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Started by Hasdeo.2013.05.31 This is Moya's logbook for Nano Japan project from 2012.6.2-2012.7.31.

- 09:00-10:00 Discussion (1)
- 10:00-12:00 Solve the problem and write the progress on pukiwiki
- 12:00-13:30 Lunch
- 13:30-14:30 Discussion (2)
- 14:30-16:30 Solve the problem and write the progress on pukiwiki
- 16:30-17:30 e-mail report and problems

- To describe the thermal conductivity of Nanotubes and graphene. The output will be an animation of atomic vibration and its propagation in Mathematica

- Keywords: Thermal conductivity, carbon nanotubes, Differential equation, Fourier Transform, Solid-state physics, Mathematica

Time and Day | Mon | Tue | Wed | Thu | Fri |

09:00-10:00 | Hasdeo | Tatsumi | Mizuno | Thomas | Nugraha |

13:30-14:30 | Thomas | Mizuno | Tatsumi | [group meeting] | Hasdeo |

Name | Lesson to teach | Misc |

Hasdeo | Phonon in Nanotubes | How to make a presentation, and Japanese class |

Tatsumi | Nanotubes | Printer and Copy machine |

Thomas | Physical Mathematics | Library |

Mizuno | Physical Computation | Computer in Lab |

Nugraha | Phonon in Nanotubes |

- Tutorial takes place in Coffee room, since visitor room will be occupied with many people

- This section is for posting questions from Moya-san and answers from other group members.
- Please list here with some simple reasons or details.
- For every problem, give a tag double asterisks (**) in the code so that it will appear in the table of contents.
- For the answer, give a tag triple asterisks (***) in the code below the problem in order to make a proper alignment.
- List from new to old.

Today, Hasdeo-san picked me up from Urban Castle Kawauchi (UCK) with Thomas-san. I learned how to get to the lab by campus bus and have been introduced to the lab, Saito-sensei and the secretaries. Hadeo-san taught me about coupled oscillators, where I learned how to solve for the motion of two masses connected by springs. The goal is to model heat in CNT's as atoms vibrating with springs. Thomas-san also lectured me and taught me some math. He taught me how to solve the 2-dimensional Laplacian using separation of variables. He also provided some insight on the applications solving the laplacian. So far, everyone seems very nice and I am very excited to start working on thermal conductivity, which was a surprise.

Today, I walked from Urban Castle Kawauchi to the lab and managed to find my way, but I might have strayed a bit! I came early to skype my family back home, but began my lessons with Tatsumi-san at 9:00. He taught me about the graphene and carbon nanotube lattice and how vectors compose the unit lattice to form the Chiral Vector and Translational Vector. He also showed me formulas which describe the nanotube lattice. For homework, I was assigned to build a carbon nanotube out of paper and I have already drawn the Chiral Vector, but have not finished the job as I need to borrow scissors and tape. I also spoke with Saito-sensei and discussed the oscillator between two walls. I have a much better understanding of this situation and Saito-sensei assigned me to work on a similar model including a drag force. I believe I understand this problem, but am not to sure about the graphs which show resonance. After lunch, Mizuno-san introduced me to Mathematica. I do not understand it that well, but for homework I am to research it online and learn different functions. I also spent some time playing with the functions and getting the hang of working with differential equations and plotting. I am also supposed to work on an animation, but this seems rather difficult at the time. Saito-sense also showed me how to calculate different aspects of the CNT today. I learned a lot from our meeting and am very excited to work on the problems he sets up for me. I am to work on a time dependent oscillating function for homework tonight and hopefully I can get this one right and continue to expand.

I walked to the lab again today and met with Mizuno-san again to discuss Mathematica. He taught me about Rules and Patterns in programming and showed me several functions in mathematica. For homework I am to study graphics and attempt to make a figure of a particle between springs. I am also to study animation and manipulation, so I can modify this graphic. These are not very easy tasks as I do not know much about programming and I plan on looking for material to help me on mathematica. I have not begun the homework yet as I met with Saito-sensei to discuss more on a particle between two springs with an applied force. I believe I am starting to get the hang of solving these differential equations as I am beginning to recall what I learned last semester in my Differential Equations class. Homework from Saito-sensei involved me recalculating the solutions to the equations and plotting them on mathematica. I think I have successfully plottted them, but plan to ask Saito-sensei if it is a correct graph. I will try to solve the differential equation of the particle with friction and later try to derive the calculations for the properties of the CNT that Saito-sensei showed me yesterday. After lunch, I worked on the plot of the solution on mathematica and went online to learn different functions of mathematica. I learned some shortcuts in typing and how to edit graphics, but I still have no idea how to make good graphics or animations.I met with Tatsumi-san and he explained some basic CNT properties like chiralities and metallic/semiconductor conditions. After this we discussed relationships between energy and temperature and energy and wavelength. We then went on to attempt to solve the Heat Equation. I understood the steps to solve the heat equation up until we had to solve for the constants. Solving for the constants required some ugly integrals with summations and trigonometry tricks that I do not know. I hope to look into this more when I go home and get a better understanding of this. Afterwards I continued to study the motion of the particle and work on its plot in Mathematica. I showed this plot to Saito-sensei and he explained the physical interpretation of the graph which dealt with beats and periods. he also went on about the imaginary part of damped oscillations. I have some homework for tonight on the imaginary solution as the imaginary part is key to understanding the transformation of heat in these situations.

