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This is Eric's logbook for Nano Japan project from 2012.6...
#contents
* Daily schedule [#daily]
- 09:00-10:00 Discussion (1)
- 10:00-12:00 Solve the problem and write the progress on...
- 12:00-13:30 Lunch
- 13:30-14:30 Discussion (2)
- 14:30-16:30 Solve the problem and write the progress on...
- 16:30-17:30 e-mail report and problems
* Goal of the project. [#goal]
- Consider the time evolution of a special vibration (rad...
- Keywords: Coherent phonon, radial breathing mode, carbo...
* Schedule for discussion [#discussion]
|Time and Day|Mon|Tue|Wed|Thu|Fri|h
|09:00-10:00|Sato|Nugraha|Tapsanit|Tatsumi|Nugraha|
|13:30-14:30|Saito|Simon|Hasdeo|Simon|Tapsanit|
- Please note that:
All appointment should be done by communicating each othe...
--If Eric-san asks you what he needs, please answer it wi...
-- If you do not have any materials to be taught, please ...
-- If Eric-san could not answer this question, it means t...
-- If Eric-san can answer within 2 mins, it means that yo...
* Questions and Answers [#QA]
- This section is for posting questions from Eric-san and...
- Please list here with some simple reasons or details.
- For every problem, give a tag double asterisks (**) in ...
- For the answer, give a tag triple asterisks (***) in th...
- List from new to old.
** Q: About Brillouin Zone [#Q-BZ]
Hey guys! So I believe this is where I should post questi...
From google I have an ok idea of what Brillouin zones are...
If anybody has any quick words of advice for how to under...
Thanks so much and see you guys in a couple of weeks!
Eric
*** Answer (by Tapsanit) [#A-BZ]
Please consider my answers one by one in order to underst...
- What is the Bloch'theorem written in page. 17 of Saito'...
-- A: The electron in solid can behave as wave and its wa...
- What is the Brillouin zone? (solved in the discussion)
-- A: We must understand the reciprocal lattice before an...
- What is the reciprocal lattice that define the Brilloui...
-- A: As mentioned above, the electron in solid is a kind...
$\vec{b}_i\cdot\vec{a}_j = 2\cdot\pi\delta_{ij}$, where $...
It is recommended to try using this relations by deriving...
** Q: About copy machine [#Q-copymachine]
Can I use a copy machine or printer?
*** A: (not solved) [#A-copymachine]
Yes, and they are across the hall from my room.
** Q: About library [#Q-copymachine]
I would like to know where the library is and how to use ...
*** A: (not solved) [#A-copymachine]
The library is on the 7th floor. To check out a book I wr...
* Report [#report]
This part is basically written by Eric-san. Any other peo...
Here the information should be from new to old so that we...
** July 20 [#m4fdb092]
This morning I continued to write and prepare my presenta...
** July 19 [#df3357d7]
Today I continued to work on my presentation, poster and ...
** July 18 [#ya0149c1]
Today I worked on my power point slide for Thursday, on m...
** July 17 [#s4e745b2]
Today was spent writing. In the morning I coninued to typ...
This afternoon I continued to do this, and also began to ...
** July 13 [#i022d706]
Today I continued to write my reports, and to work on an ...
** July 12 [#m31e2133]
Today I continued to write the reports and think about th...
** July 11: [#e68d0b5e]
Today I met with Kono-sensei, Sarah-sensei and Matherly-s...
We also coninued to think about the Klein-Gordan equation...
For dinner I ate some delicious seafood with Saito-sensei...
**July 10: [#a685dcb6]
Today I continued to consider the klein-gordan differenti...
However, I do not know why the klein-gordan equation seem...
This afternoon I went to the very useful Mathematica semi...
**July 9 [#b95a3b62]
After an unforgettable weekend in Hiroshima and Kyoto I h...
Next I talked with Saito-sensei who reminded me of the in...
After going to lunch, I prepared some more questions for ...
In the afternoon I talked again with Saito-sensei and sho...
The next step is to investigate this function further by ...
Next, I must create mathematica programs to mimic the con...
**July 4 [#u832e234]
This morning Tapsanit-san came and reviewed with me cutti...
Yesterday evening Nugraha-san told me about numerical sol...
