12 December 2008

UAW/Republican auto bailout insanity

Consider the following snippet (emphasis mine):
U.A.W. in Center of Dispute Over Bailout Failure - NYTimes.com
Late Thursday, the Senate did not take up an assistance measure passed by the House, after hours of negotiations between Senate Republicans with the auto companies and the U.A.W. The sticking point apparently was the union’s refusal to agree to lower wage and benefit rates as soon as next year.

Representatives for the union, which had already accepted a series of cuts in its current contract, sought instead to push any more concessions back to 2011, when the U.A.W.’s contract with Detroit auto companies expires.

In a statement Thursday night, the union said it was “prepared to agree that any restructuring plan should ensure that the wages and benefits of workers at the domestic automakers should be competitive with those paid by the foreign transplants. But we also recognized that this would take time to work out and implement” using programs like buyouts and early retirement offers to bring in new workers at lower rates.
It can be (albeit simplistically) be translated into:
"Yeah yeah yeah. We know our non-market salaries are high enough that it's driving the company down. Yeah, the union will accept pay cuts. But we want bought out/paid off before any of us actually have to work for market wages. Oh, and by the way, millions of other people's jobs be damned."
Interesting that the Republicans killed it, and now that it's Bush who may come swooping in from left field. Especially funny/sad is that the executive action to save things will probably give the U.A.W. what they want. That's likely to overwhelm the domestic automakers yet again even if a current bailout can save them.

09 December 2008

Nice Nutcracker article on Michelle in the Austin Decider

The Austin Decider ran a fun piece on the role of snow within Ballet Austin's Nutcracker.  Michelle was the chosen snowflake:
House Lights: Backstage at The Nutcracker

07 December 2008

Fall 2008 :: Probability Theory I Concepts

I'm a week away from finishing the first half of a year-long probability theory sequence at U.T. I (finally) managed to keep a concepts cheat sheet up to date for a course:

Probability Theory I: CAM 384K Concepts

Part of my motivation has been that while Durrett's text is useful, it is very difficult to find specific definitions and theorems within it while working problems.

25 November 2008

Wasted Days

Today I received a questionnaire asking for total number of contributions in the following categories over the past academic year:

  1. Refereed Papers
  2. Non-refereed Papers
  3. Books
  4. Book Chapters
  5. Presentation at learned societies/symposia
  6. Invention disclosures
  7. Copyrighted Software
  8. Patents Filed
  9. Other Scholarly Works
to each of which I responded with a big, fat zero. It is early for resolutions, but I aim for '09 to be full of accomplishments that can be measured instead of my usual results (e.g. "Oh! Duh! That's what that equation means. I should'a known that already...").

19 November 2008

A B-spline verification test case

Update (16 Dec): The B-spline derivative code made it into GSL's 1.12 release

I'm trying to get B-spline derivative capabilities added to gsl. Though I could find lots of implementations of B-spline derivatives for fixed polynomial order, finding derivatives for arbitrary order B-splines turns out to be a gap in many libraries (with PPPACK being the notable exception).

It also turns out that finding a good, concrete verification test case is a pain too. Hopefully gsl will pick up my patch and no one will have to implement these again. But, if you should find yourself in that situation, here's some Mathematica that provides both symbolic and numeric results for quadratic B-splines and their derivatives on a particular set of knots:

A verification case for B-Spline implementations, including derivatives

12 November 2008

Handcrafted memory layout: a case study in magic number mayhem

Observe, in the code snippet below, that no fewer than 27 subtly different aliases have been created for the same chunk of memory...

Semantics/Syntax: The @ sign instructs the compiler to have the variables named varsc and vars share storage much like C's union construct. The symbolic keyword acts like a macro definition.

    dynamic complex(64) varsc[(nx+2)/2,ny,37] 
          @ real(64)    vars[     nx+2,ny,37]   
    symbolic mic[i,j,l]        = varsc[i,j,l]
           , rhoc[i,j]         = varsc[i,j,4]
           , engyc[i,j]        = varsc[i,j,5]
           , drho_dxic[i,j,l]  = varsc[i,j,l+5]
           , dengy_dxic[i,j,l] = varsc[i,j,l+8]
           , dmi_dxic[i,j,l,m] = varsc[i,j,11+(l-1)*3+m]
           , rhsc[i,j,l,m]     = varsc[i,j,25+(l-1)*3+m]
           , rhs_rhoc[i,j]     = varsc[i,j,21]
    symbolic mi[i,j,l]         = vars[i,j,l]
           , rho[i,j]          = vars[i,j,4]
           , engy[i,j]         = vars[i,j,5]
           , drho_dxi[i,j,l]   = vars[i,j,l+5]
           , dengy_dxi[i,j,l]  = vars[i,j,l+8]
           , dmi_dxi[i,j,l,m]  = vars[i,j,11+(l-1)*3+m]
           , rhs_rho[i,j]      = vars[i,j,21]
           , dui_dxi[i,j,l,m]  = vars[i,j,11+(l-1)*3+m]
           , pres[i,j]         = vars[i,j,22]
           , tmpt[i,j]         = vars[i,j,23]
           , mu[i,j]           = vars[i,j,24]
           , tau[i,j,l,m]      = vars[i,j,25+(l-1)*3+m]
           , q1[i,j]           = vars[i,j,9]
           , q3[i,j]           = vars[i,j,11]
           , rhs[i,j,l,m]      = vars[i,j,25+(l-1)*3+m]
           , dmu_dx2[i,j]      = vars[i,j,6]
           , dtmpt_dx2[i,j]    = vars[i,j,7]
           , d2tmpt_dx22[i,j]  = vars[i,j,8]
           , d2ui_dx22[i,j,l]  = vars[i,j,8+l]

10 November 2008

Overnight trip to Mason, TX

I just got back from an overnight motorcycle trip with my friend Paul.

