Thursday, May 31, 2012

Commemorating Hannes Alfven's Achievements (2)

We continue now looking at more of Hannes Alfven's achievements with this 70th anniversary year of his research letter on Alfven waves. Two quick ones first:

1) Alfven postulated that there must be a galactic magnetic field, otherwise cosmic ray distributions would not be limited to galactic dimensions.  Most thinking at the time rebelled at this, under the conviction that if space was a vacuum it couldn't possibly sustain or carry the electric current needed to generate a magnetic field. Much later, the galactic magnetic field was verified.

2) Alfven warned that the concept of a "frozen in magnetic field" for a plasma, had to be treated very cautiously. In particular, the concept was based on idealized conditions and assumptions not always fulfilled in a real plasma. With his studies of the aurora, he became convinced that the frozen in concept could be very misleading.

Only later, was the concept tied to a quantitative basis via the magnetic Reynolds number (R_m).  If R_M >> 1 then any magnetic diffusion can be ignored and we have the frozen in condition. R_m is expressed as:

R_m = L V(A)/ n

where L is a typical scale length, V(A) is the Alfven velocity and n the magnetic diffusivity.

Thus, using the computed value of R_m for a given plasma, one could calculate if the field was frozen in or not.

3) Another major contribution of Alfven's was the guiding center approximation and adiabatic invariance. Before Alfven's guiding center approximation, the computation of electron orbits in the Earth's dipole magnetic field was an almost superhuman task, requiring enormous time and computing resources.

Alfven's genius was to separate the motion of the trapped particle into a gyration transverse to the local magnetic field and a drift of the center of this gyration, which he called 'the guiding center".

If we consider a charged particle (say of charge q) in a uniform and constant magnetic field (B). the governing equation of motion for charged particles is:

m (dv/dt) = q(v X B)

The motion here is such that v is always perpendicular to the force acting on the particle so:
v ⊥ F, implying circular motion.

Readers can pick up from this point and get an extensive insight into the guiding center approximation and also obtaining one of the adiabatic invariants - from this earlier blog:

Note in particular how the magnetic moment u, of a gyrating particle is what is being called an adiabatic invariant (this is always a property that does not change when the magnetic field changes very slowly on the time scale of the gyration). Since then, two more adiabatic invariants have been found, and have since become an indispensable tool in plasma physics.

Romney's Budget Plans To Add $47 Trillion to Deficit by 2050

Actually, I had to re-read the forecast given in the May 5th issue of The Economist, to be sure I'd seen it correctly. But there it was on page 32. If Mitt Romney wins the election, and Republicans take back the Senate (which they likely will on the coat tails of Romney) and the Tax Bagger GOP keeps the House then they'd (retroactively) make ALL Bush tax cuts permanent. Factoring in the existing interest, and that yet to be compounded from the permament cuts (which a Ryan budget promises to tilt even more to the rich) then we can estimate that in 38 years, by 2050 - we will have added $47 trillion to the deficit.

Of course, Romney and Co. will have to know savage domestic cuts would be the only things likely standing between keeping the austerity hounds at bay or breathing down the U.S. collective throat. Hence, if the Bush cuts are made permanent, then look to cuts across the board to subsidized housing, to schools, to food stamps, and likely to Medicare and Social security.

We will have the Wolf at the door, and he will be garbed in Republican red.

Anyway, we'll wait and see. Hopefully, more people will come to their senses before November and not allow Mitt and Repugs to have a one party state to do with as they please. Remember, they never earned their badges in the first place, opting to impede almost everything Obama has done since his inauguration.

Lastly, the Milquetoast Dems share some blame in all this, and the possible horrific future on offer. Had they stopped playing poltics and killed the Bush tax cuts for all, as opposed to mounting a supercilious defense of middle class cuts to the exclusion of the wealthiest (knowing the Goopers would never agree) we'd not now be staring oblivion in the face should Romney and the GOP win in November. The Zombie cuts would have been dead, likely never to rise from their grave again.

Maureen Dowd Needs To Stop Fretting Over the 'End of the World'

In her most recent column, New York Times columnist Maureen Dowd confesses to an unhealthy obsession with end of world scenarios. As she puts it:

"I'm worried about those two small asteroids that buzzed the Earth this week, those two big earthquakes in Italy and the countdown to doomsday on Dec. 21 as prophesied in the Mayan Calendar.  Will Planet X or Niburu collide with the Earth before Christmas? Will a solar flare cause a geomagnetic reversal of the north and south poles/ Will a black hole swallow us up?'

First of all, Dowd need not worry at all about the near miss of the two small asteroids. Even, if they had struck the damage would have been around the lowest threshold of the Torino scale that calibrates asteroid impact effects. The asteroid she needs to fret over is the one to deliver Earth sterilizing impact. This would leave a devastated area of up to 50 square million kilometers, as gouged out by an object of at least three fifths of a mile diameter - as opposed to a few hundred feet.

Yes, the explosive release, at 100,000 megatons equivalent,  would be enough to do away with most life on Earth, but....the collision frequency is less than once every 250,000 years. So Maureen ought to be able to sleep at night.

As for the Mayan, 2012 malarkey....what can I say and how many times do I need to say it? Again, any reversal of the Earth's magnetic field (which is not that far away, but I'd say not as near as Dec. 21 this year) has absolutely nothing to do with any alignment of the Milky Way's dark rift with the Sun as forecast by a Mayan calendar (or more accurately, recent interpretations of said calendar). To suggest such a connection is to practice unwarranted extrapolation which is not based on any credible astrophysical or astronomical data.

The tragedy is that by focusing on fake catastrophes like the Mayan 'end of daylight', people will cease to attend to the real threats by taking actual actions now. Say like cutting back on consumption of fossil fuels to abate or delay the onset of the worst greenhouse gas warming.  But more on this in a bit.

Maureen also need not fret over "Niburu" colliding with Earth, before Xmas, or ever, because Niburu is basically a mythical entity with no science to support it.  It probably originated, as much of this crap does, with some wannabe scholar who went overboard in seeking to make cosmic connections with ancient mythologies (in this case Sumerian). Thus, Zecharias Sitchin hatched "Niburu" as an unknown planet X beyond Neptune. But since it's a figment of Sitchin's imagination more than anything else, I wouldn't lose too much sleep over it.

What about a solar flare causing a reversal of the geomagnetic north and south poles? Hardly! In any case, based on magnetometer measurements we know the respective poles are weakening which usually portends field reversal. But these are part of a normal cycle, not necessitated by any sort of catastrophic event.

Just at the transition point for reversal, the Earth's magnetic field will effectively be zero Gauss, which will mean our magnetosphere will cease to exist as a protective barrier against highly charged particles, ions - say barrelling in from flares on the Sun. Whereas before the particle would be trapped and forced to oscillate back and forth in a closed field around Earth, see e.g

in zero Gauss conditions, no such impediment will be provided, so that radiation in the form of those charged particles will barrel directly through the Earth's atmosphere to the ground. Does this mean the 'end of the world'? Nooooooooo.......only that if you choose to leave your house during times of high solar activity and hence incident radiation, you take what chances you may......analogous to those brave (foolish) souls who dare to stay in the Sun for hours on end.