This afternoon Hasdeo-san came and taught me about the sa...
**July 3 [#i1a0bfcc]
Today I learned many things about the coherent phonon pro...
To find a solution of the wave equation I should use four...
**July 2 [#rep20120702]
Today Saito-sensei has returned from his travels. Meeting...
This afternoon Saito-sensei continued to help me with the...
To Do:
- Prepare a report/powerpoint presentation on what I have...
- Make travel plans for Shikoku and the south
- Edit for English Tatsumi-san's work when he gives it to...
**June 29 [#rep20120629]
This morning Nugraha-san came and helped me to consider m...
Nugraha-san also gave me some papers to read about the co...
Tapsanit-san came in during the afternoon and taught me a...
Finally, I was considering the problem of how the velocit...
**June 28 [#rep20120628]
This morning Tatsumi-san and Ominato-san came and helped ...
I have studied several solutions to the wave equation, su...
This afternoon Hadeo-san gave me data he had calculated f...
I think that it is time to move further along in the prob...
**June 27 [#rep20120627]
This morning Tapsanit-san came and continued to teach me ...
For the rest of the day I considered the problem of the e...
Also in the afternoon Hasdeo-san reviewed the Method of L...
I then reconsidered solving the equation of motion by han...
I've been learning a ton but am starting to get a little ...
**June 26 [#rep20120626]
Today I continued to consider the problem of solving for ...
Additionally, I have been learning about delta functions,...
An hour ago I brought the problem to Nugraha-san and Hasd...
I considered a few other small problems and read a little...
**June 25 [#rep20120625]
This morning I skpyed with Professor Stanton-sensei, and ...
Once I understand the solution of Q(t) I can expand to a ...
Today I also reconsidered the problem of approximating th...
I also worked a little bit on Hasdeo-san's homework of bu...
**June 22 [#rep20120622]
Saito-sensei and Nugraha-san explained to me the method o...
We ate a delicious lunch of soba noodles and tempura.
In the afternoon Tap-san taught me more about fortran and...
To do:
- Solve the wave equation for an applied force. Study fou...
- Read the chapter on Fourier transforms given to me by N...
- Complete the fortran assignment for Hasdeo-san. (doing ...
- Read Tap-san's thesis and check the english.
**June 21 [#rep20120621]
Tatsumi-san and Ominato-san taught me about LaGrange's eq...
I went to Japanese class, and then finished preparing for...
Now that I have presented I will develop a schedule for t...
Weeks:
June 25-29: Solve 1D wave equation for an applied force. ...
July 2-6: Consider the wave equation solution as it relat...
Kyoto, Midterm meeting
July 9-13: Prepare for presentation to Kono-sensei when h...
July 16-20: Begin to write up results. Hopefully I'll hav...
July 23-27: Write up results. Enjoy the last week in Send...
**June 20 [#rep20120620]
This morning Tapsanit-san continued to teach me about the...
In the afternoon Hasdeo-san continued to teach me about F...
To Do:
- Prepare for the presentation tomorrow!!!
- Fortran programming assignment for Hasdeo next week: Fi...
- Understand to mathematics of waves.
**June 19 [#rep20120619]
Today was a very productive day, and heavy on the math. M...
First thing in the morning Saito-sensei explained to me h...
Nugraha-san then came and gave me tips on how to prepare ...
Florian-san also came in during the afternoon and talked ...
To Do:
- Prepare a powerpoint presentation for Thursday
- Continue to study Gaussian wavefunctions from Nugraha-s...
- If I have time, improve the mathematica carbon nanotube...
**June 18 [#rep20120618]
Week three begins. Professor Stanton-sensei skyped me in ...
I continued to work on animating functions of applied for...
When I became tired of thinking about differential equati...
I met again with Saito-sensei who taught me that the spee...
To Do:
- Understand the solution of the wave equation well enoug...
- Solve the equation of motion for the force given to me ...
- Begin to prepare a powerpoint presentation for Thursday...
**June 15 [#rep20120615]
This morning I continued to think about how to create an ...
Next, Nugraha-san came in and continued to teach me about...
The lab ate a delicious lunch of soba and vegtable tempura.
After lunch Tapsanit-san continued to teach me the theory...
Next Ominato-san came to go over the solutions to the pro...