We'd wanted to travel further west than Mason, but a late start and a large helping of pie in downtown Mason caused us to rethink our plan.  Hanging out at The Old Peanut Mill Steakhouse and Fort McKavett Social Club filled most of Saturday evening.  Nice place.

The roads that crisscross the Guadalupe river are beautiful this time of year:

The VFR turned over 50K miles on the trip.  Paul, as always, did a great job with the route and navigating.  Both days were a mix of unused high speed sweeping turns along with some intermittent choppy surface connections across ridges and into each successive valley.

05 November 2008

Good? Bad? Over.

Done deal:

I've got to admit I'm pleased with the outcome. Hopefully state and local races won't shock the system so badly that they inhibit smooth day-to-day operation.

02 November 2008

Two more of my IBM patent applications published

I just noticed that these two patent applications just appeared publicly...

(20080198748) System and Method for Burst Traffic Smoothing for SIP Processing Elements
A system and method for burst traffic smoothing for Session Initiation Protocol (SIP) processing elements are provided. A dispatch queue management engine determines whether a received packet is a TCP or UDP packet. If the packet is a TCP packet, the packet is automatically added to the dispatch queue. If the packet is a UDP packet, a value for a drop function f is generated and a random or pseudo-random number r is generated. If r has a predetermined relationship to f, then the UDP packet is added to the dispatch queue, otherwise the UDP packet is discarded. The value for f is based on the current dispatch queue load, the network quality, the retransmission rate, and the allowable drop rate. Thus, the determination as to whether to drop UDP packets or not is configurable by an administrator and also adaptable to the current network and dispatch queue conditions.
(20080229245) Multiple Sorting of Columns in a Displayed Table in a User Interactive Computer Display Interface Through Sequential Radial Menus
Multi-sorting of displayed columns representative of a tabular display is carried out by displaying a table of a plurality of columns, selectively displaying a first radial menu having a plurality of sectors, each sector representative of one of the plurality of columns, enabling a user to select one of the sectors, and responsive to a user selection of a sector for displaying a second radial menu of the plurality of sectors wherein the selected one sector is disabled, e.g. eliminated. This is continued through a sequence of subsequent radial menus until the user has selected the intended set of sequential columns for the multiple sorting.
The second one, because I worked with a friend whose last name starts with a W, is probably the first (and only) application where I'll ever see 'Ulerich et al.'

Compressible DNS within PECOS

On Monday a bunch of DOE people are in town for the 1st annual review of the Predictive Engineering and Computational Sciences (PECOS) center at UT Austin. Because I'm partially funded through the center, another student and I put together a poster for this Monday afternoon:

Just in case embedded Scribd hiccups, here's a link to the poster.

28 September 2008

U.T. needs to ditch driving on campus

This past week U.T.'s Parking & Transportation Services proclaimed

...Beginning Wednesday, September 24th, there will be a Travis County Sheriff
Officer located at the intersection of Speedway and 24th Street.  This
officer is being placed at this intersection to provide a secure crossing
environment for pedestrians and vehicular traffic....

As safety is our primary concern, all pedestrians in this area should heed
the warning signs and utilize sidewalks for travel, including the east side
of Speedway between Dean Keeton and 24th Street and the south side of 24th
Street between Speedway and Inner Campus Drive.  Please do not walk in the
street or along the closed west sidewalk area of Speedway as construction
traffic in this area is very heavy and pedestrians create potentially
hazardous situations
Having just spent two days at ACL with tens of thousands of pedestrians, I'm pretty sure the people on foot aren't the most preventable root cause of hazardous situations. If some smelly hungover dude accidentally staggers sideways and body checks you while you cross 24th street, you'll still make it to class.  Promise.

The problem is that U.T. stupidly encourages driving across 24th street. Take a look. Those cars? Those aren't construction. The traffic consists of people parking and physical plant vehicles. The intersection becomes hazardous when impatient drivers nudge through a sea of thousands of students on foot mixed with bicycles. Guys with hard hats driving triple diesels aren't the problem vehicles. It's the regular cagers expecting to treat a college campus like any other street.

Students should, of course, be courteous to drivers. But cross campus traffic should be forced to travel north two blocks, across the four lane 26th street, and then two blocks south to San Jacinto. U.T. is not an urban campus, and it should capitalize on that fact by creating pedestrian-only areas where possible. 24th and Speedway would be a great place to start.

26 August 2008

Less than rewarding ways to spend one week

I finally learned that

MATLAB uses the apostrophe operator (') to perform a complex conjugate transpose, and the dot-apostrophe operator (.') to transpose without conjugation¹.
despite my unshakable-yet-painfully-mistaken belief that the converse was true.

One nice outcome— the .' versus ' distinction caused an oscillating phase symptom that made me go through my formulation in detail. I added the derivation as as a nonlinear example on Wikipedia's spectral method page. It will be interesting to see how long the edit survives.

Frustratingly, MATLAB's M-script is only half a hair more predictable than PHP. That ones(1); ans(1) returns one but ones(1)(1) is a syntax error boggles my mind.

21 August 2008

Patent number 7,406,606

12 August 2008

Forbes: Austin ranks #1 hardest drinking city in America

"Austin, Texas, is famous for its parties. People flock from around the world to attend events like the annual South by Southwest film and music festival. And when they get there, chances are they make like the locals and throw back a few cold ones--because Austin may be the hardest-drinking city in America."