Today I arrived at the lab early and worked on solving the damped oscillator equation and plotting the solution in mathematica. I successfully plotted the solution and was able manipulate the variables, so I could study the physical event. However, Saito-sensei would later explain this graph in more detail giving me a much better understanding. I meant with Thomas-san and he had me solve the 3-D Laplacian with boundary equations. This problem worked into a real ugly system of equations, but I understood the concept behind it. I continued to reteach myself some differential equations with Thomas-san and he later explained his presentation to me. He taught me about the solving the Laplacian in spherical coordinates, but I couldn't quite understand it and I plan on looking into it again. I then attended to 'group meeting' and I got to learn from Thomas-san's and Nugraha-san's presentations.I learned about the tough standards Saito-sensei has for presentations and a little about CNT's that Nugraha-san talked about. Later on, Saito-sensei explained the damped oscillator and has assigned me to study a coupled oscillator. I think I successfully modeled the non-damped homogeneous solution, but I have had some trouble solving the driven equation and plan to ask Hasdeo-san or Saito-sensei for help later. The goal is still to understand the transfer of energy through the springs.

Today I met with Nugraha-san and he helped me solve the driven coupled oscillator that Saito-sensei assigned me. He taught me a better trial solution to use which let me understand the phase difference. However, I think we set up our differential equations wrong and I plan on solving them again. Nugraha-san also introduced infinite coupled oscillators. We have not yet introduced a force to them, but have worked on solving the differential equations. He explained the wavevector and lent me a book to that will help explain what I learned. He assigned me to study an infinite series of different coupled masses. I plan to work on this over the weekend and show it to him when I have time. I met with Saito-sensei as well and he showed me the error in our differential equations for the coupled oscillator and introduced some concepts behind the wavevector and optical/acoustic phonons.

Today,Hasdeo-san helped me finish the homework that Nugraha-san had assigned. This was to solve for the displacement of particles (coupled by springs) in an infinite lattice where the lattice cell is constructed of two particles of different mass as opposed to one. We found the solutions to the system of differential equations and he introduced the concept of zone boundaries and which phonons are acoustic or optical. I understand the math behind these conclusions, but am still rather confused by the physical meaning of frequency as a function of the wavevector. After discussing the acoustic and optical modes, Hasdeo-san introduced the model of thermal conductivity for a crystal lattice. He taught me how the transfer of energy is related to the phase shift in the two particles. I still do not completely understand this concept and plan on studying it more. After lunch I went with Thomas-san and he introduced the laplacian in polar coordinates. We had some trouble converting the initial definition, but I asked Saito-sensei for helped and he helped me work my way through. With some help from the internet, I understand the process of converting it and will begin to studying solving the differential equation. Hasdeo-san also came to my room again and discussed the thermal conductivity again and how it relates to the velocity of the center of mass. For homework, I am to study how heat transfer relates to the phase of different atoms in the atomic lattice.

Today Tatsumi-san was absent, but I managed to work on the problems that were assigned to me yesterday. First I worked on plotting the dispersion plot where frequency is a function of wavevector for a two atom periodic lattice. While I attained the right plot, I am still rather lost behind the meaning of the plot. I am still confused as to the strict definition of a phonon and how the modes are determined at various k and w values. After achieving this graph, I began to work on Hasdeo-san's homework which consisted of calculating a constant which describes heat transfer in the lattice. I managed to calculate this lattice,but am still confused as to how the relationship is attained. I managed to plot the relationship of the constant vs frequency and learned the characteristics of this relationship. However, I do have some questions regarding the imaginary part of the solution and what it means for the conductivity to approach 'negative infinity'. Next I want to attempt to solve for this constant with forces at both walls and then to work on achieving this constant for a periodic lattice.