Last night, I spoke with a number of students from other countries and enjoyed discussing the way that they saw America. It is a bit of a long story, but suffice it to say that I ended up in a conversation with a Canadian, a Russian, three French people, and a bunch of the people in my program. I learned about their views on American stereotypes, American culture, and American foreign policy.
The Russian man told me that many Russians like South Park because that show freely expresses ideas. He liked a lot of American movies but I had not heard of many of them. The only one that I recognized was the Imaginarium of Doctor Parnassus.
According to the French man, there was support for the war in Afghanistan and he pointed to the fact that the French military is there as well. He repeatedly pointed to situations where the French and US military were working together. He also pointed out that England and France needed the large military of the US to be able to have a presence in many countries at once. He was strongly against the war in Iraq and he pointed out that there are many ruthless dictators all over the world so why did the US choose Iraq in particular.
I enjoyed conversing with these people in a mixture of French and English. I tried to listen to their conversations in French but again they would generally speak too fast for me to understand. I also feel like they did not speak loud enough for me to hear them unless they were talking to me directly (perhaps I need to continue to try to clean out my ears).
Lastly, these people had intelligent views on stereotypes. When I first asked the question about stereotypes, all of them said something to the effect of we know that those aren't true so we don't like to say them. They had met people from the US and they did not fit their stereotype. But after they insisted, they told me about how Americans can be loud. They also pointed to Texans.
At lunch today, I discussed stereotypes with the people that I work with. They were much more willing to tell us about American stereotypes. One of the more interesting ones is the idea that Americans do not have any culture. So when I think of American culture, I think of movies, TV shows and food. However, when they spoke of culture, they thought of art and history. I thought that was an interesting difference.
One big update from work is that it seems to me that the project that I was working on during the start of the summer is not going to work out. Basically, I was looking into a measurement technique and it seems that the method will not be useful to the lab. So I am going to stop working on this project soon and I will be moving on to another project for the rest of the summer. I will be looking into improving their optimization algorithms for the mirrors that they are using. I am pretty excited about this project because it is something that I have been wanting to learn about for a while.
I feel good about experience so far because I am accustomed to difficulty in research and I still learned useful things. After doing research last summer and struggling through physics labs this year, I am comfortable with research not going smoothly. Additionally, I feel like I learned a lot from this experience. I learned matlab and got experience searching for and sifting through literature for my project. More than anything, I am happy to start a new project.
Wednesday, June 29, 2011
Sunday, June 26, 2011
Exploring Opera, Time with cousins, Pantheon, and GRE
I have been busy so I will be breaking things up:
In exploring the area around Opera, a touristy area, I was able to discover many fascinating shops. To give some background, I have a bunch of traveler's checks. It is somewhat of a pain to use these, but it ended up being nice to have some since my debit card got frozen since I made a train reservation to Switzerland. Anyways, I went from one bank to another in order to find where I could exchange them. Eventually, somebody suggested that I go to the Opera train stop. Right as I emerged from the metro stop, I was greeted with the hustle and bustle of tourists clamoring over the beautiful Opera house building. I walked around and took a number of pictures. The currency exchanges in the area are blatantly in the business to rip off tourists as some places charged 10 percent plus a fee of 5 euros. After going to about 5 places, I found an exchange where the fee was only 2 percent. Since I went all the way out here, I decided to go walking around. I explored a number of children's shops. My wanderings let me to a passage with a number of cool shops. My favorite was an oriental antiquities shop. They had such an amazing collection: there were ivory, gold and wood sculptures in addition to a large collection of jewelry, tapestries, and oriental weapons! As I have concluded in the past, wandering away from the tourist traps has led to some of my best experiences here.
In walking through the Louvre slowly and enjoying a long dinner with my cousins, I saw again that I get more out of what I do by experiencing it slowly. So my aunt, uncle, and younger cousin, Meg, Harold, and Hannah, respectively visited Paris this weekend. First, we went to the Louvre. I was happy to see that my family members were happy with going through the Louvre slowly. I felt like I was able to appreciate the art more than when I went with other kids. Among other things, we discussed the progression of perspective as shown by portraits of the baby Jesus. The Louvre is just so amazing. Each section of the Louvre might as well be its own museum. We also slowly perused at paintings from smaller European countries. I enjoyed looking closely at the paintings and at least attempting to appreciate all of the work that went into each masterpiece. After that, we went out to dinner to a place that specialized in the cuisine from the Auvergne region. We enjoyed a long meal with an appetizer, main dish, dessert and some wine. I feel like I can enjoy a good bottle of wine with a meal now. It was nice to have a slow dinner for a change where we were able to talk. I hope to go on one or two more nice dinners like this where I get to try food from a new region. The only difficulty is that there is no way that I could read the menu: my aunt and uncle who have extensive experience in french cuisine still struggled to read the menu.
