Awesome circumhorizonal arc last weekend!

This was so cool.  Last Sunday while taking my daughter to her tennis lesson, we noticed a neat rainbow-like apparition in the sky above the tennis center.  But the sun was high above it, not behind us, and there was no rain or mist, only high cirrus clouds, so it couldn't be a rainbow.  I knew that while rainbows are the most common colorful refraction feature we see in the sky, there are many other less common features in the same category.  I had to look it up but found this one is called a "circumhorizonal arc".  It falls along a circle (except like rainbows we often only see a portion of that circle, in an arc) that's 57.8° from the Sun, which accounts for the Sun being so high in the sky, and also for the fact that we can only see them in summertime since the Sun is lower in the sky in winter.  Surprisingly though, in spite of our warm summertime it's little ice crystals high up in the sky that the light is refracting through to cause this effect (which accounts for the high-up cirrus clouds in the sky that day too).

Circumhorizonal arc, Seattle area, Sunday 25 June 2017, 1:30pm local time:

(that light dot at bottom of the right photo is just a camera artifact that appeared whenever I tried to include the bright Sun in the photograph)

What I also found interesting about this arc was that apparently it's typically seen along with a 22.1° halo around the Sun as well, but ours didn't have the 22.1° halo.  (See for example the picture below copied from the Wikipedia page on circumhorizonal arcs.)

There are all sorts of these types of features that can show up in the sky given the right conditions, with neat geometric derivations (for example one of my favorite Walter Lewin physics lectures is the one where he really clearly derives the 42° geometry for rainbows).

(from Atmospheric Transmission, Emission and Scattering, edited by Thomas G. Kyle)

A handful neat webpages that I've seen about these circumhorizonal arcs are:

• the Wikipedia page on circumhorizonal arcs
• the Wikipedia page on circumzenithal arcs
• a nice page about both 22 halos and circumhorizonal arcs
• and the circumhorizonal arcs page on the beautiful Atmospheric Optics website, which shows great photos of all sorts of different sky features like these.

Server with the fringe on "top"...

Just stumbled on a much nicer, expanded version of the *nix command line tool top (process listing/manager tool), called htop.  Cool - what I especially like about it is its little graphical display of cpu usage meters for each individual processor in a machine; the rest looks similar to top but with highlighting and extra features - and all configurable.  And you can scroll up and down the processing listing too!

Looks like it's installed by default already on my Ubuntu machines, but not on my Macs.  (And for the record I think the output formatting in the OSX version of top is awful anyway!)  For that I found this guy's webpage offering a precompiled OSX binary (but you could compile it yourself if you prefer, see link at bottom of his page).

Here's a screenshot of what it looks like on one of our 8-processor Ubuntu cluster nodes...

(apologies for the title pun, couldn't help myself.  ;-)

Fortune cookie

Ha ha ha!  Look what it said in my fortune cookie the other day as I was writing about the quirks of my nonlinear inversion...  The fortune cookie described the trouble exactly!

Bright Lights, Big City, Fast Electrons!

There's a neat photo decorating a bus stop near my home - one of those motion-blur shots where the artist intentionally moved the camera while taking the picture.  Looking at the whole picture on the bus stop you can tell it's of a city-scape (Seattle's presumably, given where the bus stop is and the title of the photo listed on it).  Kudos to photographer Anna-Mária Vág who is listed as the creator of this neat snapshot.

So it's pretty, but here's what I especially further like about it, being a physicist and electrical engineer before that.  Look closely at a zoom-in of the photo (or the original above for that matter):

Not only do we see blurred streams of light in this photo, but we also see that the lights are blinking on and off and on again.  That's because our power, and thus most of our lighting, runs on AC - alternating current - which takes the form of a sin wave going on and off (brighter and dimmer) 60 times per second, or 60Hz.  Besides photos like this, another common place you'll see this is if you're using a pair of binoculars to look at a nighttime cityscape, and move the binocs around in a circle or back and forth.

