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# [.net] .NET Direct Disk Access

This topic is 3727 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Does .NET provide any APIs for direct disk access? For example, writing raw sectors onto a floppy disk? I kind of doubt that it allows for this kind of low-level access, but I thought I would check. I couldn't find anything in MSDN.

##### Share on other sites
Not likely. You'll probably be PInvoking to Win32 -- or even raw NT syscalls -- for this one.

Dim fs As System.IO.FileStream = New system.IO.FileStream("\\.\PhysicalDriveN",IO.FileMode.Open,IO.FileAccess.ReadWrite)Dim bw As New System.IO.BinaryWriter(fs)' Do work herebw.Flush()bw.Close()fs.Close()


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# Macos – Easiest way to create a new text file in a Finder window on OSX

findermacos

OK, so if I'm browsing directories in OS X Finder, what's the easiest way to create a new text file?

Right now I have to either open TextEdit, click around until I get to the same directory I'm in, or I have to open a terminal window, cd to the directory, and touch blahblah.txt. I'm spoiled by the right-click menu in Windows.

tell application "Finder" to make new file at (the target of the front window) as alias

format: plain


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# Max height of a concrete column

1. May 9, 2016

### Quantum Singularity

1. The problem statement, all variables and given/known data
For a concrete column of constant cross sectional area, what is the maximum possible height if the compressible strength is 2.0 x 107 N/m2? The density of concrete is 2.3 x 103 kg/m3.
2. Relevant equations
$$\frac{F}{A}$$
3. The attempt at a solution
I am not really sure what I am doing wrong, or what I have to do differently, but so far I have tried a few different things.
First I tried setting the force equal to 2*102, and trying to solve for height:
$$\frac{2*10^7}{2.3*10^3*9.8}\approx890$$
This was incorrect however. From there, I tried adding a π to the denominator, but that didn't work. I then tried taking the square root because I realized the r term was squared. After that I realized the r term doesn't even really have a place in the equation because I am looking for height, not radius. How do I correctly approach the problem? I honestly have no clue what I am doing here.

2. May 9, 2016

3. May 9, 2016

### SteamKing

Staff Emeritus
The first thing is to understand what the numbers mean that you are given. In your attempted calculation above, you should always do a check of the units in the result to see if these agree with the answer you are supposed to obtain.

The maximum compressive stress of the concrete is 2.0 × 107 N/m2, which you would presumably obtain from the equation σ = F / A.

It is given that the column is uniform, so this suggests that A is a constant.

What other quantity is needed to give the stress in the column?

Given the density of the concrete (2.3 × 103 kg/m3), how would you determine the maximum stress in the column? Where would this stress be located?

4. May 9, 2016

### Nidum

edit : removed redundant post

5. May 9, 2016

### Staff: Mentor

The cross sectional areas cancel out. The compressive stress on the bottom is just the hydrostatic relation $\rho g h$.

6. May 9, 2016

### Quantum Singularity

I would think that the stress would be located in the center of the column. From the equations in my book, I only see where force and area are the quantities shown. The equation it gives me for force near the beginning of the chapter that this is reviewing equates it to length, a delta l, and a young's modulus number, which I don't think helps me either.

This is a review for my final, so I am able to see the answers, and it shows the answer as being 89m, instead of the 890m that I got, unless I am just missing something on units somewhere. It is really annoying seeing the error like that with it being a factor of 10 off.

7. May 9, 2016

### SteamKing

Staff Emeritus
This column is presumably standing vertically, as most columns are wont to do.

Why would you think that the stress in a vertical column would occur in the middle? Draw a free body diagram of a vertical column to check.

You don't need to know Young's modulus to solve this problem.

You can always check the book answer to see if it matches the information given in the problem statement. Answers in the book have been known to be wrong.

8. May 9, 2016

### Quantum Singularity

That is what I am thinking might be the case, but that would mean my professor is wrong because it is his final exam review. As for the free body diagram, I have decided to abandon the problem and the rest of the review for now because the exam is tomorrow and this professor hasn't cared enough to actually teach me anything of value. I have some other homework I need to do before the final anyways, and because the final curves and everyone else in the class has the same problems as me, the stuff I am having problems with shouldn't hurt me too bad. Thanks for the help though, hopefully next semester I can get someone who actually wants to teach physics.


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# Switch debouching using interrupt

#### jab99407

##### Member
Hello

I want to toggle LED by Switch Button using timer interrupt. I want to understand how timer interrupt use for Switch debouching

#### rjenkinsgb

##### Well-Known Member
One way is to use a byte as a counter.

In the interrupt routine:
If the switch is pressed, count up if the counter is less than a certain value.
If the switch is released, count down if it's above zero.

When the counter reaches the maximum value, consider the switch pressed. When it reaches zero, consider it released (setting or clearing a bit).

Use another bit as an "image" of the debounced switch signal; if the switch pressed is on and the image is off, it's a new press.
Increment another counter.

Either way, then copy the debounced input to the image.

The low bit of the second counter is the "toggle" bit you can use to control your LED.

There are many other ways, that's just the first I thought of.

#### jab99407

##### Member
One way is to use a byte as a counter.

In the interrupt routine:
If the switch is pressed, count up if the counter is less than a certain value.
If the switch is released, count down if it's above zero.

When the counter reaches the maximum value, consider the switch pressed. When it reaches zero, consider it released (setting or clearing a bit).
Can you help me with pseudo-code

I have written one

Code:
void main (void)
{

while (1)

{

}

}

// interrupt for 1 ms
void interrupt(void)
{
if(FlagSet)
{
if (switch === 1) //If the switch is pressed, count up

count++;

if (switch === 0) //If the switch is released, count down

count--;

ClearTFlag
}
}

#### Pommie

##### Well-Known Member
I use an interrupt to count mS and check keys every 20mS. Works perfectly.

Mike.

#### rjenkinsgb

##### Well-Known Member
Can you help me with pseudo-code
OK, your code extended to match my idea above.

Code:
void main (void) {
while (1) { }
}

// interrupt for 1 ms

void interrupt(void) {
if(FlagSet) {
if ( switch == 1 && count < 10 ) //If the switch is pressed, count up
count++;

else if ( switch == 0 && count > 0 ) //If the switch is released, count down
count--;

if ( count == 10 ) {
switchstate = true;

if (switchimage == false) {
state++;
}
else if (count == 0 )
switchstate = false;

switchimage = switchstate;

output = state & 0x01;

ClearTFlag
}
}

#### rjenkinsgb

##### Well-Known Member
You could also reset the counter instantly if the input was off & only verify the on state.
It's relatively complex, but allows for a programmable debounce time and consistent response time.

If input response is not critical and you want to sample at a slower rate, so more than any possible contact bounce duration, you can just compare the present state to the previous state and take it as valid if they are equal.

(Then copy the present state to the previous state store, for the next interrupt).

#### Ian Rogers

##### User Extraordinaire
Forum Supporter
Switch de-bouncing is overthought.. If its a high speed switching pulse, then I use a state machine.. But if it's your finger operating the switch.. well delay for 250mS as your input cannot be fast..

I have a keypad... I wait for a press.. Then delay 150mS.. Then beep a speaker for 150mS.. Then I know to let go of the button.. This way I get a decent key repeat..

If it is indeed a high speed mechanical switch they reckon 20mS but it will depend on your particular application..

One application I have is photosensor input from lifting forks on a fork truck... I wait for the switch.. toggle internal buffer, then wait for it to clear... then toggle internal buffer this way I can deduce state very similar to quad input.. Worked well for me for years..


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# All Questions

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# The making of a LaTeX pre-processor with Haskell - Part II

16 February 2015

In the previous part, the progam could parse text for emphasized and bold characters. So there’s some functionality, except that it doesn’t do anything useful like produce output. In this part, I’ll implement parsing links Markdown stlye (this is really more of an implementation of Markdown than anything else at the moment), and then turn the parsed text into something useful!

To start off with, I removed the ability for bold emphasized text. This is largely because there’s no plan on how to deal with embedded styles, so I’d rather not start now. Implementation of link parsing exists in the link function, which is very similiar to the other parsers, except it produces two strings. Suprisingly easy to put together in this case, and illustrates the parsing process a bit more clearly. Here is the resulting code:

So not a whole lot changed. without too much effort its resonably easy follow the parser from bodyText.