It is a bit harder to draw any conclusions about my travels today, but suffice it to say that it reinforces the point that I like to go through things slowly and I was pleased to see that some, but not many, of the students feel similarly. We started by going to some gardens. One particular person in our group planned the trip so we more or less went to see what she saw. It was hot and bright so I didn't particularly enjoy the gardens. It would have been nice to have a picnic though. Then we continued on to the Pantheon- a majestic building that contains the remains of some of Paris's "great men." Boasting large sculptures, frescos depicting hordes of people and ceilings that went hundreds of feet into the air, the inside of the pantheon was awe-inspiring. The lower level of the building contained a crypt that housed many of the influential thinkers of Paris. At this point, we split up and we each went around and looked at who we wanted to. I was able to read the French descriptions and although I was not able to understand everything, I was able to get the gist of the descriptions. Seeing these people makes me desire to know more French history and philosophy. Another notable point is that of the hundred or so people interred in the Pantheon, there are only two women. I also enjoyed reading about the history of building the Pantheon and how it had been used over the years.
My GRE preparation is going along smoothly and I am starting to notice that it is impacting my thinking in a positive way. I have been looking at a lot of vocabulary and I have a little notebook where I write all the words and definitions so that I can study them wherever I go. I feel that I am recognizing a lot of words in the practice materials that I am doing but I have trouble free-recalling the words that I am working with. The other major area of preparation is on the essay portion. I am working with a tutor and he has had a lot of helpful suggestions. It seems to me that if you write a straight-forward essay, then you get a 4. In order to make the essay better, you need to situate your argument in some context. For instance, I spoke about current problems necessitating generalists in the context of renaissance scientists. Further, by mixing in some impressive vocabulary, you can push your score to a 5 or 6. Really the idea is that you want to set yourself apart in some way with a flourish of your vocabulary and historical knowledge. I feel like it is a up to luck whether or not I can think of some historical or artistic example in order to situate my essay. Overall, I think all of this is a bit silly because I think straightforwardly, but I can see how these elements make an essay stronger. Additionally, I have to focus on writing strong introductory sentences and creating fluid transitions. I am pleased with how my preparation is going.
That's that for now. The weeks are pretty busy with work and I am having a lot of good experiences over the weekends. Next weekend I am going to Switzerland!
In exploring the area around Opera, a touristy area, I was able to discover many fascinating shops. To give some background, I have a bunch of traveler's checks. It is somewhat of a pain to use these, but it ended up being nice to have some since my debit card got frozen since I made a train reservation to Switzerland. Anyways, I went from one bank to another in order to find where I could exchange them. Eventually, somebody suggested that I go to the Opera train stop. Right as I emerged from the metro stop, I was greeted with the hustle and bustle of tourists clamoring over the beautiful Opera house building. I walked around and took a number of pictures. The currency exchanges in the area are blatantly in the business to rip off tourists as some places charged 10 percent plus a fee of 5 euros. After going to about 5 places, I found an exchange where the fee was only 2 percent. Since I went all the way out here, I decided to go walking around. I explored a number of children's shops. My wanderings let me to a passage with a number of cool shops. My favorite was an oriental antiquities shop. They had such an amazing collection: there were ivory, gold and wood sculptures in addition to a large collection of jewelry, tapestries, and oriental weapons! As I have concluded in the past, wandering away from the tourist traps has led to some of my best experiences here.
In walking through the Louvre slowly and enjoying a long dinner with my cousins, I saw again that I get more out of what I do by experiencing it slowly. So my aunt, uncle, and younger cousin, Meg, Harold, and Hannah, respectively visited Paris this weekend. First, we went to the Louvre. I was happy to see that my family members were happy with going through the Louvre slowly. I felt like I was able to appreciate the art more than when I went with other kids. Among other things, we discussed the progression of perspective as shown by portraits of the baby Jesus. The Louvre is just so amazing. Each section of the Louvre might as well be its own museum. We also slowly perused at paintings from smaller European countries. I enjoyed looking closely at the paintings and at least attempting to appreciate all of the work that went into each masterpiece. After that, we went out to dinner to a place that specialized in the cuisine from the Auvergne region. We enjoyed a long meal with an appetizer, main dish, dessert and some wine. I feel like I can enjoy a good bottle of wine with a meal now. It was nice to have a slow dinner for a change where we were able to talk. I hope to go on one or two more nice dinners like this where I get to try food from a new region. The only difficulty is that there is no way that I could read the menu: my aunt and uncle who have extensive experience in french cuisine still struggled to read the menu.
It is a bit harder to draw any conclusions about my travels today, but suffice it to say that it reinforces the point that I like to go through things slowly and I was pleased to see that some, but not many, of the students feel similarly. We started by going to some gardens. One particular person in our group planned the trip so we more or less went to see what she saw. It was hot and bright so I didn't particularly enjoy the gardens. It would have been nice to have a picnic though. Then we continued on to the Pantheon- a majestic building that contains the remains of some of Paris's "great men." Boasting large sculptures, frescos depicting hordes of people and ceilings that went hundreds of feet into the air, the inside of the pantheon was awe-inspiring. The lower level of the building contained a crypt that housed many of the influential thinkers of Paris. At this point, we split up and we each went around and looked at who we wanted to. I was able to read the French descriptions and although I was not able to understand everything, I was able to get the gist of the descriptions. Seeing these people makes me desire to know more French history and philosophy. Another notable point is that of the hundred or so people interred in the Pantheon, there are only two women. I also enjoyed reading about the history of building the Pantheon and how it had been used over the years.
