Large Hardon Collider

[Eliseos]

Ugh, Fourier Transforms. My Modern teacher spent only a lecture on those, and expected us to know them after that, and we hadn't had a class that taught those. While I was trying to do my homework on them, I found a section in my circuit analysis book on them, so it made a little more sense, but not much lol. Especially when he randomly transforms a cos function to (1/4 e^iwt + 1/4e^-iwt +1/2) or whatever it is. I think the worst part about it, was he wasn't teaching the material from a book, but from his own lecture slides. I tried reading about them on wikipedia, but reading anything on that site that is math related makes absolutely no sense since it is always at a higher level of math.

[Kryssan]

Well, that's only one form of it, to be true, the first reactor kinetics equation which is the derivation of the neutron life cycle with respect to prompt neutron lifetime. There are several more. However, all reactor theory equations can be traced to either the kinetics equations, the period equation, or a few of the specialty equations like the inhour equation. Honestly the inhour equations are a bit heady for me, but I was never good at analyzing based on graphical proofs. Never really sat down and tried to puzzle my way through the inhour equations, the kinetics/period equations and their forms are all you really need. From there you just assume what you want the conditions of the core to be and plug and chug. Since core geometry is relatively fixed for a core that isn't damaged, you can assume design parameters are constant. The only things that should be changing then are the terms in the reactivity balance and the kinetics/period equations, all of the variables of which you should be able to solve for with the information you assume.



The stuff I have trouble with currently is fracture mechanics... I'm no mechanical engineer, and I'm not really a good electrical engineer either. Reactor theory is my strong suit - I can look at what a core is doing and based on its actions tell you the general idea of what is going on inside. I wish I could use the real equations, but for the time being I'm still forced to use approximations because my mathematic knowledge has degraded greatly from lack of use/application. But the actual design data/parameters that go into formulating core geometry and fuel/poison loading is out of my league currently. Not sure if I'll ever go there, to be honest. Lets not even get started on the electrical side of the house; as previously mentioned elsewhere on these forums, I don't really know all that much about the generators or the grid or how they all work. If it isn't a digital circuit, I'm probably lost. I know the basics, enough to provide a general overview and solve problems involving them if I'm given just variable and conditions to solve for, but that's about it.

[Woozie]

By the way, Eliseos, If you need any help in Modern Physics or have any questions about conceptual or mathematical aspects of QM, post here (assuming this is your first exposure to the mathematics of QM, you're bound to have a lot of questions to ask. No one gets it their first time). We'd all be happy to help. And you might end up sparking a huge debate over why Max is wrong about hidden variables. (Max and I used to argue about this in spam all the time. I don't believe there are hidden variables, but he does. Under certain restrictions on the variables, QM doesn't necessarily disallow hidden variables, so there's no way to really resolve the question. It's more philosophical than scientific as long as the person arguing for hidden variables allows their variables to be non-local and can formulate their theory to be consistent with QM and any Bell Experiments [like Bohemian's Interpretation]. If you're new to QM, I don't expect you to understand everything I just said yet, but the people in this topic will make sure you eventually do understand all of this).

Even if you think you understand it, you should probably ask questions anyways. Heck, if this is your first exposure to it, you should be very worried if it doesn't confuse you (or very proud. Who knows, you might be the next Feynman). Your book probably wont go over the real theory behind the measurements and what they mean. I can explain it to you now if you want, or you can wait until you're a little more familiar with the Schrodinger equation (again, assuming this is your first exposure to it. I have no clue if you've studied this before or not). Many of the aspects of measurement are more philosophical or unresolved, but I can at least explain it in terms of the postulates of Quantum Mechanics.

[Woozie]

Honestly the inhour equations are a bit heady for me, but I was never good at analyzing based on graphical proofs.

So when you say this, am I to assume that the inhour equation is an equation based on empirical data? i.e. is it like "These are our postulates. These are our laws. Therefore, based on these, we get: inhour equation" or is it more like "we've done this a experiment a kajillion times and this graph was always the result, so we fit an equation to this curve and call it the inhour equation"?

[Kryssan]

Inhour equation:


http://www.aethernavale.net/Media/images/inhour.PNG


The inhour equation is only applicable for static conditions, and was used really early in the reactor theory days. Its a bit archaic, but a lot of people still like it because the graphical interpretations of the inhour equation are something you can see. Personally, I find it easier to just stick with reactor period, as reactor period can be used in all cases.


http://www.aethernavale.net/Media/im...nhourgraph.PNG


Shown as an example.






This however is the equation for reactor period:


http://www.aethernavale.net/Media/images/period.PNG

As you can see, its a lot more managable. I have no idea why the inhour equation is still around outside of reactor theory history lessons, but meh. Period is not limited by static conditions or waiting for the delayed neutron precursor groups to decay into the asymptotic state shown by the graphical solutions, and I find it to be far more managable.