The next thing to do is make the parser return LaTeXified text. This turned out to be more simple than I thought, though it helps that all I am doing it returning strings. All that was required is to wrap the content in the return statements with LaTeX commands, and altering the main function simply concatanate the resulting parsed text:

Running it with input.htex as This is not in italics. *But this is.* **This is bold.** This is not bold. (Description for a link)[link]. This is not in bold italics. results in

This is not in italics. \emph{But this is.} \textbf{This is bold.} This is not bold. \href{link}{Description for a link}. This is not in bold italics.

Easy! It’s not quite right, since you can’t just run LaTeX on it on the output, but that requires a bit more thinking to manage package handling and other preamble bits.

### Where to?

At this point, I could continue and create a fully fledged pre-preprocessor, but would this satisfy a true need for it. As I said in the previous part, LaTeX syntax is somewhat verbose for a lot of uses. What I can see my pre-processor doing is allowing users to only need content to create pdfs, with some customization via something like a YAML header (like Jekyll), allowing for a bit of a “hands off” experience. Pandoc already allows for the creation of LaTeX files from Markdown, so what further use would a slightly different Markdown derivative be?

Templates are another possible extension, but this functionality is already available in Pandoc, and can be implemented fairly easily with Python using Jinja. One problem with templates is that with the seperation of content and design, the content must be written without regard for where it is in the page. This reduces to having to edit a .tex file anyway.

This all applies to normal text, not math notation since there’s no real alternative markup. Which is real shame since latex is over a bit too verbose what you need it for (especially if you’re writing any calculus). To suit the needs of ordinary text, in my experience with helping create my partners masters thesis in LyX, all that’s needed it a good framework to handle bibliographies and references.

So with all of the above, I’m going leave this project as is. On the plus side, what if you could write math in Haskell? Say, if you wanted to typeset

as LaTeX? This doesn’t look too diffucult, and could produce the output:

Looks fairly trivial to do. How about some calculus? How would you represent

in Haskell? This example is a bit complicated complicated math wise, since we don’t know what \theta is as a function, and \lambda may not be invertable, so rearraging is not so easy. In addition, both side of the equations have functions applied to \theta. But luckely, we don’t care about the math, but the typesettings instead! Inside of a LaTeX (or even html file), one could have:

Where the type definitions are:

Then a parser could use type introspection (for variable names/operations) alongside evaluating equationOne, which maps names to LaTeX commands contained within a text file.

In this case, the Haskell version is a bit longer, and it’s readability compared to the LaTeX version is debatable. But one thing it does allow you to do is reuse functions quickly (without using those bloody backslashes everywhere!). For instance, if say you wanted to rewrite the above to a system of differential equations, all you would have to do is write

One other way that may work is to take working mathematical functions and rely heavily on type introspection to get the meta-data. But in the case of the above differential equation, theta is unknown and may not have a closed form. So you would need some method of saying theta is a function that explicity depends on x, y, and z. Using this method opens up support for incorperating other languages, but I’m not sure there’d be a reliable way of implementing it considering considering the diverse ranges of languages used in the computing world. I’ll stick to the former method and see where it takes me.


text:
## Casting out 9s

Math help on Congruences, Modulo, Fermat's Theorem, Fermat's Last Theorem (FLT), Euler's Theorem, Euler Totient Function, Divisors, Multiples, Prime Numbers, Prime Number Theorem, Distribution of Prime Numbers, Dzeta Function, Riemann Hypothesis, Algebraic Number Theory, Analytic Number Theory on My Math Forum.
Math problems in Number Theory

### Casting out 9s

I want to prove whether or not 65,547,012/26,436 = 2479 + (12,168/26,436) using casting out of 9s.

I know how casting out 9s works with multiplication. However, I do not know how to apply the concept to division with a remainder/decimals. Please help me get started. Thanks!
SlamDunk
Newcomer

Posts: 17
Joined: Mon Apr 16, 2012 2:22 pm

### Re: Casting out 9s

The dividend excess is 3. The final excess from the remaining values is $$$3\times 4$$+0=3$. The values check.
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
Global Moderator

Posts: 11250
Joined: Thu Jul 01, 2010 3:14 am
Location: St. Augustine, FL., U.S.A.'s oldest city

### Re: Casting out 9s

Ok I see that the dividend is 6+5+5+4+7+0+1+2 has a remainder of 3 when divided by 9. I also see that 2+6+4+3+6 has a remainder of 3 and that 2+4+7+9 has a remainder of 4 and that you multiply both of those.

The fraction is what is getting me. How do you know it has remainder of 0?
SlamDunk
Newcomer

Posts: 17
Joined: Mon Apr 16, 2012 2:22 pm

### Re: Casting out 9s

12,168 is divisible by 9 and 26,436 is divisible by 3 but not 9, so you can at least conclude that the quotient is divisible by 3.
Pari/GP: this is the program I probably mentioned in my post. Windows users can get it at http://pari.math.u-bordeaux.fr/pub/pari ... -2-6-1.exe

CRGreathouse
Global Moderator

Posts: 12072
Joined: Sat Nov 25, 2006 9:52 am
Location: UTC -5

### Re: Casting out 9s

65,547,012 = 2479·26,436 + 12,168

then use the method:

3 = 4·3 + 0 = 3
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
Global Moderator

Posts: 11250
Joined: Thu Jul 01, 2010 3:14 am
Location: St. Augustine, FL., U.S.A.'s oldest city

### Re: Casting out 9s

Thanks Mark. That is very clever and makes perfect sense.
SlamDunk
Newcomer

Posts: 17
Joined: Mon Apr 16, 2012 2:22 pm

### Re: Casting out 9s

I will be honest and admit I had never heard of this method before and had to look it up.
Living in the pools, They soon forget about the sea...— Rush, "Natural Science" (1980)

MarkFL
Global Moderator

Posts: 11250
Joined: Thu Jul 01, 2010 3:14 am
Location: St. Augustine, FL., U.S.A.'s oldest city


text:
# Is it a bad idea to use PGP encryption for structured/predictable data?

I'm working on an app and need to encrypt some structured data. The data will be turned into a string form (JSON) before getting encrypted.

The data format I'm using will always start with a { character and end with a } character. Does this make encryption less secure? Are there any methods for more securely encrypting a JSON string?

• PGP should work just fine. It is meant to take any sort of data as input and securely encrypt it. – mikeazo May 2 '15 at 1:24


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How To Develop A Home loan Calculator For Free in Microsoft Excel

One of the truly awesome components elements of Microsoft Excel is the works Microsoft has produced for you to utilize. This implies that instead compared to need to establish a work from the ground up you could utilize pre-built ones to do a wide variety of jobs such as Structure your very own Home loan Calculator. The Home loan Calculator or PMT work is simply among numerous Monetary Works offered.

Okay, so ways to develop a home loan calculator…

The initially point we need to do is to begin by establishing a couple of fundamental headings. So allows start by beginning a brand-new workbook and clicking in the initially cell A1. Participate in cell deal with A1 the going - Regular month-to-month Lending Payments. Following off, participate in cell deal with A2 - Quantity of Lending, cell deal with A3 - Rate of passion Price, cell deal with A4 - Size of Lending and after that in A6 - Regular month-to-month Payment.

In instance home loan calculator, we'll take the Lending Quantity, Rate of passion Price and Size of Lending and determine your Regular month-to-month Payment. Alright so in the matching area B1 go into the worth of $200,000 and make certain you style the area as a money. In cell B2 go into a worth of 9.25% and style the area as a portion and after that lastly go into in a worth for the Size of the Lending as 25. The worth you participate in the Size of the Lending area remains in years. Currently its time to produce the formula that will do your computation for the Regular month-to-month Payment. The work we'll utilize for this computation is called the PMT work. The PMT work constantly returns a unfavorable number so among the points we'll have to do is to transform it right into a favorable number, however a bit on that particular later on. There are 3 disagreements we'll utilize for this formula and they are - = PMT(Monthly Rate of passion Price, Variety of Resettlements, Quantity Borrowed) So to exercise the Regular month-to-month Rate of passion Price we just take the worth in B3 and split it by 12 - B3/12. The PMT work deals with the fundamental of the variety of resettlements you're mosting likely to make, so if we are mosting likely to make regular month-to-month resettlements on our home loan we just take the variety of years in cell B4 and increase it by 12 - B4 *12. This implies that to determine the Regular month-to-month Payment for our home loan we have to go into the complying with formula - = PMT(B3/12, B4*12, B2) Currently as I stated previously, the PMT work constantly returns a unfavorable worth, so to transform this right into a favorable worth we just kind the PMT work with the Outright Work encapsulating it as revealed listed below - = ABS(PMT(B3/12,B4*12,B2)) Just kind the formula over right into the cell B6 and push the go into essential. You should currently style the cell deal with B6 as a money and you could do that by just pushing the Buck Sign on the Format Toolbar. As quickly as you go into the formula and push go into you ought to obtain an outcome of$1712.76. If you don't obtain this response, just return and make certain that you have went into the formula properly.

