Tuesday, November 13, 2018

The Life and Works of Leonhard Euler in Context of Russian History

Leonhard Euler was undoubtedly one of the most influential mathematicians and, indeed, the greatest physicist of his era. Paul Hoffman summed up Euler’s life in this manner: “In the eighteenth century, the Swiss wizard Leonhard Euler, who fathered thirteen children, wrote eighty volumes of mathematical results, many reportedly penned in the thirty minutes between the first and second calls to dinner.” [1] While he is most noted for what is now called Euler’s equation, e iθ = cos(θ) + isin(θ), he was also “the first person to derive an equation of state for a gas from a kinetic-molecular theory. . .he invented the achromatic lens . . . he designed and built an apparatus for measuring the refractive index of a liquid[. . .] his hydrodynamics was the first field theory.” [2] In addition to that, one cannot forget that beyond being a great mathematician, Euler did revolutionary work in the field of physics. A. P. Aleksandrov, President of the Academy of Sciences of the USSR in 1983 accurately itemized Euler’s contributions. “I will merely remind you of the fact that in modern textbooks on higher mathematics and mechanics, one finds a multitude of methods, formulae, and theorems bearing the name of Euler. In that regard, perhaps, he has practically no equal.” [3]

Euler was born on 15 April 1707 near Basel, Switzerland to Paul and Marguerite
Euler. His father was a Protestant clergyman, and his mother’s family was also religious. They wished him to continue the family tradition of joining the clergy. Although a devout clergyman, his father was also deeply interested in mathematics and went to lectures taught by Jakob Bernoulli, later befriending such notable mathematicians as Jakob Hermann and Johann Bernoulli. Euler’s father also introduced his son to mathematics at an early age.

Shortly after Euler’s birth, the family moved to the village of Riehen, where his father became the pastor. He was given some education at home, including math lessons from his father, and then sent to live with his grandmother in Basel so that he could attend the school there. However, they did not offer courses in mathematics. In 1720, Euler entered the Basel University.

Once there, Euler was introduced to Johann Bernoulli. Due to Bernoulli’s schedule, he was unable to teach Euler all the time, but he gave Euler books to read, and arranged for Euler to come and ask him questions. As Euler noted, “I was given permission to visit [Johann Bernoulli] freely every Saturday afternoon and he kindly explained to me everything I could not understand.” However, Euler was loathe to waste his precious time with Bernoulli and tried to figure out how to solve most of the questions he had on his own.

In 1724, he was awarded his Masters degree, having given a speech completely in Latin comparing Newtonian and Cartesian philosophies. After graduating, Euler studied theology, just as his father expected. However, Euler continued to study mathematics with Johann Bernoulli and soon befriended the sons and nephew of his mentor, including Daniel and Nicolaus II Bernoulli. Mathematics became such an addiction that Euler soon neglected his studies in Hebrew and Greek. His father could not deny Euler something that he himself also loved, and so Euler was given permission to study solely mathematics.

In 1725, Daniel and Nicolaus II Bernoulli accepted positions in physiology and mathematics respectively at the newly founded St. Petersburg Academy. Emperor Peter I had died, and his wife Catherine I carried out the founding of the academy six months after Peter’s death. According to the historian John H. Appleby, the idea of a Russian academic society originated under the rule of Tsar Alexis. Dr. Samuel Collins, physician to the Tsar, wished to correspond with the London Royal Society. This led to meetings with Robert Boyle, who over the years was “supplied with a mass of data about the effects of cold and freezing, as well as Russian natural history.”[4]

Peter I’s later visit to England resulted in contact with the London Royal Society,
where he learned the art of seamanship from Edmund Halley. Peter I was also successful in recruiting British engineers and mathematicians for the School of Mathematics and Navigation in Moscow.

