Error originates: RdWrOT: IFlag = 2 Data mismatch
Search? I only get here. And the results aren’t exactly useful …

你给出的信息太少了,能不能多贴一点出来?

Anyway this almost always seems to be a problem with the collision of the previous and current route. Often I have to increase the number of optimization or SCF cycles because my systems are large and I do optimizations with diffuse functions, which tend to be pretty ill-behaved. Here’s the total head of the log:

******************************************
Gaussian 03: AM64L-G03RevE.01 11-Sep-2007
29-Mar-2009
******************************************
%chk=freq_min60.chk
%nprocshared=8
Will use up to 8 processors via shared memory.
%nproclinda=16
Will use up to 16 processors via Linda.
%mem=100MW
Default route: MaxDisk=200GB
----------------------------------------------------------------------
# freq=restart b3lyp/6-31+g(d) geom=allcheckpoint guess=read int=fmmna
toms=300 scf=tight
----------------------------------------------------------------------
1/10=4,30=1,35=1/3;
99//99;

GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Berny optimization.
Restoring state from the checkpoint file "freq_min60.chk".
Title: min60
Route: # opt b3lyp/6-31+g(d) geom=allcheckpoint guess=read int=fmmnat
oms=300 optcyc=1000 scfcyc=1000
RdWrOT: IFlag = 2 Data mismatch
MaxStp (old) = 504 MaxStp (new) = 2
MaxJob (old) = 1 MaxJob (new) = 1
RdWrOT: Data mismatch on MaxStp/MaxJob
Error termination via Lnk1e in /apps/steele/g03-E.01/l103.exe at Sun Mar 29 01:19:04 2009.
Job cpu time: 0 days 0 hours 0 minutes 13.6 seconds.
File lengths (MBytes): RWF= 49 Int= 0 D2E= 0 Chk= 56 Scr= 1
Command exited with non-zero status 1


I’m posting this more so this error comes up in Google to Vdov so maybe, maybe someone can tell me about it (no one, including people who really know the software well, has been able to provide an acceptable explanation thus far). If the two routes are both optimizations, for instance, you can usually get around this error by eliminating the opt cycle specification in the new restarted route. But if you’re moving the guess and geometry to some new calculation, it’s nearly impossible to get around this. The solution is almost always to create a formatted checkpoint file (formchk) and convert back (unfchk), so the route disappears. You could also obviously do this by specifying the new geometry as a Z-matrix in the initial calculation, but I much prefer to read my initial guess from the checkpoint, so this is not a good option in many cases. Starting the calculation and then restarting from the new binary checkpoint file usually does the trick, as there are appear to be no collisions in the route cycles.

Anyway, cheers. Hopefully someone who knows something about this will let me know.

Let’s say you have a system composed of N different species and you’ve got your xtc trajectory file from the run. Then let’s say you want to know about average cluster sizes of one of the species in the simulation. For some programs in gromacs (not g_clustsize, the one in question here) this is fairly easy because the software lets you specify, either through the program options itself or through an index file, what you’d like to consider. With others though, especially those with options for dealing with molecule statistics explicitly, that don’t allow you to do this for whatever reason. So, a workaround is necessary.

First, edit your input mdp file and topology with extreme prejudice, eliminating or commenting out references to anything you’re not interested in. For instance, in my files, I need to remove all water and ions. I call all these new files “fake” versions of the real files.

$ diff fake_fullmd.mdp fullmd.mdp
15,16c15,16
< xtc_grps = protein ; sol na+ cl-
< energygrps = protein ; sol na+ cl-
---
> xtc_grps = protein sol na+ cl-
> energygrps = protein sol na+ cl-


$ diff fake_topol.top topol.top
163a164,166
> SOL 9529
> NA+ 10
> CL- 10


Make sure you have an index file if you don’t already:

$ make_ndx -f conf.gro


Then dump the first frame of the real simulation. The program (trjconv) will ask you which parts of the frame you’d like to dump.

$ trjconv -f traj.xtc -o fake_protein.gro -s b4md.tpr -n index.ndx -dump 0
...
Select group for output
Group 0 ( System) has 37968 elements
Group 1 ( Protein) has 1568 elements
Group 2 ( Protein-H) has 784 elements
...
Select a group:


Now generate the new input binary for your “fake” system.

$ grompp -f fake_fullmd.mdp -c fake_protein.gro -p fake_topol.top -o fake_b4md.tpr


Convert your trajectory, again selecting whichever part of the trajectory you’re interested in.

$ trjconv -f traj.xtc -o fake_protein.xtc -s b4md.tpr -n index.ndx
...
Select group for output
Group 0 ( System) has 37968 elements
Group 1 ( Protein) has 1568 elements
Group 2 ( Protein-H) has 784 elements
...
Select a group:


Now you’re ready to run your analysis! It won’t actually use the index file you specify here (since you’re only looking at molecules with the -mol option), though it requires it for some reason that eludes me.

$ g_clustsize -f fake_protein.xtc -s fake_b4md.tpr -mol -n index.ndx


And there you have it. Cluster statistics for an arbitrary subset of your system. Cheers.