America's Hard-Drinking Cities - Forbes.com

09 August 2008

Stenchikovs's talk

This Thursday past I listened to a talk by Professor Georgiy Stenchikov. Stenchikov works with the Intergovernmental Panel on Climate Change (IPCC) crew that won the Nobel recently. On Thursday he spoke of the effects that aerosols (fine particles) have in the upper atmosphere. Apparently higher concentrations of aerosols in the stratosphere reflect incoming solar radiation and reduce global temperature. Their effect can be observed when a massive volcanic eruption drops global temperature by a small amount. Stenchikov and his collaborators have created global climate models capable of reproducing this volcanic effect.

Stenchikov's talk focused on artificially increasing the aerosol content of the upper atmosphere to combat CO2-related global warming trends. Apparently it's an idea from the late 70's. Stenchikov quite literally ran 40 year simulations where humans sprayed megatons of aerosols into the stratosphere to see if we could reduce the temperature. The verdict? It works, but if we ever stop the process, global warming comes back with a vengeance.

That's some scary shit. By "that" I mean nearly every implication of living in a day when such a plan is a genuine topic of interest.

31 July 2008

Summer Vacation '09

Next year's vacation should be one interesting trip-- two weeks in Russia, floating from Moscow to Saint Petersburg.

26 July 2008

Impinging shock results for a 5 degree wedge at Mach 8.2

After a dead-end-full month of futzing with Gridgen, DPLR, and Tecplot 360, today I finally got a result worth showing:

This is a simulation of a hypersonic experiment performed by Kussoy and Horstman in 1991. A flat plate and an angled wedge are placed in a Mach 8.2 flowfield. Starting from the upstream tip of the flat plate (not shown), a turbulent boundary layer develops along the plate's length. An attached shock occurs at the wedge tip, and the shock interacts with the plate's turbulent boundary layer. Kussoy and Horstman looked at how surface pressure and heat flux at the plate varied with the wedge angle. Here I'm comparing their surface pressure data with my simulated numbers for the 5 degree wedge case. Agreement isn't that bad (eyeball norm), especially given the paper's experimental error bounds and how new I am to this whole process.

I was surprised to see the simulated pressure gradient is sharper than the experimentally obtained gradient. I suspect that

  • I goofed when specifying the turbulence transition point along the flat plate, or
  • perfect air assumptions weren't appropriate, or
  • Baldwin-Lomax wasn't the right turbulence model to use, or
  • I've not done any averaging and the flowfield has turbulence, or
  • any one of a number of other things.
I'm elated to be in the why-isn't-this-what-I-expect stage instead of playing the why-is-the-solver-blowing-up game.

22 July 2008

Using GNU screen with gnome-terminal's custom shell command

GNU screen is a nice tool. It becomes more valuable when it's omnipresent, but until today I've been too lazy to get configured the way I want it:

  1. I want screen started within every new gnome-terminal.
  2. When a new terminal starts, I want a fresh screen window with a fresh shell.
  3. When I close a terminal window, my screen session should persist.

The first ups screen's usefulness since its capabilities are now always a keystroke away. The second mimics my new-terminal-window-is-a-new-task mentality. The third keeps me from accidentally losing work when I close a terminal window.

First, I needed to add several options to my ~/.screenrc:

# Useful settings (among many others)
autodetach on
multiuser on
startup_message off
# Startup commands for a new session
screen -t local
select local

Next, because gnome-terminal's custom command facility doesn't allow anything too fancy (e.g. multiple commands, variable expansion), I had to create a small bash script called gnome-terminal-command.sh:

#!/bin/bash -i
# First, construct a new window identifier
WIN_ID=`date +%R:%S`
# Second, start a new window in the screen session using that identifier
screen -xRR -X screen -t "${WIN_ID}"
# Third, prevent existing terminals from switching to the new session
# Thanks to nassrat for this tip
screen -xRR -X other
# Now, use screen to connect to the new window within this process
exec screen -xRR -p "${WIN_ID}"

Lastly, I told gnome-terminal to use gnome-terminal-command.sh under Edit -> Current Profile -> Title and Command . Check "Run a custom command instead of my shell" and give gnome-terminal-command.sh in the Custom command input box. Older versions of gnome-terminal (e.g. version 2.18.1) allow the script to be somewhere in your path. Newer versions (e.g. 2.22.1) seem to require a full path to the script. This is puzzling.

Testing it out...

  1. Start gnome-terminal and you get a screen session with one window called 'local'.
  2. Open a second gnome-terminal and you get a new screen window whose title is the current time.
  3. Close the second window and you see two screen windows persisting in the first gnome-terminal.
  4. Open a third gnome-terminal and you get yet another new screen window.
  5. Hit Control-D three times in the third window to end each of the screen windows. All of your gnome-terminals will simultaneously close.

During testing, it'll help if you have an informative screen status line. Should you run into serious troubles, you can undo the changes by using gconf-editor to tweak use_custom_command and custom_command under apps/gnome-terminal/profiles/Default.

16 July 2008

I've been here for too long

I walked in this morning after a small breakfast, still hungry. While putting my lunch away, I noticed a large container of dill pickle spears. The type provided in bulk by BBQ joints when they cater. Exactly the type of food that lingers in the fridge near the grad student cubicles.

Ignoring the complete grossness of consuming pickles alongside cheap instant coffee, I immediately wondered how long they'd been there and if they'd be safe to eat. I snapped to the conclusion that, well, they are pickles and are therefore pickled after all.

I caught myself just as my hand lifted towards the container, shivered, collected my instant coffee, and moved on.