As for being swallowed by black holes, not likely! There are no candidates that would meet the Earth-swallowing range within at least 12,000 light years.

Dowd next waxes her fear onward based on a new novel "Age of Miracles" by Karen Thompson Walker that "makes you look around warily as you walk down the street" - according to Maureen. But why? Well because this novel has evidently found a way to roll all the assorted fears into one - starting with Earth's rotation slowing, days and nights stretching the length of weeks, the Earth's magnetic field withering and "gravity going kerflooey" as temperatures become either boiling or freezing.

All of which is sophisticated hogwash. Evidently, the author of the novel got the idea after learning that the infamous 2004 Indonesian quake sped up Earth's rotation and knocked 3 milliseconds off each day. That is 3/1000 of a second.

So, hey, why not extrapolate the other way and imagine something that causes Earth's rotation to maybe 56 or 100 hours instead of 24, so weeks are now 2 or 4 times longer than they used to be Then, Voila! The Earth loses its magnetic field, and temperatures go crazy while gravity "goes kerflooey". Sorry, ain't gonna happen! Even if Earth's rotation was slowed a factor ten beyond what it is now, say taking 240 hours to make one revolution, one would not behold the disasters proposed by Thompson.

And would gravity change? Uh nooooo. Because the gravitational intensity g is given by:

g = GM/r^2

where G is the Newtonian gravitational constant, 6.7 x 10^-11 Nm^2/kg^2, r is the radius of Earth, r = 6400 km or 6,4 x 10^6 m and M is the Earth's mass, 6.4 x 10^24 kg. Then one obtains g = 9.80 m/s^2.

The only way the gravitational intensity changes (and recall weight is defined as w = mg), would be if the Newtonian constant itself changed, or the Earth's actual mass or radius.  And incidentally, none of this has a bearing on temperatures!

So much for another entry into the reasons why all American need to take a basic physics course.

Where Maureen veers closest to a grounded worry, is when she recalls how hot it's been lately, with thousands of records broken. But instead of rightly connecting this to global warming, which it ought to be (never mind what the meteorologists keep yapping about highs) she veers off into an old Twilight Zone episode where the Earth "spins out of its orbit and moves closer to the Sun".

Makes for intriguing reading for sure, but hardly necessary to get humans to take proper stewardship of their home world.

Fact is, we shouldn't have to resort to scaring the shit out of people using elaborate sci-fi scenarios or depictions when real ones (such as ever increasing CO2 levels from man made activities) are quite capable of doing the trick.

Maureen, take note!

Wednesday, May 30, 2012

Does the Caribbean Really Plan to Take on the U.S. in the Rum Wars? Believe It!

One thing I learned very soon after arriving in Barbados for my Peace Corps service, is that rum is almost a religion. Rum distilleries- refineries (most expats call them 'refineries') are hallowed ground, as they are throughout most of the English-speaking Caribbean, and no sane human - American or other - would even think of arriving in Barbados, say, with a bottle of Bacardi's

First, rum refining comprises the largest remaining driver for the consumption of sugar cane that grows in abundance. Given the world's diminishing taste for sugar (including health reasons) the only large remaining outlets are for sugar-based ethanol, e.g. in Brazil, or for rum manufactured in the Caribbean conglomerate known as the "Cariforum nations".

Second, rum comprises the region's largest agriculture -based export industry - which generates $500 m in foreign exchange each year. Foreign exchange is what keeps all of these island states afloat, because without it, they'd not be able to afford the food imports.....and without the food imports, most islanders would descend to a level of malnutrition common to sub-Sahara Africa.

So, it was with more than the usual interest that an item appearining in the Caribbean press (Jamaica Gleaner, Barbados Advocate, Trinidad Guardian)  some 3 weeks ago, alerted Caribbean folk that they may soon have to wage a pitched battle with the U.S. ...over, yes, RUM!  Specifically, CARICOM Secretary General Irwin LaRoque disclosed in a news conference that the Cariforum alliance had begun a process which would eventually, if unresolved, lead to Cariforum hauling the USA before the World Trade Organization, WTO).

The source of the miff? The U.S. Government's selective application of a cover-over program which repatriates 98 percent of all rum excise duties (raised on rums sold in the U.S.) back to the producing U.S. territories of Puerto Rico and the  U.S. Virgin Islands.   Estimates from 2010 put this unfair repatriation at $450 m.

These offhand deals, made by the respective neo-colonial governments (of Puerto Rico and the USVI) have been struck with the likes of Bacardi and Serrales. It is galling to Caribbean governments which derive no similar special deals based on repatriating duties. In effect, as one writer (David Jessop)  has pointed out, the U.s. congress has enabled the USVI and Puerto Rican development programs to divert hundreds of millions of dollars to primarily provide a development program for the largest distilled spirits companies in the world.

In this sense, the U.S. - maybe wittingly, maybe unwittingly - is damaging one of the few competitive industries that Cariforum nations have and in Jessop's words, "which helps underpin the economic viability of small and vulnerable Caribbean states". And this is on top of an already seething anger and distrust that's erupted since the (now deposed) French idiot Sarkozy remarked at an economic conference that Barbados' offshore banking is ignoble and abets criminals and it ought to be "punished" by the OECD.  Add in the rum fracas, and you have lots of West Indians ready to chew titanium at the offhand way they've been treated by the big Western powers.

The issue is even more close to the hearts of Caribbean folk, since as Jessop has noted :

"Unlike the product of large, multinational distilling groups, the success of Cariforum producers does not result from artificial tax breaks, transfer pricing or subsidy. Instead it is an industry dominated by small local distillers whose product is export-oriented, brings much needed foreign exchange and adds value to primary agriculture.while providing signficant levels of tax revenues to governments struggling to deliver social programs"

Which is very true, since we know the Cariforum nations have one of the most progressive tax systems in the hemisphere, and unlike the faux democrats in the US of A, none of them would ever approve any form of unbalanced tax cuts, or any tax cuts, period.

But isn't it chutzpah of the first order to believe a consortium of small island nations, can take on a Goliath like the U.S. allied with its powerful multinationals who have money to burn? Maybe not! Jessop again:

"This is why rum has always been a product worth fighting for as Europe knows to its cost and the U.S. is soon to discover".

Perhaps this will be the Cariforum nations' counter punch to the U.S. dragging it before the WTO over a banana dispute back in 1998. (The U.S, allied with Chiquita Banana, insisted that despite colonial history and associations, Europe had no right to pay Caribbean nations special, higher prices.)

In any case, this would be the perfect equalizer.

Commemorating Hannes Alfven's Achievements (1)

As most researchers, workers in plasma physics are aware, this year marks the 70th anniversary of a ground breaking research letter ('Existence of electromagnetic -hydrodynamic waves') in Nature, that was to change the face of physics forever. Though only a half page long, it was the content that mattered, describing a new type of low frequency oscillation for a magnetized plasma.