To do:
-Make a good animation of waves. With periodic boundary c...
-Solve Nugraha-san's wave problem.
**June 14 [#rep20120614]
This morning I continued to work on developing a code in ...
Next Tatsumi-san came and explained to me how the waveve...
I helped to make lunch, and in the afternoon I listened t...
**June 13 [#rep20120613]
First I put the numerically calculated constants in the s...
Then morning Tapsanit-san taught me about the refractive ...
We defined the complex refractive index n~ = n +iK, where...
In the afternoon I spent more time studying the solution ...
Then I accompanied my fellow lab-mates to the grocery sto...
To do:
-Complete the animation on mathematica of the vibrating w...
-Once this is done, make a POV-ray animation
-Complete the problems from Ominato-san
-Think about the solution to the equation of motion that ...
**June 12 [#rep20120612]
This morning Nugraha-san taught me more about computer pr...
Also in the morning I compared a gaussian force (f=Ae^(-t...
Next Saito-sensei taught me about the equation for a wave...
In the afternoon Florian-san also taught me more about di...
To Do:
-Solve for the coefficients of the solution to the wave e...
-Consider when a force is applied to the string. Look for...
-Finish the problems given by Ominato-san
-Type up the derivation of the recursion formula used to ...
-Type up notes from today.
**June 11 [#rep20120611]
Today Saito-sensei taught me how to find a solution for t...
Saito-sensei taught me how to use the equation feature of...
The Mathematica function is: TeXForm[f(t)]
Make sure to always use a capital letter X. Insert the fu...
On LaTeX I created a summary of the solution we found and...
Here we have the equation of motion for an applied force,...
\[ \ddot{Q} - k\dot{Q}+\omega^2Q = F(t) \]
\[ \ddot{Q} - \omega^2Q = A e^{-\frac{t^2}{\alpha^2}} \]
We Assume a solution of form:
\[ \Sigma_{n}^{\infty} C_{n}t^{n}e^{-\frac{t^2}{\alpha^2}...
For Odd Coefficients we have where m=2n+1, m grater than ...
\[ C_{2m+1}=\frac{1}{4m^{2}+2m}[C_{2m-1}(\frac{8m-2}{\alp...
And for Even Coefficients where m=2n, m greater than or e...
\[ C_{2m}=\frac{1}{4m^{2}-2m}[C_{2m-2}(\frac{8m-6}{\alpha...
Saito-sensei and I also talked about how best to model th...
Saito-sensei suggested modeling the force as either a pol...
To Do:
-The Fortran assignment for Hasdeo-san
-The problems for Ominato-san
-Think about the wave equation for Saito-sensei, and the ...
-Continue to document my work on LaTeX
-Check the accuracy of the coefficients generated by the ...
**June 8 [#rep20120608]
This morning Nugraha-san came and we talked a little bit ...
We then talked a little bit about Fortran and Nugraha-san...
In the afternoon Tapsanit-san came in and we constructed ...
Finally, we looked at the Fortran task given by Hasdeo-sa...
To Do:
-Complete the fortran programming assignments given by Ha...
-Solve the diffeq for a parabolic force, and then conside...
-Learn LaTeX
-Solve the problems given by Ominato-san
-If I have time, work through the BU Fortran tutorial
-If I have time, read the pages given by Tapsanit-san
**June 7 [#rep20120607]
In the morning Tatsumi-san and Ominato-san explained to m...
To somewhat review what Tapsanit-san taught me yesterday ...
At 10:30 I accompanied Hasdeo-san to Japanese class where...
In the afternoon I went to the group meeting where Simon-...
Later in the afternoon, Ominato-san and Tatsumi-san retur...
\[ m\frac{dv}{dt}=e(E+\frac{1}{c}v X H)-(\frac{m}{T})v \]
We derived v(t) when H=0, and then for the steady state s...
We then Derived $\sigma$ (the conductivity) based on the ...
\[ j=nev= \sigma E \]
Next, we derived v(t) for a more general case and put int...
\[ j= \sigma E \]
Ominato-san explained the classical Hall effect and we br...
E=+/- sqrt((cp)^2+(mc^2)^2) were E is a parabolic functio...
To Do:
-Finish the problems given by Ominato-san, and rewrite go...