20 June 2008

One of these things is not like the others

Fidelity periodically pushes a particular mutual fund. Recently it's their Fidelity Trend Fund. They usually put up a growth since inception chart:

I'm scratching my head over the Apple iPod appearing here. I mean they're nice and all. I have one. But alongside the lunar landing and the fall of the wall?

16 June 2008

Brown Applied Mathematics Report Released

Just recently released through SIAM, the Brown Report discusses how the U.S. Department of Energy wants applied mathematics to evolve to fit the its needs. One of the panel members, J. Tinsley Oden, is the director of my applied mathematics program at U.T. The timing of the report is interesting — this past Friday we had several folks from Sandia on campus for a meeting as part of the PECOS center. The odds are pretty good that I'll spend next summer at Sandia.

08 June 2008

Video Compression and Turbulence Don't Mix

At least not well. While trying to re-learn basic fluid mechanics I ran across some mid-60's instructional films made by the National Committee for Fluid Mechanics Films. The excellent material presentation and quality of the experimental setups has helped me regain some intuition. The retro-educational aspects are outstanding: black and white video, coke bottle glasses, professors in full suits, gesturing at concepts with a pipe, etc.

Sadly though, the films have been stored in the usual compressed way. For laminar flow visualization, this works fine. Unfortunately, the film on turbulence suffers from nasty compression artifacts that obscure the time-dependent, chaotic structure this video was designed to illustrate. It'd be interesting to know if there are domain-specific codecs that would adequately capture chaotic motion here, or if all compression approaches would suffer a similar fate. In theory, you probably could capture the isotropic small scale structure and then overlay that atop a normal video codec to get acceptable results.

07 June 2008

Passed my Quals

Possibly the sweetest words I've read in a long time:

Congratulations! You have passed all three CAM Preliminary Examinations....

We saw Eddie Izzard last night at the Paramount Theatre. Damned good stuff. I'm very much looking forward to a DVD release of a specials.

02 June 2008

Fortran Compiler Output

Intel 10 Fortran Compiler
Oh swell, thanks. Err, I mean "remark: THANK YOU".

31 May 2008

Qualifying Exams Over

Tuesday, Wednesday, and Friday morning I had qualifying exams for my graduate program. I was happy with Wednesday's exam. I wish I'd nailed one more question on each of the other two exams. I'll receive a pass/fail verdict in about three weeks. Regardless of the outcome, I'm happy to be moving on to other stuff.

28 May 2008

First Grant!

I've got many in process, but to my knowledge this is the first one that's gone all the way through. Thankfully the claims pack more punch than the abstract. In theory this one covers the charging infrastructure for plugging my electric car into your power outlet and routing the billing back to my electricity bill.

United States Patent 7,376,631
King, et al. May 20, 2008
Method, apparatus and computer program product for reporting energy consumption


Energy consumption meters are associated with owners who hold accounts with a power supplier. The meters are assigned meter identifiers and identifiers for their respective owners. Such a meter may be a parent meter having associated submeters. In response to being plugged into a power source from the power supplier, such a meter reports its owner identifier and meter identifier to the supplier. Also, in response to being plugged into a power source supplied by one of the parent meters, a meter communicates with the parent meter. This establishes that the parent meter is associated with the submeter. The submeter measures energy delivered reports this to the power supplier. Also, the indicated association of the submeter to the parent meter is reported to the power supplier. The receipt of this information enables the power supplier to debit and credit owner accounts in a manner permitting temporary associations of meters.

Inventors: King; Jennifer E. (Boulder, CO), Peterson; Robert R. (Rockledge, FL), Richter; Jon F. (Austin, TX), Spivey; Ian P. (Cambridge, MA), Stading; Tyron Jerrod (Austin, TX), Ulerich; Rhys (Austin, TX)
Assignee: International Business Machines Corporation (Armonk, NY)

Also mine and publicly in process are

App Number Title
20070106795 Automatic orchestration of dynamic multiple party, multiple media communications
20070061326 Receiving display station on a communication network for accessing and displaying network documents associated with a television program display in which the text stream of the TV program on the display station provides user selectable links to predetermined network source sites
20070008892 Method and system for testing branch execution and state transition logic in session initiation protocol application modular components
20060268858 Communication system supporting two-way on-hold functionality
20060187902 Method and apparatus for session initiation protocol application design, development, execution and integration
with the television program display one being the best of the bunch. There's a complete technology startup complete with exit strategy rolled into it if you read between the lines.

09 May 2008

TACC Scientific Software Day next week

I am very much looking forward to TACC's scientific software program next Thursday and Friday. Especially the talks on visualization, dynamic clusters, parallel IO, and the second day tutorial on SciPy from the guys at Enthought. Registration is still open (and still free) for anyone interested.

18 April 2008

Automagically showing printer friendly article versions

Most articles are surrounded by advertisements, navigational links, and other kruft (Example ). Most magazines are smart enough to have a "printer friendly" link somewhere. Usually these versions are much more online friendly too (Example).

Anyone want to write a Greasemonkey script that'll automagically follow the first "print me" link found on a page and then cancel any potential printer dialog that appears? Also, it'd be nice to have it append a small floating <div> on the print version page with a back link to the bypassed regular article view.


Shuffle puts Toots and the Maytals Alidina into my head about once every two months. It always sticks there for at least a week. No one can sing the eternal lyric "yeah" like Toots:

Alidina, go out and do the work
alright alright

Alidina, lazy lazy
Alidina, crazy crazy
Alidina, go on and do the work

Just the week before last week I saw you
standing out at the mother's corner looking inside
and you alidina, want to do the work
alright alright

Just the day before yesterday I saw you
walking on the long train line, doing nothing
and you, Alidina, want to do the work
alright alright
Of course I can't find an online source for the song besides Amazon's preview at Last.fm. No "yeah" lyrics in that though. Figures.

