By operating integration of energy over E_g to E_g-1 on energy dependent neutron diffusion equation, we can get definitions of some group constant like group absorption cross section, group scattering cross section weighed by flux.
For diffusion coefficient, it's weighed by gradient of flux, not flux itself. It is reasonable because the diffusion depends on gradient of flux, not flux.
It's interesting that we have flux dependence( or gradient of flux) , which we have not known yet, in the definition of group constants. This is called a recursive problem. To tackle this, we assume the spatial part and energy part of flux is separable. And then, we further assume that we know the energy dependence. For example, we assume a Maxwellian-Boltzmann distribution for thermal neutrons.
Since the difficulty of group parameter constants are already solved, we can easily write down the two group diffusion equation. What following is similar in one group. We will have two kind of problems, source problems and criticality problems.
2009年4月29日 星期三
class review NPRE 455 4/23
Topics: Neutron transport equation
Starting from expanding flux dependence to even include direction and energy. ø( position, energy, direction, time), we write down the neutron balance equation. And then, omit direction dependence first and focus on energy dependence from now on.
ø( vector r, E, t)
Notice that not only flux has a energy dependence, some parameters like cross section, velocity or diffusion coefficients are also energy dependent now.
Some changes in neutron balance equation:
1. Fission neutrons come from fission reactions of neutrons of all energy.
2. Losing neutrons by scattering from objective energy to any other energy.
3. Gaining neutrons by scattering from any other energy to objective energy.
Then we define g group of flux ø_g by integrate the flux from E_g to E_g-1. By this, we have the neutron balance equation of group g.
For example, we had taken a look of two group, G=2. Some simplifications are used like up-scattering, fission neutrons being all fast
Starting from expanding flux dependence to even include direction and energy. ø( position, energy, direction, time), we write down the neutron balance equation. And then, omit direction dependence first and focus on energy dependence from now on.
ø( vector r, E, t)
Notice that not only flux has a energy dependence, some parameters like cross section, velocity or diffusion coefficients are also energy dependent now.
Some changes in neutron balance equation:
1. Fission neutrons come from fission reactions of neutrons of all energy.
2. Losing neutrons by scattering from objective energy to any other energy.
3. Gaining neutrons by scattering from any other energy to objective energy.
Then we define g group of flux ø_g by integrate the flux from E_g to E_g-1. By this, we have the neutron balance equation of group g.
For example, we had taken a look of two group, G=2. Some simplifications are used like up-scattering, fission neutrons being all fast
2009年4月19日 星期日
2009年4月16日 星期四
The speed of taking notes
These weeks, I found I took the notes too slowly to have them done in time in class.
I wondered if it's just a coincidence but I happened to sit on the back seats when it happened.
Why the difference?
The only explanation coming across my mind is the TRAVELING of LIGHT!
Since the front seats are much closer to the blackboard, the time the light needed to travel from blackboard to my eyes, positioned in the front seats, is apparently less then it is for the back seats. I need more time to gather information on blackboard if I choose the back seats and that's why I took notes more slowly.
2009年4月14日 星期二
Seven rabbits in a row
Yesterday was a raining day. Not heavy kind of rain, but misty.
On my way home, near the EE quad, I saw rabbits.
Nothing special about rabbits, actually, I had seen wild rabbits on the first day I arrived UIUC.
But this time, oh my, there are seven of them.... That is huge.
Maybe there is a party of rabbits or something.
Maybe they like the rain.
Maybe the grass in moisture is more delicious.
Or, because of me? Probably not.
2009年4月12日 星期日
2009年4月10日 星期五
Wow~it's already April
Time flies. scaring.....
About one month later, I will jet back to Taiwan.
That also means that it's almost a year for my studying abroad.
Sigh..........
I would only say it's the busiest year of my life.
However, there is not too much exciting new things knocking my brain.
Not much research, not much inspiring ideas....
Most courses I took this year were already taken in Taiwan before. Just a improved skill and a better feeling of the subject. I hope I could take more challenging courses next semester.
On the other hand, I found that I studied faster now, but think things less. Do keep in mind that thinking and curiosity is the most important.
About one month later, I will jet back to Taiwan.
That also means that it's almost a year for my studying abroad.
Sigh..........
I would only say it's the busiest year of my life.
However, there is not too much exciting new things knocking my brain.
Not much research, not much inspiring ideas....
Most courses I took this year were already taken in Taiwan before. Just a improved skill and a better feeling of the subject. I hope I could take more challenging courses next semester.
On the other hand, I found that I studied faster now, but think things less. Do keep in mind that thinking and curiosity is the most important.
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