NOTE: There actually are slightly more elegant ways of doing this, but this is perfectly sufficient for simple situations, like clustering of some molecule in some other explicit medium.

So, of course, people need to know how to do parallel simulations with this code. In all major package managers 4.0.2 hasn’t made it through any appropriate channels, so people have to build it themselves. Unlike most major scientific packages, building Gromacs is absurdly simple. Things are quite beautiful actually.

Anyway, my point isn’t to extol the virtues of Gromacs but rather to suggest that if something doesn’t work, do the initial work to figure out the problem and exhaust at least the most obvious problems with the software before throwing your hands up in the air. Problem with MPI? Test it first! Anyone working with MPI should at the very least be able to look up how to write a basic MPI application.

An example:

#include "stdio.h"
#include "mpi.h"

int
main(argc, argv)
int   argc;
char  *argv[];
{
  int  rank, size, length;

  char name[MPI_MAX_PROCESSOR_NAME];

  MPI_Init(&argc, &argv);
  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
  MPI_Comm_size(MPI_COMM_WORLD, &size);
  MPI_Get_processor_name(name, &length);

  printf ("process %d of %d on %s\n", rank, size, name);

  MPI_Finalize();

  return 0;
}

If you’re on a modern Debian or Ubuntu build with OpenMPI installed (pretty much the standard MPI implementation you should be using), then build.

$ mpicc.openmpi -o hello hello.c
$ mpirun.openmpi -np 4 hello
process 1 of 4 on enskog
process 2 of 4 on enskog
process 3 of 4 on enskog
process 0 of 4 on enskog

I do love my MPI. And Gromacs does dynamic load balancing now … so freaking fast.

Cheers.

Cheers.

UPDATE: Verdict: lame. See comment #1.

The article capitalizes on the tendency of popular songs to evolve from long and content-rich ballads to highly repetitive texts with little or no meaningful content.

[...]

“…our ancient ancestors invented the concept of refrain” to reduce the space complexity of songs, which becomes crucial when a large number of songs is to be committed to one’s memory.

[...]

Finally, progress during the twentieth century—stimulated by the fact that “the advent of modern drugs has led to demands for still less memory”—leads to the ultimate improvement: Arbitrarily long songs with space complexity O(1), e.g. for a song to be defined by the recurrence relation.

We’ve really taken the concept to heart in modern popular music haven’t we? See here for explanation and here for the original paper.

Cheers.

For all its size, one of the areas where I have been left completely unsatisfied is in support for threads. Yes, of course POSIX threads are there and I’ve had some success implementing them in some of my older, now completely obsolete C code which I never want to look at again. It’s baffling to me that there is nothing in the STL which develops some nice thread classes. I know there are at least 2 (if not more) very experienced C++ programmers who read vdov.net, and I’m looking for advice. Have you looked at some developed thread classes and if so what have you thought? Recommendations? I would really rather not have to write my own thread classes from scratch (especially since accessing the C pthread library would be a nightmare here), as this is both utterly useless for my research and, well, I’d probably screw it up with near-fledgling knowledge of the language.

Cheers.

A (very) Brief History of Superconductivity:

Superconductivity is mostly associated with (and named for) materials that have zero electrical resistance. If I had a superconducting power line, that would mean that I lose zero energy transmitting electricity wherever I want it to go. In case things get confusing in the technological future and the buzz words get out of control, a word of advice: never buy a superconducting heater. Superconducting materials have other interesting properties; they don’t allow magnetic field lines to pass through them (unless you’re a type II above H), and there’s a gap in the density of states. The first phenomenon allows for levitation demos, which are fun, and maglev trains—also fun. The second property is responsible for some tech gadgets like SQUIDs, which are the most accurate magnetometers possible (not just available). For a long time, superconductivity was a mystery, and still is in many ways. It was discovered in 1911 (which was right after Einstein’s famous theory of special relativity) by H. K. Onnes or a series of his fired graduate students. The story:

Heike Kamerlingh Onnes had some graduate students. He asked his students to measure the resistance of mercury down to liquid helium temperatures. Each time a graduate student came to Onnes’ office to tell him that the resistance of mercury suddenly dropped to zero at 4.2K, that student was fired. Finally, after going through a half-dozen idiotic graduate students, Onnes went down to his lab and measured the resistance of mercury himself. He found that the resistance suddenly dropped to zero at 4.2K. He won a Nobel prize for his work in 1913. (1911 paper + image ref)

No one could explain the phenomenon. More superconducting materials were found, including lead (T=7K) and niobium nitride (T=16K). Finally in 1957, Bardeen, Cooper, and Schrieffer presented a plausible theory (BCS theory) involving what are now known as Cooper pairs—two electrons that pair through the vibrations of the crystal lattice at low temperatures. (Remember electrons usually hate each other…via Coulomb forces.) For some reason BCS theory doesn’t work for the more recently discovered high-temperature superconductors (1986+); there are a lot of people working on that problem (see Woodstock of Physics). However, BCS theory works very well for many materials, and for others it forms a pretty good starting point. For our purposes here, Cooper pairs can be thought of as the “heralds” of superconductivity. As far as BCS is concerned, if they’re there, it’s superconducting, if they’re not, it’s not superconducting. As a technical note, phase coherence among the Cooper pairs is also required.