The awesome component regarding this Home loan Calculator is that you could return and alter any type of among the worths in B2, B3 and B4 which are the Lending Quantity, Rate of passion Price and Size of Lending to exercise what your regular month-to-month home loan payments will be.

The awesome component regarding this easy device is that it informs you truly rapidly whether obtaining huge quantities from the financial institution deserves it and whether you could truly pay for that home loan. Why not inspect out what your payments will be if your rate of passion price increased by 2 or 3%, it could be truly fascinating to see the effect on your budget plan.

Easy devices such as this could conserve you countless bucks and could likewise assistance you see what modifications rate of interest will have by yourself budget plan. It's definitely beneficial structure on your own a Budgeting Spreadsheet and the home loan calculator to exercise simply what you truly could pay for particularly in these uncertain times.


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# Tritium & Deuterium. Coil Torque

#### Tritium and Deuterium

Please find  energy that is necessary to remove a neutron of tritium ($^3H$) to give a deuterium atom ($^2H$) and a neutron.

The rest energy for: neutron = 939.565 MeV, proton = 938.272 MeV, deuterium = 1875.613 MeV

$3H +energy = 2H +1n$

atomic masses are (all are taken from wiki)

$M(3H) =3.01604 uam =2817.143 MeV$ for tritium

$M(2H) = 2.0141 uam = 1881.27 MeV$   for deuterium

$M(1n) = 1.00866 uam = 942.142 MeV$

because

$1 uam =1.6605*10^-27 kg =1.6605*10^-27*(3*10^8)^2 / 1.6*10^-19 =934.053 MeV$

$(E =m*c^2)$

$Energy = 1881.27 +942.142 -2817.143 = 6.269 MeV$

#### Coil Torque

A planar solenoid with 4 turns and a surface of $4.75*10^{-3} m^2$ has a current of $i=1.58 A$ in the xz plane as shown.  This coil is situated in an external magnetic field $B = (1.86i – 3.79j – 3.36k) mT$

(a) For this system please find the magnetic potential energy.

b) Please find the magnetic torque of magnetic field $B$ on the solenoid. What is the magnetic potential energy of the coil-magnetic field system?

The magnetic energy of the system is just

$U = -m*B$

where m is the magnetic moment vector of the coil, B is the external magnetic field and * is the dot (scalar) product between vectors.

For a single loop of current I the magnetic moment is given by the equation:

(http://en.wikipedia.org/wiki/Magnetic_moment#Current_loop_representation)

$m =I*S$

Therefore for the entire solenoid:

$m =N*I*S =4*1.58*4.75*10^{-3} =30.02*10^{-3} =3*10^{-2} A*m^2$

The direction of $m$ is perpendicular to the surface of the loop:

$m = 0.03*j A*m^2$

Now the magnetic energy is just

$U = -(0.03*j) *(1.86*i -3.79*j -3.36*k)*10^{-3} =0.03*3.79*10^{-3} =0.1137*10^{-3} J$

b)

The magnetic torque is defined as

(http://en.wikipedia.org/wiki/Magnetic_moment#Definition)

$T = m x B$

$T =\begin{vmatrix} i& j& k&\\ 0& 0.03& 0& *10^{-3}\\1.86& -3.79& -3.36\end{vmatrix}=$
$=(-3.36*0.03*i -1.86*0.03*k)*10^{-3} = – (0.1008*i +0.0558*k)*10^{-3}; N*m$


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# Quantum Computing - Relationship between Hamiltonian and Unitary model

When developing algorithms in quantum computing, I've noticed that there are two primary models in which this is done. Some algorithms - such as for the Hamiltonian NAND tree problem (Farhi, Goldstone, Guttman) - work by designing a Hamiltonian and some initial state, and then letting the system evolve according to the Schrödinger equation for some time $t$ before performing a measurement.

Other algorithms - such as Shor's Algorithm for factoring - work by designing a sequence of Unitary transformations (analogous to gates) and applying these transformations one at a time to some initial state before performing a measurement.

My question is, as a novice in quantum computing, what is the relationship between the Hamiltonian model and the Unitary transformation model? Some algorithms, like for the NAND tree problem, have since been adapted to work with a sequence of Unitary transformations (Childs, Cleve, Jordan, Yonge-Mallo). Can every algorithm in one model be transformed into a corresponding algorithm in the other? For example, given a sequence of Unitary transformations to solve a particular problem, is it possible to design a Hamiltonian and solve the problem in that model instead? What about the other direction? If so, what is the relationship between the time in which the system must evolve and the number of unitary transformations (gates) required to solve the problem?

I have found several other problems for which this seems to be the case, but no clear cut argument or proof that would indicate that this is always possible or even true. Perhaps it's because I don't know what this problem is called, so I am unsure what to search for.

• Every polynomial-time algorithm in one corresponds to a polynomial-time algorithm in the other, but it's not clear the degree of the polynomial will be the same. Hopefully somebody will come up with references. These results were proved in the early days of quantum computation, and there should be better proofs of these theorems now. – Peter Shor Jul 6 '14 at 1:25
• does this relate to what is known as the Heisenberg vs Schroedinger picture of QM which relates to how the operators are defined? also if it isnt covered in Nielsen & Chuang then that would seem to be a major oversight! the NAND tree paper uses "hamiltonian oracles" which seem to be introduced by Farhi/Gutmann 1998. here is a nice survey article on Hamiltonian oracles by Mochon 2007 – vzn Jul 6 '14 at 15:58
• The book link you provided is actually the textbook we used in my undergraduate course in Quantum Information Processing. The book is really geared towards the Unitary approach (within the context of oracles as well), but not so much in the context of Hamiltonians. My undergrad course was focused from a cs perspective and not a physics perspective, which is why I am most familiar with the Unitary model. – user340082710 Jul 8 '14 at 15:47
• The paper you provided as well is a good reference in general, but I don't believe it addresses my question either. Lastly, I've taken a look at the Heisenberg vs Schroedinger picture of QM, and it does look related, but I believe my question is different (though I could be wrong - It was a hard to follow the Wikipedia entries). – user340082710 Jul 8 '14 at 15:49
• I think there are different ways to interpret your question and instead of answering all interpretations, I'd like to ask you the following: Could you be more precise about the version of the Hamiltonian model you have in mind? What is the measure of complexity in this model? (i.e., what is it that counts how difficult it is to solve a problem in the Hamiltonian model?) How is the input to the problem given? Is it given explicitly or do you have to query the input via an oracle? – Robin Kothari Jul 10 '14 at 0:27


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# zbMATH — the first resource for mathematics

Quasirecognition by prime graph of $$^2D_p(3)$$ where $$p=2^n+1\geq 5$$ is a prime. (English) Zbl 1172.20015
Summary: As the main result, we show that if $$G$$ is a finite group such that $$\Gamma(G) =\Gamma(^2D_p(3))$$, where $$p=2^n+1$$, ($$n\geq 2$$) is a prime number, then $$G$$ has a unique non-Abelian composition factor isomorphic to $$^2D_p(3)$$. We also show that if $$G$$ is a finite group satisfying $$|G|=|^2D_p(3)|$$ and $$\Gamma(G)=\Gamma(^2D_p(3))$$, then $$G\cong{^2D_p(3)}$$. As a consequence of our result we give a new proof for a conjecture of W.-J. Shi and J.-X. Bi [Lect. Notes Math. 1456, 171-180 (1990; Zbl 0718.20009)] for $$^2D_p(3)$$. Applications of this result to the problem of recognition of finite simple groups by the set of element orders are also considered.

##### MSC:
 20D06 Simple groups: alternating groups and groups of Lie type 20D60 Arithmetic and combinatorial problems involving abstract finite groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
Zbl 0718.20009
Full Text:


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# How to explain the products of the nucleophilic aromatic substitution of 1-chloro-3-methylbenzene with NaOH?

I guess this reaction is a nucleophilic aromatic substitution where $\ce{ONa-}$ is the nucleophile $\ce{Cl-}$ the leaving group, is that right?

Methyl group is a ortho-, para- director. So why should I have a meta product here? Don't we need an electron withdrawing group ($\ce{NO2}$ , carbonyl) in a NAS-reaction which is at ortho or para positions to the leaving group?

