK is to run on a two-core or four-core processor such as an Intel i3, i5 or i7 based Laptop, with Linux (Slackware) as the operating system, and OpenMP as the task coordination mechanism. I usually run several jobs, with various parameter choices, exploring some material model. Each job might take from a few hours to a couple days, depending upon the fineness of the grid used for modelling. On a supercomputer cluster, I have in the past run up to 100 jobs concurrently, with a selection of parameter choices, in order to develop an understanding of how the parameters affect the calculation results for the material.
More recently I have been running jobs sequentially, using a more directed exploration of the parameter space vs model results. That latter approach allows for more interaction with the investigation as it progresses, and leads to better intuition. One of my beliefs is that the dynamic tension between improving calculation speed and improving model and math, leads to better understanding. That belief goes back decades, to some success I had in number theory problems by using the tension between calculation and description. To do the work faster, instead of using a faster computer, one can replace parts of the problem description with better math. Eventually, sometimes, the problem collapses into good math and a fairly rapid calculational model. I have a hope in the back of my wish list that certain DFT, QCD, and Molecular Dynamics problems will someday be discovered to have such simplifications.
Anyway, given that approach, I was interested in perhaps using the RasPi as an ELK machine, thereby leaving my main Linux laptop free for other work. The RasPi (couple of links below) has impressive specs, with the model 2B, the current product, having a quad-core processor, 1 GB memory, 8 GB to 32 GB of local disk (depending on the sD photo card installed) with net 4 GB to 28 GB of free storage for user files, an ethernet port, four usb ports for keyboard, mouse, etc, and … best of all … very modest cost. RasPi comes with Linux (Debian based) and a copy of Mathematica. Although I don’t use Mathematica at present, having “paid my dues” already by learning Maple, and not wishing to have to re-learn the quirks of a new tool unless necessary, the low cost access to Mathematica is a nice plus, of possible future benefit.
So, I ran some timing tests. The results in summary: ELK installs on RasPi with no difficulty (details below) and runs its post-install tests successfully. However, RasPi is slow in running ELK, taking 79 elapsed minutes to complete the collection of 18 test calculations. The “top” and “1” command sequence shows that all four of the processor threads were active, so the problem may lie with some other aspect — for example, speed of the sD card or the low (1 GB) memory resulting in less in-memory-buffer file access. Whatever. In contrast, my Intel i5-core based laptop (Lenovo ThinkPad T420 with disk replaced by a 1 TB drive, and Slackware installed instead of Windows) completes the test calculations in 8 minutes. With a 10x speed difference, the ELK approach is not cost effective. It might cost about $600 to get ten stripped down RasPi boards (with board itself, with only power and ethernet connected, and controlled via ssh login sessions), whereas the T420 laptop cost only $300 refurbished. So, I will stick with laptops. However, I look for the next generation of RasPi boards. I think it is an excellent product. There are other applications besides ELK. GROMACS, for molecular dynamics calculations, for instance, might be suitable for the RasPi. For the future.
Some details about the RasPi setup may be helpful to record, for others. The RasPi in Canada is available from canakit.com and one can find other suppliers elsewhere. I was pleased with the speed of delivery from Canakit. I got the full kit, eg with Wifi dongle, but one just needs a stripped down kit for second and subsequent RasPi boards. I replaced the 8 GB sD storage card with a 32 GB sD card, with the latest operating system version (Nov-2015) downloaded from the RasPi support website. The OS boots to an X-Windows screen, and one logs in as user “pi”. To get root access and a command line, I used “sudo passwd root” and set my own password on the root user. Then one can work a bit easier. The aptitude utility was used to install the software needed for ELK, including “aptitude xxx” commands where xxx was these in sequence: “update”, “search fortran”, “install gfortran”, “search openmp”, “install libblacs-openmpi1”, “search lapack”, “install liblapack3”, “search fft”, “install fftw3”. ELK was set up to use the GNU fortran compiler (gfortran), etc.