-Consider the differential equation given by Saito-sensei...
-Finish the graphs for Nugraha-san.
-Finish the graphs for Hasdeo-san and the cascading numbe...
I learned a tremendous amount of theory today. My underst...
** June 6 [#rep20120606]
- Tapsanit-san explained the Brillouin zone of a 1D latti...
In the afternoon Hasdeo-san explained further about Fortr...
To Do:
1. Get a correctly formatted w(k) graph to Nugraha-san AN...
2. Solve Saito-sensei's differential equation by learning...
3. Solve Hasdeo-san's problems:
- plot the cascading list of integers
- graph two fxns (different parabolas) using Fortran
- output fxn data in column form
** June 5 [#rep20120605]
- Nugraha-san explained the problem of an infitie 1D seri...
Also, Florian-san showed me how to use the POV-Ray softwa...
- The homework is: by friday complete a graph of w(k) for...
Also, solve the diff eq for a Gaussian.
If I have time consider the infinite 1D series of spring ...
** June 4 [#rep20120604]
- Sato-sensei showed me around the campus and installed X...
- Hasedo-sensei introduced me to Fortran language and we ...
- Solved the differential equation for f(t)=(bt)/a=x''+w^2x
Solution is: f(t)=(b/(aw^2))(t-(1/w)sin(wt))
Could look into the eqn and new initial conditions for...
to do:
- Solve the same diff eq for f(t)=Ae^(-t^2/a^2)
- Clean up the solution for the reciprocal lattice from l...
** Task from Tapsanit (Bloch's theorem and reciprocal lat...
+ Check that the $\Psi(\vec{r})= e^{i\vec{k}\cdot\vec{r}}...
-- Answer:
Bloch's theorem is:
\[
T_{\vec a_i}\Psi = e^{(i\vec{k}\cdot\vec{a_i})}\Psi
\]
Here $T_{\vec a_i}$ is a translation operator: $T_{\vec a...
Then, also note that $u(r)$ is a periodic function. We ha...
\[
T_{\vec{a}_i} \Psi(\vec{r}) = \Psi(\vec{r} + \vec{a}_i)
\]
\[
= e^{(i\vec{k} \cdot (\vec{r} + \vec{a}_i))} u(\vec{r} + ...
\]
\[
= e^{i\vec{k} \cdot \vec{a}_i} [e^{i\vec{k}\cdot \vec{r}}...
\]
\[
=e^{i\vec{k} \cdot \vec{a}_i}\Psi\left(\vec{r}\light)
\]
The Bloch theorem is satisfied.
+ Derive the unit vectors of reciprocal lattice, $\vec{b}...
-- Answer: Here we use
\[ \vec{a}_i = {\rm unit~vector~of~real~lattice} \]
\[ \vec{b}_i = {\rm unit~vector~of~reciprocal~lattice} \]
\[ \vec{a}_i\cdot\vec{b}_i = 2\pi \]
\[ \vec{a}_i\cdot\vec{b}_j = 0 \quad {\rm if} \quad i \ne...
From Eq. (2.22) of CN book:
\[
\vec {a}_1 = \left(\frac{\sqrt{3}}{2}a,\frac{a}{2}\right...
\vec {a}_2 = \left(\frac{\sqrt{3}}{2}a,-\frac{a}{2}\right)
\]
\[ \vec{a}_1\cdot\vec{b}_1 = a_{1x}b_{1x}+a_{1y}b_{1y}=b_...
\]
\[ \vec{a}_2\cdot\vec{b}_1 = a_{2x}b_{1x}+a_{2y}b_{1x}=b_...
\]
\[b_{1y}\frac{a}{2}=b_{1x}\frac{a\sqrt{3}}{2}
\]
\[b_{1x}\frac{a\sqrt{3}}{2}+b_{1x}\frac{a\sqrt{3}}{2}=2\pi
\]
\[b_{1x}=\frac{2\pi}{a\sqrt{3}}
\]
\[b_{1y}=\frac{2\pi}{a}
\]
\[
\vec {b}_1 = \left(\frac{2\pi}{a\sqrt{3}},\frac{2\pi}{a}...
\vec {b}_2 = \left(\frac{2\pi}{a\sqrt{3}},\frac{-2\pi}{a...