Because of the reforms that Peter I had implemented, there was a great interest
in science, and Peter I wished to form a scientific society of his own, patterned off of such models as the Royal Society of London, the Académie des Sciences in Paris, and the Berlin Academy of Sciences. The idea took a firmer hold when Peter visited Paris in 1717 and was introduced to many of the famous scientists of the time. Peter I was also elected a member hors de tout rang. In addition, Arnold van der Hulst dedicated his doctoral dissertation from Leyden University to Peter. 5 Peter’s old friend, Aleksandr Menshikov also helped aid Peter’s interested in the sciences; in 1714, Menshikov was unanimously elected a member of the Royal Society in London, and praised by Isaac Newton for “the help he had rendered to Peter....in the dissemination of excellent books and sciences.”[6]

However, one cannot discount the importance of the correspondance between Peter I and Gottfriend Wilhelm Leibniz of the Berlin Academy of Sciences. Indeed, the St.Petersburg Academy “bore remarkable similarities to Leibniz’s own Berlin academy and to his vision of a global system of academies.” [7]
Due to the lack of Russian scholars, the academy naturally wished to employ as many young Western scientists as possible. Besides the Bernoullis, the Basel mathematician Jakob Hermann, also a family friend of the Eulers, was given a position in St. Petersburg.

Before leaving, the Bernoullis promised to find Euler a position with them.
While the Bernoullis settled in St. Petersburg, Euler published his first two papers, both dealing with problems in analysis that were published in Acta eruditorum. In addition, he competed in a prize competition sponsored by the Académie des Sciences. While he did not win, his analysis on mast placement in sailing ships received an honorable mention–even though Euler did not have the advantage of being able to actually observe the sailing ships.Over a 30 year span, Euler won the prize twelve times for a variety of different entries.

In 1726, Nicolaus II Bernoulli died of appendicitis. Daniel Bernoulli succeeded his brother as chair of mathematics and recommended Euler for the now-empty position in the physiology department. Euler accepted the offer, agreeing to journey to St. Peterburg when the weather was better. In the meantime, he set about learning anatomy and physiology “in characteristically industrious fashion–albeit from a geometrical point of view.” [8] He also unsuccessfully applied for the vacant chair of physics at the University of Basel. Nicolaus Fuss, assistant and grandson to Euler, claimed in his Encomium of Euler that Euler turned down the position. [9] Ferdinand Rudio, who was chosen to
be editor of the 1911 printings of Euler’s complete works, notes that Euler never had the opportunity to turn it down, as the candidates were selected by lottery, and Euler’s name was not in the lottery. However, according to the historian Ioan James, even with the backing of Johann Bernoulli, Euler was turned down from the beginning, partly due to his age. [10]

Having being unsuccessful in Basel, Euler traveled to St. Petersburg, arriving on 17 May 1727. The country was thrown into upheavel, and resulted in Peter II becoming emperor. However, he was only twelve, and heavily influenced by his grandmother, Evdokia, the first wife of Peter I, who was heavily opposed to all of his reforms. Due to the anti-Western atmosphere, the funding for the Academy was cut, and many of the scholars there were forced to leave, such as Jakob Hermann, or take up additonal means of income. Euler himself began training to be a medic in the navy. However, things were straightened out and Euler was given a position in the mathematics department.

In 1730, Peter II died of smallpox and Anna Ioannovna was installed as ruler by Vasily Dolgoruky and Dmitry Golitsyn. They attempted to impose restrictions on her rule, but two weeks later, she tore up the document. Empress Anna, previously the Duchess of Courland, had spent enough time in Germany that she was very Western-oriented, and was considered to be “too German” by her subjects.
In 1733, Daniel Bernoulli returned to Switzerland, leaving Euler as his successor in the chair of mathematics. Having become financially secure, Euler married Katharina Gsell, the daughter of a Swiss painter who had come to St. Petersburg during Peter I’s rule. Their first son was born in 1734, and a second was born in 1740. He also purchased land on Vasilevskii Island, which was not far from the Academy. In 1738, he became blind in one eye, but even that did not stop his mathematical productivity.
While in St. Petersburg, Euler solved a variety of problems, most notable that of the Königsberg Bridge. The problem asks if it is possible to cross all seven of the bridges in Königsberg only once. Euler proved in an extremely elegant fashion that it could not be done. He also worked with the department of geography to map Russia and did foundation work combining Newtonian dynamics with analysis. Additionally, he published several papers on the calculus of variations and worked on gamma-, beta-and zeta-functions, as well as topics in infinite series, number theory, topology and introductory astronomy.