It is interesting that the ELK test runs produce some warning messages regarding IEEE floating point arithmetic errors: IEEE_INVALID_FLAG, IEEE_OVERFLOW_FLAG, IEEE_UNDERFLOW_FLAG, IEEE_DIVIDE_BY_ZERO. These exceptions are discussed in a post at SourceForge, URL given below. Although I found the specific recommendations of that post to be ineffective, the insight into cause, and why it “does not matter”, is useful — see the third comment in that post. It is something that can guide investigation. Running ELK on Slackware / Intel i5-core with gfortran does not produce those errors, though it produces identical test results. I think that is simply because floating point exception warnings have been turned off in the latter configuration.
That’s it about RasPi and ELK. Each device/program is worth one’s attention if it matches one’s objectives, as these do with my objectives. Neither is perfect, but they are understandable, affordable, open for improvement, and a net benefit for serious work.
URLs below.
Best wishes,
Ken Roberts
25-Jan-2016
For ELK density functional theory calculational software:
http://sourceforge.net/projects/elk/
For Raspbery Pi supply, and for community projects website:
https://www.element14.com/community/welcome
https://www.raspberrypi.org/
Discussion of ELK tests producing IEEE floating point exceptions:
http://sourceforge.net/p/elk/discussion/897820/thread/e87237ad/
[end]
Neon Cactus
This neon cactus has been around my house for about 25 years. It serves as the night-light in the main room. Last week, it died, and that led to some investigation of the details…
The cactus is made from a “neon” sign tube, which glows brilliant green. The pale green color in the photo is an artifact of my camera. The transformer is hidden within the metal pot, and covered with a large amount of fish tank gravel, to support the transformer and the base of the neon tube. The toothiness along the neon tube is achieved by little bits of clear silicone caulk applied along the glass.
Inside the metal pot, there are two sets of connections: from the transformer to the neon tube, and from the power cord to the transformer input. The supply to the tube (output of the transformer) is rated at 3000 volts and 20 milliamps — enough to give someone a dangerous jolt, I believe. We are fortunate that we have never had a house guest who emptied his beer into the metal pot.
The cause of the failure last week was the transformer overheating. After 25 years, it deserves a rest — and has taken a permanent break. Power consumption of about 50 watts x 24 hours = 1.2 kwh/day = approx operating cost 30 cents/day at modern rates. Less than a single movie admission ticket per month. So it costs to operate a neon cactus, yes, but it is not out of line with other entertainment.
Rather than replace this neon cactus art with another neon construction, or hunt all over for a new transformer, I think it will be more in tune with the times to look for some LED or other pixel-based art. One might, for instance, mount a photo frame where the cactus was, and set up a suitable permanent or slowly cycling slide show fed from a USB stick. A bit of consideration and searching on the net and asking friends, should produce an abundance of good ideas.
Best wishes,
Ken Roberts
28-Dec-2015
Solar Cells 3
In this post I’ll talk about the one diode model for solar cells. A solar cell produces a current because, under illumination, exciton pairs — electrons and holes — are produced, and before the electrons and holes can recombine, they flow towards and out through the contact terminals of the solar cell.
A solar cell can be described by a “lumped parameters” model. There is a current source, which represents the current which the solar cell’s material would produce, under standard illumination, in the absence of any losses due to reverse flows or contact resistance. The reverse flow, or recombination of excitons, is represented as a diode in parallel with a shunt resistance. There is also another resistance in the model, due to the contact resistance and other limitations on the flow of electrons to outside the solar cell. That latter resistance is modelled as a resistor in series with the current source / diode / shunt resistor triplet.
Here is a circuit diagram. It’s easier to see an unambiguous circuit than to follow the verbiage in the previous paragraph. The output current and voltage produced by the solar cell are I and V. These two related quantities are measurables. One actually has several values of I and V — for instance Isc the short circuit current (when V is zero), and Voc the open circuit voltage (when I is zero), both under standard illumination. As well one can obtain a value Idk, the dark current when there is no illumination and the solar cell has a bias voltage V applied. However, the other parameters in the circuit diagram are components of the model, to be determined by choosing those parameters to fit the actual I-V curve measurements (see characteristic curve in prior post) against the model. Rs is a series resistance, Rp is a shunt resistance, Iph is the photocurrent, and I0 and n are diode parameters — to be discussed in the next paragraph. Actually, given the current direction convention in the circuit, the output of the solar cell is -I not I. That is just a convention, but it accounts for the shape of the I-V curve in previous post, which looks like a letter J. Solar cells (good ones, at least) are described as having a J-shaped I-V curve, so I have adopted a current direction convention which makes the curve look like a letter J.