I am a bit confused about the shown picture.

• Could be because of ipso substitution. This link might help. – Avyansh Katiyar Feb 14 '18 at 15:18
• thank you for the link. the ipso subst leaving group seems to be at ortho or para positions as ı mentioned. but in the reaction ı provided it is at meta. that is what is confusing me – Taylan Feb 14 '18 at 15:24


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In this tutorial we will see how to run a relatively big system in the Hopper supercomputer (at NERSC in California), and how to measure its performance. There are a few key things you need to know about how to interact with the machine. To log in, run ssh trainX@hopper.nersc.gov in your terminal, substituting the actual name of your training account. Be aware that since this machine is far away, you should not try running X-Windows programs! You submit jobs by the qsub command, ‘‘e.g.’’ qsub job.scr, which will put them in the queue for execution when there is free space. You can see what jobs you currently have in the queue by executing qstat -u $USER, so you can see when your job finishes. A status code will be shown: Q = waiting in the queue, R = running, C = complete. You can cancel a job by qdel + the job number, as written by qstat. The job script (‘‘e.g.’’ job.scr) specifies parameters to the PBS/Torque queuing system about how many cores to use, what commands to run, etc. # Running the ground state We will need the input file, job submission script, coordinates file, and a pseudopotential for Mg (for the other elements we will use the default ones that come with Octopus). The pseudopotential is available in the Octopus directory at jube/input/Mg.fhi. You can copy the files on hopper directly from /global/homes/d/dstrubbe/octopus_tutorial to your scratch directory as follows:  cd$SCRATCH
cp -r /global/homes/d/dstrubbe/octopus_tutorial .

The input file (inp ):

CalculationMode = gs

#### System size and parameters

Spacing = 0.20

Units = ev_angstrom
XYZCoordinates = "xyz"
%Species
"Mg" | 24.305 | spec_ps_fhi | 12 | 3 | 2
%
ExcessCharge = 0

XCFunctional = gga_x_pbe + gga_c_pbe

ExtraStates = 18
Eigensolver = rmmdiis
LCAOAlternative = yes
SmearingFunction = fermi_dirac
Smearing = 0.1
Mixing = 0.15

#### GS
MaximumIter = 300
EigensolverTolerance = 1e-8
ConvRelDens = 5e-8

#### Saving memory

SymmetriesCompute = no
PartitionPrint = no
MeshPartitionPackage = metis

ExperimentalFeatures = yes

Submission script job.scr with 24 CPU processor cores:

 #!/bin/bash
#PBS -q regular
#PBS -l mppwidth=24
#PBS -l walltime=0:30:00
#PBS -N testing_chl
#PBS -V

cd $PBS_O_WORKDIR aprun -n 24 octopus_mpi &> output_gs_24  To run:  qsub job.scr  Coordinates file xyz . Take a look at it (on your local machine) with visualization software such as xcrysden to see what kind of molecule we are dealing with. Expand: xyz file When your job finishes, take a look at the output to see what happened and make sure it completed successfully. Then we can do time-propagation. # Running the time-dependent profiling We change the input file accordingly. Change the CalculationMode from gs to td, and add the following lines:  ##### TD T = 18 dt = 0.003 TDPropagator = aetrs TDTimeStep = dt # Profiling ProfilingMode = prof_memory TDMaxSteps = 30 FromScratch = yes  Now it is the time to do exactly the same TD run, changing the number of CPU processor cores. You have to change the XXX to powers of 2, 2^x. Start at 64 (which will be fastest) and divide by 2, in steps down to 4. (Running on 2 or 1 cores may not work.)  #!/bin/bash #PBS -q regular #PBS -l mppwidth=XXX #PBS -l advres=benasque.348 #PBS -l walltime=0:30:00 #PBS -N testing_chl #PBS -V module load octopus/4.1.2 cd$PBS_O_WORKDIR
aprun -n XXX octopus_mpi &> output_td_XXX

Different profiling.000xxx folders will be created with each execution. We need to process them, mainly to be able to plot the information they contain. For that we can run the next script. It runs fine without any argument, but we can have more control in the files that it is going to process by using the following arguments: “analyze.sh 64 000004 2”. The first argument is the biggest number of CPU processor cores that is going to be considered. The second optional argument is the number of the reference file that is going to be used. The third one is the starting number, i.e. the smallest number of CPU cores to consider.

 #!/bin/bash

## Copyright (C) 2012,2014 J. Alberdi-Rodriguez
##
## This program is free software; you can redistribute it and/or modify
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
##
## analyze.sh

# Define the biggest number of processors.
if [ -z "$1" ]; then last_proc=64 else last_proc=$1
fi

# Define the reference file/folder
if [ -z "$2" ]; then ref=000004 else ref=$2
fi

# Define the starting value
if [ -z "$3" ]; then start=1 else start=$3
fi

#Initialise the output file
echo "-  " > profile_$start for ((num=$start;num<=$last_proc;num*=2)); do echo$num >> profile_$start done rm -f tmp1 # Analyze all profiling.XXXXXX/time.000000 to get the time per subroutine count=0 for function_name in$(less profiling.$ref/time.000000 | awk '{print$1}')
do
if [ $count -lt 4 ]; then count=$((count + 1))
else
echo $function_name >> tmp1 -iterate over power of two profilings for ((num=$start;num<=$last_proc;num*=2)); do folder=printf 'profiling.%06d\n'$num
x=$(less$folder/time.000000 | grep "^$function_name " | awk '{print$3}' )
zero=_"$x"_ if [ "$zero" != "__" ]; then
echo $x >> tmp1 else echo "0" >> tmp1 fi done paste profile_$start tmp1 > tmp2
rm tmp1
cp tmp2 profile_$start fi done echo "The result is in the \"profile_$start\" file"

At this point we should run “analyze.sh 64 000004 2”. Thus, we will create files named “profile_2”. You can take a look at the following columns in the profiling data:

• TIME_STEP; the iteration time. It has a good scaling.
• COMPLETE_DATASET; the whole time of the execution. In general it decreases, it is more obvious in a real execution, where the initialization time is the same and execution one is bigger.
• SYSTEM_INIT; initialization time. We were able to stop the increasing time, and now is almost constant independently of the number of processes.
• POISSON_SOLVER; execution time for the Poisson. It is somehow constant in this case, but now with the other solvers and domain parallelization.
• RESTART_WRITE; time for writing the restart files. It depends much in the system status, more than in the number of running processes. Could be heavily decreased if it is written to the local drive.

Now we can plot it using the following script:

 #!/bin/bash

## Copyright (C) 2014 J. Alberdi-Rodriguez
##
## This program is free software; you can redistribute it and/or modify
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
##
## plot_function.sh

if [ $- -eq 0 ]; then function="TIME_STEP" else function=$1
fi
echo $function column_number=$( awk -v fun=$function ' { for(i=1;i<=NF;i++){ if ($i == fun)
{print i+1 }
}
}' profile_2 )

script_dir="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )" sed "s/REF/$column_number/g" $script_dir/plot_ref > plot_base sed -i "s/FUNCTION/$function/g" plot_base
gnuplot plot_base

We also need this auxiliary file:

 ## Copyright (C) 2014 J. Alberdi-Rodriguez
##
## This program is free software; you can redistribute it and/or modify
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
##
## plot_ref

set t postscript eps enhanced color solid
set output "gnuplot.eps"

set xlabel "MPI processes"
set ylabel "t (s)"
set logscale yx 2

plot "profile_2" u 1:REF w linespoint t "FUNCTION 2^x"

Something else you can try is 12, 24, 48 and 96 cores, because each of the nodes has 24 cores. In this case, you would need “analyze.sh 96 000003 3” to make “profile_3”, and then in the plotting script,

 plot "profile_2" u 1:REF w linespoint t "FUNCTION 2^x", "profile_3" u 1:REF w lp t "FUNCTION 3·(2^x)"

## Parallelization in domains vs states

We can divide up the work among the processors in different ways, by dividing up the points into domains for each processor, or dividing the states into groups for each processor, or a combination of both. Try out different combinations by adding to your input file

ParStates = 2
ParDomains = 12

and run on 24 cores, with different numbers in the first two fields whose product is the total number of processors (‘‘e.g.’’ 6 x 4, 3 x 8, …).