However, in 1741, the political situation took a turn for the worse. Empress Anna had died, and the throne had passed to the son of her niece, Ivan. Since he was not even a year old when he succeded to the throne, his mother, Anna Leopoldovna was installed as regent. Elizaveta, the daughter of Peter I, took control of the throne in a coup less than a year later. Her pro-Russian policies cast suspicion on many of the foreign scholars. [11]
Things were so oppressive that Euler and his family accepted an offer from Friedrich the Great. The Prussian ambassador had been courting Euler for at least a year, but Euler had asked for a larger offer before he was willing to leave. When the political situation changed, Euler’s mind also changed. By this time, Friedrich the Great had agreed to Euler’s conditions of a higher salary than what was originally offered, and so Euler made the necessary arrangements to leave for Berlin as soon as possible.

While conditions in Berlin were less than satisfactory–Friedrich the Great did not
make any provisions for Euler who had to live on credit for two years after his arrival–they were still better than being in Russia. Friedrich the Great intended for Euler to bring the Berlin Academy back to its former glory, as it had languished during the rule of Friedrich Wilhelm I. However, he did not give it the necessary funding for a few years, so in the meantime, Euler began publishing almanacs to fund the Academy and collecting famous mathematicians for it. Euler himself was still receiving a 200 rouble pension from the St. Petersburg Academy as part of an agreement that he would still send them papers to publish.

In 1746, Friedrich the Great established the French scholar Pierre de Maupertius as head of the academy. He was specifically impressed with de Maupertius’ social graces. Euler possessed no such skills and was considered plebian and contemptible by Friedrich, who only tolerated Euler because the works he published brought acclaim to the academy. Another black mark against Euler was caused by Voltaire, a great favorite of the king, clashed with Euler and often ridiculed him.

Despite these differences, Euler quite clearly preferred Prussia to Russia. When asked by the queen why he barely talked to her, Euler responded: “Madam, in the country I have just come from, one is hanged if one speaks.” Because of Friedrich’s interests, Euler also took up work in hydraulic engineering, which is appropriate since he did groundbreaking work on hydrodynamics while in St. Petersburg. He also worked with celestial mechanics, receiving yet another prize from the Académie des Sciences. On average, he published about ten papers per year, half published by the St. Petersburg Academy, the other half published by the Berlin Academy.

A debate with the mathematician d’Alembert about the logarithm of negative numbers caused Euler to both define the logarithmic function and to start work in complex number theory. Yet another debate between Euler, d’Alembert and Daniel Bernoulli, concerning the boundary conditions to solutions in mathematical physics showed the depth of Euler’s insight. D’Alembert attempted to prove that the only way to solve the system was to impose restrictive boundary conditions, which Euler debated. However, it was not until 1935 with Sergei Sobolev’s work on generalized functions that it could be proven that Euler was indeed correct. In 1755, Euler published his Differential Calculus,
which was financed by the St. Petersburg Academy, and not Berlin.


However, the political situation in Berlin took a turn for the worse. After de Maupertius’ death in 1759, the king passed over Euler, whom he distrusted, for the position of president of the Academy, and offered it to d’Alembert, who refused. However, during the Seven Years War, Euler became head in all but name. The Russian crown continued to respect Euler much more than the Prussian king. When the Russian army devastated one of Euler’s properties, he was offered a greater recompense than the damage done.