So, what about the diode? The standard diode model is called the Shockley model, and is described in many places on the net and in books. For an extended discussion focused on the particular context of solar cells see, for instance, “The Physics of Solar Cells”, by Jenny Nelson, chapters 1 and 6. The basic idea of a p-n junction diode is that current flows in one direction based upon the bias voltage across the diode, but it is offset by a thermal counterflow. The current through and voltage across the diode, say Idiode and V1, are related by the equation
Idiode = I0 [exp(q V1 / n k T) – 1]
where T denotes absolute temperature (degrees Kelvin), k denotes Boltzmann’s constant, and q is the magnitude of the electron charge.
There are two parameters in the Shockley diode model: I0 and n. The parameter n is called the “ideality factor”, and is 1 in an “ideal” diode, on the order of 1.05 for a real diode, and somewhere between 1 and 2 for a diode model used for a solar cell. As you can see, the assumption that a solar cell can be modelled using a diode is a bit of a stretch, but it is good enough for most practical purposes. It has the great advantage that there is lots of circuit modelling software for diode circuits. The parameter I0 is chosen to fit the data.
Now, one can write an equation to relate I and V for the one diode model of a solar cell. The voltage drop across the entire solar cell is V = I*Rs plus V1; that is, V1 = V – I*Rs. The current through the shunt resistance is V1/Rp. The current through the diode is Idiode as per the formula above. Putting everything together, and taking account of the sign conventions, one ends up with the equation
I = I0 [exp(q (V – I Rs) / n k T) + (V – I Rs)/Rp – Iph.
This equation is exact, at least insofar as the Shockley diode model and the other components in the one diode model are adequate as a description of actual solar cells. If one chooses a value of V, one can solve for the corresponding value of I. And vice versa. So the I-V curve corresponding to this equation can be drawn, and one can adjust the five parameters I0, Rs, Rp, n and Iph to fit the solar cell model to the actual I-V curve for a solar cell. (The parameters q and k are constants, and the parameter T reflects the working context of the solar cell, so they do not have to be adjusted to fit the model to the data.)
However, choosing a value of V and solving for I means solving an implicit equation. Likewise, choosing a value of I and solving for V also means solving an implicit equation. It would be nice to have an explicit equation, I = f(V) or V = f(I), either one. The difficulty is that I and V each appears both in linear terms and in exponential terms in the model equation above.
Those sorts of equations, involving exponentials and linear terms in a variable, often can be solved using the Lambert W function, and this equation is one which can be solved. The basic solutions were found by Jain and Kapoor in 2004 (see refs in working paper for the journal reference), and I will not bother to transcribe them here. J&K give explicit equations for both alternatives, I = f(V) and V = f(I). Because it is the V = f(I) form which turns out to be best for extending to the two diode model to be considered later, I will show the V = f(I) form here:
V = f(I) = I Rs + (I + Iph + I0) Rp
– (n k T / q) LamW((q / (n k T)) I0 Rp exp[(q / n k T) Rp (I + Iph + I0) ] )
where LamW() denotes the principal branch of the Lambert W function.
That’s a mess, I know. But at least it is an explicit expression. Given a value of I, one can calculate V. That calculation process is much less time-consuming than iterative refinement to solve an implicit equation of the form function(V,I) = 0.
However, there’s a problem. That particular formula V = f(I) can experience arithmetic overflow. And that’s where our working paper comes in. I’ll discuss some computational considerations, for the one-diode model, in the next post.
By the way … Merry Christmas !