\]
End:
This is Eric's logbook for Nano Japan project from 2012.6...
#contents
* Daily schedule [#daily]
- 09:00-10:00 Discussion (1)
- 10:00-12:00 Solve the problem and write the progress on...
- 12:00-13:30 Lunch
- 13:30-14:30 Discussion (2)
- 14:30-16:30 Solve the problem and write the progress on...
- 16:30-17:30 e-mail report and problems
* Goal of the project. [#goal]
- Consider the time evolution of a special vibration (rad...
- Keywords: Coherent phonon, radial breathing mode, carbo...
* Schedule for discussion [#discussion]
|Time and Day|Mon|Tue|Wed|Thu|Fri|h
|09:00-10:00|Sato|Nugraha|Tapsanit|Tatsumi|Nugraha|
|13:30-14:30|Saito|Simon|Hasdeo|Simon|Tapsanit|
- Please note that:
All appointment should be done by communicating each othe...
--If Eric-san asks you what he needs, please answer it wi...
-- If you do not have any materials to be taught, please ...
-- If Eric-san could not answer this question, it means t...
-- If Eric-san can answer within 2 mins, it means that yo...
* Questions and Answers [#QA]
- This section is for posting questions from Eric-san and...
- Please list here with some simple reasons or details.
- For every problem, give a tag double asterisks (**) in ...
- For the answer, give a tag triple asterisks (***) in th...
- List from new to old.
** Q: About Brillouin Zone [#Q-BZ]
Hey guys! So I believe this is where I should post questi...
From google I have an ok idea of what Brillouin zones are...
If anybody has any quick words of advice for how to under...
Thanks so much and see you guys in a couple of weeks!
Eric
*** Answer (by Tapsanit) [#A-BZ]
Please consider my answers one by one in order to underst...
- What is the Bloch'theorem written in page. 17 of Saito'...
-- A: The electron in solid can behave as wave and its wa...
- What is the Brillouin zone? (solved in the discussion)
-- A: We must understand the reciprocal lattice before an...
- What is the reciprocal lattice that define the Brilloui...
-- A: As mentioned above, the electron in solid is a kind...
$\vec{b}_i\cdot\vec{a}_j = 2\cdot\pi\delta_{ij}$, where $...
It is recommended to try using this relations by deriving...
** Q: About copy machine [#Q-copymachine]
Can I use a copy machine or printer?
*** A: (not solved) [#A-copymachine]
Yes, and they are across the hall from my room.
** Q: About library [#Q-copymachine]
I would like to know where the library is and how to use ...
*** A: (not solved) [#A-copymachine]
The library is on the 7th floor. To check out a book I wr...
* Report [#report]
This part is basically written by Eric-san. Any other peo...
Here the information should be from new to old so that we...
** July 20 [#m4fdb092]
This morning I continued to write and prepare my presenta...
** July 19 [#df3357d7]
Today I continued to work on my presentation, poster and ...
** July 18 [#ya0149c1]
Today I worked on my power point slide for Thursday, on m...
** July 17 [#s4e745b2]
Today was spent writing. In the morning I coninued to typ...
This afternoon I continued to do this, and also began to ...
** July 13 [#i022d706]
Today I continued to write my reports, and to work on an ...
** July 12 [#m31e2133]
Today I continued to write the reports and think about th...
** July 11: [#e68d0b5e]
Today I met with Kono-sensei, Sarah-sensei and Matherly-s...
We also coninued to think about the Klein-Gordan equation...
For dinner I ate some delicious seafood with Saito-sensei...
**July 10: [#a685dcb6]
Today I continued to consider the klein-gordan differenti...
However, I do not know why the klein-gordan equation seem...
This afternoon I went to the very useful Mathematica semi...
**July 9 [#b95a3b62]
After an unforgettable weekend in Hiroshima and Kyoto I h...
Next I talked with Saito-sensei who reminded me of the in...
After going to lunch, I prepared some more questions for ...
In the afternoon I talked again with Saito-sensei and sho...
The next step is to investigate this function further by ...
Next, I must create mathematica programs to mimic the con...
**July 4 [#u832e234]
This morning Tapsanit-san came and reviewed with me cutti...
Yesterday evening Nugraha-san told me about numerical sol...