As with many novel insights, the content was long disregarded (or openly dismissed) mainly because the new waves couldn't be demonstrated experimentally at the time. However, over decades and as experimental - lab techniques grew more refined (including experiments conducted in the space environment via satellites and on Space Shuttles) the novel waves we call "Alfven" soon began to occupy an important role in space and plasma physics.

It helps at this stage to examine a bit of the nature of Alfven waves, conceived by Hannes Alfven, and which were finally experimentally demonstrated in lab plasmas by 1960.

Alfven waves, by the way, are the most important waves propagating in the solar atmosphere, as well as the Earth’s magnetosphere (underpinning the coupling between it and the ionosphere). They are important in that they efficiently carry energy and momentum along the magnetic field.

One way to get a handle (of sorts) on Alfven waves is to look at the analogy with mechanical waves – say propagating along a string put under tension. Consider the reference frame or coordinate system:

^ y

Say x marks the direction of propagation in the above coordinate system, and y is the direction of transverse (wave) displacement. Then the vertical force component is:

F_y = - T(@y/ @x)
where T is the tension and the bracketed quantity is the partial of y with respect to x. Thus, just as the restoring force for a mechanical wave is the string tension T, the restoring force for an Alfven wave is the magnetic tension. This magnetic version of “tension” accelerates the plasma and is opposed by the inertia of the ions (mainly from proton masses m(p))

Now, the wave speed on a string is related to u (mass per unit length), and T such that:

v = (T/ u) ^½

and as we can see,  increasing the string tension increases the wave speed in an analogous way to what magnetic tension does for the Alfven wave. The magnetic tension analog can be expressed (as we shall see) as: T(M) = B^2/ u_o

where B is the magnetic induction and u_o is the magnetic permeability for free space, u_o = 4 π x 10^-7 H/m)

Examining the origin of these waves always starts with setting out the basic equations for what we call “ideal MHD”, e.g. one of the equations is: @B / @t = Curl (v X B). We then introduce small perturbed quantitites (e.g. imagine introducing a small perturbation into the plasma velocity such that v_o -> v_1, which will also subject the mass density, fluid pressure and magnetic field to perturbation), such that:

rho = rho_o + rho_1

v = v_1
B = B_o + B_1

p = p_o + p_1

and we substitute these back into the original ideal MHD equations  Then, after using a LOT more math (which I will spare readers) we end up with the general Alfven wave quation:
 w^2 v_1 – c_s^2 (kv_x)k* + B_o/ u_o rho_o [k X k* X (v_1 X B_o)] = 0

where w denotes the plasma frequency, k is the wave number vector (k* the vector orientation) and the other quantities are as before, and c_s is the ion sound speed.  One will then take the preceding equation and resolve it into x, y components, viz.

x-component of wave:

w^2 v_x – c_s^2 k^2 v_x + B_z k^2/ u_o rho_o [v_zB_x – v_xB_z] = 0

y-component of wave:

w^2 v_y - B_x^2 k^2 v_y/ u_o rho_o = 0

or simply:

w^2 = [B_x^2/ u_o rho_o] k^2

where the quantity in brackets is the Alfven velocity or alternatively written:

v(A) = [w/ k] = B_x / [u_o rho_o]^½

v(A) = B_o/ [u_o rho_o]^½

since B_o is in the x –direction

A more refined and useful form is obtained by incorporating the x and z-components and solving the resulting simultaneous equations, then doing some simplification to get:

w^2 = ½[(c_s^2 + v(A)^2k^2 +/- [(c_s^2 + v(A)^2 k^4 – 4 c_s^2 v(A)^2 cos^2(Θ) k^4]^1/2

Now, if one plots the preceding using (for the vertical axis ): c_s^2 + v(A)^2  and for the horizontal B_o (e.g. x) one will get what is called “Friedrich’s diagram”


Visualize superimposed on the above axes, the following graphs:

1) a small “dumb bell” or figure-8 shaped graph centered at the origin. This will be for what we call “slow mode” waves

2) a single larger lobe that envelopes the smaller right lobe of the dumb bell. This will be for Alfven waves proper.

3) A circle- shaped graph surrounding both 1, 2 above. This will be for what we call the “fast MHD” mode.

The critical thing to note here is that the fast mode is the only MHD wave able to carry energy perpendicular to the magnetic field. This has important ramifications for solar flares, as well as magnetospheric effects (such as the aurora). Meanwhile, the phase velocity (w/k) of the slow mode wave perpendicular to the magnetic field is always zero. In the limit where the sound speed c_s^2 < < v(A)^2, and the Alfven speed v(A)^2 << c_s^2, the slow wave disappears. (Which you can easily validate and confirm for the equation in w^2)

Other properties, points to note:

- the velocity perturbation v_1 is orthogonal to B_o

- the wave is incompressible since DIV v_1 = ik.v_1 = 0

- the magnetic field perturbation (B_1) is aligned with the velocity perturbation. Since both are perpendicular to k and B_o

- the current density perturbation (J_1) exists as a current perturbation perpendicular to k and B_o e.g.

J_1 = k X B_o

- when c_s^2 << v(A)^2 the fast mode wave becomes a compressional Alfven wave. This has a group velocity equal to its phase velocity w/k

Why the maddening complexity with these waves and being able to quantify them? Mainly because Alfven used both the electromagnetic theory of James Clerk Maxwell in combination with hydrodynamics (or fluid dynamics) which hitherto had been established as separate disciplines of physics. But by marrying them via the sort of steps outlined above (to do with Alfven waves) Alfven succeeded in opening up an entirely novel area called magnetohydrodynamics.

Oddly, and ironically, at the time they were conceived these waves had no practical basis, or applications. But by the 1950s, when thermonuclear research took off, they emerged as it became possible to generate high temperature plasmas artificially on Earth.  The rest, as they say, is history.

Next: Some further contributions of Hannes Alfven.

Tuesday, May 29, 2012

Drone Makers to Public: Stop Whining Already! Drones is GOOD Guys!

The drone manufacturing industry, under the aegis of The Association of Unmanned Vehicle Systems International, (AUVSI)  the industry’s trade group in Washington, is pissed off and they aren't going to take it anymore! This is after facing growing hostiliity to drone implementation on both the left and the right. Conservative columnist Charles Krauthammer, for example, called for a ban on drones in U.S. airspace. Then two conservo two other commentators endorsed the idea of shooting down unmanned aircraft flown by U.S. law enforcement agencies.

Meanwhile, many on the left, have correctly pointed out the inherent dangers posed by these flying robots in U.S. airspace, since he FAA, has not yet issued rules for unmanned aviation systems - especially maneuvering in proximity to large commercial airports such as Denver's (where a near collision occurred about 2 weeks ago. Moreover, air safety experts also have raised questions about the ability of sensors aboard unmanned aircraft to properly detect a nearby plane, and to assure immediate action to avoid a midair collision.

Michael Toscano, president of the AUVSI isn't bothered as he argued in a recent interview that:

"“Car crashes kill 35,000 people a year, but we don’t talk about banning cars. We need to be honest about the costs and the benefits.”