## PFFT Poisson solver

Another thing you can try is to compare the PFFT (parallel FFT) Poisson solver against the one we were using before (look in the output file to see which one it was). You will need to use this aprun line in your job script instead of the previous one:

 aprun -n XXX /global/homes/j/joseba/octopus/bin/octopus_mpi &> output_td_XXX

in order to use a different octopus compilation that uses that library, and add these lines to your input file:

PoissonSolver = fft
FFTLibrary = pfft

Compare some runs against one on a similar number of processors that you did previously. How does the time for this solver compare? You can also try ordinary FFTW (not parallel) with

FFTLibrary = fftw

## Parallelization of the ground state

We can also try different parameters and algorithms to see their effect on the speed of the ground-state calculation, for 24, 48, or 96 processors. Look each up in the variable reference to see what they mean, and see which of the options you were using in the previous runs.

• parallelization in domains vs states (as above)
• Eigensolver = rmmdiis, plan, cg, cg_new, lobpcg.
• StatesOrthogonalization = cholesky_serial, cholesky_parallel, mgs, qr
• SubspaceDiagonalization = standard, scalapack
• linear-combination of atomic orbitals (LCAO) for initial guess: LCAOAlternative = yes, no. In this case, add MaximumIter = 0 to do just LCAO rather than the whole calculations.


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# cf.Field.domain_axis_key¶

Field.domain_axis_key(*identity, default=ValueError(), **filter_kwargs)[source]

Returns the domain axis key spanned by 1-d coordinates.

Specifically, returns the key of the domain axis construct that is spanned by 1-d coordinate constructs.

Parameters
identity: optional

Select the 1-d dimension coordinate constructs that have an identity, defined by their identities methods, that matches any of the given values.

If no values are provided then all 1-d dimension coordinate constructs are selected.

A value may be any object that can match via the == operator, or a re.Pattern object that matches via its search method.

Note that in the output of a dump method or print call, a construct is always described by an identity that will select it.

default: optional

Return the value of the default parameter if there is no unique construct.

If set to an Exception instance then it will be raised instead.

filter_kwargs: optional

Keyword arguments as accepted by Constructs.filter that define additional construct selection criteria.

New in version (cfdm): 1.8.9.0

Returns
str

The key of the domain axis construct that is spanned by the data of the selected 1-d coordinate constructs.

Examples

>>> print(f.constructs())
Constructs:
{'dimensioncoordinate0': <CF DimensionCoordinate: time(1) days since 1964-01-21 00:00:00 >,
'dimensioncoordinate1': <CF DimensionCoordinate: pressure(23) mbar>,
'dimensioncoordinate2': <CF DimensionCoordinate: latitude(160) degrees_north>,
'dimensioncoordinate3': <CF DimensionCoordinate: longitude(320) degrees_east>,
'domainaxis0': <CF DomainAxis: size(1)>,
'domainaxis1': <CF DomainAxis: size(23)>,
'domainaxis2': <CF DomainAxis: size(160)>,
'domainaxis3': <CF DomainAxis: size(320)>}
>>> f.domain.domain_axis_key('time')
'domainaxis0'
>>> f.domain.domain_axis_key('longitude')
'domainaxis3'


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# with Omer Blaes, Shigenobu Hirose Scott Noble, John Hawley, Kris Beckwith - PowerPoint PPT Presentation

Understanding Thermal Stability of Radiation-Dominated Disks and Radiative Efficiency of Global Relativistic Disks. with Omer Blaes, Shigenobu Hirose Scott Noble, John Hawley, Kris Beckwith. Understanding Thermal Stability of Radiation-Dominated Disks. =. =. 1. 6. 2. 1. 2. 2. 1. =.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

with Omer Blaes, Shigenobu Hirose Scott Noble, John Hawley, Kris Beckwith

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### Including a Pressure/Magnetic Energy Correlation --- After the Fact

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Independent of n

### Which Variables Really Control the Stress?

As suggested by the structure of shearing-box simulations, S and W are the truly fundamental variables wherever the inflow time is the longest timescale.

Magnetic field intensity, and secondarily, the pressure, follow, with dissipation of magnetic energy driving the pressure, as regulated by the radiative loss rate.

### Origin of Traditional Efficiency Numbers:the Novikov-Thorne model

• Full GR

• Time-steady, axisymmetric, vertically-integrated

• Energy and angular momentum conservation

• Boundary conditions—

energy: prompt radiation carries off dissipation

angular momentum: zero-stress at ISCO

h = ut(ISCO)

### MHD Stresses Don’t Know to Stop at the ISCO

(Thorne 1974): “In the words of my referee, James M. Bardeen (which echo verbal warnings that I have received from Ya. B. Zel’dovich and V.F. Schwartzman), ‘It seems quite possible that magnetic stresses could cause large deviations from circular orbits in the very inner part of the accretion disk….’”

It follows that the Novikov-Thorne radiative efficiency numbers may not be the last word when magnetic stresses are important.

=

1

2

·

¸

²

²

j

j

L

1

1

¡

+

¡

½

²

=

(

)

(

)

2

2

H

H

º

r

T

L

¡

u

=

º

¹

¹

### Numerical Procedure

• Extend HARM (GR/MHD, total-energy, conservative) from 2-d axisymmetric to 3-d

• Introduce toy-model optically thin cooling function:

(1) rapidly radiates (almost) all the heat generated

(2) allows aspect ratio regulation

a/M = 0.9

H/r = 0.1

T = 15000 GM/c3

### Surface Brightness in the Fluid Frame

averaged over 10000—12000M

### Preliminary Summary

• There is noticeable radiation beyond N-T

• Dependence on H/r, a/M to be explored


text:
Is the gas heated or cooled?

1. Jul 19, 2016

Vibhor

1. The problem statement, all variables and given/known data

2. Relevant equations

PV = nRT

3. The attempt at a solution

$PV^2 = constant$

Differentiating both the sides we get , $V^2dP + 2PVdV = 0$

Now , using this along with $PdV+VdP=nRdT$ , we get $PdV = - nRdT$ .

Since $dV$ is positive , $dT$ is negative which means the temperature falls or gas is cooled .

Is this the correct way to analyze the problem ?

Thanks

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• gas.PNG
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2. Jul 19, 2016

Staff: Mentor

Yes.

3. Jul 19, 2016

Vibhor

Thank you .

Please check the attached image containing the official solution . Do you think the analysis done in it is correct ? I could not understand it .

Attached Files:

• solution.PNG
File size:
20.5 KB
Views:
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4. Jul 19, 2016

Staff: Mentor

For the same fractional increase in volume the final pressure is lower, so the temperature must have decreased rather than staying constant. It's equivalent to what you did mathematically, but I like the way you did it better.

5. Jul 20, 2016

andrevdh

A gas does positive work when it expands.
The internal energy is used for this resulting in a decrease in the gas's temperature, unless heat is supplied to cancel this.
When just enough heat is supplied to cancel this we get that Boyle's law is upheld, or put another way the gas is kept at a constant temperature by a heat source.
This means that the heat into the system is used to do the work or produce the expansion.
In this case the gas has to expand even more to keep the product constant (V2).

6. Jul 20, 2016

Staff: Mentor

There is no need to invoke internal energy or the first law to address this problem. This can be done strictly as an ideal gas equation analysis.

7. Jul 20, 2016

Vibhor

8. Jul 20, 2016

Staff: Mentor

I saw it, but I wasn't able to figure out exactly what they are asking.

9. Jul 20, 2016

Vibhor

Ok

10. Jul 20, 2016

TSny

Another approach is to substitute $P = nRT/V$ into $PV^2 =$constant to get $TV =$ constant.

11. Jul 20, 2016

Vibhor

Fantastic ! You made my work in OP look silly .


text:
Article | Open

# Imaging spectroscopy of solar radio burst fine structures

• Nature Communicationsvolume 8, Article number: 1515 (2017)
• doi:10.1038/s41467-017-01307-8
• Download Citation
Received:
Accepted:
Published:

## Abstract

Solar radio observations provide a unique diagnostic of the outer solar atmosphere. However, the inhomogeneous turbulent corona strongly affects the propagation of the emitted radio waves, so decoupling the intrinsic properties of the emitting source from the effects of radio wave propagation has long been a major challenge in solar physics. Here we report quantitative spatial and frequency characterization of solar radio burst fine structures observed with the Low Frequency Array, an instrument with high-time resolution that also permits imaging at scales much shorter than those corresponding to radio wave propagation in the corona. The observations demonstrate that radio wave propagation effects, and not the properties of the intrinsic emission source, dominate the observed spatial characteristics of radio burst images. These results permit more accurate estimates of source brightness temperatures, and open opportunities for quantitative study of the mechanisms that create the turbulent coronal medium through which the emitted radiation propagates.