In 2007, my lab observed Cooper pairs in insulating thin films (ref). This result indicates that superconductivity can exist in insulators. In case that doesn’t strike a harsh chord, remember the etymology of the word ’superconductor’: zero electrical resistance. We seem to have found a contradiction. How is it possible that an insulator can be ’superconducting’? To convince you of our results, I’ll describe our experiments.

Thin Film Experiments on Nano-honeycomb Substrates:

Geometry
In my lab we measure the resistance of very thin films at really low (sub Kelvin) temperatures. We also make our films on substrates that have holes in them, so that the films we make look like sheets of honeycomb (see picture to the right). This geometry restricts the motion of electrons (or Cooper pairs). Imagine a bulk piece of superconducting material with Cooper pairs happily swimming around in 3-dimensions. Now slowly shave the material down to a nearly 2-dimensional sheet, then poke holes all over it. Given this scenario, you might understand how unhappy the Cooper pairs are in our films. We look at electric transport in this reduced geometry because it provides a way to test the limits of superconductivity. It is in the limit of weak superconductivity that we hope to learn in detail how the phenomenon comes about.

Superconductor-Insulator Transition: unholey vs. holey
Although I described the structure of our films by ’shaving’ away slices of a 3-dimensional block and then poking holes in it, we actually make our films in the opposite direction: by evaporating metal atoms onto the honeycomb substrates. We can make films so thin that they no longer superconduct. In these extremely thin films (~ 4 or 5 atoms thick), the resistance actually increases as the temperature is lowered, and it is presumed that the resistance is infinite at zero temperature. As more material is slowly added we watch the curve change. At a very specific thickness, the material will begin to superconduct as the temperature decreases. This process is shown in the figure to the left (Y. Liu et. al.) in a uniform bismuth film on a smooth substrate (no holes) and is known as the Superconductor-Insulator Transition (SIT).
(note: in this field, the words ‘insulator’ and ’superconductor’ always refer to the zero-temperature resistance value. While this is a useful classification, it can be confusing. For example, a true insulator has an infinite resistance–we never measure infinite resistances, but we can see that in some films the resistance tends toward infinity as the temperature goes to zero. We call this film an insulator.)

In our holey films the superconductor-insulator transition looks a little bit different, and is shown in the graph below the first. You could make the statement that the shape of our transition is different from the one on a smooth substrate in two dimensions because poking holes in two dimensions makes something of a a 1d-2d hybrid geometry. Or for those with less malleable imaginations: 2d with some additional restrictions.

At the transition’s edge
So far, we have made very weak superconductors. The films that do superconduct only just superconduct. Since we are already on the line between a superconductor and an insulator, we want to take a closer look and try to figure out why the insulator decides to become a superconductor at some thickness (or vice-versa). The answer might be found by studying the films very close to the transition thickness, and it turns out that there are many interesting things to be looked at. We will talk about one of them here: magnetoresistance oscillations.

The effect of magnetic field on holey films
Say we make a film of a certain thickness in the graph above (“a.” for example). We know that it has holes in it, so the currents that run through the film have to go around the holes. If we turn on a very small magnetic field perpendicular to the film, the magnetic field lines will penetrate the film at a right angle and also go straight through the holes. We note that the field lines bend the trajectories of the electrons. If the film is not superconducting, the field lines bend the electron trajectories uniformly throughout the film. However, in superconducting films, some of the electrons will end up circling around the holes (for reasons discussed below). I’d also like to introduce the idea of magnetic flux: each hole now contains some amount of magnetic flux, which is described by B*A when the field is perpendicular to a material’s surface; here, B is the magnetic field and A is the area of the hole. We could just as easily draw a circle somewhere in the film and calculate the amount of magnetic flux through that arbitrary circle.

If we repeat the analysis presented above with film c. instead of film a., a few things change. The obvious change is that the film in question is now a superconductor (at low temperatures). If it is also a type I superconductor (as many are), or a type II superconductor below H, the Meissner effect applies and magnetic field lines are no longer allowed to penetrate the film itself. (We will only discuss this case for our superconducting films.) In fact, the superconductor will set up currents that exactly cancel any magnetic flux that was planning on penetrating the film, and the resulting situation is that all of the magnetic field lines go through the holes in the film. Now each hole contains some magnetic flux, and if you were to arbitrarily draw a circle in the film, you would find that the magnetic flux in your circle is zero (as long as you do not encircle any holes). Now it is clear that the electrons in the film are deflected only around the holes, since this is where the field lines are sequestered. Some of them could even end up circling around the holes.