My GRE preparation is going along smoothly and I am starting to notice that it is impacting my thinking in a positive way. I have been looking at a lot of vocabulary and I have a little notebook where I write all the words and definitions so that I can study them wherever I go. I feel that I am recognizing a lot of words in the practice materials that I am doing but I have trouble free-recalling the words that I am working with. The other major area of preparation is on the essay portion. I am working with a tutor and he has had a lot of helpful suggestions. It seems to me that if you write a straight-forward essay, then you get a 4. In order to make the essay better, you need to situate your argument in some context. For instance, I spoke about current problems necessitating generalists in the context of renaissance scientists. Further, by mixing in some impressive vocabulary, you can push your score to a 5 or 6. Really the idea is that you want to set yourself apart in some way with a flourish of your vocabulary and historical knowledge. I feel like it is a up to luck whether or not I can think of some historical or artistic example in order to situate my essay. Overall, I think all of this is a bit silly because I think straightforwardly, but I can see how these elements make an essay stronger. Additionally, I have to focus on writing strong introductory sentences and creating fluid transitions. I am pleased with how my preparation is going.
That's that for now. The weeks are pretty busy with work and I am having a lot of good experiences over the weekends. Next weekend I am going to Switzerland!
Sunday, June 19, 2011
Notre Dame, ENSTA Party, Wine Tasting, Musee Rodin and redeeming qualities of the GRE
So this might be a long post... I have been feeling pretty busy lately so I have been putting of this blog. So
Last weekend, most of the group went to Marseilles. The rest of us who stayed in Paris had a relaxing weekend and we tried to catch up on sleep. On Sunday, I went to Notre Dame. While I enjoyed seeing the amazing stained glass windows, I was somewhat saddened by way that the church had become so touristy. The windows were fantastic as ever. Given that the church was completed by 1345, I am impressed by the ability of the French people at the time to construct such a fantastic building. Granted, it took about 200 years to complete, but the windows and all of the sculptures were amazing. Again, I found the impact of the tourism to be displeasing. The area was flooded by tourists taking pictures and everywhere you looked, there were little trinkets that you could buy. There were also advertisements for the church's program to help other countries spread about that were asking for donations. Of course I am not religious but I picture a church as a place where one would go to get closer to god and not an institution that fawns over tourists.
I have been busy studying for the GRE so I did not do that much during the week. However, on Thursday night, I went to a party with some of the students who welcomed us to Paris when we first arrived. It was the last hurrah before their final exams started so the event was understandably crazy - they held a shopping cart race where they threw water ballons, pies, milk and many other strange things at the competitors. My favorite part of the party was talking to the french students. I described the various things that I have been doing in Paris to them and some of my general impressions of Paris all in French! Everybody was very friendly and spoke slower to me in French so I was able to understand them. I left a lot earlier than most of the people who went to the party so I missed some fun things but overall it was a great time. I am glad that I decided to go.
This Saturday, I went to a wine tasting with most of the other students. My goal was to attempt to see what people like about good wines. The "Tour de France of Wine" featured six wines from around France and an expert wine maker to explain the wines. Overall, it was a good experience. I enjoyed hearing about the technique of wine tasting - one of the more pompous things that one can do- and the amazing amount of skill that goes into making great wines. You can read about it more online, but proper wine tasting involves many steps. One starts by looking at the color and viscosity of the wine from which you can predict certain properties of the wine. Then one swirls the wine to let out some of the aromas and to oxidize some of the wine. Then you taste a little wine and swish it about in your mouth. There are different stages of the taste which some pompously entitle the attack phase, the evolution phase, and the finish. Our particular guide did not use these terms but they came up frequently on the internet. I was impressed with how there were subtle differences in the tastes of the wines. I felt that the wines were okay but I have never had that much wine so perhaps it is not a taste that I have acquired yet. I felt that I got some appreciation for the work that goes into making the wines but I still don't quite see why people find wine to be so fantastic. After drinking all of that wine, I felt the alcohol a bit but I again I didn't really like the feeling of being a bit tipsy. I felt like I was talking a bit louder than normal and that my balance wasn't quite the same but I still felt as outgoing and the same levels of social anxiety (which is typically quite low for me) as I normally do. This was a good experience for me but it didn't change my views that much on drinking - others seem to enjoy it a lot but I don't have much of a desire to drink. I am glad to see that my extreme aversion to alcohol at the start of college has relaxed to a more reasonable view.
Today, I went to Musee Rodin because I wanted to see the place that so many people have recommended to me. I was glad to go to a smaller museum where I could both appreciate fantastic pieces of art and not be overwhelmed by too many pieces of art. After you enter, there is a beautiful outdoor courtyard that displays some of Rodin's more famous works. Among others, the thinker, the gates of hell, and the three shades are situated in a beautiful garden. Rodin was able to capture emotion in his sculptures - the main quality by which I judge art. Inside a renovated hotel, there was a sizable collection of Rodin's other sculptures and a few other paintings like a Van Gogh painting and a Renoir painting as well.
The trip was more relaxed than usual because I went with one other student who has a similar energy level to mine. I liked that we went through the art relatively slowly and that we were able to see pretty much all of the art in three hours. I have found it very overwhelming to go to the Louvre where there are so many masterpieces that I cannot really appreciate any of them. In the future, I do want to go to a museum and do an audio tour. Even though I went through this museum slowly, I could have spent much more time reading about the history. I feel that I have to have at least one museum experience where I take a sufficient amount of time to learn about the history. In order to accomplish this, I think that I need to go alone because it does not seem like this appeals to the people in our group.