This afternoon Hasdeo-san came and taught me about the sa...
**July 3 [#i1a0bfcc]
Today I learned many things about the coherent phonon pro...
To find a solution of the wave equation I should use four...
**July 2 [#rep20120702]
Today Saito-sensei has returned from his travels. Meeting...
This afternoon Saito-sensei continued to help me with the...
To Do:
- Prepare a report/powerpoint presentation on what I have...
- Make travel plans for Shikoku and the south
- Edit for English Tatsumi-san's work when he gives it to...
**June 29 [#rep20120629]
This morning Nugraha-san came and helped me to consider m...
Nugraha-san also gave me some papers to read about the co...
Tapsanit-san came in during the afternoon and taught me a...
Finally, I was considering the problem of how the velocit...
**June 28 [#rep20120628]
This morning Tatsumi-san and Ominato-san came and helped ...
I have studied several solutions to the wave equation, su...
This afternoon Hadeo-san gave me data he had calculated f...
I think that it is time to move further along in the prob...
**June 27 [#rep20120627]
This morning Tapsanit-san came and continued to teach me ...
For the rest of the day I considered the problem of the e...
Also in the afternoon Hasdeo-san reviewed the Method of L...
I then reconsidered solving the equation of motion by han...
I've been learning a ton but am starting to get a little ...
**June 26 [#rep20120626]
Today I continued to consider the problem of solving for ...
Additionally, I have been learning about delta functions,...
An hour ago I brought the problem to Nugraha-san and Hasd...
I considered a few other small problems and read a little...
**June 25 [#rep20120625]
This morning I skpyed with Professor Stanton-sensei, and ...
Once I understand the solution of Q(t) I can expand to a ...
Today I also reconsidered the problem of approximating th...
I also worked a little bit on Hasdeo-san's homework of bu...
**June 22 [#rep20120622]
Saito-sensei and Nugraha-san explained to me the method o...
We ate a delicious lunch of soba noodles and tempura.
In the afternoon Tap-san taught me more about fortran and...
To do:
- Solve the wave equation for an applied force. Study fou...
- Read the chapter on Fourier transforms given to me by N...
- Complete the fortran assignment for Hasdeo-san. (doing ...
- Read Tap-san's thesis and check the english.
**June 21 [#rep20120621]
Tatsumi-san and Ominato-san taught me about LaGrange's eq...
I went to Japanese class, and then finished preparing for...
Now that I have presented I will develop a schedule for t...
Weeks:
June 25-29: Solve 1D wave equation for an applied force. ...
July 2-6: Consider the wave equation solution as it relat...
Kyoto, Midterm meeting
July 9-13: Prepare for presentation to Kono-sensei when h...
July 16-20: Begin to write up results. Hopefully I'll hav...
July 23-27: Write up results. Enjoy the last week in Send...
**June 20 [#rep20120620]
This morning Tapsanit-san continued to teach me about the...
In the afternoon Hasdeo-san continued to teach me about F...
To Do:
- Prepare for the presentation tomorrow!!!
- Fortran programming assignment for Hasdeo next week: Fi...
- Understand to mathematics of waves.
**June 19 [#rep20120619]
Today was a very productive day, and heavy on the math. M...
First thing in the morning Saito-sensei explained to me h...
Nugraha-san then came and gave me tips on how to prepare ...
Florian-san also came in during the afternoon and talked ...
To Do:
- Prepare a powerpoint presentation for Thursday
- Continue to study Gaussian wavefunctions from Nugraha-s...
- If I have time, improve the mathematica carbon nanotube...
**June 18 [#rep20120618]
Week three begins. Professor Stanton-sensei skyped me in ...
I continued to work on animating functions of applied for...
When I became tired of thinking about differential equati...
I met again with Saito-sensei who taught me that the spee...
To Do:
- Understand the solution of the wave equation well enoug...
- Solve the equation of motion for the force given to me ...
- Begin to prepare a powerpoint presentation for Thursday...
**June 15 [#rep20120615]
This morning I continued to think about how to create an ...
Next, Nugraha-san came in and continued to teach me about...
The lab ate a delicious lunch of soba and vegtable tempura.
After lunch Tapsanit-san continued to teach me the theory...
Next Ominato-san came to go over the solutions to the pro...