In superconductors* it turns out that magnetic flux, like charge, is quantized and only comes in packets of a certain size. (Despite statistics, no American family actually has 2.5 children.) This means that the holes in a superconducting film require certain amounts of magnetic flux. One, two, three, four… packets of flux, but not one and a half. However, we can vary the applied magnetic field continuously—meaning that I can turn on the magnetic field to a value that would provide 1.5 packets of magnetic flux per hole or whatever non-integer value I like… Something must give in order to satisfy the physical law of flux quantization. Luckily, we have neglected the electrons in this flux calculation thus far. As stated above, some of the electrons will circle around the holes; in a superconductor, this means that some electrons will circle around the holes in pairs. In other words, some Cooper pairs will circle around the holes. Electrons carry electric charge, and moving electric charge gives an electric current (by definition). Finally, electric current moving around a circle generates some magnetic flux. This is the mechanism by which the current in the film compensates for non-integer values of magnetic flux in the holes. If my magnet is trying to put a non-integer value of magnetic flux through a hole, Cooper pairs will circle around the hole in a number that exactly cancels the excess flux (or perhaps compensates for the missing flux needed to get to the next integer).

We must now ask ourselves how we expect to see the compensation process described above, and what that might tell us about the status of our films in their transition from insulators to superconductors.

Experimental aside: probing mechanisms
The problem with modern experimental physics seems to be in translation between the ‘physical’ and the ‘observable.’ It is most convenient (and some people may argue more ‘real’) to speak about physics microscopically. i.e. ‘The electrons go around the holes,’ or ‘The proton splits into 3 quarks,’ etc. However, the microscopic happenings of a material are rarely what is being observed. Rather, scientists use macroscopic probes into the microscopic world. Our probe for the thin film experiments is the macroscopic resistance of the film. As another example, the probe for detecting a muon decay is often a scintillator that emits photons when bombarded by a muon or an electron; the photons can then be amplified and detected. The trick to a good macroscopic probe is in finding one that will reveal a property that could only be caused by one particular microscopic action. Or at least, you’d like to be able to argue away all other possible microscopic scenarios that could result in your macroscopic observation.

Resistance in a changing magnetic field: a probe for Cooper pairs
Using the resistance of the film as our probe, let us try to infer what the microscopic happenings in the film do in a changing magnetic field. We’ll discuss three different stages toward the development of superconductivity (three different films): the strongly insulating (labeled a. in the figure), weakly insulating (b.), and superconducting (c.). The strongly insulating film is the thinnest, and the superconducting film the thickest.

In film a. the material is strongly insulating. We expect that when we turn on the magnetic field, the field lines will be allowed to penetrate both the holes and the film, and therefore we do not expect that flux quantization will be important here. Now, every time an electron attempts to move it just gets shoved back to its previous position because of scattering (collisions) due to the magnetic field lines. As the field is increased further, the density of field lines will increase, and the number of electron collisions/deflections will also increase. In the end, we only see the materials magnetoresistive properties, and learn nothing else by using our special geometry.

Onto the thickest film, and a more interesting case, film c. Since film c. superconducts at low temperatures, we will guess that flux quantization will butt in as we get closer to the superconducting state (at low temperatures), let’s try to figure out what the resistance might look like as the magnetic field is increased from zero.

We hold the temperature at some constant value that is close to the transition temperature (but above it). In zero field, we know that the resistance is some low value. When we turn on a small field, the ‘pro-superconducting’ part of the film starts to shove that magnetic flux into the holes by creating currents that circle around the holes. These electrons then tend to get in the way of the electrons that are just trying to get from one side of the film to the other—the resistance goes up. It reaches a maximum when the field I apply to the film is equivalent to trying to put 1/2 of a flux quantum in each hole. Then the supercurrents have to work their tails off trying to keep the flux out of the film, while they are also required to keep an integer amount of flux in each hole. The ‘traversing’ electrons have the most difficult time getting through the film in this situation (imagine this going on with people in a crowded train station. the electrons are people, some of them trying to travel and some of them working. I don’t know what would represent the magnetic flux. Maybe this analogy is better suited for the Harry Potter train station, but even there it’s a bit of a stretch…).

Contrarily, the traversing electrons have the easiest time getting through the film when the flux quantization rule for the holes is already satisfied by the amount of magnetic field applied by the user (me), i.e. I apply the equivalent of one flux quantum per hole. In this situation, the electrons working to make the supercurrents have much less to do and the traversing electrons have much less to run into. Graphically, this process results in magnetoresistance oscillations, shown in the graph below (the x-axis represents the applied magnetic field, and the y-axis represents the resistance of the film).

But I’ve pulled a fast one on you. The data shown above, which requires Cooper pairs and flux quantization to explain (which, in turn, require superconductivity), are not data from film c. The data shown above were taken on film b.—an insulating film. Thus, by these arguments, we have shown the presence of Cooper pairs in insulators.

Various terms have been used to describe this state, both theoretically and experimentally. “Bosonic insulator” is one, “superinsulator” is another. Though “superinsulator” is certainly a better buzzword, I think that it is somewhat misleading. The term “superconductor” is descriptive, however “superinsulators” are not necessarily excellent insulators. The state that we are discussing is that in which insulating behavior is facilitated by Cooper pairs.