After the War, Friedrich took greater interest in the Academy and established a sort of dictatorship. Euler disliked this, and due to his poor relationship with Friedrich, combined with several offers from the St. Petersburg Academy, he left for Russia in 1766. While the king was reluctant to let him go, he had nothing positive to say about Euler’s work, or the man himself, whom he referred to as “my one eyed cyclops.”
On his way to Russia, Euler recieved an invitation from Prince Czartoryski to visit the Polish King, Stanislaw Poniatowski, a former lover of Catherine II. Since Poniatowski was an enlightened intellectual, he was much more interested in studying than ruling, one of the reasons why Catherine II had placed him on the Polish throne. Euler spent ten days visiting the Polish court, finding the king to be extremely kind and generous. Euler saw those qualities as the outward manifestation of the king’s ”spiritual and intellectual qualities” [12] and was impressed for the rest of his life.

Catherine II was delighted to have Euler back and welcomed him warmly. She paid him a much larger salary than what was agreed on and met both of Euler’s conditions, that his son Johann-Albrecht be given a postion in the Academy and that his son Christofor be given a promotion in the Russian army, following his release from the Prussian army, where Friedrich refused to promote him.

Not long after Euler had arrived in St. Petersburg, he fell ill and became completely blind. This was not enough to stop him from his beloved mathematics, however, and he continued to publish just as much as before. Among the books published was his Dioptrics, which constituted three volumes of the theory behind telescopes and microscopes. In fact, his productivity increased–in 1775, he wrote the average of one paper a week. Devastation struck again in 1771 when a fire that broke out destroyed his St. Petersburg home and almost caused his death. Fortunately, he was rescued from his burning home by Peter Grimm. In 1773, Euler’s wife, Katharina died. Since his family was very large and required a wife, he was married in 1777 to her half sister, Salome-Abigail Gsell.

In 1766, Count Kirill Razumovskij was stripped of his priveleges of the President of the St. Petersburg Academy, and the directorship was replaced by a council consisting of Euler, his son Johann-Albrecht, Semyon Kotel’nikov, Johann Lehman and Stepan Rumovskij, as well as Jakob Stählin. Euler worked on thoroughly reorganizing the Academy. The plan was for Euler to administer the affairs until a new director was named. Euler made a lot of progress thanks to the previous work of Mikhail Lomonosov who advocated giving the scholars more freedom than they had previously been granted. Later in 1766, Count Vladimir Orlov was appointed as the director of the Academy. Euler was still in charge of most of the organization and administration, until he and his son resigned in February 1774, saying that they were better off teaching in the Academy.

Orlov remained as director until December, at which point he was replaced by the poet Sergei Domashnev. Neither Orlov nor Domashnev understood nor respected science–the directorship was a reward for their participation in Catherine II’s coup. Domashnev was described by Count Sigismund Ehrenreich Redern of the Berlin Academy as ”[the director]...is against all scholars, regards the academy as useless, and believes with Rousseau that science would make the world only more evil.” 13 In 1782, Domashnev removed Kotel’nikov from his position at the academy for no reason whatsoever. His response to the protest by the rest of the academicians was silence. Euler then resignedin protest.

Upon hearing of the conflict, Catherine II investigated the affair and had Domashnev removed. On 24 January 1783, she appointed Princess Yekaterina Dashkova to be director. While Princess Dashkova protested she was not qualified, Catherine II insisted. However, Princess Dashkova wished to bide by the rules that Euler, Kotel’nikov, Lehman and Rumovsij had drawn up and waited until she had been formally elected to make any changes.

Princess Dashkova paid great respect to Euler, whom she said was “without any
doubt the greatest geometer and mathematician of his age, besides being familiar with every branch of science: his industry was such that even after he lost his sight he continued his researches and made discoveries, dictating his work to Mr. Fuss, who was married to his grand-daughter.” [14]

On Monday, 30 January 1783, Princess Dashkova was formally presented to the St. Petersburg Academy. In her Memoirs, she writes that she begged Euler to accompany her to the Academy. She showed her great regard for Euler by telling him “to sit down where he thought fit, for any place he occupied would always be the first.” [15] That would be the last time his presence graced the Academy–on 18 September 1783, Euler had a massive hemorrhage and died almost immediately. Up until the very moment of his death, he was very active intellectually. That morning, he had been working on the mechanics associated with balloon flights, and in the afternoon, he had been making calculations on the orbit of the newly discovered planet Uranus.