Oh just terrific! So, as long as the drone -aircraft collisions don't snuff out more than the number perishing in autmobile crashes, Toscano is just fine with them. And what exactly are the benefits? I dismissed these so-called benefits in my first blog about the issue:

Stated "benefits" cited including: environmental monitoring, fire protection, surveillance of suspected criminals....checking power lines and tracking equipment.  But all of these can be done at much less expense and without requiring unmanned drones. For example, multiple street video cameras mounted all over can now track criminals anywhere. Moreover, the "fusion centers" provided under the Patriot Act make this as easy as companies tracking people using 'cookies' on the web. Nor do we need to risk commercial passenger safety by putting thousands of the blasted things in our skies for the specious reasons cited. In the end this is all bullshit, and the real purpose of this law is to provide an outlet for the defense industry drone manufacturers who will no longer have U.S. occupations within which to ply.

But Mike Toscano isn't taking it on the nose.asserting that the AUVSI would go on a PR offensive against critics. Toscano made the PR strategy sound like something straight out of Edwin Bernays reality-management textbook — or George Orwell's 'Newspeak' from 1984.. The AUVSI wants to bombard the American public with positive images and messages about drones in an effort to reverse the growing perception of the aircraft as a threat to privacy and safety. Didn't ya know that small drones made up like little flying Avengers can even babysit your kids? And they can generate serenades or nursery rhymes too!

According to Toscano:

"We’re going to do a much better job of educating people about unmanned aviation, the good and the bad,”

Right and we know where the emphasis will be.  Already Toscano and his mates are preparing the main boilerplates for language change, for example seeking to replace the harsh word 'drone' (which conjurs up images of Afghani babies being incinerated by Hellfire missiles fired from predator drones) to 'remotely piloted vehicles”. Sorry, maestro! But if your vehicle has to be directed from afar it's not being "piloted"! It's a zombie, a drone!

Meanwhile, Medea Benjamin of 'Code Pink' has highlighted the same pernicious origin of this drone law that I noted in my 'Elements of the Corporatocracy': That is, as in the case of the Medicare Modernization Act of 2003 -letting lobbyists actually write the legislation and the congress whores merely sign on. In the same way, according to Benjamin:

"They’ve been able to write the drone legislation and get their lackeys in Congress to push it through and get the president to sign it. But they are going to have to work harder and harder as we ramp up our efforts to educate the public.”

My bet is on the anti-drone side to educate more clearly and deliberately than the drone spin meisters can.

Meanwhile, Missy Cummings, a professor of aerospace engineering at Massachusetts Institute of Technology, insists that the recent controversies about drones mark a new phase in public thinking.
We’ve just reached a tipping point and now people are starting to think about and talk about these issues, That’s a good thing.”
What's not a good thing is how our slimey congress critters actually think they can slide this crap right past our noses and make it stick. They all ought to be ashamed of themselves, but when laws are dicatated by the corporate paymasters you know a once great Republic is already on its last legs. The very fact that the billions needed to produce these damned things could have been used instead to hire back 365,000 teachers nation wide.

The drone makers barely realize how shameful they are, and the fact they need to hire PR hacks to push their crap is further proof.

Monday, May 28, 2012

Notes from a Dad's Entry into War

I only recently located the earliest notes giving an account of my dad's entry into the battlefields of World War Two. On this Memorial Day, I'd like to share them. They leave the reader with a sense of the incomplete but we do know from his Army records he was engaged in five major battles in New Guinea (including the Battle of Buna, see e.g.

 as well as in the Phillippines. We also know his company faced some of the toughest, most disciplined Japanese combat troops that the Empire of Japan fielded. They also fought you face to face, including with mounted bayonets, not via proxy devices. And they fought to the death.

Anyway, here are those initial notes of a young volunteer soldier headed to War:


January 16th, 1942 – I left Camp Robinson, Arkansas on a troop train. We went by way of St. Louis and Chicago. On Sunday nite, January 18, we arrived at Indiantown Gap, an Army Camp in Penn.

January 20th, 1942 – about 12:30 P.M. we arrived at port of embarkation in Brooklyn, N.Y. We walked from the troop train to the U.S. Army Transport, “Thomas H. Barry”. This being the first ship I had ever seen, was very large, and there were 5,000 officers, nurses, and enlisted men aboard, when we pulled anchor on the cold morning of January 23.

The “Barry” carried approximately 25 guns, and from the beginning of the trip, I felt sure that we were well protected.

Ours was the first largest convoy of troop ships to cross either ocean. The first few days on the water were quite interesting and I somewhat enjoyed it. But as the days became longer, and the ocean rougher, it was a damnable experience for us all. We had only salt water for showers, and shaving, and our drinking water was rationed, one quart a day. Our food was terrible, and most generally we could expect rice and scrambled watery eggs for breakfast, and stew for supper. We were fed only twice a day.

We passed most of our time playing games, reading, and listening to lectures on what to do, if we were attacked by the enemy.

One Sunday Morning many of us on deck saw one of our Navy destroyers sink an enemy submarine about three miles out from our ship. Depth charges were used.

I had my first and only scare one morning after being at sea for about a fortnight. One of my buddies and I were playing Checkers on the deck – when all at once there’s a loud blast – as though the “Barry” was torpedoed! One of our lieutenants told us to get inside and tighten out life-belts. I was too afraid to speak! I heard guns on the ship firing and my only thought was “God save us!”

After what had seemed hours, but only a few minutes, we learned that our convoy was having an “attack drill”!

February 1st, 1942 – We sail into the Panama Canal, which is our first stop since leaving Brooklyn, eight days ago. Going through the canal and “locks” was very interesting to me. It took our ship eight hours to go through the canal. Panama, as we saw it from the Barry, looked very beautiful with the many coconut trees lining the shores. After taking on supplies, we leave the canal Feb. 2 for our destination, Australia!

Feb. 4th, 1942 – we crossed that famed line, commonly known as the equator! We received our equatorial rights, and were initiated into the “King Neptune Court”.

Several weeks later we drop anchor at a South Sea Island, called Bora Bora. Hundreds of Natives came up to our ship in their rugged canoes, or LAKATOI’S, as they are known. Many of us Americans gave them money and toilet articles for fruits, coconuts, pineapples, etc., that we so badly wanted. We were here only six hours, to refuel.

After 35 hellish days and nights on the Atlantic and Pacific oceans, we reach our destination, Melbourne, Victoria, Australia, on Feb. 28, 1942! We marched off the “never-to-be-forgotten” Barry, and boarded an electric train which took us to our new camp, “Royal Park”. This place is paradise! We are fed good, and we’re permitted to go into the city on the second day after arriving. Everyone is very friendly toward us “Yanks”, and they invite us to their homes, parties, dances, etc. The Australians speak English, but they have so much more “slang”, and speak faster and indistinctly. It was difficult at first to understand them, but we soon “caught on”. The Australian girls had rather be with an American, than an Australian soldier, anytime! Odd? Yes, but true. Several of the nice girls that I met asked countless questions about the United States. I admire them for their loyalty to the Australian Commonwealth and their desire to do all they can, to help win this war.

Melbourne was in a “brown-out” every nite, and as I walked down the streets after a show, I would pass young girls and boys singing “Bless ‘em all”, “I’ve Got Sixpense”, etc. From the beginning, I liked Australia very much. The winters seldom get below freezing and the summer months are December, January and February.