Best wishes,
Ken Roberts
25-Dec-2015
Snow Crystals 2
Imagine my surprise to see a mainstream media article about snow crystals! Here is the link.
https://www.rt.com/news/326738-designer-snowflakes-lab-california/
It describes the snow crystals grown by Ken Libbrecht in his Caltech lab, and has some great photos.
The text of the article is also worth a read.
Best wishes,
Ken R.
22-Dec-2015
Solar Cells 2
A solar cell produces an electric current when its material surface is illuminated. In order to standardize the methods of measuring solar cell performance, and comparing different cells, certain conventions are adopted. For instance, standard illumination, which is the amount and wavelengths of the light falling on the solar cell’s surface.
A typical solar cell might have an area of 2.2 cm^2. Sometimes the current produced by a solar cell is quoted as so-many amps (or milliamps or microamps) under standard illumination. That statistic is appropriate when considering a particular solar cell or comparing two models of solar cells. Other times the current produced by a solar cell is quoted as a “current areal density”, that is, so many amps per square centimeter of solar cell material. That statistic is appropriate when considering a proposed solar cell material, or comparing two types of material or two choices of processing options for preparing solar cells using a particular material.
Solar cells are assembled into modules, which are groups of individual solar cells connected together (eg, in series) pre-packaged for easy handling. Modules are built into arrays, which make up solar panels; the panel includes the structural framework. Solar panels are the structures one notices on roofs and in fields.
The context of our recent work has been a mathematical model which is used for describing individual solar cells. As you can see there are many other aspects of solar cells and solar panels which are worth investigation (and have been investigated). Our work is just one part of the efforts of thousands.
I’m no expert on solar power. But I want to share the bits of information (or misunderstanding!) which I’ve gathered during my work. In the rest of this post I’ll describe some general aspects of solar cell performance. The details of the math model I’ll discuss in other posts — or you can go directly to the working paper at Researchgate if you want.
There are two measurements on the performance of a solar cell which are relatively easy to make: Isc = the short circuit current, and Voc = the open circuit voltage. Isc is determined by the amount of current the solar cell will push when it is under standard illumination and its contacts are shorted (no voltage difference); that current is largely determined by the series resistance within the solar cell. Voc is determined as the voltage difference between the contacts of the solar cell, again under standard illumination, when the load is missing — ie, an open circuit (no current flowing), or the voltage into an infinite load. Under other loads, there is a current less than Isc, and a voltage difference less than Voc.
The “I-V characteristic” for a solar cell is the curve which relates the current and the voltage. The graph shows a typical example, for a silicon solar cell manufactured about 3 decades ago. The current is shown as a negative number because of the convention used in the test circuit. What you can see in this curve is that this solar cell has Isc about 102 milliamps and Voc about 520 millivolts. The solar cell puts out a fairly constant current, between 102 milliamps and 95 milliamps, regardless of the load resistance, as long as the voltage drop does not exceed say 420 millivolts. That is, the load resistance can be up to say 420/95 = 4.3 ohms. As the load resistance goes higher, the solar cell’s current output drops rapidly towards zero. A load resistance of about 4.3 ohms, for this solar cell, is the “sweet spot” when the I*V product is a maximum. Power equals I*V (for direct current circuits like a solar cell), and hence that sweet spot is known as the “maximum power point” or MPP of the solar cell. The “fill factor” or FF of the solar cell is the ratio between the I*V product at the MPP, and the Isc*Voc product.
The maximum power point can shift if the illumination on the solar cell changes. For example, if the solar cell falls into shadow. The calculations to determine the MPP for an array of solar cells, for load balancing, can represent a lot of work. The MPP can be estimated by searching, varying the load slightly, but sometimes the power curve will have multiple peaks, and automated searching may not find the optimal operating conditions. It is important to have a good mathematical model for the I-V characteristic, in order to rapidly find the MPP under changed illumination. Further, that model should be suitable for implementation on very inexpensive microprocessors, such as may be used in a field installation. That’s where the method which S. R. Valluri and I recently described in our working paper is likely to be most useful.
That’s it for this post. More later!
Best wishes,
Ken R.
20-Dec-2015
Logic, Astronomy, Science, and Ideas Too 