So a quick update on the GRE. I have been continuing to study an hour or two a day. I feel that my preparation is going pretty well but it would be nice to have more time. I can pay $50 to move my test day to as late as July 13th (whereas I am currently planning to take in June 27th). As I see it, the reason to take it now is that I would be able to do more fun things during the rest of my trip. The upside is that I would certainly do better on the test if I had two more weeks to prepare. Additionally, I do feel that what I am doing is useful. I should be able to formulate a clear and organized argument in a short amount of time. I should feel comfortable deconstructing an argument. I should have the ability to read through a dense passage and quickly determine the structure and the purpose of the author. I will make this decision in the next few days. I do wish that I had more experience doing these things at college but I have not taken that many humanities classes.
That's all for now.
Last weekend, most of the group went to Marseilles. The rest of us who stayed in Paris had a relaxing weekend and we tried to catch up on sleep. On Sunday, I went to Notre Dame. While I enjoyed seeing the amazing stained glass windows, I was somewhat saddened by way that the church had become so touristy. The windows were fantastic as ever. Given that the church was completed by 1345, I am impressed by the ability of the French people at the time to construct such a fantastic building. Granted, it took about 200 years to complete, but the windows and all of the sculptures were amazing. Again, I found the impact of the tourism to be displeasing. The area was flooded by tourists taking pictures and everywhere you looked, there were little trinkets that you could buy. There were also advertisements for the church's program to help other countries spread about that were asking for donations. Of course I am not religious but I picture a church as a place where one would go to get closer to god and not an institution that fawns over tourists.
I have been busy studying for the GRE so I did not do that much during the week. However, on Thursday night, I went to a party with some of the students who welcomed us to Paris when we first arrived. It was the last hurrah before their final exams started so the event was understandably crazy - they held a shopping cart race where they threw water ballons, pies, milk and many other strange things at the competitors. My favorite part of the party was talking to the french students. I described the various things that I have been doing in Paris to them and some of my general impressions of Paris all in French! Everybody was very friendly and spoke slower to me in French so I was able to understand them. I left a lot earlier than most of the people who went to the party so I missed some fun things but overall it was a great time. I am glad that I decided to go.
This Saturday, I went to a wine tasting with most of the other students. My goal was to attempt to see what people like about good wines. The "Tour de France of Wine" featured six wines from around France and an expert wine maker to explain the wines. Overall, it was a good experience. I enjoyed hearing about the technique of wine tasting - one of the more pompous things that one can do- and the amazing amount of skill that goes into making great wines. You can read about it more online, but proper wine tasting involves many steps. One starts by looking at the color and viscosity of the wine from which you can predict certain properties of the wine. Then one swirls the wine to let out some of the aromas and to oxidize some of the wine. Then you taste a little wine and swish it about in your mouth. There are different stages of the taste which some pompously entitle the attack phase, the evolution phase, and the finish. Our particular guide did not use these terms but they came up frequently on the internet. I was impressed with how there were subtle differences in the tastes of the wines. I felt that the wines were okay but I have never had that much wine so perhaps it is not a taste that I have acquired yet. I felt that I got some appreciation for the work that goes into making the wines but I still don't quite see why people find wine to be so fantastic. After drinking all of that wine, I felt the alcohol a bit but I again I didn't really like the feeling of being a bit tipsy. I felt like I was talking a bit louder than normal and that my balance wasn't quite the same but I still felt as outgoing and the same levels of social anxiety (which is typically quite low for me) as I normally do. This was a good experience for me but it didn't change my views that much on drinking - others seem to enjoy it a lot but I don't have much of a desire to drink. I am glad to see that my extreme aversion to alcohol at the start of college has relaxed to a more reasonable view.
Today, I went to Musee Rodin because I wanted to see the place that so many people have recommended to me. I was glad to go to a smaller museum where I could both appreciate fantastic pieces of art and not be overwhelmed by too many pieces of art. After you enter, there is a beautiful outdoor courtyard that displays some of Rodin's more famous works. Among others, the thinker, the gates of hell, and the three shades are situated in a beautiful garden. Rodin was able to capture emotion in his sculptures - the main quality by which I judge art. Inside a renovated hotel, there was a sizable collection of Rodin's other sculptures and a few other paintings like a Van Gogh painting and a Renoir painting as well.
The trip was more relaxed than usual because I went with one other student who has a similar energy level to mine. I liked that we went through the art relatively slowly and that we were able to see pretty much all of the art in three hours. I have found it very overwhelming to go to the Louvre where there are so many masterpieces that I cannot really appreciate any of them. In the future, I do want to go to a museum and do an audio tour. Even though I went through this museum slowly, I could have spent much more time reading about the history. I feel that I have to have at least one museum experience where I take a sufficient amount of time to learn about the history. In order to accomplish this, I think that I need to go alone because it does not seem like this appeals to the people in our group.