Also recently stuck for more than several days were Punk Rock Girl by The Dead Milkmen and, for the sheer purpose of embarrassing me when I forgot myself and hummed it, the Muppet version of the Fraggle Rock theme song.

13 April 2008

Somebody's gotta say it before it can ever be fixed

Being from a post-steel western Pennsylvania city, I'd say Obama nailed it. It's not the most savory of portrayals, but that doesn't make it inaccurate.

Mr. Obama made the remarks at a closed-door fund-raiser in San Francisco last Sunday — before a very different crowd from those he has been courting in Pennsylvania and Indiana — after he was asked why he was not doing better in Pennsylvania. Polls there show him narrowing the gap with Mrs. Clinton but still lagging behind.

“You go into these small towns in Pennsylvania and, like a lot of small towns in the Midwest, the jobs have been gone now for 25 years and nothing’s replaced them,” Mr. Obama responded, according to a transcript of the fund-raiser published on Friday on The Huffington Post Web site.

“And they fell through the Clinton administration, and the Bush administration, and each successive administration has said that somehow these communities are gonna regenerate and they have not,” Mr. Obama went on. “And it’s not surprising then they get bitter, they cling to guns or religion or antipathy to people who aren’t like them or anti-immigrant sentiment or antitrade sentiment as a way to explain their frustrations.”

By Saturday morning, Mr. Obama was trying to contain the political damage after a series of late-night and early-morning strategy calls in which advisers decided he had to acknowledge that he made a mistake.

from On the Defensive, Obama Calls His Words Ill-Chosen

The fun part is now that the pretense of protection for the old industry and old economic models have gone away, those areas are reinventing themselves in the service economy. They're doing a great job, and many businesses which could go to the east coast megalopolis are moving to western Pennsylvania specifically because the operating costs are low while the quality of the labor pool is very good.

10 April 2008

Qualifying exam concepts index

Some concepts appearing in Areas A, B, and C qualifying exam packet, poorly categorized and in no particular order. May will be a fun month.

Area A: Applicable Mathematics

  1. Arbitrary coordinate transforms computed via Jacobian ratios
  2. Banach contractive map theorem
  3. Canonical isomorphisms
  4. Cauchy Integral Theorem for complex integrals
  5. Change of variables in an ODE
  6. Chebyshev spaces
  7. Computing Laplace transforms using the Residue Theorem
  8. Computing flux through the surface of a volume
  9. Computing mass moments of inertia
  10. Computing the eigenvalues and eigenvectors of an operator, matrix or otherwise
  11. Concept of norm-equivalence and equivalence of resulting topologies
  12. Conformal mapping and solution of Laplace/Poisson equations
  13. Construction of weak variational form given strong form, plus equivalence proof
  14. Continuity, uniform continuity, Lipschitz continuity
  15. Contraction mapping theorem used for existence/uniqueness of an IVP
  16. Convergence, uniform convergence, and weak convergence
  17. Conversion of Del & Laplacian to cylindrical and spherical coordinates
  18. Conversion of integral limits and differentials to alternative coordinates
  19. Definition of metrics, norms, and inner products
  20. Determining a radius of convergence for a power series solution
  21. Determining if an operator is self-adjoint
  22. Direct sum of two vector spaces
  23. Eigenfrequencies and mode shapes for the wave equation
  24. Equivalence of topology given difference metrics
  25. Equivalence of ways to define a topology, including stronger/weaker comparison
  26. Euler-Bernoulli equation
  27. Euler-Lagrange equation in a Variation setting, especially the derivation
  28. Exact sequence definitions and implications
  29. Fixed point problem concepts, especially for integral equations
  30. Fourier transform and inverse transform
  31. Fredholm Integral Equations
  32. Gateaux differentials
  33. Gauss' Divergence Theorem
  34. Green's Theorem
  35. Hamel basis, and basis in infinite dimensional vector spaces
  36. Identify complex poles and classify their order
  37. Inductive use of Holder and Minkowski inequalities
  38. Inner product space definition
  39. Integral of a nonnegative function over a measurable set is zero iff f = 0 a.e.
  40. Irrotational fields and corresponding scalar potentials
  41. L^2 and \ell^2
  42. L^2 definition and how it relates to quotient spaces
  43. Lagrange multiplier methods for constrained minimization
  44. Laplace transform and inverse Laplace transform
  45. Laplace transform of the delta distribution
  46. Lebesgue Dominated Convergence Theorem
  47. Line integral calculation of the first and second kind
  48. Linear subspace definition
  49. Method of images?
  50. Minimization problem settings
  51. Notions of being "well-defined"
  52. Perturbation approaches
  53. Picard method
  54. Proof of Cauchy-Schwarz
  55. Proof of Holder and Minkowski Inequalities, applications to L^p spaces
  56. Proof that interior of A is the complement-closure-complement
  57. Properties that hold almost everywhere
  58. Quotient spaces
  59. Real eigenvalues and orthogonal eigenvectors for self-adjoint operators
  60. Separation of variables and use of Sturm-Liouville Theory
  61. Series convergence for matrices T like x{i+1} = T xi + b, spectral radius
  62. Show that the distance function is always continuous
  63. Showing that a vector field is divergence free
  64. Solenoidal fields
  65. Stokes' Theorem on a particular domain, including verifying its correctness
  66. Surface integral calculation
  67. Telegrapher's equation
  68. Topology on a set, including interior and closure definitions and properties
  69. Topology on discrete sets, e.g. neighborhoods, closed sets, separability
  70. Use of Fourier Transform in boundary value problems
  71. Use of Holder and Minkowski to demonstrate elements in L^p
  72. Vector space definition
  73. Weierstrass Theorem