Part II of this two-part series will further discuss Cooper pairs in insulators and will introduce other groups’ research on the topic. It will also include the gracious insults alluded to above; it is always interesting when science overlaps with anything involving interactions between people. In Part I, I hope that I have stimulated some interest in the topic of “superinsulators” without overwhelming the reader. I would also be happy to hear comments/criticisms/complaints.

Footnote:
*I say “in superconductors” specifically because that is the only application of this rule. Flux quantization comes about by requiring the superconducting wave function to be single-valued. This is good news because if I claimed flux quantization were true for any regular materials it wouldn’t make sense. You could have a slab of wood with magnetic field lines going through it and I would be telling you, “you can’t draw a circle that small because of flux quantization” when you can clearly draw whatever size circle you please. Anyway, I hope I’ve convinced you that flux quantization only makes sense in superconductors.

Typically, such books are shorter than those I use for reference and much longer than a wikipedia article – they are in between. I’ve taken to calling these books “tweeners” (n., pl., pronounced tee-wieners), as in “they are be-tween-ers”. Another possible term was “t’ain’ts” (n., pl., a contracted contraction of it with ain’t), as in “t’ain’t a wikipedia article and t’ain’t a reference book”. While I prefer the equally appropriate term t’ain’t, the unfortunate (inappropriate) slang meaning justifies avoiding this collision of terminology (no link). There are also less severe collisions with “tweener”:

Let it be understood that I am not referring to a tweener, n., (1) a person capable of playing multiple positions in a sport, (2) a person that falls between two age generations, (3) a bowling form, (4) a hobbit between the ages of 20 and 32 or (5) a man that looks like a woman or vice versa.

Currently, I’m reading A.I. Khinchin’s “Mathematical Foundations of Statistical Mechanics”. It’s definitely a tweener! As far as I know, the readers (and writers) of vdov.net are a diverse group. Do you have a tweener? Are you man, woman, man that looks like a woman, woman that looks like a man or hobbit enough to share it?

If you simply break the box up into 8 pieces, the easiest possible way to do this is just to simply cut through the planes of the box. The faces of the global box do not exist on processor boundaries, as I apply boundary conditions on all these faces. Each cutting plane has 200 x 200 faces, so you don’t need a CS or math degree to know that the number of processor faces in this case would be 120,000. Is this what METIS gives you? No! It gives you 164,033 processor faces. What the hell?

Here’s a little graph of what this looks like (excuse my very quick and dirty xfig’ing). The width of the boundaries is directly related to the number of processor-processor faces between each decomposed domain.

While there is some obvious symmetry here (within a certain level of approximation), this yields far from the cleanest solution. While METIS may be fantastic for complex domains, it doesn’t do well with simple domains with obvious symmetry. Further, each domain should have a maximum of 3 processor-processor boundaries! It’s important to note here that in fact each processor has 3 major processor-processor boundaries (each node has 3 wide connections — this tell us that METIS is in fact roughly trying to get to the optical structure described above). It’s all the little connections that would be removed with some knowledge of the basic full domain structure. I understand and perhaps believe that this could all be due to some convergence criteria in the method which I am unaware of (in my reading of the papers on the subject and the code itself I haven’t found any such parameter), though still, I see no reason why some from-end part of the algorithmic implementation shouldn’t take into consideration the symmetry of the large and subdomain groups.

Cheers.

[UPDATE after the jump]

UPDATE: Here are two images from the processor 1 set. I think everyone should be able to see what I mean now.

How in the spirit of chemistry did she know?! So I asked. She replied “I can just tell.” Baffling! Then I looked down and realized the first corollary and theorem, in my developing theory of how to not behave like a theorist (hereby termed atheorism):

Corollary 1: Chicken noodle soup shrapnel on a shirt is neither necessary nor sufficient to indicate someone is a theorist.

Theorem 1: Chicken noodle soup shrapnel on a male wearing a t-shirt that says “Visionary Women: Challenging assumptions and inspiring change” from 1993 is sufficient but not necessary to indicate the male is a theorist.

It turned out that I had forgotten to bring dining utensils with my dinner to work. Slurping Campbell’s chicken noodle soup seemed like a good idea at dinner time. Forgetfulness is also typical theorist behavior and will be a later theorem, when my sinful theorist nature catches up with me.

Sincerely,
A devoted atheorist

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a prominent place in chemistry — an aberration which is happily almost impossible — it would occasion a rapid and widespread degeneration of that science.

Awesome. I don’t think that Mr. Comte would be very happy with me or a number of people here at Vdov.net.

Slashdot: Scientists solve the mystery of traffic jams

This is fine and well, but unfortunately these people fail to mention the most important work on the subject which initially came from the theory of nonlinear wave equations, and was more or less solved in 1974. It was summed up in a classic text on linear and nonlinear waves so titled and written G. B. Whitham. The book is out of print but it’s around on Amazon as well as other stores and any self-respecting science library should have this book sitting on the shelves. The main problem is one of wave propagation leading to “shock fronts” in traffic. If one person brakes for no reason, shock waves develop and travel backwards (for most flow problems) relative to the moving frame of the cars. Consider a velocity function for cars as a function of the density.