So a quick update on the GRE. I have been continuing to study an hour or two a day. I feel that my preparation is going pretty well but it would be nice to have more time. I can pay $50 to move my test day to as late as July 13th (whereas I am currently planning to take in June 27th). As I see it, the reason to take it now is that I would be able to do more fun things during the rest of my trip. The upside is that I would certainly do better on the test if I had two more weeks to prepare. Additionally, I do feel that what I am doing is useful. I should be able to formulate a clear and organized argument in a short amount of time. I should feel comfortable deconstructing an argument. I should have the ability to read through a dense passage and quickly determine the structure and the purpose of the author. I will make this decision in the next few days. I do wish that I had more experience doing these things at college but I have not taken that many humanities classes.
That's all for now.
Tuesday, June 14, 2011
Simulation Working? Yes Practical? No
So I have finally gotten the simulations to work. To review, here is the idea:
I have a design of a multilayer mirror (eg. 4 nm of one substance, 3 of another...). Then we have a program that can simulate the reflectivity and the phase delay of that mirror. The goal of my program is to take simulated reflectivity data and use that to calculate phase using the Kramers-Kronig relationship, and compare that to the simulated phase delay.
As you can see, the results are pretty good. Over a wide range of energies, the two graphs are quite close. But there are still a lot of problems to deal with. As I have mentioned before, there are complex frequencies with zero reflectivity that come into the KK relation. They must be taken into account.
The algorithm that I wrote to find these was effective and found two complex zeros E1=97.0+0.5i and E2=68.7+3.6I. This method requires you to know the magnitude of the reflectivity for complex frequencies. Of course this is not practical so I will be looking into how others have attacked this problem.
The other issue to mention is that I used quite a large energy range in this calculation. (The simulated data was 10 eV to 120 eV in steps of 0.5 eV. Then the data used to calculate the KK relation was 10 eV to 100 eV with steps of 1 eV). I will have to play around with the energy range in order to achieve something practical. Also the energy range has a significant impact on the graph so I will look into what gives an accurate result.
Another complication to mention is that the calculation is actually off by a factor of pi. This has to do with the fact that the complex zeros introduce a factor of pi for frequencies that have a real part that is much larger than the real part of the zero.
Just for myself, it is important to note that this was a good exercise in debugging. Basically, I needed to find the simplest thing to test in my program and work up. It occurred to me that I could think of a simple function to plug into my numerical integrator that would allow me to check if it was working. This helped me work out a few problems. Next, I realized that I did not take the logarithm of the reflectivity so I eventually realized that when looking at my code. The complex zeros would have been hard to know about if I hadn't read a fair number of papers (many of the papers on this subject don't really mention them).
I have a design of a multilayer mirror (eg. 4 nm of one substance, 3 of another...). Then we have a program that can simulate the reflectivity and the phase delay of that mirror. The goal of my program is to take simulated reflectivity data and use that to calculate phase using the Kramers-Kronig relationship, and compare that to the simulated phase delay.
As you can see, the results are pretty good. Over a wide range of energies, the two graphs are quite close. But there are still a lot of problems to deal with. As I have mentioned before, there are complex frequencies with zero reflectivity that come into the KK relation. They must be taken into account.The algorithm that I wrote to find these was effective and found two complex zeros E1=97.0+0.5i and E2=68.7+3.6I. This method requires you to know the magnitude of the reflectivity for complex frequencies. Of course this is not practical so I will be looking into how others have attacked this problem.
The other issue to mention is that I used quite a large energy range in this calculation. (The simulated data was 10 eV to 120 eV in steps of 0.5 eV. Then the data used to calculate the KK relation was 10 eV to 100 eV with steps of 1 eV). I will have to play around with the energy range in order to achieve something practical. Also the energy range has a significant impact on the graph so I will look into what gives an accurate result.
Another complication to mention is that the calculation is actually off by a factor of pi. This has to do with the fact that the complex zeros introduce a factor of pi for frequencies that have a real part that is much larger than the real part of the zero.
Just for myself, it is important to note that this was a good exercise in debugging. Basically, I needed to find the simplest thing to test in my program and work up. It occurred to me that I could think of a simple function to plug into my numerical integrator that would allow me to check if it was working. This helped me work out a few problems. Next, I realized that I did not take the logarithm of the reflectivity so I eventually realized that when looking at my code. The complex zeros would have been hard to know about if I hadn't read a fair number of papers (many of the papers on this subject don't really mention them).
Saturday, June 11, 2011
Versailles
So the main thing that I want to talk about in this post is my trip to Versailles.
When we first got to Versailles, we were greeted with a regal statue of Louis the 14th. Then we saw the brilliant golden fences. I was amazed at how much gold there was everywhere. This palace is really a testament to the wealth of the French monarchs (and perhaps a warning about their extreme arrogance...).
So the line to get in was very long. We decided that it would be a good idea to pretend that we were students from the EU. That way we would get free admission. I didn't like this idea too much but they didn't give us that hard a time even though we didn't actually have identification from another country- we used our international students cards. Luckily they didn't know that University of Michigan wasn't in the EU...
My overall reaction to the palace was that it was unbelievable that such a palace exists. The extravagance is almost impossible to describe. One of the more impressive aspects is that there were fabulous statues everywhere. Also the rooms of the king and queen were really outrageous (the queen won out on the most opulent room... good for her?!)