Area B: Numerical Analysis and Scientific Computation

  1. Adaptive integration
  2. Best approximation results for projections
  3. Cholesky factorization
  4. Construct matrix condition numbers based on perturbed matrices and vectors
  5. Cost analysis of common matrix operations
  6. Definition of a norm and norm equivalence
  7. Demonstrating that eigenvalue computation has no closed form solution
  8. Determining an orthonormal basis, the LQ decomposition
  9. Determining equispaced interpolating subdomains with some error bound
  10. Determining the rank of a matrix in finite precision arithmetic
  11. Effect of matrix rank on Gram-Schmidt
  12. Eigenvalues and eigenvectors
  13. Estimation of an interval given information at a finite number of points
  14. Existence and uniqueness of an interpolating form given particular information
  15. Finite difference construction based on Taylor truncation, including stability
  16. For Galerkin-like minimization methods, show that error is "orthogonal"
  17. Forward and backward error analysis
  18. Gaussian elimination error propagation when used without pivoting
  19. Gaussian quadrature and the use of orthogonal polynomials
  20. Gershgorin Circle Theorem
  21. Gram-Schmidt, including how floating error arises
  22. Hermite matrices and their properties
  23. Householder transforms/rotators
  24. LU Decomposition
  25. Lagrangian interpolating polynomials
  26. Linear independence, linear combinations
  27. Linear least squares, properties, the normal equations, including computing
  28. Modified Gram-Schmidt
  29. Operational identities in finite precision arithmetic
  30. Partitioning of symmetric positive definite matrices
  31. Positive and negative definiteness, and relation to eigen- and singular values
  32. Proof of Taylor-like error estimate for an interpolating polynomial error bound
  33. Proof that Gaussian n-point quadrature is exact for polynomials of order 2n-1
  34. Proofs Cline made a fuss about :)
  35. Properties of a matrix norm, including the sub-multiplicative one
  36. Properties of an induces matrix norm
  37. QR Factorization
  38. Rank and Nullity Theorem
  39. Residual matrices
  40. Richardson extrapolation, acceleration rates, and required regularity
  41. Runge-Kutta methods for solving initial value problems
  42. Separation of a 2-tensor into a symmetric and antisymmetric part
  43. Shifting of Gaussian quadrature rules through affine transformations
  44. Similarity and congruence transformations
  45. Simpson's rule
  46. Singular value decomposition and how it relates to rank, nullspace, and range
  47. Singularity to working precision, and the distance to nonsingular matrices
  48. Special matrix structures, e.g. symmetric, banded, diagonal, skewsymmetric
  49. Spline construction, including cubic Hermite splines
  50. Trapezoidal rule and relationship to Lagrange polynomials
  51. Two definitions of matrix norms and how they relate to minmag and maxmag
  52. Use of QR factorization in the least squares problem
  53. Ways to test if a matrix is positive definite, and correctness guarantees
  54. Why/when is QR preferred over Gram-Schmidt

Area C: Mathematical Modeling and Applications

  1. Balance laws
  2. Boltzmann Transport Equation
  3. Calculus of variations applied to simple problems
  4. Cauchy's principal and the Cauchy stress tensor
  5. Cauchy-Green deformation tensors
  6. Computing deformation gradient, tensors, and principal deformation directions
  7. Conservation laws and their derivations
  8. Darcy's law and its derivation
  9. Definitions of basic continuum mechanics concepts
  10. Derivation of Navier-Stokes equations, including term-by-term interpretation
  11. Determine lattice specific energy
  12. Developing model of water through a rigid trough
  13. Energy density calculation given a potential
  14. Energy per particle
  15. Formal homogenization assuming periodic small scales, including anisotropics
  16. Green strain
  17. Lattice energy calculation
  18. Main sources of non-numerical error in simulations
  19. Main steps in constructing a mathematical model
  20. Mathematical formulation of Schrödinger's equation, constraints, and solutions
  21. Multiscale/matched asymptotic approaches
  22. Nondimensionalization of the transport equation
  23. Optimization and the adjoint problem, classes of optimization/control problems
  24. PDE types (e.g. Parabolic, Hyperbolic, Elliptic) for 1st and 2nd order
  25. Permeability constants
  26. Piola transformation
  27. Stokes' equation
  28. Well-posedness of second order, linear differential equations


We kept the stray cat we found around for about five days, but it just wasn't working. Michelle and I realized the only reason we wanted a cat was because we couldn't have a dog. That fact combined with the severe lack of litter box placement options in our condo caused us to cave and take Cracky Stubbs to the local animal shelter.

08 April 2008

Finite element shape function comparison

Part of a term project for one of my classes, this Mathematica notebook shows some of the nice functional aspects of Mathematica. It also shows how far I'll go to avoid manually integrating even simple polynomials.

03 April 2008

When people can't accept responsibility...

...you get fun stuff like Bear May Have Survived If Fed Acted Earlier, CEO Says. Not saying the death of an investment bank isn't a complex issue exacerbated by lots and lots of unknowable details, but it'd be nice to hear a "Man, did I screw up" from the CEO whose entire company went kaput in record time.

Money quote:

"Schwartz said the Fed's rescue effort on March 14 didn't help, partly because it singled out the firm in trouble, which exacerbated the panic about Bear Stearns."
"We were obviously holding our own until the Fed spilled the blood that drew the sharks."