Among the many places of interest, I went to Coffee lounges to hear different orchestra’s, Melbourne’s famous St. Kilda Beach where thousands of people swarm and Tuna Park, where one may find rides, shows, and amusements of every kind. I visited Flinder’s Street Railroad station, the busiest in the world – and there it really isn’t safe to turn around and go back!

Our work in Melbourne wasn’t hard. Usually in the morning we would drill, or take a hike to some part of Melbourne. Sometimes

We would be on a work detail at the docks (at Port Melbourne) , and we had guard duty at times. We were free about every nite to go to town, or a tent show at camp.

April 17th, 1942, our good times ended in Melbourne, the 43rd Engineers were separated and we’re to go to nearer to the front. We, of Co. E, are put on a large freighter, and as I write this now, it’s my understanding that we are to go New Guinea to engage the Japanese. Our first stop is to be Brisbane. We have a better “set up” here than we had on the “Barry”. Our meals are very good and we have plenty of good water. It should not take over another week to reach Brisbane.

Sunday, May 27, 2012

Russian Angst Increases Over U.S. "Missile Defense" Plan

The recent words of a Russian Defense Minister (Denver Post, May 25), to the effect that the Russians will have to double or treble their existing nuclear missile warhead capacity to neutralize the planned U.S.-NATO missile shield for eastern Europe is certainly grounds for serious worry. To be sure, it has the makings of a new nuclear arms race just as we were making progress in removing warheads and disassembling missiles in the former USSR. And for what? Well, for no good reason!

As I noted in earlier blogs, e.g.

This proposed shield, which is planned by NATO (Why does this anachronism even exist any more? The only plausible reason is to act as a buffer or cover for U.S. militarist actions.) would be completed in four phases by 2021  and the cover story or PR is that "it's meant to counter a potential threat from Iran". Trouble is, the system - which uses Aegis radar systems and interceptors on ships- is set up right on Russia' border in nearby Poland. Since the Russkies kept their side of the deal and expedited the dissolution of The Warsaw Pact (the putative counter to NATO in the Cold War Years), the U.S. - despite warning from expert Russianologists, has made ever more pacts with former Russian satellites and expanded NATO to Russia's doorstep. This is stupid, ill-conceived.

Indeed, one can't blame the Russians for their mounting paranoia that the system allegedly to be used to stop Iranian missiles is really designed to undermine Moscow's nuclear deterrent.. As one Russian minister observed, obviously it would be of use since (irrespective of the claimed purpose) it "would give the West the ability to shoot down Russian missiles in situ" (WSJ, 'Moscow Raises Alarm Over Missile-Defense Plan for Europe', May 4, p. A14). Thus, the Russians rightly worry that the proximity of this system to their border gives the U.S. an excellent opportunity to down Russian missiles in the boost phase.  If this idea catches on, and there's good reason it can, one can pardon the Russians for believing the U.S. is setting up for a first-strike capability.

In his book 'Particles and Policy', physicist Wolfgang Panofksy pointed out the only true system of security for Russia and the U.S. was MAD: Mutually Assured Destruction. Thus, it became an axiom that neither nation would do anything to jeapordize the stability ensured by MAD using reckless moves which might be interpreted to seeking to gain leverage in the MAD world.

The objective truth is that this proposed missile system is merely a destabilizer with absolutely no known benefit. Even the Poles, who are destined to house one or more systems have gone on record to state that any such system isn't needed. Stefan Niesiolowski, chairman of the defense committee in the Polish Lower House of Parliament pointedly observed such a missile system is not needed in Poland. As he pointed out ('Missile Gaffe Leaves Europen Unfazed', WSJ, April 22,  p. A8):

"There's no military threat and we haven't had a situation as secure as this in 300 years. The level of U.S. military engagement in Poland therefore is not of top importance."

Then WHY do it?

The answer is simple: the military -industrial complex ensconced in the U.S. wants to invent ever more specious reasons to piss away ever more billions of our taxpayer dollars. (Which is also why they want to have 30,000 unmanned drones airborne by 2015, since Afghanistan use is winding down). THEN...the deficit hawks can pick up the yelp to cut social programs because of all the deficits created by "entitlements". Except they aren't caused by "entitlements" but by: a) unpaid for Bush tax cuts and b) wasteful military spending!

While a Report by the Defense Science Board issued last year speculates that "there are no fundamental roadblocks to the system", it then monkey-wrenched the claim by elaborating profound problems with the system including cost overruns (which, of course, the defense contractors love).  Meanwhile, former Pentagon nuclear weapons' tester Philip Coyle  warned that the issues raised in the Report "would require substantial and costly changes, if they can be surmounted at all:"

As for Panofsky, he makes it clear in his chapter 'MAD vs. NUTS', that no such missile shield systems are in any way practical or feasible. And even if by some serendipity they temporarily were,  a determined adversary could easily find the means to neutralize the system- as Russia proposed to do with Reagan's 'Star Wars' by having missiles deploy thousands of metallic fragments as decoys.

Russia, for its part, rightfully demands a legally binding guarantee that the system won't be used against it. But the U.S. asserts (ibid.) "it can't agree to formal limits on missile defense".

Oh really? Then why should the Russians believe the system isn't really designed to be used against them? Again, the U.S. miltarists - driven by Paul Nitzke's feral document NSC -68  (mandating empire building)  end up putting their feet into their mouths, and at the same time possibly detracting from global nuclear security for all of us, if the Russians increase the megatonnage of their warheads in response.

The ironic aspect of it all, as Morris Berman notes (Dark Ages America: The Final Phase of Empire, W.W. Norton, page 118) is:

"Nitze emphasized the importance of perception, arguing that how we were seen was as crucial as how militarily secure we actually were. This rapidly expanded the number of interests deemed relevant to national security”.

Of course, the US of A has no patent on such perceptions, and if the Russians also believe they're entitled to theirs, they can be forgiven for taking steps to thwart the deployment of a missile shield embodied in U.S. "perceptions" of self-interest. Especially given the shield is to be set up right under their noses!

Saturday, May 26, 2012

Want Your Gov't Back? Bring Back the Original Filibuster!

Let's see: A bill to curb CO2 emissions quashed in the Senate though it had more than 50 votes, the appointment of Elizabeth Warren as Head of the First Consumer Protection Division, quashed in the Senate though the pro-votes excceded 50, the original Dodd -Frank bill which demanded an exchange for risky derivatives, again over 50 votes but no passage, and finally, a 2009 credit card oversight bill that would have easily passed with just over 50 votes - having to have an insane "rider" attached (allowing people to carry guns into National Parks) in order to make the filibuster-free threshold.

What gives? Well, what gives is a paralyzed government that's now been perverted from the intent of the framers of the Constitution-  who viewed the filibuster only as an extreme measure to disrupt or impede the passage of legislation.  And to ensure that it would only be used sparingly, they demanded the Senator(s) who would prevent legislation actually stand on the Senate floor and occupy time by reading from some extensive source. For a fictional portrayal, see the Jimmy Stewart movie, 'Mr. Smith Goes To Washington'- wherein Stewart's character had to speechify until literally blue in the face to attempt to halt a vote.