[Woozie]

Ugh, Fourier Transforms. My Modern teacher spent only a lecture on those, and expected us to know them after that, and we hadn't had a class that taught those. While I was trying to do my homework on them, I found a section in my circuit analysis book on them, so it made a little more sense, but not much lol. or whatever it is. I think the worst part about it, was he wasn't teaching the material from a book, but from his own lecture slides. I tried reading about them on wikipedia, but reading anything on that site that is math related makes absolutely no sense since it is always at a higher level of math.

See, lol. This is exactly what I mean. The physics teacher spends one hour on something that would normally take a whole course to really understand, and then you're expected to use this formula. Your only choice is to pretty much memorize the formula so you can plug in the variables. But, as you already know, memorizing formulas is the worse thing you can do in math. You have to understand the formula and how it's derived, what it really means, and how to really use it. When you're forced to memorize the equations, you really haven't learned anything. If he was going to bother teaching fourier analysis at all, he may as well have gone ahead and went over it in detail (i.e. more than just one lecture).

And yeah, wikipedia is kinda useless for learning new stuff. It's more for looking at stuff you already know as a way to check or refresh your knowledge.

Fourier Series -- from Wolfram MathWorld

This site is usually a lot better when it comes to learning stuff that you've never seen before. Though the best idea might be to go to the library and get a book on Advanced Engeineering mathematics or a mathematical methods of physical sciences (Peter O'Neil and Mary Boas are the best. I like Peter O'Neil better. He seems like more of a mathematician to me. Physicists never explain things as well as a mathematician does, though Boas was still very good).

Especially when he randomly transforms a cos function to (1/4 e^iwt + 1/4e^-iwt +1/2)

This actually comes from Euler's equation, which you may remember from high school if you were lucky enough to have a teacher that went over it.

Euler's equation states

http://latex.codecogs.com/gif.latex?...eta+isin\theta

It's easy to understand why this is the case when you write sin, cos, and e as infinite series. Check wikipedia or your calc2 book. The proof in Wikipedia is easy enough to understand. You literally just rearrange the terms of the infinite series.

Well anyways

http://latex.codecogs.com/gif.latex?...+isin(-\theta)

Remember, Cos is an even function. It is symmetric across the y axis.

http://latex.codecogs.com/gif.latex?...a)=cos(\theta)

as for sin, it is antisymmetric. Sin is called an odd function. Notice that

http://latex.codecogs.com/gif.latex?...)=-sin(\theta)

You can understand both of these results just by looking at their graphs, their unit circles, or their taylor series.

So we have

http://latex.codecogs.com/gif.latex?...st%20sin\theta

We now know that:

Equation 1: http://latex.codecogs.com/gif.latex?...st%20sin\theta

and

Equation 2: http://latex.codecogs.com/gif.latex?...st%20sin\theta

So let's add equation 1 and equation 2 together (noticing that the sin's have different signs):

http://latex.codecogs.com/gif.latex?...ta})=cos\theta

That very last equation is what your professor used.

[Kryssan]

Wow, that looks absolutely horrid in BS theme Woozie. I can barely make that out. This is why I just left the white background on mine.

[Woozie]

Yeah, you're right, the reactor period equation looks much easier to use.

[Woozie]

Wow, that looks absolutely horrid in BS theme Woozie. I can barely make that out. This is why I just left the white background on mine.

My bad D: I'm using silverblue. It looks perfect in silverblue.

Edit: Wow, I see exactly what you mean lol.

[Eliseos]

Equations

See, that makes a lot more sense. He had another brief lecture on Euler's formula before the Fourier Transform lecture, but again it was mostly abstract stuff, and he went through it expecting we all knew it prior to that. My homework this week is on special relativity, and deriving some of the transformations. I'll probably post some questions on here, and some basic sanity tests to make sure I'm doing the math right.

The semester is already starting to creep up on me lol. Next week I have a quiz on Monday(SQL, should be easy), an exam on Tuesday (vector analysis), two exams on Wednesday (Modern Physics and Circuits II) plus a lab report (Circuits II) and homework due (Modern), and an exam on Thursday (Theory of Computation h8 h8 h8).

[Woozie]

See, that makes a lot more sense. He had another brief lecture on Euler's formula before the Fourier Transform lecture, but again it was mostly abstract stuff, and he went through it expecting we all knew it prior to that. My homework this week is on special relativity, and deriving some of the transformations. I'll probably post some questions on here, and some basic sanity tests to make sure I'm doing the math right.

The semester is already starting to creep up on me lol. Next week I have a quiz on Monday(SQL, should be easy), an exam on Tuesday (vector analysis), two exams on Wednesday (Modern Physics and Circuits II) plus a lab report (Circuits II) and homework due (Modern), and an exam on Thursday (Theory of Computation h8 h8 h8).

Wow, your exam schedule is even worse than mine.

[Kryssan]

See, that makes a lot more sense. He had another brief lecture on Euler's formula before the Fourier Transform lecture, but again it was mostly abstract stuff, and he went through it expecting we all knew it prior to that.