Euler once said he would leave the St. Petersburg Academy so much work that they would be working on it twenty years after his death. This was not the case. It took 47 years to publish everything Euler had left behind, and even then, unpublished works were still being discovered. In addition, the work he had been doing the afternoon of his death aided in the discovery of the planet Neptune.

His passing was mourned by everyone. The members of the Academy all contributed to a fund to have a marble bust of him placed in the Academy. Even today, he is noted as one of the most influential mathematicians of all times. His work has applications in every field, even fields that did not even exist during his time. The 1748 debate with d’Alembert over the boundary conditions of vibrating strings specifically demonstrates this. Sobolev’s work on generalized distributions lead to Laurent Schwart’s Theory of Distributions, which provided the formation of the Dirac delta function. In addition, Euler’s work with continued fractions led to what he called non-analytic functions, the
topic of fractal geometry. Given that almost every equation on the undergraduate level was proven or formulated by Euler, Pierre-Simon Laplace was absolutely correct to say, “Lisez Euler lisez Euler, c’est notre maı̂tre á tous.”

Bibliography
1. John H. Appleby, The Founding of St. Petersburg in the Context of the Royal
Society’s Relationship with Russia, The Royal Society, vol. 57, 2003, pp. 273-284
2. Rudolf Feuter, Commentarii mathematici Helvetici, Zürich : Orell Füssli Verlag,1929
3. Sergej Wawilow, Isaac Newton, Neues Österreich Zeitungs- und Verlagsgesellschaft m.b.H., 1948
4. Leonhard Euler; Rudolph Fueter; Adolf Krazer; Ferdinand Rudio; Paul Stäckel, Leonardi Euleri Opera omnia. Sub auspiciis Societatis Scientiarum Naturalium Helveticae edenda curaverunt F. Rudio, A. Krazer, P. Stäckel, Lipsiae et Berolini, 1911
5. Leonhard Euler, Letters of Euler to a German Princess, Bristol: Thoemmes, 1997
6. William Dunham, Euler: The master of us all, Mathematical Association of
America, 1999
7. N. N. Bogoliubov; G. K. Mikhailov; A. P. Iushkevich, Euler and Modern Science, Mathematical Association of America, 2007
8. Robert E. Bradley; Charles Edward Sandifer, Leonhard Euler: life, work, and
legacy, Amsterdam; Boston: Elsevier, 2007
9. I. M. James, Remarkable Mathematicians; from Euler to von Neumann, Washing-
ton, DC: Mathematical Association of America; Cambridge, UK; New York: Cambridge
University Press, 2002
10. Alexander Vucinich, Science in Russian Culture: A history to 1860, Stanford,
Calif., Stanford University Press, 1963
11. Michael D. Gordin, The Importation of Being Earnest: The Early St. Petersburg
Academy of Sciences, The History of Science Society, vol. 91, 2000, pp. 1-31
12. Paul Hoffman, The man who loved only numbers : the story of Paul Erdõs and the search for mathematical truth, New York: Hyperion, 1998
13. Robert E. Bradley; Lawrence A. D’Antonio; Charles Edward Sandifer, Euler at 300: An appreciation, Mathematical Association of America, 2007
14. William Dunham, The genius of Euler: Reflections on his life and work, Mathematical Association of America, 2007
15. Charles Edward Sandifer, The early mathematics of Leonhard Euler, Mathematical Association of America, 2007
16. Dieter Suisky, Euler as Physicist, Berlin: Springer, 2009
17. Lindsey Hughes, The Romanovs: Ruling Russia, 1613-1917, London; New York: Hambledon Continuum, 2008
18. E. R. Dashkova; Kyril FitzLyon; Jehanne M. Gheith; A. Woronzoff-Dashkoff,
The Memoirs of Princess Dashkova, Durham: Duke University Press, 1995

Rufus


Friday, July 22, 2016

finding my gemini MDFs!