29 March 2008

Stupid Google caught me with the bike uncovered...

Found out through Austin Metblogs that Google just added Austin, Texas Street View coverage. The data is recent. Eerily, they caught me with the cover off the bike.


A cat showed up on our doorstep today, and the neighbors know nothing other than that this one's been around a day or two and is seemingly sweet. We've been talking about a cat or dog for months and months. The critter's timing couldn't be better (for it anyway). Still, we're attempting to do the right thing and make sure if there's a willing owner, he/she can get the cat back.

P.S. "Cracky Stubbs" if we end up keeping him.

P.P.S. Only (no?) good came come of this.

18 March 2008

Notes on "Review and assessment of turbulence models for hypersonic flows"

On the heels of the recent PECOS center announcement and my recent advisor choice, I'm taking some baby steps to prepare for my first summer of graduate research. On a recommendation from Prof Moser, I'm reading through a 2006 survey of hypersonic turbulence models by Roy and Blottner and cooking up naive questions/notes:

  1. What are the effects of "hypersonic mixing layers"?
  2. For a hypersonic flow result that uses ideal gas relations, what are the general effects of introducing non-ideal constitutive laws for gas behavior?
  3. What are the additional challenges behind predicting the natural transition to turbulence in hypersonic versus other flows?
  4. DNS is computationally expensive, and RANS/LES are comparatively cheap. How much cheaper are they for the same flow parameters and grid?
  5. The article sounds like many people cook incompressible turbulence models and then expand them with compressible terms. Does anyone work in reverse and treat the incompressible as a special case of a compressible model?
  6. What are the differences between the full Navier-Stokes, thin layer Navier Stokes, parabolized Navier-Stokes, viscous shock layer, and boundary layer equation formulations? When are each of them preferred? What are their effects on uncertainty in the simulation results?
  7. What is the reason for artificially limiting the production-to-dissipation ratio of turbulent kinetic energy? How could any model requiring this kneecapping give reasonable results?
  8. What's the background behind "... for computational fluid dynamics simulations, the residual reduction levels correlate quite well with the actual iterative error in the flow properties" ?
  9. Is there an open database of turbulence results in the way that the bioinformatics community makes its raw data available for consumptions? E.g. ERCOFTAC
  10. Which of the cases listed on pages 477-8 and in ERCOFTAC are of most interest to us in PECOS? Expect Holden reference 43 to be of interest.
  11. What are the particulars between Van Driest II theory? What causes Roy and Blottner to up the bound to 5% from 3%? See references 133 and 134.
  12. What is wall skin friction?
  13. What approaches are used to transform flat plate turbulence results to other geometries? E.g. sharp cone as mentioned on page 479.
  14. What are the differences between the "perfect gas model" and ideal gas model?
  15. Almost all of the experimental results discussed are under Mach 12. Will we run into problems with validating against lower Mach results and then simulating higher Mach numbers?
  16. Details surrounding "the elliptic mathematical character of the separated flow region, these pitot surveys should be used with caution".
  17. What is a turbulent Prandtl number?
  18. What are incompressible coordinates?
  19. I need to review concepts of fully developed boundary layers. And other concepts. Badly.
  20. What exists besides RANS/LES approaches to model turbulence effects? Are there other schools of thought around dealing with the computational complexity of the Navier-Stokes equations?
  21. Which of the models listed in Table 4 are relevant to the current PECOS efforts? Did any of the models/areas survive/persevere in the funding dry spell over the last decade?
  22. Is the distinction between one and two equation models primarily done for computational cost reasons?
  23. Any good background on general theory of turbulence from a lay perspective? Any historical reading on the evolution of turbulence research from both a mathematical and engineering point of view?
  24. Roy and Blottner require integration to the wall in all reviewed models and don't examine "wall functions"? Why?
  25. Lots of the two equation models are based on a k-epsilon or k-omega foundation. Are these classifications or common ancestors which then tend to be further specialized/improved? See reference 152 and the revised model in 153. See reference 159 and 6.
  26. There is lots of mention of "adverse pressure gradients" when talking about the advantages of k-omega over k-epsilon models. What qualifies as an adverse pressure gradient?
  27. In modeling turbulence, is the general goal to have the minimal error with respect to quantities of interest? Or is it to be bounding/conservative so that model results can be "safely" applied to engineering problems? Generally, do people take an engineering or a science mindset when constructing and using turbulence models?
  28. Can models be designed to emphasize accuracy of some quantities of interest? Or are they more of a try-it-out-and-see-what's-good approach?
  29. Why is grid refinement recommended as the next checkmark to add to model validation studies? What causes researchers to generally either not do it or to not report detailed results when they do?
  30. See reference 156 for Rodi's k-epsilon model, which seems to have good results according to the conclusions in section 4.6. What causes it to work well? What causes its weaknesses upstream of the interaction region?
  31. What is shock unsteadiness?
  32. What are the reasons for model sensitivity to y^{+} spacing?

07 February 2008

Rare Magazine Perspective

Rare Magazine publishes from Austin, Texas. It covers the local scene, shops, and events. For February the published a set of short pieces on area couples. Rare wanted to include a Ballet Austin company dancer, and Michelle was picked. By association, I got picked too.

The full February 2008 issue is available online. I cherry picked the pages containing our piece, which you can read better if you click on the pages to zoom in (done using Issuu). Enjoy.