In the photo we see that although the buildings are separated by wide distances, most of their lighting is not only blinking, but blinking in phase - meaning in sync with each other.  If you took a better snapshot than mine of this photo, and then placed a ruler on it to draw lines between the bright (or dark) parts of the streaks, you'd see most of them make nice straight lines, all the way across the photo of the city.  The electrons zipping over the electrical supply wires for the city are moving @#$% fast to accomplish that.  They're not quite moving at c, the speed of light in a vacuum we talk about in relativity discussions etc. - they're going slightly less than that because these electrons are moving through copper wires.  But it's still really darned fast!

I said "most" of the ruler lines make nice straight lines - some are a bit off, yet still appear in sync with each other - what's going on there?  It turns out not only is the city running on AC power, but it's actually running on three supplies of AC power at once; they call this "three phase power".  The three phases are 120° off from each other, i.e. if you add up the phase angle of all three you get 360°, which allows for a convenient and efficient trick for running the wiring for the power as well as for turning on industrial motors.  The blink patterns in this photo that are not right in a line with each other appear to be roughly 1/3 off from the others, which is consistent with that 120° and 240° business.

Cameras and binocs aside, you may even find that when standing under some types of street lights (or looking at certain car/bus taillights, or modern car nighttime dashboards, or digital projectors, etc), and glance your eyes back and forth, you'll see them blinking directly yourself without further aid.  Which frankly is really @#$% annoying when you're trying to concentrate on something else, like driving.  But what the heck, at least it gives you a moment to appreciate some of this neat stuff, and to realize just how fast those electrons are moving!

A&S for the 21st century

Sweet, I just discovered that the old classic 1000-page mathematical reference Abramowitz and Stegun has been updated and distributed for the new millennium (well, and century too) in a more modern way.  It's all there free on its own NIST website (the National Institute of Standards and Technology were the ones who published A&S in the first place back in the 1960s).  Here it is right here:

http://dlmf.nist.gov

It was released just two years ago, with both a book version and this online version, which as far as I can tell is a superset of the book.  Here are the three coolest practical aspects of the website version:

1. next to each equation there's a permalink so you can reference a link straight back to the original section of the equation reference
2. and perhaps even better, also next to each equation there's a link to the TeX source for the equation, so you don't even have to rework it all up in TeX again yourself when using it.
3. and even better than that! - ALSO in each section is a list of links to modern software references for finding software libraries & codes to compute the quantities discussed in each section.  (typically in Fortran; note for each code the link puts you at a bibliography entry for a relevant journal paper, but at the right of that ref there's another link that'll get you to the code and other related documents)

NIST Digital Library of Mathematical Functions

(Note the Riemann zeta function used in their cover plot - for these 3D plots you can even interactively go zip around in them via VRML and X3D)

Self-explanatory

Alas this is snipped out of a real geophysics research paper - an important and seminal one at that (Dahlen et al's "banana-donut" paper on ray sensitivity kernels).  So freakin' typical and stereo-typical at the same time...

Tradeoff using central finite differences

Arggg!  (But yay!)  Well my collaborator and I finally figured out why the spectra we were computing were unexpectedly rolling off in the higher wavenumber end.  We were calculating spectra of the derivative of our data series, and were using central finite differences to approximate that derivative.  We'd figured that central differences were more accurate than forward differences and so we were using those (via Matlab's gradient() function), but we realized - ahem, in hindsight - that there's an important tradeoff to be aware of there.  Since the central differences approximate the derivative using the point before and after the present point, it's effectively averaging over three points, and gives you a low-pass filtered version of the derivative.  Forward (and backward) first finite differences do this too but over fewer points (two instead of three) so it's not so big an effect.  The central diffs caused a big enough effect to be a problem in our work, while the forward diffs do not.  Note it depends what aspect of the derivative is most important to you though - phase offset vs frequency rolloff.

In the end we computed the derivative more directly anyway by transforming to the wavenumber domain and multiplying by ik, just to avoid the whole issue.  At any rate, I noticed Terry Bahill (retired from Univ Arizona) has a nice brief paper that sums it up well.  @#$%, can't believe I didn't notice this earlier...