I think a general theme in many of the trips that we've been taking is that there is just so much to appreciate and we don't have the time to really appreciate the sites. I would love to learn all about the history of Versailles and the psychology behind the man who made it so extravagant. I felt like we rushed through all of the exhibits. Another theme that I've noticed is that my general historical knowledge is lacking. Many sculptures are related to Greek mythology and many paintings depict stories from the bible. It would be nice to have enough knowledge of these things to be able to recognize that a sculpture is showing, for instance, the abduction of Persephone.
But even though I am recognizing a lack of knowledge, I doubt that I will take steps to learn more about these areas. I just feel that I am too busy. I think that I would like to go back to some of these places on my own in the future. I would like to do the audio tours. I would enjoy learning more about the history of the paintings.
Another general conclusion about these trips is that I value relaxing. In accordance with the French style pace of life, I love to just sit down and enjoy looking around. I was pleased that I was able to convince our group to sit on the grass for about a half hour. I hope that I will get to do more relaxing in the future.
Socially, I feel that I am striking a good balance. I appreciate that people seem to respect the fact that I want to carefully balance my time and that I need to factor in GRE studying. From my perspective, it seems like I am able to do things with other people every few days. For instance, I have been making pasta for myself for the past few nights, but I took one night off to go to dinner with the group at the on campus cafeteria in order to hang out. Overall, it seems like I am over thinking these things and that I am getting along with the group. I really did have a good time at Versailles and a big part of it was doing touristy things with the other people here.
Anyways, I have two more days this weekend to do fun things. Half of the students in the program are going to southern France. So hopefully the rest of us will do some fun things as well. But most of all, I am looking forward to sleeping in tonight.
Another aside is that I do feel like my GRE preparation is going well. I took a computer adaptive test through princeton review and I hit my goal on the verbal. The essays didn't seem to go so well. I had trouble thinking about ideas for the essay and I didn't start out with a solid outline. Furthermore, I got nervous throughout the essay since the ideas were not coming together well. Also in general, I have to work on the essay that is to evaluate an argument. I do this so rarely now in a formal sense that I am not sure how to structure the essay. I have been doing a lot of vocab and I think that helps me get handful of questions correct on the verbal. The most helpful thing in studying is just getting familiar with the question types and how to go about them.
Another thing that has been on my mind related to the GRE is that I feel that the test prep sites negatively impact poorer people. $450 effectively gets you an increase of 100 to 200 points (out of 800). Granted you have to put in the time, but if that is prohibitively expensive for you, then you are at a huge disadvantage. It is too bad that they don't offer better free test materials. Luckily I have been able to find enough practice materials to last me until I take the test in about two weeks.
When we first got to Versailles, we were greeted with a regal statue of Louis the 14th. Then we saw the brilliant golden fences. I was amazed at how much gold there was everywhere. This palace is really a testament to the wealth of the French monarchs (and perhaps a warning about their extreme arrogance...).
So the line to get in was very long. We decided that it would be a good idea to pretend that we were students from the EU. That way we would get free admission. I didn't like this idea too much but they didn't give us that hard a time even though we didn't actually have identification from another country- we used our international students cards. Luckily they didn't know that University of Michigan wasn't in the EU...
My overall reaction to the palace was that it was unbelievable that such a palace exists. The extravagance is almost impossible to describe. One of the more impressive aspects is that there were fabulous statues everywhere. Also the rooms of the king and queen were really outrageous (the queen won out on the most opulent room... good for her?!)
I think a general theme in many of the trips that we've been taking is that there is just so much to appreciate and we don't have the time to really appreciate the sites. I would love to learn all about the history of Versailles and the psychology behind the man who made it so extravagant. I felt like we rushed through all of the exhibits. Another theme that I've noticed is that my general historical knowledge is lacking. Many sculptures are related to Greek mythology and many paintings depict stories from the bible. It would be nice to have enough knowledge of these things to be able to recognize that a sculpture is showing, for instance, the abduction of Persephone.
But even though I am recognizing a lack of knowledge, I doubt that I will take steps to learn more about these areas. I just feel that I am too busy. I think that I would like to go back to some of these places on my own in the future. I would like to do the audio tours. I would enjoy learning more about the history of the paintings.
Another general conclusion about these trips is that I value relaxing. In accordance with the French style pace of life, I love to just sit down and enjoy looking around. I was pleased that I was able to convince our group to sit on the grass for about a half hour. I hope that I will get to do more relaxing in the future.
Socially, I feel that I am striking a good balance. I appreciate that people seem to respect the fact that I want to carefully balance my time and that I need to factor in GRE studying. From my perspective, it seems like I am able to do things with other people every few days. For instance, I have been making pasta for myself for the past few nights, but I took one night off to go to dinner with the group at the on campus cafeteria in order to hang out. Overall, it seems like I am over thinking these things and that I am getting along with the group. I really did have a good time at Versailles and a big part of it was doing touristy things with the other people here.
Anyways, I have two more days this weekend to do fun things. Half of the students in the program are going to southern France. So hopefully the rest of us will do some fun things as well. But most of all, I am looking forward to sleeping in tonight.