01 February 2008

Data is the New Long Distance Redux

From a Newsweek article by Steven Levy called "The Net Meter Is Running", the cable companies are investigating imposing different costs for different total monthly bandwidth usage. Not surprisingly, they're following the wireless footprint for how to milk money from consumers:

Currently, [Time Warner Cable] envisions offering plans capped at 5, 10, 20 and 40 gigabytes. Five gigs gets you barely two movies and a couple of TV shows, not counting the normal Web surfing, music streaming and e-mail. . . . Bell Canada, which meters service in some plans, charges customers who go over the limit $7.50 per each additional gigabyte. . . . A high-def movie (typically four gigs) could cost you $30 more. (Bell Canada offers an Unlimited Usage Insurance Plan for $25 a month.)

Levy puts forward how plans like this could benefit company bottom lines by effectively reducing consumer choice:

... [Time Warner Cable's] main interest is cable television. An increasingly important component of that business is distributing video on demand. TW's competitors in that arena are Internet companies that intend to do the same thing. The Time Warner plan tilts the field in its own favor. Let's say I want to watch the indie film "Waitress." I may have the choice to order it on my cable box or rent it from iTunes. Each might cost me $3. But if I'm metered, renting it from iTunes might mean that I exceed my monthly limit, perhaps incurring a penalty that's more than renting the movie.
Capped monthly broadband plans are as awful as wireless data plans. Adding bandwidth usage costs is like turning the internet into one large 1-900 service.

In Austin, Time Warner affiliate and its competitor Grande both offer tiered upstream and downstream bandwidth. I'm fine with that pricing plan because it doesn't increase my cost for the other services I use on the internet (though Time Warner suspiciously offers nothing between reasonable-cost/way-too-little-speed with high-cost/way-too-much-speed). Over the last ten years, the cable operators have deliberately avoided commoditization of their services— the broadband "Model T" hasn't gotten any cheaper despite an overwhelming increase in the number of people who have one. Holding broadband costs constant despite improved economies of scale via an expanding customer base is questionable. Actively investigating how to make more money from providing less service through monthly bandwidth caps is reprehensible.

22 January 2008

Data is the New Long Distance

I just finished a two year Verizon Wireless contract. They frantically called me, informed me my contract was up, and walked me through a month-to-month agreement. The only change was that their "Mobile Web" feature went from $5/monthly to free. Free! Sweet! Then I listened to the big long details where the customer service rep informed me they didn't debit my airtime minutes for the usage. Charges now run $1.99/megabyte for Mobile Web usage unless you spend $15+ monthly on an all-you-can-eat option.

That straw, the allure of SIM cards, and the fact that Verizon has the lousiest, P.O.S. software on their phones (contact me if you're interested in a rant) made me switch to at&t yesterday. I paid attention to at&t's data charges— either $15+ monthly for a smörgåsbord or $0.01/kilobyte. Similarly crazy in price.

An example of the sheer monstrosity of it all:

  • Assume you didn't pay the $180+ annually these companies want for unlimited data plans
  • Assume you bought a 2 gigabyte microSD card for your phone.
  • Assume you filled up your microSD card
All of these seem reasonable. After all, you're already paying hundred of dollars annually to be able to use the phone you've purchased. For 2 gigabytes/2,048 megabytes/2,097,152 kilobytes of a la carte data:
  • Verizon would charge you $4,075.52 to fill a 2 gigabyte microSD card at $1.99/megabyte.
  • at&t would charge you $20,971.52 to fill a 2 gigabyte microSD card at $0.01/kilobyte.

The wireless carriers may rationalize this ridiculousness by saying that they can better forecast data network needs when customers buy unlimited plans. But then again, how much forecasting information do you get on "unlimited" plans?

Monthly a la carte data plan pricing should cap out at the monthly unlimited plan rate. After using $15 bucks of a la carte data in one month, just bump me to unlimited already. Say that up front. Don't be shady. Sheesh.

20 January 2008

Manipulating amarok remotely using dcop and ssh

Following my friend Ian's recommendation, I moved all of my music onto an amarok installation a couple of years back. Great program, great features, simple to use, nicer for multi-user installations since the database can be shared, able to have automagic playlists like what-haven't-I-listened-to-in-awhile, etc. I can't recommend it highly enough.

Often, I play music from our desktop but work on my laptop. With purely random playlists, two problems arise when listening remotely:

  1. Ack! That's horrible. Next song, please.
  2. What song is this exactly?

Amarok provides an dcop interface that allows CLI access to lots of information. If your remote SSH shell isn't part of the same dcop session (not likely), you need an extra bit of magic to use it.

In my setup, I can answer those two problems with these commands:

  1. dcop --user `whoami` --all-sessions amarok player next
  2. dcop --user `whoami` --all-sessions amarok player nowPlaying
and can setup a remote 'tail' with a fancy one-liner like: while echo -n; do for info in path year artist album track title rating sampleRate score labels trackPlayCounter; do echo -en "${info}:\t"; dcop --user `whoami` --all-sessions amarok player ${info}; done; sleep 10; clear; done where the --all-sessions option solves the different-dcop-session problem and --user `whoami` is required alongside it.

07 January 2008

Vacation Shorts

A small collection of short videos taken while on vacation with Michelle. When happy or hyperactive, she can be hilarious to watch.

Give Me Spinning

Taken shortly after New Year's while visiting a friend in Santa Cruz, we stopped at a park. It was raining, windy, and getting nastier. Straight from the car, Michelle took off frolicking:

Eating Donuts in College Station

Taken while on a Nutcracker Bon-Bon audition trip to College Station, TX, we stopped at a donut shop one morning. Notice the 2 and a 1/2 step donut eating maneuver, and the huge grin she gets once the bite is safely performed:

Poo on Your Jeans

Taken outside some of the bigger museums in Amsterdam, Michelle calmly notices that I've got dog crap all over my left pant leg:

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