## Introduction

During sporadic periods of activity, the Sun produces the largest magnetic energy release events in the solar system: solar flares and coronal mass ejections (CMEs). Flares emit radiation across the electromagnetic spectrum from gamma- and X-rays1 to radio waves2. Solar radio bursts originate from the acceleration of electrons in the relatively tenuous (electron number density $n≲1 0 8$ cm−3) solar corona, a region that, because of its low plasma density, produces very low, and hence undetectable, levels of X-ray and Extreme Ultra-Violet (EUV) emission. The radio bursts produced in such regions are, however, easily observable and thus provide unique diagnostics of electron acceleration and propagation in the outer corona and surrounding heliosphere. They provide information on the impulsive initial evolution of solar eruptions, information that is essential to the overall understanding of such events and hence to developing an effective system of space weather prediction and mitigation.

Most of the brightest solar radio bursts are due to coherent radio plasma emission processes:3 the injection of non-thermal electrons into the solar corona leads to the generation of Langmuir plasma waves through the electron-electron two-stream instability3, and these plasma waves are converted into radio emission at both the plasma (fundamental) $f p e ≃9×1 0 - 3 n cm - 3$ MHz and second-harmonic (f H = 2f pe) frequencies. Radio bursts produced by electrons moving away from the Sun along open magnetic field lines are known as Type III bursts. The fine frequency structures, so-called Type IIIb bursts, are commonly believed to be caused by density inhomogeneities in the background plasma4,5. The radiation propagates through the solar corona where it is both refracted6 and scattered by turbulent plasma processes7,8, hence understanding these propagation effects is critical to a correct interpretation of solar radio burst images9,10,11. Because coherent plasma emission produces radio waves at frequencies close to the local plasma frequency11,12,13, propagation effects are particularly significant and must therefore be carefully considered in determining both the intrinsic properties of the surrounding plasma (e.g., density, magnetic field, density gradient, and turbulence) and of the emitting high-energy electron beams (e.g., location, energy).

High-time resolution one-dimensional scans14 or single-frequency images15 have demonstrated that Type III radio sources expand with time. This could (for such single-frequency observations) be due to either propagation effects or intrinsic variations in the structure of the Type III burst15,16,17. Further, imaging observations with the Culgoora radioheliograph18,19 have also revealed an interesting enigma for the events at the limb: sources of fundamental emission are radially shifted outwards with respect to harmonic emission (and hence are apparently situated at different heights in the solar atmosphere), although the physics of the responsible coherent plasma emission mechanism requires that they are produced cospatially3. This is particularly puzzling, since the refraction of radio waves shifts sources radially inwards and, since the fundamental component is refracted more than the second-harmonic component, the fundamental component should appear lower19. Although a variety of possible resolutions of this paradox have been presented20,21, a possible resolution that is consistent with the observed increase in source size with time involves radio wave propagation effects9,11, which could10,22,23 shift the observed positions of fundamental radiation upward (radially outward). However, to date there have been no observations that permit the decoupling of propagation effects from intrinsic source variations, and hence there has been no quantitative assessment of the reasons behind this paradox.

Here we report imaging spectroscopy observations of fine frequency structures associated with a solar radio burst24. These observations with high spatial and temporal resolution demonstrate radio wave propagation effects in the solar corona.

## Results

### Overview of the observations

The radio burst on 2015 April 16 around 11:57 UT was simultaneously observed by one of the largest decameter arrays, the LOw Frequency ARray (LOFAR)25 and by the URAN-226 (Ukrainian Radio interferometer of National Academy of Sciences). The latter provides corroborating observations at other frequencies, polarization information, and valuable cross-calibration for the LOFAR observations between 30 and 32 MHz.

The dynamic spectrum (radio flux in the frequency-time plane; Fig. 1) shows two main burst components, each characterized by a rapid decrease in frequency with time; the first burst passes through 20 MHz at $≃$11:57:00 UT and is followed a few seconds later by another burst which passes through 20 MHz at $≃$11:57:04 UT. The first burst is radiation at the fundamental plasma frequency, while the second burst is harmonic emission from the same electron beam forming a so-called type IIIb-type III pair27,28 (for example, at 11:57:00 UT the emission in the first burst is concentrated at frequencies around 20 MHz while the emission in the second burst is concentrated around 40 MHz.)

The Type III burst in this event is rather typical;19,28 for example, the peak flux density between 32 and 40 MHz is 100–200 solar flux units (sfu) (1 sfu = 10−22 J s−1 m−2 Hz−1), and it has circular polarizations of ~15% and <5% for the fundamental and harmonic components, respectively. The rapid downward drift of frequency with time is a defining characteristic of solar Type III bursts;19 it results from the rapidly decreasing ambient density (and hence decreasing plasma frequency away from the Sun) as the emitting electron beam propagates upward through the decreasing density of the solar atmosphere. Since the plasma frequency $f∝ n 1 ∕ 2$, it follows that $( 1 ∕ f ) df∕dt= ( 1 ∕ 2 n ) dn∕dt= ( 1 ∕ 2 ) ( dln ( n ) ∕ d r ) ( d r ∕ d t ) =v∕2L$, where $L= ( dln ( n ) ∕ d r ) - 1$ is the density scale height and v = dr/dt is the vertical component of the velocity of the exciting electron beam. Using the Newkirk29 density model of the solar corona as a typical model, the characteristic density scale height is $L≃0.3 R ⊙ ≃2×1 0 10$ cm at a level in the atmosphere corresponding to plasma frequencies around 32 MHz. Therefore, the observed frequency drift rate $df∕dt≃7$ MHz s−1 at the f = 32 MHz point in the fundamental frequency burst component corresponds to $v= ( 2 L ∕ f ) ( d f ∕ d t ) ≃1 0 10 cm s - 1 ≃c∕3$, where c is the speed of light. The speed c/3 is a typical speed for the  ~ 30 keV electrons that excite Type III bursts19,30.

The expanded view in Fig. 1 shows that the fundamental component of the burst consists of multiple fine-structured striae; such fine structure is the characteristic signature of Type IIIb bursts24 (the number of striae increases with decreasing frequency, so that below ~30 MHz, the frequency structure of the burst looks quasi-continuous). These fine frequency structures are believed to be due to small-scale density fluctuations4,28,31,32 that modulate the resulting radio emission; they have full width at half-maximum (FWHM) durations around 1 s at a given frequency (Fig. 1). The presence of these fine striae in the fundamental component of the burst provides an estimate of the characteristic size of the emitting volume (intrinsic emission source size), which can then (see below) be compared to the source sizes obtained from direct imaging in order to evaluate the effects of radio wave propagation on the observed source size. Specifically, the individual striae (see the zoomed-in dynamic spectrum in Fig. 1) have FWHM frequency widths Δf ~ 0.3 MHz. Although the relationship between Δf and the size of the radio emitting source is model dependent5, and in particular depends on the angle between the direction of beam propagation and the direction of the density gradient, an order-of-magnitude estimation based on the plasma emission mechanism suggests that the limited frequency range corresponds to a vertical extent $Δr≃2L ( Δ f ∕ f ) ≃4×1 0 8$ cm. We note this would be the size of a density inhomogeneity leading to an enhanced level of Langmuir waves, while the electron beam generating the Langmuir waves is extended over a much larger distance4,31. Such a characteristic size of the fundamental emitting source extends over an angle $θ≃0.1$ arcmin at the Sun and hence subtends a very small solid angle ($Ω≃1 0 - 2$ arcmin2) on the sky. The harmonic emission is likely to form over a much larger region in physical space33, a feature that is also evident from the dynamic spectra—the fundamental component has clear striae, but the harmonic is rather smooth.

### Imaging

LOFAR imaging observations were made using 24-core Low Band Antenna stations with tied-array beam forming25,34,35,36,37, an observing mode that provides images with sub-second time resolution and unprecedented frequency resolution in order to resolve the individual striae in the Type IIIb burst. The array of 127 tied-array beams cover the sky out to $~2 R ⊙$ with a mosaic beam spacing of  ~ 0.1 degrees. We note that tied-array mosaic imaging is different from the traditional method of producing images from interferometric visibilities. The LOFAR core size of $D≃3.5$ km provides an angular resolution $λ∕D≃9$ arcmin at 32 MHz (wavelength λ = 9.4 m) and the dirty beam FWHM area A LOFAR was $≃110$ arcmin2 at the time of the observation. The flux was calibrated against the Crab nebula both before and after the burst observations; in addition, the Sun-integrated flux was compared with URAN-2 data, which showed agreement within a factor of  ~ 2. The temporal modulation of the URAN-2 flux also demonstrated excellent agreement with the observed fine frequency structures, excluding instrumental effects.