Now? The requirement that an objecting Senator "hold the floor" has gone the way of coonskin caps and muskets. Today, in these times, an ojecting Senator need only place a cell call from his jacuzzi in the Senate gym and make clear his "intent to filibuster".  The expedient and efficient has overtaken Constitutional principle and the result? Gridlock!

Because the filibuster has ceased to be a real manifestation of a Senator actually holding the floor, we have seen the spectacle of a 60-vote majority now regularly needed to pass nearly all legislation. In another words, our government's law making processed has been monkey-wrenched.

Fortunately, last week, a challenge to the pseudo-filibuster was filed in federal court. The lawsuit argues (correctly, in my humble opinion) that the framers who wrote the Constitution, insisted only on specific and rare instances when a supermajority would be needed and hence the current version of the filibuster ignores the principle of majority rule - thereby requiring 60 votes for even trivial legislation.

My prediction is that this challenge will likely lose, on account of Article 1, Section 5 of the Constitution allowing each chamber of congress to create its own rules.

My own suggestion then, is for the Senate itself to man-up and take the nation's business (rather than party affiliation) to heart, and change the filibuster rule to what it was in the 1950s, 60s. That is, allow it, but mandate the objectors have to do what the old time Senators did and get their butts out on the Senate floor and read, and read, and read.

In other words, no more filibusters on the cheap! The result will return the device to how it was originally envisaged: a rare tool employed when all else fails to block legislation viewed as pernicious. At least if that is done. we may get back to some semblance of a government that works.

Friday, May 25, 2012

Near Collision of Aircraft with Unmanned Drone Over Denver: Anyone Paying Attention?

In a blog in February:

I portrayed a scenario in the near future in which a commercial aircraft collides with a large unmanned drone with massive loss of life. Now, it seems, the future may have almost arrived with the news from last week of a near collision between a corporate jet and what was described as “a large remote controlled aircraft” in Denver airspace. Obviously, while some have their eyes set on the snooping aspect of donres this incident highlights the challenges facing aviation authorities in the safety dimension.

But have our lawmakers listened? Paid attention? Nope! They've just approved a law to have up to 30,000 of these unmanned devices wafting through our skies by 2015. Obviously, all these paid whores are doing it because the military-industrial complex has notified them that if they want more campaign largesse, they better cough up the goods, because after all, the drone-makers need an outlet for their machinery after Afghanistan winds down and Karzai finally kicks our butts out.

So this way, the military industrial complex is afforded a new avenue for increased manufacture (and jacking up deficits), on the home front! Anyway, as reported by a Denver TV station last week, the pilot of a Cessna flying at 8,000 feet over Denver told air traffic controllers he had just seen an unidentified object pass by.

A remote controlled aircraft, or what?” a nervous-sounding pilot said in conversation captured by, a website that monitors air traffic control traffic. “Something just went by the other way … About 20 to 30 seconds ago. It was like a large remote-controlled aircraft.”

An FAA spokesman in Washington said, “We reviewed radar and audio communications but found no unidentified targets in the area where the Citation pilot was flying, and no other pilot reported seeing an unidentified aircraft.”

Jeebus peace! So you mean to tell me the FAA's wizards can't even discern IF an unmanned vehicle is in possession of anyone or if that missing drone was involved in a near collision with official, human-piloted air craft? Wow! If that's so, we really are in deep shit.

But a bit of FAA research would have disclosed that the only entity known to have permission to fly drones anywhere in the vicinity is University of Colorado’s Center for Unmanned Aircraft Systems, which has FAA authorization to fly drones over 59 separate 20 x 20-mile areas 50 miles east of Denver, according to a school website. This is a wake up call, folks, especially if the FAA can't even keep track of who or where they authorized to fly these damned things.

Stay tuned, and in the meantime maybe email your congress rats and ask them what they were thinking when they approved unmanned clutter in our airspace, threatening official, manned aircraft, even as the feds purport to still be concerned over security in our skies. Something here stinks, and it ain't in Denmark! What I do know is that financially we've got very much bigger issues to deal with - including rebuilding infrastructure- which ought to precede a $1.2 billion domestic drone manufacture program!

What I Learned While On Blog Hiatus (3)

When last we left off, we had seen the putative basis for a linearly evolving non-dimensional shear d(x) which could be mapped onto the x-y plane overlaid on a solar active region. See e.g. the diagram in:

As we change the (dimensionless) shear through progressive numerical substitutions, the shear gradient m increases so that the dimensionless shear kφ  increases to a maximum of 1, then decreases. Likewise, in doing this, one finds the line y = mx altering with m to yield evolving arcade footpoint axes (in relation to the potential or y = 0 configuration) of the arcade when in the potential or current free condition.

 We are left with incorporating three functions:

1) d(x) = x sinh b

2) B n (x) = x / R o [ B  ( R o ) ]


3) v(φ,W) = a sin (φ ) exp [1 - 2[φ ]/ W

into one partial differential equation, e.g.

u_t + au_x = 0

which is amenable to an efficiently generated numerical simulation algorithm.
Note first that (2) can be recast as:

x =  B N (x) [R o  [ B  ( R o ) ]

And  we can choose as a first value for a: a =  dx(kφ,W) /dt

where v (φ, W) in (2) is now dx(kφ,W) /dt

The final functional solution which we obtain for possible discretization after obtaining its PDE and after substituting for x in x sinh b, is:

u(x,t) =  [ B n (x) [R o [ B ( R o ) ]  sinh b +  dx(kφ,W)/dt

And we note that the dimensionless shear kφ is actually a time -dependent function of the gradient, e.g. m(t).

Alas, the complexity of the (differentiated) equation became evident as I went through several initial runs merely testing for errors and stability for two methods, the finite difference and spectral method (which uses Fourier series)).  What did I learn ?   Well, that I bit off a bit more than I could chew in a 2 1/2 week project. But hey, at least I made a start!

Three Cheers for the Defenders of Atheists in Barbados

When any minority group in a nation has aspersions cast upon it, it is important that rational and ethical citizens object strenuously, lest that out-group be further demonized into inhuman entities. And we saw what befell such groups in the Third Reich. Thus, I must extend kudos to both John Wickham and B.C. Pires who courageously took the Editors of The Barbados Nation to task for their scurrilous April Editorial demeaning all atheists inhabiting that island nation.

The main part of The Nation editors' rant was in asserting there was no place in the island (as a 'Christian nation")  for atheists who were  rendered "base and ignoble" beings by their disbelief. Of course, any editor who'd write such claptrap in a major national newspaper has to be himself questioned concerning base and ignoble motives.

Thankfully, sometime columnist John Wickham pulled the editors up for their blatant hypocrisy: taking them to task for claiming to respect unbelievers, while labeling them "base and ignoble". Meanwhile, B.C. Pires in his separate Nation column noted that Barbados "is no longer a Christian nation, if it ever were". Pointing the large Jewish and Muslim contingent, as well as nearly 15%  of the 280,000-odd populace who are either professed agnostics or atheists. (Well, at least some of the battles I waged against over the top religionists in 1990 in the island's papers appears to have borne fruit.).

