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Well, that "any direction" answers seems to conflict with experiments from 1920-30's, I wonder why did they find a preferential angle...

Thanks for the reply. I slightly forgot, what we were tought again and again, that photon interaction with matter can only occur via 3 processes (in which electrons occur anyway...). So in some sense, it's not the photon, it's the electron that's the culprit (alhthough it is the photon who...

I was looking for information on how the photo electrons are emitted when under X-ray radiation. In this ancient review paper here http://journals.aps.org/pr/pdf/10.1103/PhysRev.30.488 [Broken] they state that the most common angles for non polarized X-ray beams (of various energies) range...

mathman, could you give examples where a same energy photon and electron would give different results in terms of biological damage ?

The title was too long, original question was: Why is the relative biological effectiveness (RBE) of photon and electron the same ? I was suspecting the charge of electron to possibly have some effect... Also, in biological matter, would there be a difference between photon damage and...

Ah, it's more clear now ! I don't really like the oversimplifications made. It makes sense why one has reflectors then. So basically, it is crucial how you make the pellets, how many of them are in a rod and how many rods per assembly. I think when I get too looking properly at cross sections...

Thanks for the analogy, I think I get it why the delayed ones do the work (because every text booork website tells you the same, but I am yet to find an answer about what happens to prompt neutrons). So IGNORE delayed neutrons (I think the question title is a bit misleading now...) My...

Thanks for the answer, but it is still not clear to me, how these prompt neutrons are controlled in the reactor ? I mean, maybe I am missing something - the prompt neutrons come from fission of your fuel and delayed come from fission from your FP. But how do you control the prompt neutrinos, to...

Hi all, I've been seeing this again and again, that delayed neutrons are the ones that are allowing thermal nuclear reactors to work etc. etc. What I do not understand is how are prompt neutrons controlled and how delayed ones are allowed to "do their thing" no problem ? Wiki says...

I did not notice I deleted that part. I got x = 1 - Ct (I did it by differentiating, and equating the logs. Are we still talking about the same problem as in the picture ? Because it says the shock forms at t=1, x=1. Anyway, never mind. I understand nothing. Thanks for your help anyway!

So x vanishes for t = 1/C... So the x intercept. If C is the "sigma" this confuses me even further...

It should be x = K (1+t) So a straight line, for some constant K. If I use the range x is in I get that -1<t<\frac{1}{K}+1. I think I am wasting your time by now. I think it could be high school maths that's my problem. I have no idea where I get K from and no idea how this leads to shock time...

Maybe you could tell me about how you think (your thought process) when you are drawing the characteristics (especially the sloping ones) ? I have circled the ones that maybe will make life easier for both of us. Because, however I approach it, I get nonsensical line. Let's say for the first...

I am still not sure if this all helped (not that your explaining is bad, but me being daft). I am now looking at shocks and weak solutions. I (think I) know how to mechanically get weak solutions, but when it comes to drawing the characteristics for the weak solution - I'm in trouble. For...

So where was I wrong ? (I have not really seen x being set to something before (except when playing around with limits)) Did you mean it like sigma (I take it these can be interchanged for t=0) ?

I assume you mean the \sigma = 1 which will give the characteristic x = \alpha t + 1, where \alpha = u and in range from 0 to 1. \alpha = x-1/t so u = x-1/t

I assume you are asking for this: u(0,\sigma) = \sigma ? Otherwise, maybe this u(\sigma,t) = F(\sigma) = u(x,t) = F(x/(1+t)) ?

OK \sigma = x / (1+t)

Following the same idea, would it not just be x = \sigma t + \sigma ? (And I expanded the solution in my previous post). Sorry, I thought I solved the problem in the previous post.

I assume you are talking about the most recent problem, so u(0,\sigma) = \sigma and that will let us solve for x i.e. x = \sigma t + \sigma for the given limits (with now 0 \leq \sigma < 1 ). I then rearrange for \sigma = x / 1+t now look at limits 0 \leq x/1+t < 1 and then consider the...

Thank you for your help. However, I think I am just to daft to understand these. I am not sure what I do not understand. I bet it has to do with understanding the surfaces. The Monge equations, as far as I understand, are about the tangent vector ? Sort of like streamlines in fluid mechanics ...

Not really sure how to answer that, but whatever u(t=0,x) is equal to, will stay the same along the characteristic (note, that I am answering using the definition, not understanding). Is that what you are asking about ?

I really do not know, my notes said: "Note that we may choose t_{0} = 0 without loss of generality since the Monge equations are invariant under the change of variable. In other examples it may be more appropriate to choose x_{0} = 0 instead, using the same argument." I thought that the...

Solving your given Monge equations: t = s + t_{0} ; x = ut + x_{0} ; u=F({\sigma}) Then choose t_{0} = 0 (Could have equally done that to x_{0} I assume because it does not matter where we start, might as well chose 0) Then u(x,t) = F(x-us) s=t

Not sure what you mean there, but I will pretend to understand :) I'm having trouble with this question: The "shock location is obvious" for me it is only obvious if I draw the picture, maybe I should look at the limits ? But the real problem to me is understanding how were the limits...

Yes, I know how to algebraically get the expressions in the picture of the solutions I have attached. What I do not understand is why are we allowed to compare x and t ?

I think I get that (and I thought that was the whole point of characteristics, that u is the same on a characteristic). What I do not get is how we compare time t and space x...

Sorry, I have not realized that did not fit. It's u_{t}+uu_{x}=0 and u(x,0) = -1 for x<0 and u(x,0) = 1

A very simple problem that is probably the key problem for me is the fact that x and t are easily compared and interchanged. I do not understand how one can compare time and distance. For example saying u = 1 for x<-t. Should I somehow think in 3D ? This is a very simple problem with the t...

Thanks for the reply ! I just read about how parity violation in weak interactions, in particular, example of β-decay of polarised 60 Co. Although I still could not imagine parity as some trait, I think I might see the importance, I almost feel ashamed for my ignorance...