To do:
-Make a good animation of waves. With periodic boundary c...
-Solve Nugraha-san's wave problem.
**June 14 [#rep20120614]
This morning I continued to work on developing a code in ...
Next Tatsumi-san came and explained to me how the waveve...
I helped to make lunch, and in the afternoon I listened t...
**June 13 [#rep20120613]
First I put the numerically calculated constants in the s...
Then morning Tapsanit-san taught me about the refractive ...
We defined the complex refractive index n~ = n +iK, where...
In the afternoon I spent more time studying the solution ...
Then I accompanied my fellow lab-mates to the grocery sto...
To do:
-Complete the animation on mathematica of the vibrating w...
-Once this is done, make a POV-ray animation
-Complete the problems from Ominato-san
-Think about the solution to the equation of motion that ...
**June 12 [#rep20120612]
This morning Nugraha-san taught me more about computer pr...
Also in the morning I compared a gaussian force (f=Ae^(-t...
Next Saito-sensei taught me about the equation for a wave...
In the afternoon Florian-san also taught me more about di...
To Do:
-Solve for the coefficients of the solution to the wave e...
-Consider when a force is applied to the string. Look for...
-Finish the problems given by Ominato-san
-Type up the derivation of the recursion formula used to ...
-Type up notes from today.
**June 11 [#rep20120611]
Today Saito-sensei taught me how to find a solution for t...
Saito-sensei taught me how to use the equation feature of...
The Mathematica function is: TeXForm[f(t)]
Make sure to always use a capital letter X. Insert the fu...
On LaTeX I created a summary of the solution we found and...
Here we have the equation of motion for an applied force,...
\[ \ddot{Q} - k\dot{Q}+\omega^2Q = F(t) \]
\[ \ddot{Q} - \omega^2Q = A e^{-\frac{t^2}{\alpha^2}} \]
We Assume a solution of form:
\[ \Sigma_{n}^{\infty} C_{n}t^{n}e^{-\frac{t^2}{\alpha^2}...
For Odd Coefficients we have where m=2n+1, m grater than ...
\[ C_{2m+1}=\frac{1}{4m^{2}+2m}[C_{2m-1}(\frac{8m-2}{\alp...
And for Even Coefficients where m=2n, m greater than or e...
\[ C_{2m}=\frac{1}{4m^{2}-2m}[C_{2m-2}(\frac{8m-6}{\alpha...
Saito-sensei and I also talked about how best to model th...
Saito-sensei suggested modeling the force as either a pol...
To Do:
-The Fortran assignment for Hasdeo-san
-The problems for Ominato-san
-Think about the wave equation for Saito-sensei, and the ...
-Continue to document my work on LaTeX
-Check the accuracy of the coefficients generated by the ...
**June 8 [#rep20120608]
This morning Nugraha-san came and we talked a little bit ...
We then talked a little bit about Fortran and Nugraha-san...
In the afternoon Tapsanit-san came in and we constructed ...
Finally, we looked at the Fortran task given by Hasdeo-sa...
To Do:
-Complete the fortran programming assignments given by Ha...
-Solve the diffeq for a parabolic force, and then conside...
-Learn LaTeX
-Solve the problems given by Ominato-san
-If I have time, work through the BU Fortran tutorial
-If I have time, read the pages given by Tapsanit-san
**June 7 [#rep20120607]
In the morning Tatsumi-san and Ominato-san explained to m...
To somewhat review what Tapsanit-san taught me yesterday ...
At 10:30 I accompanied Hasdeo-san to Japanese class where...
In the afternoon I went to the group meeting where Simon-...
Later in the afternoon, Ominato-san and Tatsumi-san retur...
\[ m\frac{dv}{dt}=e(E+\frac{1}{c}v X H)-(\frac{m}{T})v \]
We derived v(t) when H=0, and then for the steady state s...
We then Derived $\sigma$ (the conductivity) based on the ...
\[ j=nev= \sigma E \]
Next, we derived v(t) for a more general case and put int...
\[ j= \sigma E \]
Ominato-san explained the classical Hall effect and we br...
E=+/- sqrt((cp)^2+(mc^2)^2) were E is a parabolic functio...
To Do:
-Finish the problems given by Ominato-san, and rewrite go...