So I had to learn IRAF and it was definitely not the most natural thing to me. But, I got the SOAR data reduced...eventually. (This view of Cerro Pachon is pretty cool!)

SOAR!
So for the Gemini data, I had to download a separate package of tools, and run them. One of the postdocs was kind enough to give me his scripts for processing GMOS data, but he was doing multiobject stuff, and I only have one. So hopefully I won't have to make too many changes. I did learn how to run my own .cl scripts.
Gemini telescope (2007 press release photo)

For running a task with a parameter file, for instance lacosmics, I need to just put two lines in:
reset lacos_spec=/path/to/cl/file/ and then
task lacos_spec=lacos_spec$lacos_spec.cl

For your own scripts with no parameters, you can just load in "task $thisprep=scriptincurrentdir.cl" and you will be able to run it!

 So for my data currently, I changed the script so that it read the file headers and separated the data based on whether it was an object, flat, or arc, and the dithered wavelength, and then runs gprepare on them. I do want to go through and remove the image files from when they were centering the object on the slit.

But after a few snags, this all seems to be working nicely, except gprepare is warning me that there are no MDFs--Mask Definition Files. Now I believe these came when I downloaded the Gemini tools, so I am hoping it is something as simple as changing the path to them. Because of the whole AstroConda/Ureka thing, I am worried that the Gemini tools just won't work, but that hasn't been an issue so far.

Thursday, July 14, 2016

Notes on "Sunspot Rotation as a Driver of Major Solar Eruptions in NOAA Active Region 12158"

Paper

Authors:
P. Vemareddy, X. Cheng, B. Ravindra


Abstract:

NOAA active region 12158 has a sigmoidal structure which develops under the influence of the magnetic non-potential fields (magnetic fields produced from the electric fields present in the coronae above active region) of  a rotating sunspot (active region).
https://solarmonitor.org/index.php?date=20140910&region=12158
Measurements are taken from HMI (Helioseismic Magnetic Imager) and AIA (Atmospheric Imaging Assembly) (aboard SDO), and show the erupting feature began in the rotating sunspot (moves at 0.5 deg/hr). Evolution of the non-potential field corresponded with the rotation. Was approximated by time series of force free equilibria. The nonlinear force-free field "NLFFF" magnetic structure of the sunspot is what caused the sigmoid structure. 


High rigidity Forbush decreases: due to CMEs or shocks? - Babu, Arun et al. arXiv:1304.5343 [astro-ph.SR]
Field lines from around the sunspot make up the body, and lines from the middle make a  flux rope structure. 

Two CMEs (coronal mass ejection) occurred in the active region during the rotation. During the first event, the coronal current concentrations were enhanced, and degraded during the second, both consistently with the photospheric net vertical current. Magnetic energy is released for both cases. 

This paper suggests that the magnetic connections of the sigmoid are driven by the slow sunspot rotation, which transforms the "highly twisted flux rope". An exceedingly critical twist in the flux rope probably leads to the loss of equilibrium and thus triggers the onset of the two eruptions.

1. Introduction:

Major solar eruptions are believed to be powered by free energy stored in the stressed magnetic fields of active regions (ARs). The fields transport magnetic energy and helicity  during the evolution of ARs by flux emergence from the sub-photosphere and shearing motions at the photosphere. 







Image credit: NASA


Sunspot rotations last long enough (days) and could be efficient mechanisms to inject helicity and energy. There has been an increase in the number and quality of observations of rotating sunspots. Numerical MHD simulations have also helped to investigate the relationship between sunspot rotation and eruptive activity (such as CMEs) by studying flux ropes. They have shown that the photospheric vortex motions can twist the core magnetic field in an active region up to a point where equilibrium can no longer be maintained and thus the twisted core field (flux rope) erupts. It will erupt as a confined flare or CME.  Recent models show the rotating sunspot as a trigger.


In 2012, Vermareddy et al showed correspondence of sunspot rotation with many non-potential parameters. 