Another aside is that I do feel like my GRE preparation is going well. I took a computer adaptive test through princeton review and I hit my goal on the verbal. The essays didn't seem to go so well. I had trouble thinking about ideas for the essay and I didn't start out with a solid outline. Furthermore, I got nervous throughout the essay since the ideas were not coming together well. Also in general, I have to work on the essay that is to evaluate an argument. I do this so rarely now in a formal sense that I am not sure how to structure the essay. I have been doing a lot of vocab and I think that helps me get handful of questions correct on the verbal. The most helpful thing in studying is just getting familiar with the question types and how to go about them.
Another thing that has been on my mind related to the GRE is that I feel that the test prep sites negatively impact poorer people. $450 effectively gets you an increase of 100 to 200 points (out of 800). Granted you have to put in the time, but if that is prohibitively expensive for you, then you are at a huge disadvantage. It is too bad that they don't offer better free test materials. Luckily I have been able to find enough practice materials to last me until I take the test in about two weeks.
Thursday, June 9, 2011
Things are Coming Together...
Things that I did today:
(Got Principal Value Integral Package to work)
So today, I got a matlab package to work that integrates principal value integrals. The code was written poorly but I adjusted it so that I could pass a function handle to the method that did the integration. From what I can see, the integral does not contribute much to the phase. The larger contributions seem to come from the extrapolation terms.
(Thoughts about extra terms due to complex zeros of R)
In the actual phase graph, there seems to be a jump discontinuity. Looking at the equation for the phase, it seems like this is due to a complex zero in the reflectivity. (The arctan term gives a jump discontinuity if the real part is small).
(Learning how to Calculate Reflectivity)
Anyways, now I've been looking into the code that lets you calculate the reflectivity. The relevant topic is called "the transfer matrix method" (see http://en.wikipedia.org/wiki/Transfer-matrix_method_(optics) ). The idea is that if you have a layered structure, you look at the electric field and the derivative of E with respect to the normal to the surface and the propagation of the waves can be described by multiplying the E, dE/dz vector by a matrix.
(Derivation of KK Relations)
Also one question that came up yesterday is why are the complex zeros of reflectance relevant in the equation. So the derivation of the KK relationship using complex variables is very nice and can be found here: http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation (see derivation). The basic idea is that you take a contour integral of f(omega')/(omega'-omega) that goes along the real axis and then a semicircle in the upper half of the complex plane (with a little indent around omega). If there are singularities, you have to surround those with little loops to take them into account when you deform the integration contour.
(Algorithm to find complex zeros)
So I adjusted the program that is used to calculate reflectivity given a frequency so that it can pass it into a root finding algorithm. I wonder if I will be able to find the zeros of this function.
Anyways, I feel pretty good about my project because I am understanding things and I have a lot of things that I can do.
(Got Principal Value Integral Package to work)
So today, I got a matlab package to work that integrates principal value integrals. The code was written poorly but I adjusted it so that I could pass a function handle to the method that did the integration. From what I can see, the integral does not contribute much to the phase. The larger contributions seem to come from the extrapolation terms.
(Thoughts about extra terms due to complex zeros of R)
In the actual phase graph, there seems to be a jump discontinuity. Looking at the equation for the phase, it seems like this is due to a complex zero in the reflectivity. (The arctan term gives a jump discontinuity if the real part is small).
(Learning how to Calculate Reflectivity)
Anyways, now I've been looking into the code that lets you calculate the reflectivity. The relevant topic is called "the transfer matrix method" (see http://en.wikipedia.org/wiki/Transfer-matrix_method_(optics) ). The idea is that if you have a layered structure, you look at the electric field and the derivative of E with respect to the normal to the surface and the propagation of the waves can be described by multiplying the E, dE/dz vector by a matrix.
(Derivation of KK Relations)
Also one question that came up yesterday is why are the complex zeros of reflectance relevant in the equation. So the derivation of the KK relationship using complex variables is very nice and can be found here: http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relation (see derivation). The basic idea is that you take a contour integral of f(omega')/(omega'-omega) that goes along the real axis and then a semicircle in the upper half of the complex plane (with a little indent around omega). If there are singularities, you have to surround those with little loops to take them into account when you deform the integration contour.
(Algorithm to find complex zeros)
So I adjusted the program that is used to calculate reflectivity given a frequency so that it can pass it into a root finding algorithm. I wonder if I will be able to find the zeros of this function.
Anyways, I feel pretty good about my project because I am understanding things and I have a lot of things that I can do.
Wednesday, June 8, 2011
Continued Research Ideas
One paper that I have found seems to be helpful in that it discusses using the KK relations for a thin film. The generalized relation that takes into account the singularities that occur for complex frequencies is
Theta_R(omega)= - omega/Pi INT [0,Infinity] (ln R(omega') )/(omega'^2-omega^2)d omega'
+ 2 SUM arctan (omega-a_j)/b_j
where a_j+i* b_j are the zeros of R(omega).
(1) These zeros are difficult to find experimentally. I wonder if I can modify the code for the simulation in order to allow for complex frequencies. (I do not know what the equations are like but it seems at least possible to do this).
Some other things that are important to do are:
(2) Think of an appropriate way to extrapolate in the LOW frequency region. The issue is that even outside the region where the mirror that I am working with was optimized, there is some significant reflection in the 10 to 30 eV range. My professor said that this isn't too surprising because in addition to the peaks that come from constructive interference, the metals that they use just reflect those frequencies. Experimentally, this could be problematic because you can only go so low with the energies in the synchrotron. Regardless, I hope to get some sort of bound on the error that this produces.