-Consider the differential equation given by Saito-sensei...
-Finish the graphs for Nugraha-san.
-Finish the graphs for Hasdeo-san and the cascading numbe...
I learned a tremendous amount of theory today. My underst...
** June 6 [#rep20120606]
- Tapsanit-san explained the Brillouin zone of a 1D latti...
In the afternoon Hasdeo-san explained further about Fortr...
To Do:
1. Get a correctly formatted w(k) graph to Nugraha-san AN...
2. Solve Saito-sensei's differential equation by learning...
3. Solve Hasdeo-san's problems:
- plot the cascading list of integers
- graph two fxns (different parabolas) using Fortran
- output fxn data in column form
** June 5 [#rep20120605]
- Nugraha-san explained the problem of an infitie 1D seri...
Also, Florian-san showed me how to use the POV-Ray softwa...
- The homework is: by friday complete a graph of w(k) for...
Also, solve the diff eq for a Gaussian.
If I have time consider the infinite 1D series of spring ...
** June 4 [#rep20120604]
- Sato-sensei showed me around the campus and installed X...
- Hasedo-sensei introduced me to Fortran language and we ...
- Solved the differential equation for f(t)=(bt)/a=x''+w^2x
Solution is: f(t)=(b/(aw^2))(t-(1/w)sin(wt))
Could look into the eqn and new initial conditions for...
to do:
- Solve the same diff eq for f(t)=Ae^(-t^2/a^2)
- Clean up the solution for the reciprocal lattice from l...
** Task from Tapsanit (Bloch's theorem and reciprocal lat...
+ Check that the $\Psi(\vec{r})= e^{i\vec{k}\cdot\vec{r}}...
-- Answer:
Bloch's theorem is:
\[
T_{\vec a_i}\Psi = e^{(i\vec{k}\cdot\vec{a_i})}\Psi
\]
Here $T_{\vec a_i}$ is a translation operator: $T_{\vec a...
Then, also note that $u(r)$ is a periodic function. We ha...
\[
T_{\vec{a}_i} \Psi(\vec{r}) = \Psi(\vec{r} + \vec{a}_i)
\]
\[
= e^{(i\vec{k} \cdot (\vec{r} + \vec{a}_i))} u(\vec{r} + ...
\]
\[
= e^{i\vec{k} \cdot \vec{a}_i} [e^{i\vec{k}\cdot \vec{r}}...
\]
\[
=e^{i\vec{k} \cdot \vec{a}_i}\Psi\left(\vec{r}\light)
\]
The Bloch theorem is satisfied.
+ Derive the unit vectors of reciprocal lattice, $\vec{b}...
-- Answer: Here we use
\[ \vec{a}_i = {\rm unit~vector~of~real~lattice} \]
\[ \vec{b}_i = {\rm unit~vector~of~reciprocal~lattice} \]
\[ \vec{a}_i\cdot\vec{b}_i = 2\pi \]
\[ \vec{a}_i\cdot\vec{b}_j = 0 \quad {\rm if} \quad i \ne...
From Eq. (2.22) of CN book:
\[
\vec {a}_1 = \left(\frac{\sqrt{3}}{2}a,\frac{a}{2}\right...
\vec {a}_2 = \left(\frac{\sqrt{3}}{2}a,-\frac{a}{2}\right)
\]
\[ \vec{a}_1\cdot\vec{b}_1 = a_{1x}b_{1x}+a_{1y}b_{1y}=b_...
\]
\[ \vec{a}_2\cdot\vec{b}_1 = a_{2x}b_{1x}+a_{2y}b_{1x}=b_...
\]
\[b_{1y}\frac{a}{2}=b_{1x}\frac{a\sqrt{3}}{2}
\]
\[b_{1x}\frac{a\sqrt{3}}{2}+b_{1x}\frac{a\sqrt{3}}{2}=2\pi
\]
\[b_{1x}=\frac{2\pi}{a\sqrt{3}}
\]
\[b_{1y}=\frac{2\pi}{a}
\]
\[
\vec {b}_1 = \left(\frac{2\pi}{a\sqrt{3}},\frac{2\pi}{a}...
\vec {b}_2 = \left(\frac{2\pi}{a\sqrt{3}},\frac{-2\pi}{a...
\]
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