Yeah, I understand this all too well. I hate it when people dub down material and expect you to either know it or brute force memorize it rather than teaching it. Then again, I find the more I learn about nuclear power the more of it I've learned by teaching myself than by sitting through any classroom lectures. The only exceptions to that would be when I lucked out in the past during my internship and got seminars from the surviving scientists that worked for the Manhattan Project. There was this one crazy guy that gave the most awesome reactor safety seminar I loved to death, who walks around carrying a piece of uranium fuel from the original pile in a lead glass cube in his pocket.



On topic, though, this is why my Calc III teacher was the awesome. He'd walk in every day, pull out the textbook, and go "So, this is what I'm supposed to cover today... blahblahblah so boring *toss book* I think we'll learn about this instead...". He was my introduction to fun math. Shame it took so bloody long to get there, and I really need to get back on learning it. 6 years of not having touched a Calc textbook is no good at all. Need a new sliderule though, my old Logarex has a broken cursor and maligned scales that are smudged from use. It was only an all plastic rule though, so was to be expected with a couple years of use. Still using it but it's so brutal atm, I'm holding the cursor together with tape. It had 23 scales though, and I don't want to lose that functionality. Looking at getting one of the virtually unbreakable 26 scale Deci-Lons offered by K&E this next time up. Probably going to call my contact for them on Monday and see about ordering one.

[Eliseos]

Yeah, I understand this all too well. I hate it when people dub down material and expect you to either know it or brute force memorize it rather than teaching it. Then again, I find the more I learn about nuclear power the more of it I've learned by teaching myself than by sitting through any classroom lectures. The only exceptions to that would be when I lucked out in the past during my internship and got seminars from the surviving scientists that worked for the Manhattan Project. There was this one crazy guy that gave the most awesome reactor safety seminar I loved to death, who walks around carrying a piece of uranium fuel from the original pile in a lead glass cube in his pocket.

That's awesome lol. And yet, people still are afraid of nuclear power, like it's going to deform their hands or something.

On topic, though, this is why my Calc III teacher was the awesome. He'd walk in every day, pull out the textbook, and go "So, this is what I'm supposed to cover today... blahblahblah so boring *toss book* I think we'll learn about this instead...". He was my introduction to fun math.

I like my vector teacher this semester. The book he had us get is one of those Schaum's outlines. He makes us start the problems before lecturing on the material, and then he'll do examples after we can't get any further, and explain the theory with the examples. The book is structured in a similar manner. They have a brief one page summary of the theories in the chapter, then the actual meat of the math is explained in the example problems that are solved. It's a lot more active of a learning experience than listening to someone lecture for an hour and fifteen minutes at a time. Plus, it's actually working. I'm learning faster and better than I normally do.

Wow, your exam schedule is even worse than mine.

My entire weekend will be having my head in some book, desperately hoping for that "aha!" moment(s).

[Thuronn]

Reactor kinetics equations are always fun, real or ideal. True facts.
http://www.aethernavale.net/Media/images/1rke.PNG
.

= 7

And does anyone know the date this is coming back online? They said mid-November, if i remember correctly.

[Kryssan]

= 7

And does anyone know the date this is coming back online? They said mid-November, if i remember correctly.

42, silly. Sheesh, how did you get 7?



And as for the LHC...

[Eliseos]

God damn, so exciting. I can't believe how fast the past year has gone.

[Woozie]

That's awesome lol. And yet, people still are afraid of nuclear power, like it's going to deform their hands or something.

Well, radioactivity can cause super powers, which can lead to the government building giant sentinels to destroy you. So it is pretty dangerous overall.

[Eliseos]

Well, radioactivity can cause super powers, which can lead to the government building giant sentinels to destroy you. So it is pretty dangerous overall.

Ah...right...I forgot about that...oh well, on with the radioactivity!

[Kryssan]

Radiation is as much a part of our everyday lives as is breathing. Its just a shame the first thing people think of is glowing green barrels of goo. Although, admittedly, tablesalt will glow a light blue when irradiated.... hardly the point though. Maybe one day the word nuclear won't be the prelude of a scare tactic/control mechanism...

[Eliseos]

Alright, I have a question about a homework problem of mine. I think I have the answer, but for some reason it seems that it shouldn't be this easy. Anyway, the question is:

Einstein reported that as a boy he wondered about the following puzzle. If you hold a mirror at arm's length and look at your reflection, what will happen as you begin to run? In particular, assume you run with speed v=0.99c. Will you still be able to see yourself? If so, what would your image look like, and why?

As I think about it, you would see exactly the same image of yourself as you would as if you were standing still. You and the mirror share a reference frame, so there is no length contraction/time dilation between the mirror and yourself (assuming you could hold the mirror still while running that fast, and be able to run that fast!). Am I thinking about this correctly, or am I way off and missing something important?