It’s quite simple to assume that must be a decreasing function of which starts from some maximum value at and decreases to zero as , and the maximum density flow occurs at some specific value of . Guess what? Actual observations peg the value of at about 255 vehicles per mile and the maximum flow density at about 80 (or 1500 vehicles per hour). Amazingly these values scale in a near linear fashion as lanes are added to the flow on a simple highway. It turns out the maximum flow rate is actually achieved at about 20 miles per hour. If we then develop a simple expression for the propagation velocity:

Since the derivative of the velocity function is less than 0, propagation of shock waves in a traffic flow travel backwards, and according to Whitham, “warn the drives of disturbances ahead”. Unfortunately this has some pretty negative consequences for you and I, the driver, who will inevitably be fed up with random stoppages in the road for no particular reason. Whitham continues to make some elementary arguments on the status of a wave near the stoppage density of traffic on a road. It turns out that the second derivative of the density flow function is less than zero, which means that a local increase of density propagates backwards, and shock forms somewhere behind the initial disturbance.

Now I’m sure that people have made some improvements in the mathematical description of this problem since the pioneering work of Whitham, but don’t be fooled: pretty much everything you read about “new developments” in this area in the popular media have been solved for more than 4 decades.

Cheers.

Where is the surface tension, is the radius of the sphere, is the permittivity and is the electric field. The following derivation follows simply by application of a little algebraic gymnastics and Maxwell’s equations/stress tensor (where is the charge density and is the total number of charges).

Therefore,

This is remarkably similar to the actual Rayleigh limit (the only difference being a multiplier coming from the fact that this is in fact a sphere), which is given by:

UPDATE: There has been a briefing by the Pentagon which has video of the missile launch, the “kill,” and a brief analysis. The launch occurred on time with no delays due to weather (only 2-3 foot seas). It looks like the shoot down was successful and the hydrazine tank was, in fact, destroyed along with the satellite. The collision occurred at 153 nautical miles above the Earth (~283km).
UPDATEII: Also, what do you know… it looks like there is already amateur photography of the debris field and the hydrazine trail, courtesty of Rob in Maui, Hawaii.

As many of you may know the US military is planning on shooting down a rogue spy satellite in a decaying orbit. It is designated USA-193. The satellite failed immediately after launch and was reported by amateur satellite watchers to have a decaying orbit. The official reason for shooting down the satellite rather than allowing it to deorbit on its own is that the ~5000 pound satellite contains about 1000 pounds of frozen hydrazine propellant that could potentially deorbit into parts of North America. It has been confirmed that the USS Lake Erie, a Ticonderoga class guided missile cruiser, will fire a modified SM-3 missile to intercept the satellite. This may occur sometime within a couple hours of this post, but it looks like weather might delay the shot. Despite assurances from the US, there has been wide speculation that the reason for shooting down the satellite is to test US anti-satellite (ASAT) capabilities, specifically as a reaction to the unannounced test by the Chinese which destroyed a weather satellite dubbed FY-1C in early 2007.

The deployment of military weapons into space has been a matter of concern since the Cold War and the aptly named “Outer Space Treaty” has been ratified by 98 nations. The treaty specifically bans the deployment of weapons of mass destruction into space but does not make prohibitions against ASAT weapons. Both the US and China have tested ASAT technology using the “purposeful miss” method where a missile is fired with the intention of coming within a close distance of a satellite and recording the accuracy. But the last successful satellite “kill” was by the US in 1985 and the Chinese “kill” was after three probable prior attempts. Now the costs and benefits of having ASAT technology and testing it can be debated but the immediate concern is the debris created by such tests. The most significant difference between the planned US shoot down and the previous Chinese one is in the altitude of the satellites destroyed, which has a significant effect on the fate of the debris.

The company that has been tasked with doing simulations of the debris and their paths is Analytical Graphics, Inc. (AGI). They provide an enormous amount of analysis, modeling, and visualization software to the US military and NASA. They also have a lot of great visualizations that are available to the public. Specifically, they have made a bunch of press release and general interest material available about the US intercept of US 193 and the Chinese ASAT test. The biggest difference between the US and Chinese “kills” is going to be the fate of the debris. As this AGI simulation shows (sorry for the .wmv) the debris from the US “kill” will mostly degrade after only a few more orbits and are expected to only last a matter of days. This is because US 193 will be destroyed at ~250km in altitude. FY-1C was destroyed at ~650km which means its debris will not completely deorbit for literally hundreds of years. AGI has also done modeling of the Chinese “kill” and the resulting debris (see the above picture).

There is a cache of publicly available visualizations of the Chinese “kill” made by AGI here. The Chinese ASAT test is the largest orbital debris generating event in history and increased the amount of “trackable items” (larger than golf ball sized) in orbit by 22%. These debris are also going to be very long lasting considering the high altitude of the destroyed satellite. There is a simulation of the debris from this event here. (once again sorry for the .wmv) The difference in the two simulations is immediately obvious.