Again, the error made by the Nation's editors, as well as so many others (including in this country), is that of assuming because a group professes no belief in a deity, they have no morality. But this puts the cart before the horse, because it is not the existence per se of any deity that defines the Good, or the Moral, but whether in fact an act is good or moral on its merits. This is what the hate mongers don't get and likely never will.

In line with this, any persistent observer of human social interaction will note that the vast majority of people are law-abiding and decent folk who naturally practice a common-sense, utilitarian ethics similar to what has been described. No supernatural law or commandment ordains this behavior. Instead it is the conscious and deliberate recognition that the promotion of the welfare of others is directly linked to one's own welfare. Compromise others' security, and you in effect compromise your own. Undermine their welfare and you also undermine your own. No god is necessary.  This has often been articulated under the ancient Hammurabi code credo: "Do unto others as you would have them do unto you." - which, alas, many Christian mistakenly attribute to Jesus Christ.

By contrast, religious morality is predicated on some formal codification of expected human behavior in terms of absolutist propositions, not subject to debate. The typical moral code of a religionist, whether Muslim, Pentecostal, Catholic or Jewish, isn’t subject to evolution or variation based on contingencies, or externalities. This blindness probably results from a 'control' meme that proclaims the morality as ‘god-ordained’ or revealed in some scripture or other. If ordained by a god - whether Allah, Jehovah, Yahweh or whoever, it cannot be compromised or altered no matter what.

But, as Kai Neilsson has asked in his book (Ethics Without God, Prometheus, 1992):

"Is an act good because God did it, or is it good independent of such action?"

For a genuine ethical basis, any human action must be totally independent of whether a god did it (in scriptures) or ordains it. It must be good on its own merits.

A first test, as Neilsson observes, is ethical choice predicated on a humane standard. Consider: if a human parent knows his child is trapped in a burning house, s/he will try to save it however s/he can. There is no way the human parent will simply walk out and allow 'fate' or "free will" of the child to make the decision. If the human parent has an ounce of common decency s/he must intervene.
However, god-ists generally seem quite happy to let their deity off the hook, when and where it suits their fancy. Start then with the standard deity template, say espoused by most Christians. This entity is posited as both omniscient and omnipotent (all knowing and all powerful). But when churches are destroyed by tornadoes, as occurred in Ala. in 1994, all sorts of excuses are proferred - and also "it's not our place to question the Divine". Why the hell not?

If you are going to attach supreme ("omni") attributes to its chracter, then make excuses when those attributes aren't manifested, we have every right to question not only the behavior but the putative existence.

Thus it follows, even from the most generic examples (presupposing a supernatural, omnipotent force) that human ethics trumps divine ethics on its face. If it does so, then it must also trump any and all human extensions of divine ethics. Whether in the ten commandments, canon law or wherever.
Hence, it follows that human ethics and ethical standards can exist independently of invoking any divine or religious fluff, affiliations or baggage.

Ethics without god then, is ethics elevated to its highest consistent standards without the need for baffling with bullshit.

A very good article for the basis of a godless morality:

Maybe the Nation's editors should study it carefully before they next sound- off on "ignoble" atheists!

Thursday, May 24, 2012

Can We Finally Say PSA Tests Are a Waste of Time?

The latest findings reported by the U.S. Preventive Services Task Force which had culled thousands of medical reports and analyzed them, ought to show once and for all that the yearly PSA tests most older American males go through amount to a numbers game, a waste of time, and more often than not ... a treacherous ride of pain, unresolved medical conditions and expense ....through the American Medical -Industrial-PhRmA complex. Do men really want to take this trip?

Earlier, I showed the much vaunted "PSA velocity" which many American urologists rely on to determine the need for a biopsy is also not productive or reliable, viz,

In that blog I cited research originally appearing in The Journal of the National Cancer Institute, February 24, 2011 and authored by  Dr. Andrew Vickers and Hans Lilja, who concluded that PSA velocity as a guideline would be unlikely to improve patient outcomes, adding, "we therefore recommend that organizations issuing policy statements related to PSA and prostate cancer detection remove references to PSA velocity."

Now, the U.S. Preventive Task Force, comprised of some of the finest specialists, physicians in the land, have similarly come down against regular PSA tests for healthy men. As one of the Panel chairs, Virginia A. Moyer has observed in her column in yesterday's Denver Post (p. 21A):

"Science finds that there is at best a small potential benefit from prostate cancer screening and there are substantial known harms. We need a better test and we need better options. We can do better."

Indeed. Now, to see how bad this PSA test is as a gauge let's look at some of the statistics dredged out (op. cit.)  by the task force and put them into perspective:

- Of every 1,000 men screened via the PSA only ONE will avoid a prostate cancer death in the course of 10 years (the largest study ever conducted in the U.S. found no benefit at all, zero men avoiding prostate cancer death via PSA screening)

- Of the same 1,000 screened, 2-3 will suffer a serious complication of treatment including bowel blockage or rupture, blood clot, heart attack or a stroke leaving the guy a vegetable.

- As many as 40 of the same 1,000 screened will suffer erectile dysfunction for the rest of their lives which no device, medication or operation will fix

- Up to 40 will suffer from urinary incontinence and have to wear adult diapers for the rest of their days.

- And 30-40 of the 1,000 will suffer severe complications including incontinence, or urinary -other infections merely as a result of a prostate biopsy.

Even allowing for total overlap of the subsets for erectile dysfunction and incontinence, these stats mean that for every possible screened guy who avoids prostate cancer (because of the screening) up to 83 will have suffered a debilitating complication, and arguably one life-altering in the sense of taking away life quality. Thus, reading these another way, the average guy is 83 times more likely to suffer a complication somewhere along the line than he is to benefit from the screening.  (Factor in the Task Force's finding that 80% of PSA tests yield false positives at some time, and you have major cause to be concerned that too many will be snookered into over-treatment based on some uro-guru's pronouncements).

Of course, on hearing the new guidelines (actually they were reinforced since being issued last year), the American Urological Association went ape shit. They blabbered 'Oh NO! You can't do that! This is the best test we have to prevent prostate cancer!"  And as you watched them, you could just see the big dollar signs vanishing from their eyes, because make no mistake, if most men respond to these findings in a rational sense, the urologists will no longer be multi-millionaires. No longer will $1b a year be squandered on prostate biopsies (which now cost nearly as much as colonoscopies, and further - unlike colonoscopies- cannot even ensure at the 50% level you are cancer free!)

Now, is there a test which men might consider to further calm their frayed, hyper-reactive nerves, especially if they can't tolerate the thought of any kind of cancer growing (even slowly) inside them? There is, and it's called the free PSA. What it does is measure the ratio of the free prostate specific antigen in the blood to the total or bound PSA. Here's the deal: the lower the ratio the more likely there's prostate cancer.