The imaging of the radio emission was performed with time resolution $≃$50 ms, during which radio waves propagate a distance of only  ~ 1.5 × 109 cm $≃0.3$ arcmin, allowing us to accurately track variations in both the location and the areal extent of the source on sub-second timescales. For each 12 kHz-wide frequency channel we fitted an elliptical Gaussian to the LOFAR images. The ellipse centroid position (which is determined to an accuracy significantly better than the angular resolution of a single beam measurement38) and the FWHM area of each source were estimated for all frequency channels during the radio burst (Fig. 2). Figure 3 shows the size and centroid positions (with uncertainties) of both fundamental (F) and harmonic (H) images for a typical stria near 32 MHz; the FWHM areas are A F ~ 400 arcmin2 for the fundamental and A H ~ 600 arcmin2 for the harmonic. The accuracy of determining the source position and area is variable, depending on the emission flux (Methods section), and near the burst peak they can be as high as  ± 0.1 arcmin for the position and  ± 5 arcmin2 for the area (see Fig. 4). The areas and area uncertainties are well above the LOFAR resolution limit and hence the radio sources are reliably resolved (Methods section). The radio source sizes corrected for the LOFAR beam, $A { F , H } - A LOFAR$, are both four orders of magnitude larger than the emission region size $Ω~1 0 - 2$ arcmin2 as determined above from considerations of the fine frequency width of individual burst striae.

Figure 3 shows the temporal evolution of the centroid location, and the areal extent, of the fundamental and harmonic sources (both observed at a frequency of 32.5 MHz, so that the H-radiation is produced in a region with a density one-fourth that of the region emitting the fundamental—and a few seconds later, when the emission at the fundamental frequency has drifted downward to 16.25 MHz). The centroid of the fundamental frequency radiation moves in a direction roughly parallel to the local solar radius (i.e., north-west in the plane-of-image; see full-disk image in Fig. 3), whereas the centroid of the source of harmonic radiation moves in a roughly transverse direction. The motion of F and H sources due to frequency drift between 38 and 32 MHz caused by electron transport is shown in Fig. 5. Figure 4 shows the time evolution of the radial centroid positions and areas in the X–Y plane, for both F and H components (Fig. 3). The areal expansion of both F and H components is most pronounced during the decay of the burst. This is consistent with various wave scattering models6,10,11, although these models predict different motions and growth rates of the source, depending on the assumed emission and scattering anisotropies39. Therefore, we focus on times during the decay and estimate the radial velocity in the X-Y plane and areal expansion rate by fitting linear expressions $r ( x , y ) = r 0 + ( d r ∕ d t ) ( t - t 0 ) ,A= A 0 + ( d A ∕ d t ) ( t - t 0 )$ during the time intervals shown by the shaded regions in Fig. 4. The centroid of the F-emission moves radially outward at an average speed $dr∕dt≃1.8arcmin s - 1 ≃c∕4$, while its area A F grows from  ~ 420 arcmin2 to  ~ 530 arcmin2 within  ~ 0.6 sec, an average areal expansion rate $d A F ∕dt≃180$ arcmin2 s−1. On the other hand, the centroid of the harmonic component shows negligible radial motion, while its area A H grows from  ~ 600 arcmin2 to ~ 760 arcmin2 over  ~ 3 s. The average areal expansion rate is $d A H ∕dt≃50$ arcmin2 s−1, about one-fourth the areal expansion rate for the fundamental component.

We repeated this analysis for 48 well-observed striae in frequency channels between 32 and 38 MHz (Fig. 6). We excluded frequencies below 32 MHz where the striae start to overlap and images above 38 MHz due to low signal-to-noise ratio. Figure 6 shows that for all well-resolved striae, the rate of areal expansion of the fundamental source is ~(2–4) times greater than the expansion rate for the harmonic source.

Individual striae start at different times within the Type IIIb burst (Fig. 1). Each stria also initially appears at a different location on the solar disk within a broad envelope of the Type IIIb burst (Methods section). However, nearly all stria sources move radially while the harmonic component at the same frequency behaves in a completely different manner. This allows us to exclude refraction effects in the Earth’s ionosphere as an explanation for the observed motion of the fundamental stria component. Further, the very similar expansion rates inferred from observations in 235 different frequency channels, at 48 different striae spread over 2 s (larger than  ~ 1 s duration of a stria) allow us to infer with a high degree of confidence that observed regions of fundamental radiation expand faster than regions of harmonic radiation. As we argue next, this result is not supported by any reasonable variation in the intrinsic source sizes in existing models2, but is consistent with propagation-scattering effects.

An intrinsic variation of source size with time at a given frequency requires that the emitting source grows in time as larger and larger iso-density surfaces start to emit17. However, in order to produce the observed striae, which are very narrow in frequency and large in imaged sources, such a model would require two essential features. Firstly, the emitting region is distributed over a thin but large (and changing) volume, all at the same plasma frequency and thus density; any density inhomogeneities would have to be always parallel to iso-frequency surfaces, and secondly, the positions of the stria, which originate at different locations, have nearly identical centroid motions. Moreover, in such a scenario, the expansion rate is related to the structure of the iso-density surface and it is challenging to explain why the expansion has a similar rate at all frequencies, or equivalently why all the iso-density surfaces, which are spread over a height range $~0.2 R ⊙$, expand at nearly identical rates. Finally, such a model does not explain why the centroids of the fundamental and harmonic components behave differently. Therefore, we reach the rather inescapable conclusions that the emitting sources most probably have sizes comparable to the inhomogeneity scale; they are randomly located within the corona and are responsible for the individual striae; and that the observed extent of the radio burst is primarily determined not by the size of the emitting region but rather by wave propagation effects in the surrounding atmosphere.

### Radio wave propagation

A simple model6,11 for multiple scattering off density inhomogeneities does indeed produce a (linear) increase in the area of a source (in solid angle units) with time (see Equation 64 from11): $d < θ 2 > d t ∝ f p e 4 f 4 1 μ 4 ⟨ δ n ⟩ 2 n 2 ℓ$, where $⟨δ n ⟩ 2$ is the rms level of density fluctuations, l is the density inhomogeneity scale11,40, and μ is the refractive index. For a fully ionized plasma, $μ 2 ( f ) =1- f p e 2 ∕ f 2$ is frequency dependent, so the rate of areal increase for radiation near the plasma frequency will always be larger than that for radiation at the harmonic frequency, qualitatively consistent with the observations in Fig. 6. As the waves propagate away from the source into regions of lower density (and so lower plasma frequency), the (local) plasma frequency f pe becomes progressively smaller than the wave frequency f, the refractive index approaches unity for both fundamental and harmonic radiation, and the expansion rate $∝ f p e 4 ∕ μ 4$ is greatly reduced. The location of the radio source is  ~ 7 arcmin from the solar disk center, so the short temporal extent (average FWHM $Δt≃1.1$ s) of the striae constrains the radio wave broadening along the line of sight direction to be less than $cΔt≃3×1 0 10$ cm $≃8$ arcmin. Since the perpendicular to line of sight size (~20 arcmin on the plane of the sky) is larger than the line of sight 8 arcmin size, the combined effect of scattering and emission directivity3 is likely to be anisotropic, with the dominant effect being perpendicular to the line-of-sight direction. While both the fundamental and harmonic regions expand, the fundamental source is also radially moving, and this suggests a rather small intrinsic source size for the fundamental emission and a somewhat larger intrinsic source size for the harmonic emission. Indeed, the harmonic emission source is  ~ 1.4 times larger than the fundamental (Fig. 4).

## Discussion

We have reported imaging spectroscopy observations of fine frequency structures in solar Type III radio bursts. The high frequency-time resolution of these observations have allowed us to image the radio waves as they emerge from the solar atmosphere.

The observed sources have linear extents, corrected for the finite size of the LOFAR beam, of $~ ( A F - A LOFAR ) ≃ ( 17 - 22 )$ arcmin near the peak of the fundamental component (Fig. 4). The source sizes are very similar to the average source sizes $≃$20 arcmin inferred for Type III bursts at 43 MHz19 and are much larger than the intrinsic emission source sizes ~0.1 arcmin deduced from the appearance of fine temporal substructures within the burst. The simulations of LOFAR response (Methods section) show the small source required by plasma emission cannot explain the LOFAR observations. We have also found that the areal extent of the fundamental component grows more rapidly than the harmonic component, consistent with a model involving scattering off density inhomogeneities. The measured expansion rates (Fig. 6), as well as the sub-second fundamental source motion, provide valuable information on the fibreous structure of the corona10 and on the (currently poorly known) characteristics of the density turbulence spectrum6,11.