I would love to know more about the actual ability of people to model these type of events. Apparently we have the ability to detect objects the size of golf balls in orbit. The military is apparently planning on using sea based X-band radar to target and track the satellite and resulting debris. This radar can apparently detect the spin of a baseball from thousands of miles away (impressive eh?). The other really impressive part of this story is the ability of amateur satellite trackers to not only track but give pretty detailed information about classified US government (and I assume other nations as well) assets.

Oh and it does a fantastic job of optimizing elements. This was done in 30 seconds on a single processor in a ~3-4 million element tetmesh, and basically completely eliminated the bottom 2 quadrants of mesh quality (the range in “mesh quality” here (I won’t explain the details), is 0 -> 1). If you can’t see it (someone who knows please explain to me why firefox on linux screws up image scaling so bad … I’m sure there is a simple solution but I definitely don’t know it), a blown up version is here.

The first derivative of position is velocity and the second derivative of position is acceleration. What is the third derivative of position called? Hmm. I didn’t have a special purpose for this information, but I was curious. So I did some searching and found out it is called the jerk (link). I was so excited, it was as if the new phone books were here. I also found out that in the UK, the term jerk is instead sometimes referred to as jolt. Lame. [Side note: This summer I am moving to England. I will not conform.]

I shook the thermos song out my head long enough to wonder about the next derivatives. That’s right, there are more! How many of them have names? According to the physics FAQ, it has been suggested that the fourth, fifth and sixth derivatives be called snap, crackle and pop. Nothing has been proposed for higher order derivatives. The Rice Krispies terms don’t seem to have caught on. It’s a little surprising to me they haven’t. Scientists aren’t above adopting funny names or names that have funny acronyms (e.g., Proton Enhanced Nuclear Induction Spectroscopy). Do scientists hate elves? Maybe just the registered trademark variety.

That concludes my first post. I’m somebody! I’m in print! Things are going to start happening to me now.

hold on;
for k = 1:numfiles
  for l = 1:numexpt
    if (isequal(char(grp(k)),expt(l).name)) pplot(l) = ...
    plot(P(k,compa),P(k,compb),plothash_a{l}, ...
    'MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor',plothash_c{l});
    end
  end
end

Indeed, this works very well. So, let’s say instead I want to plot in 3D. So, I use the command ‘plot3′ instead of ‘plot’. Of course, one would expect this to be very simple. The part here that counts looks like:

hold on;
[...]
if (isequal(char(grp(k)),expt(l).name)) pplot(l) = ...
plot3(P(k,compa),P(k,compb),P(k,compc),plothash_a{l}, ...
'MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor',plothash_c{l});
[...]

Knowing that plot3 is the correct command, this produces a 2D plot only representative of the P(k,compa),P(k,compb) data segment. What the hell? So it turns out that if you hold a new plot with ‘hold on’, Matlab assumes you want a 2D plot. Then upon trying to plot in 3D, Matlab decides it is smarter than you are and that clearly your choice of a 2D plot outweighs your decision to use the ‘plot3′ command, and plots in 2D anyway without throwing an error. Why would ‘plot3′ tell me nothing??? I realize this is a pretty trivial complaint and there are plenty of other great examples of ridiculous crap in Matlab that makes no sense.

Anyway, done complaining. In a ton of data processing Matlab demos, the program asks you to important a series of files into a one data matrix, and does it with some very clumsy code that requires you to manually change the program every time you move to a new data set. Not really my style. Let’s say you have a bunch of data vectors organized in a series of directories (happens all the time), where the directories are representative of some data group that should be accessible as a unit. How about something like this:

repository = pwd;
expt = dir('*.enabled');
numexpt = size(expt,1);
for i = 1:numexpt
  repo{i} = strcat(repository,'/',expt(i).name,'/');
  file(i,:) = dir([repo{i} '*.csv']);
  num(i,:) = numel(file(i,:));
  files(i,:) = strcat(repo{i},{file(i,:).name});
end
expt = transpose(expt);
file = transpose(file);
num = transpose(num);
files = transpose(files);
numfiles = numel(files);
for k = 1:numfiles
  [X,Y(:,k)] = textread(files{k});
end

I use the transposes just because they are nice later in my code, they are certainly not required. I am no Matlab programmer, and I know some of you out there are, so any suggestions as to better file import mechanisms would be greatly appreciated. Short of that though, this is a million times better and far more general than the crap they put you through in the Matlab demos (specifically anything in the bioinformatics sections).

Cheers.