In general, for patients with total PSA results between 4.0 and 10.0 ng/mL, free PSA measurements may be used to improve specificity, with biopsy restricted to patients whose percent free PSA is below some cutoff (20% in the case of one ACS guideline). If the free PSA is significantly above 25%, this generally signals a benign condition called "benign prostate hypertrophy" with 90% probability, and biopsy can be eschewed.

The point is, there is a more refined test if one seeks to pursue it, but it assumes the total PSA is already over 4.0 ng/mL.

In the end, the general guidelines are if you're healthy, don't have any genetic predispositions and experience no problems there's no need to get a PSA every year. Nor do you have to become hysterical or rush for a biopsy because some urologist says so, even if the PSA level jumps. But the best option may be to ditch the numbers fetishism, period - at least until the urological gurus come up with something less ambiguous.

Can a culture that's so mesmerized by changing numbers (such as the DOW) even remotely come to that state? Who knows, but it might be worth a try at least for some of us!

What I learned While on Blog Hiatus (2)

Continuing on from the previous blog, the key issue was how to incorporate shear (φ) and velocity (v (φ,W)  parameters together with magnetic field conditions (e.g. B z =  0,  B f   =   Bo J1 (aR)/ r) into the same numerical simulation format - and to do so efficiently without having to resort to different (and possibly conflicting) simulations for shear, velocity and the  ( B z , Bf )   fields.  

A fortuitious bit of serendipity was the appearance of a paper entitled 'Efficient Algortihms for Solving Partial Differential Equations with Discontinuous Solutions' by Chi-Wang Shu, which appeared in The Notices of the American Mathematical Society (p. 615) in their May, 2012 issue.Shu gives an example of a (hyperbolic) PDE which displays attributes of the ideal sort of equation I was seeking to discretize. This was:

u_t + au_x = 0

where u = u(x,t) is a solution which depends on the spatial location, x, and time t while a is a constant (which could be the speed of wave propagation for his particular PDE, or in my case, perhaps the field line pitch, or tension).   Also the use of subscripts simplifies the writing of the partial derivatives, so that u_t, for example, is really  @u / @t where @ denotes the partial derivative symbol.

In the flare model context I had been considering, spatial location is automatically incorporated via the shear since as we saw in the (May 3rd) blog: shear is manifested via d (x) or the displacement d(x) of the footpoints (say in an arcade model). Also, it is well known (cf. E.R. Priest, Fundamentals of Cosmic Physics, Vol. 7, p. 363, 1982) that the shear can take the form d(x) = mx, where the shear gradient (m) is a montonically decreasing function, and also one can pose it in straight linear form via:

d(x) = x sinh b

where 'sinh' denotes the hyperbolic sine and b = (½ c)^½  a (kφ) cosh b, where  kφ is the dimensionless shear.  Thus, it's possible to define u(x) = x sinh b, but the problem remains for obtaining u(x,t). What 'blended' function u(x,t) might one then use? Shu provides a clue by first considering an initial condtion for his equation which is time-independent, viz.

u(x,0) = g(x)

and thence that it's easy to verify a unique solution of the original PDE is:

u(x,t) = g(x - at)

i.e. basically a shift in the initial condition with speed a. (This has a direct analogy to assorted wave equations in terms of the phase, or phase angle). In effect, one doesn't require a separate time aspect to the function u(x,t) if he's simply willing to allow shifts to occur via initial conditions at certain rates, a. So how would this translate to the shear system in an arcade model (or 2 ribbon) flare?

!     z
!     /
!  /
!/ -------------> x

One way to get around this is sketched in the diagram above, for which a 3rd dimensional shear parameter, z = mx is projected upon the xy plane (recall the context in the link from the May 3rd blog, showing a large solar active region). As we change the (dimensionless) shear through progressive numerical substitutions, the shear gradient m increases so that the dimensionless shear kφ  increases to a maximum of 1, then decreases. (As one would easily see by constructing a 3D flexible arcade model  then gradually shearing it to faithfully conform with the projections on to the x-z then x-y planes). Likewise, in doing this, one finds the line y = mx altering with m to yield evolving arcade footpoint axes (in relation to the potential or y = 0 configuration) of the arcade when in the potential or current free condition.

The final trick then is to incorporate the fields into the mix, but how to do so? One wants as a priority criterion to have any field associations, functions related at least to x, or d(x) for the shear displacement. The one proposal that seems to work is the one originally given by Priest (op. cit.) but it is limited to the normal component at the photosphere, or  ( B n ) and then:

n (x)  = x / R o   [  B f ( R o ) ]

= [x^2   +   h^2]^½   

But where to from here? In particular, how does one drag the shear velocity :

v (φ,W) = a sin (φ ) exp [1 - 2[φ ]/ W

into the simulation?

Wednesday, May 23, 2012

What I Learned While On Blog Hiatus (1)

As noted in my blog of May 3rd, I planned to undertake a 2 ½  week project in numerical simulations for a solar flare model. In that blog, I basically summarized a few of the avenues toward resolving the quantitative complexities using some form of finite difference equations. I began by targeting a differential equation given as:
DIV^2 A + d/dA {½ B(y)^2} = 0

where B(y) is the magnetic induction or magnetic component in the y direction. Historically, two problems have been defined: 1) B(y) = f(A) for whcih the functional form of the field is pre-prescribed (obviously simpler) and 2) d = d (x) or the displacement d(x) of the footpoints (say in an arch model) from the x-axis are imposed. One then follows the evolution of the field through a series of force-free equilibria.

In the ideal world, one would find that the boundaries of the model neatly blend into exterior domains and so we say there exists the possibility of continuous solutions.  Alas, such a model wasn't possible for the 2-dimensional arcade (for a two ribbon flare) that I'd originally planned.  In my particular model, the shear angle magnitude φ , was taken as a proxy for the increase in relative magnetic helicity H( r) such that:

 H (r) ~   O( φ ) = arctan (B z /Bφ  )

where the numerator and denominator denote the axial and poloidal field components respectively, each defined in terms of the relevant Bessel function. But...when one consults the appropriate Bessel functions, J0(aR) and J1(aR) one finds they must be truncated. Hence they offer discontinous boundaries, with respect to external fields, if one also intends to include the shear velocity v(φ, W). Readers can find more on Bessel functions in this earlier blog:

The boundary conditions for the arcade field, defined at the (truncated)  dimensionless radius aR = 2.4 are:  B z   =  0,   and   B f   =   Bo J1 (aR)/ r.  The choice of the boundary at aR = 2.4 is consistent with a truncated Lundqvist solution, and obviates the problem of unobserved (and unphysical) field reversals which are peculiar to Lundqvist solutions. However, it doesn't resolve the problem of meshing the shear angle with continuous velocity changes of the form:

v (φ,W) = a sin (φ ) exp [1 - 2[φ ]/ W

This inconsistency forced me into a "Hobson's choice" with the simulations: Do I pursue the discretization of PDEs yielding strict Bessel function solutions,  which at least afford some continuity, e.g. with exterior fields joining smoothly to those interior to aR = 2.4 (Dimensionally, the boundary is set equal to a radius R = 5 x 10 7  m)  or do I forego that in favor of pursuing discontinous solutions that have the capacity to introduce the critical parameter v (φ,W)?  More on this in the next instalment.