Because the intrinsic source size is so much smaller than the apparent source sizes, the brightness temperature of the source must be similarly ($A F ∕Ω~1 0 4$) larger than that obtained using the apparent source areas. A flux of 100 solar flux units at the fundamental frequency corresponds to a brightness temperature ~1014 K, which is larger than what is typically assumed2 and interestingly close to the maximum brightness temperatures observed for type III solar radio bursts33.

These results also resolve a long-standing problem in solar radio astronomy—why the fundamental and harmonic sources, which result from the same physical process, do not generally appear to coincide spatially (Figs. 2 and 3). Because propagation effects result in a large increase in source size with time, the apparent source locations of the F and H sources are controlled primarily by these propagation-scattering effects, rather than by properties of the underlying emitting sources. We encourage further tests of this conclusion through analysis of radio data in different frequency bands.

The differential rates of propagation of F and H-radiation can easily lead, within a modest time, to a systematic displacement of the apparent source centroids, which Fig. 3 shows to be in the radial direction.

These observations also allow new testing and improvement of radio wave propagation models10,11,13 in turbulent coronal plasma, tests that have hitherto not been available for the solar corona40. In particular, since the areal expansion coefficient is proportional to the size of the density fluctuations, this provides a diagnostic of the latter quantity and opens up previously unavailable opportunities for further study of various manifestations of solar activity, such as flares, coronal mass ejections and formation of the solar wind.

## Methods

### Polarization

The Sun-integrated flux densities observed by LOFAR and URAN-2 described above have been compared in Fig. 7. Polarization measured by URAN-2 is given for the same frequency.

### Radio source position and size

The imaging has been performed for 48 individual stria in 235 frequency channels and is shown in Fig. 5. The LOFAR observations were made using 24-core Low Band Antenna stations using tied-array beam forming images with sub-second time resolution. The array of 127 tied-array beams, which are the coherent sum of all the station beams, covered the Sun with  ~ 6 arcmin spacing (the data are publicly available via http://lofar.target.rug.nl). Each LOFAR beam measures the flux F i for a given position on the sky given by $x i b$, $y i b$ in heliocentric coordinates. Figure 2 shows the locations of the beams on the solar disk. The measured flux F i recorded by LOFAR is a convolution of a LOFAR beam point spread function (Fig. 8) and the true source. The positions and the flux values for each beam allow us to reconstruct the images. Iteratively finding the highest value in the array of F i , 1% of the maximum convolved with a point spread function (Fig. 8) has been subtracted from all F i until the highest value is smaller than 5% of the initial maximum. The resulting cleaned image41,42 is shown in Fig. 9. Figure 9 also compares the result of simulated LOFAR images.

In principle, one can apply the cleaning procedure to thousands of images, and then deduce the measured source parameters. However, because we are interested in the characteristic size and source position only, such an extensive calculation effort seems unjustified. Instead, we determine the areal extent and subtract the LOFAR dirty beam area. The side-lobes do not exceed 10%, so the images are weakly affected by cleaning at half-maximum level (the top right (cleaned) image looks similar to the top left (dirty) image at 50% level in Fig. 9). The simulations in Fig. 9 also demonstrate that small $≃1$ arcmin sources are inconsistent with the data.

To determine the size and the position of the source, we fit an elliptical Gaussian $S ( x , y ) = S 0 exp ( - x ′ 2 ∕ 2 σ x 2 - y ′ 2 ∕ 2 σ y 2 )$, where $x ′ = ( x - x s ) cos ( T ) - ( y - y s ) sin ( T )$ and $y ′ = ( x - x s ) sin ( T ) + ( y - y s ) cos ( T )$, where T is the rotation from the x axis, in the clockwise direction. Minimizing $χ 2$

$χ 2 = ∑ i = 1 N ( F i - S ( x i b , y i b ; S 0 , x s , y s , σ x , σ y , T ) ) 2 δ F 2 ,$

we find the Gaussian parameters for each moment of time and frequency. The inferred parameters are as follows: S 0 is the peak amplitude, x s , y s are the coordinates of the central source position, $σ x , σ y$ are the rms lengths, T is the rotation of the ellipse from the x axis. The background flux level before the burst for each frequency and beam was taken as the uncertainties on the flux δF (typically around 1 sfu). The resulting fitted Gaussian gives the source size (convolved with the LOFAR beam). The half-maximum area of the fit gives the areal extent of the source. Since we are interested in the position and the areal extent of the source we provide the expressions for the errors. The errors δx s , δy s for the source position (x s , y s ) can be written38

$δ x s ≈ 2 π σ x σ y δ F S 0 h,δ y s ≈ 2 π σ y σ x δ F S 0 h,$

where h is the angular resolution. For weakly elliptical source $σ x ~ σ y$ as presented in Fig. 2, the uncertainty on the source position gives $δ y s ≃δ x s ~0.1$ arcmin for the fundamental ( ~ 120 sfu) and $δ x s ≃δ y s ~0.6$ arcmin for the harmonic since the harmonic ( ~ 17 sfu) has 5–6 times lower flux near the peak of each component (Fig. 4).

Similarly, the error on the source half-maximum area A can be estimated

$δ A A ≈2 δ F S 0 h A$

For example, the error on the area becomes $δA∕A~$ 5% for harmonic near the peak shown in Fig. 4. The above expressions show that the accurate determination of the source positions and the areas becomes available due to high signal to noise ratios F i /δF. We further note that the results do not imply that the source has a Gaussian shape, but show that the multi-beaming measurements can provide estimates of the position better that the resolution of the instrument and the area measurements better than ’dirty’ beam half-maximum area.

### Data availability

The datasets generated during and/or analyzed during the current study are available in the LOFAR Long Term Archive, http://lofar.target.rug.nl/ and https://sdo.gsfc.nasa.gov/data/ or available from the authors upon request.

## Additional information

Change history: A correction to this article has been published and is linked from the HTML version of this paper.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Change history

• ### Correction 11 January 2018

The original version of this article contained errors in Refs 15, 27, 32, 33 and 43, which were incorrectly given with the wrong journal name “Solid Phys.” rather than the correct “Sol. Phys.”. This has now been corrected in the PDF and HTML versions of the article.

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## Acknowledgements

E.P.K., N.L.S.J. and N.H.B. were supported by a STFC consolidated grant ST/L000741/1. A.G.E. was supported by grant NNX10AT78G from NASA’s Goddard Space Flight Center and by the National Aeronautics and Space Administration Grant NNX17AI16G, issued through the Office of Heliophysics. A.A.K. was supported in part by the RFBR grant 15-02-03717. B.A. was supported by a STFC studentship grant. The work has benefited from a Marie Curie International Research Staff Exchange Scheme‘Radiosun’ (PEOPLE-2011-IRSES-295272) and an international team grant (http://www.issibern.ch/teams/lofar/) from ISSI Bern, Switzerland. This paper is based (in part) on data obtained with the International LOFAR25 Telescope (ILT). LOFAR is the Low Frequency Array designed and constructed by ASTRON. It has facilities in several countries, that are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation under a joint scientific policy. The authors are thankful to the SDO/AIA team for the data.

## Author information

### Affiliations

1. #### School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK

• E. P. Kontar
• , B. Alcock
• , N. L. S. Jeffrey
•  & N. H. Bian

• S. Yu

• S. Yu
4. #### Institute of Solar-Terrestrial Physics, Irkutsk, 664033, Russia

• A. A. Kuznetsov
5. #### Department of Physics & Astronomy, Western Kentucky University, Bowling Green, Kentucky, 42101, USA

• A. G. Emslie
6. #### Institute of Radio Astronomy, National Academy of Sciences of Ukraine, Kharkiv, 61002, Ukraine

• V. N. Melnik
7. #### Indian Institute of Science Education and Research, Pune, 411008, India

• P. Subramanian

### Contributions

E.P.K. has designed and coordinated the investigation. S.Y., A.A.K. and V.N.M. have contributed to the analysis of data and the creation of the figures. A.G.E., B.A., N.L.S.J., N.H.B., P.S. have contributed to the data analysis and the data interpretation. All authors have contributed to writing the manuscript.

### Competing interests

The authors declare no competing financial interests.

### Corresponding author

Correspondence to E. P. Kontar.

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