In a viscous only flow, the Navier-Stokes equations are simplified as the inertial components (and therefore any time derivatives) must be zero. The standard Navier-Stokes equation for a Newtonian fluid reads as,

This is a lot simpler than you think: the left hand side of the equation is characteristic of inertial forces, and the right hand size consists of a pressure gradient term, viscosity term and a body forces term (gravity, etc.). In the limit of very low Reynold’s number, these equations simplify to the Stokes equations, given as (neglecting any body forces),

With continuity equation for an incompressible fluid as,

we have a relatively nice description of the problem. So what does this all mean for microscale swimming? These Stokes equation have no time dependence and the solutions to the equations are time-reversible. So, in a viscous enough fluid at relatively low velocity, swimming in the traditional sense won’t work. Any motion in one direction will be completely countered by the equal and opposite motion. So a flapping wing or paddle is pretty useless in these types of conditions. Certainly you or I couldn’t swim at low Reynold’s number. So microscale species develop inventive ways of getting around this problem. A lot of these solutions are detailed in the classic Life at Low Reynold’s Number (I found a free link to the paper … AIP would like to charge you for it). There are many methods of solution to the Stokes equations, the details of which I will certainly not discuss here. If you want to know more about some of the more interesting ones (Boundary Element, Streamfunction or Green’s Function methods), take a graduate class in numerical methods or fluid dynamics.

This is all great and good. What the paper in PRL has done is simply apply a reasonable molecular dynamics (MD) approach to the power and efficiency of these problems. It’s an extremely simple application of MD to a pretty easily understood phenomena, and therefore perhaps appropriate here on vdov.net. In the paper, they investigate various biological and microbiotic designs (such as biflaps motion, flagellum, legs and snaking motion), and extract infomation about the power vs. efficiency of each design. This information has some pretty important ramifications, some of which might include some interesting work on the efficiency of microscale therapeutics. The paper is extremely easy to read and the majority of the conclusions drawn should be understandable to the reader without any simulation or fluids experience.

Why then, you might ask, would I care about any of this? Well it turns out this type of fluid to molecular reduction is precisely what I am trying to do to study the collisions of droplets in a spray or on a surface. The problem specification in my situation is perhaps more involved and I certainly won’t detail it here, but this is a wonderful example on how MD and computational fluids can talk to each other. Secondly, I’m looking to put more science on the vdov.net front page, and this paper seemed like a nice place to start. All of you current or future PhDs out there are welcome/encouraged to post anything interesting at any time.

Cheers.

I think I read (though I can’t seem to find the reference anywhere) an interview with Linus Torvalds recently in which he said something like the following (if you know the reference feel free to let me know, I’m pretty sure it was on Kernel Trap this year sometime):

I don’t use Debian or any other ‘low-level’ Linux flavors because I feel like Linux should be easy to use and manageable for day-to-day work, etc.

Those of you that know me well probably know that I have made nothing short of a career in the past 3 years going exactly in the opposite direction here. Recently however, I decided to take the plunge for a number of reasons. They are briefly: 1) I’ve got way too many machines to take care of these days, 2) I love Debian but on laptops I find it a bit annoying to have to configure dynamic things every time I move and 3) Recently I screwed up a bunch of my machines and decided it was time to reinstall them, 4) Being ridiculously OCD I needed to have all my machines running the same software and they all basically need to look the same. Lastly, and definitely most importantly, Ion3 was really having trouble running a lot of the software I needed to run, including Fluent (ANSYS), Gambit, Matlab, etc. So all these things together, along with my acquisition of a brand new laptop, made me decide to take the plunge and reinstall all my machines with … (drum-roll), 64-bit Ubuntu.

Generally I’m pretty happy with my choice. I loved the Ion3 window manager and Debian in general, but Ubuntu is basically Debian with some fancy crap built on top of it. So the backend is basically the same. Plus the update cycle is way better in Ubuntu … well, at least faster. As far as using Gnome, I’m not completely sold yet. I sort of like it … I guess, and I’m getting used to it. But I do miss the simplicity of Ion3. I don’t, however, miss configuring everything manually in Debian for my laptop or the huge number of problems I had with applications really not liking the Ion3 windowing model.

Oddly, Ubuntu Gusty’s (7.10) compositing window manager (Compiz Fusion 0.52) is pretty annoying. There are really no real benefits to it so far as I can tell, other than Aero/Aqua-type effects. And there are plenty of annoyances. As I first got back to reinstalling my systems, basically everything that didn’t work with Ion3 well also didn’t work with Compiz, so I had to disable it out of the box on all of my machines. Annoying.

Alec turned me on to ‘unison’ as a nice little remote folder syncing utility, which is quite wonderful. I use it now to sync my document tree between my 3 work machines (work laptop, work desktop and home desktop). It’s designed for just 2 machines but it works equally well with 3.

I also got a nice new laptop recently, a Dell Latitude D430, which is their ultra-portable business machine. I’ve used it extensively already and generally I’m quite happy with it. Ubuntu runs great on it — I haven’t really been able to detect even the slightest hitch yet — it’s got fantastic battery life and the performance sacrifices due to ultra-portability and long battery life really don’t affect me in the slightest. It’s really going to be brilliant to be able to work on a plane or while traveling, not to mention when I just need to get out of lab for any number of reasons (there are lots of them).

I’m not sure I have much else to say. Lots of real work to get done since my OP is over, as my boss wants to publish pretty soon and I really don’t have enough yet done to do that. Hopefully I’ll be writing paper #2 in February. I doubt anyone will really care about this post but it’s here for you if you like; I had to write something, this place is dead. Hey you … write something for vdov.

Cheers.

I put up my OP paper. You can take a look at it here.