2. Observations:

Used data from HMI on the sunspot and AIA for corresponding coronal activity.

3. Results: 

Vector magnetic fields from HMI show a main sunspot with positive polarity surrounded by negative polarity. The geometry of the magnetic loops has a reverse S-sigmoid shape. (Fig 1. middle column) 
 
Vermareddy et al Figure 1.



In Fig 1 col 1, the corona sigmoid region (composite image from AIA) is overlaid with magnetic contours that show that the sigmoid has roots in the rotating sunspot. The contours are used to identify the photospheric connections. The rectangular region shows "the region of rotating sunspot having roots of a sigmoid". Col 2 is the vector magnetic field of the rotating sunspot.

They used DAVE4VM to derive the velocity field of the flux motions (3rd column of fig 1). 
Vermareddy et al Figure 2: sunspot rotation. Dashed yellow lines show movement of prominent penumbral features.


The sunspot rotation was measured by watching the change of the penumbral (edge) features as the sunspot rotated around the umbral (dark) center. 


Vermareddy et al figure 4. Top row: NLFFF model, lower row: observations.
Magnetic field lines from the edge of the sunspot make up the body of the sigmoid, interior lines overlay the sigmoid. NLFFF model is close but failrs to reproduce some of the twisted lines.

As the sunspot rotates anti-clockwise, the field lines tend to retain their connectivity and appear as swirled in a clockwise direction. Static modelling cannot capture everything, but eruptions can be approximated by flux rope current channels.
Vermareddy et al figure 5
Figure 5 shows model  (col 1) vs AIA extrapolated lines (col 2), at different epochs. Column 3 shows  integrated maps of current density to find buildup of strong current concentrations. Column 4 shows an AIA image overlaid by "quashing factor" contours. 



Summary and Discussions:


A flux rope was observed during the first eruption.  The first eruption was partial, with the flare slowly reconnection and a small CME  being observed.  Consistent with the photospheric measurement of net vertical current during pre-to-post eruption, an increased coronal current concentration is being observed across the sigmoid as a fact of twisting by sunspot rotation. Flux rope is also observed during the second CME, analysis results suggest that the magnetic connection of the sigmoid are drive by slow motion of sunspot rotation, which developed to a highly twisted flux rope structure.


 The two eruptions that happened were probably triggered by a critical twist in the flux rope that caused a loss of equilibrium.The NLFFF did not completely model all features of the eruption caused by the rotating sunspot and data drive MHD models would help explain better.

Boxcar smoothing

I needed to smooth some spectroscopic data yesterday and came across a neat tutorial on using AstroPy to do it by Joseph Long. It was really delightful how quickly I was able to do it! If I have more time or have to do it again in the future, it would be interesting to see how changing the box width (I left it at 11) changes the smoothness. But my data turned out beautifully!

Tuesday, July 1, 2014

Dewdrop

“When we contemplate the whole globe as one great dewdrop, striped and dotted with continents and islands, flying through space with other stars all singing and shining together as one, the whole universe appears as an infinite storm of beauty.”

John Muir

Sunday, March 30, 2014

Boltzmann

According to Boltzmann, the question about the existence of the external
world, or matter, must be seen in the light of another problem: “does the
answer of this question complicate or simplify our image of the world
(weltbild)?” 3
 Boltzmann seems to feel necessary to avoid useless discussions, such as those frequently promoted by philosophers. Even though he recognized that there were no definitive proofs either in favor or against the existence of matter, at least at his epoch, he considered that the belief in either position to be ideology. Although he did not define what he meant by ideology, it seems correct to state that for him this word had a negative meaning. In any case, both idealism and realism are, in the end, ideologies. Another important example, certainly of negative connotation and more important than the previous one, about what seems to be Boltzmann’s viewpoint about ideology comes from solipsism. Boltzmann had a true horror of idealism, referring to it as the major madness ever created by the human mind, since idealism denies the existence of the external material world.

(http://cds.cern.ch/record/1013890/files/0701308.pdf)