For now, it seems like it is appropriate to assume that reflectivity is a constant in the high frequency region since that is a small contribution. One thing that I am not sure about, however, is how the phase acts for large x. Regardless, I should be able to get a bound on the error that comes from the HIGH frequencies.
Another nice thing that I figured out today is that instead of writing a code to integrate the cauchy principal value integrals, I was just able to find a method that should be able to do it for me. The code is written somewhat poorly so I am working on getting that to work correctly.
All in all, I do feel good about this project. It is quite a challenge, but it is important for this lab to be able to measure the phase delay for their mirrors so I am contributing something. Hopefully I will be able to get my program to do a better job of predicting the phase. If the few things that I am doing don't work, I will go to more papers and see how they approached this problem.
Theta_R(omega)= - omega/Pi INT [0,Infinity] (ln R(omega') )/(omega'^2-omega^2)d omega'
+ 2 SUM arctan (omega-a_j)/b_j
where a_j+i* b_j are the zeros of R(omega).
(1) These zeros are difficult to find experimentally. I wonder if I can modify the code for the simulation in order to allow for complex frequencies. (I do not know what the equations are like but it seems at least possible to do this).
Some other things that are important to do are:
(2) Think of an appropriate way to extrapolate in the LOW frequency region. The issue is that even outside the region where the mirror that I am working with was optimized, there is some significant reflection in the 10 to 30 eV range. My professor said that this isn't too surprising because in addition to the peaks that come from constructive interference, the metals that they use just reflect those frequencies. Experimentally, this could be problematic because you can only go so low with the energies in the synchrotron. Regardless, I hope to get some sort of bound on the error that this produces.
For now, it seems like it is appropriate to assume that reflectivity is a constant in the high frequency region since that is a small contribution. One thing that I am not sure about, however, is how the phase acts for large x. Regardless, I should be able to get a bound on the error that comes from the HIGH frequencies.
Another nice thing that I figured out today is that instead of writing a code to integrate the cauchy principal value integrals, I was just able to find a method that should be able to do it for me. The code is written somewhat poorly so I am working on getting that to work correctly.
All in all, I do feel good about this project. It is quite a challenge, but it is important for this lab to be able to measure the phase delay for their mirrors so I am contributing something. Hopefully I will be able to get my program to do a better job of predicting the phase. If the few things that I am doing don't work, I will go to more papers and see how they approached this problem.
Tuesday, June 7, 2011
A post that ended up being mostly about food
As discussed before, I feel like I have been very busy - I have a lot to balance: learning french, doing research, socializing with the other people in my program, getting settled in my living area and studying for the GRE.
Just to summarize a few notable experiences,
Yesterday, I went with two other people on a "pasta-venture." My goal was to get a pan, pasta, and some toppings. We took the train and bus to a very large supermarket (called a hypermarche/). Carrefour is basically the French Walmart. It was a lot of fun to go around and see the all of the different food sections. There was a huge cheese section, a fish section, etc. Another cool area was the french book area. There were a lot of children's books. I spent about 15 minutes reading Winnie the Pooh (or Winnie l'Ourson). It was fun to read but I did not recognize some of the grammar structures. It was 10 euros so I didn't buy it but I do have fond memories of Winnie the Pooh from when I was younger! Another fun feature of the store is that they had moving walkways to go upstairs so you could take your shopping cart. The surrounding shopping center had these as well.
When I went to the checkout, apparently I almost bought a 50 euro pot. I also didn't weigh my bananas. So I was able to use my french to say no thanks. Apparently I misread the label for the pot and it actually cost 20 euros only if I bought 50 vignettes whatever that means. I was able to get another pot.
Another thing that I have been doing is that I have been trying different French cheeses. I have always eaten a lot of cheese and so it has been fun to explore different kinds. At my lunch, I have been getting a little cheese with each meal. I also bought some cheese from the store. So far, I have had Camembert, Brie, and Roquefort. The last cheese there is one of the moldy cheeses that is supposed to be quite strong but I thought it was tasty. Tomorrow, I hope to try Munster. I also bought "mimolette jeune". It looks like cheddar but I haven't tasted it yet. I hope to continue to try different french cheeses.
Tonight, I was successful in using my pot to cook pasta and I put some cheese on it (emmental). After looking this up, it is just what we refer to as Swiss cheese. I also got two other pasta sauces. One is a tomato sauce with Ricotta, and another is tomato sauce "basquaise" I just chose it randomly when I was there. Apparently it is a sauce with tomatoes and hot peppers. All in all, I am looking forward to making more pasta!
I have been trying to spend less money lately in general so I think that I will be doing well now that I am settled. For breakfast, I have a few cereal bars (they were quite cheap at that store), for lunch, it is subsidized so that is cheap, and dinner will be cheap with the pasta. I will go out occasionally but not everyday like I was doing at the start of the trip.
Also I am not sure if I have talked about the lunch at work. So basically, around 12, the whole lab moseys over to the lunch area. There is typically a long line so we talk a bit. When you are in line, you pick up a tray and put various dishes on your plate. A typical lunch for me includes: a hot plate with a meat and rice or pasta, a small salad, some fruit, a dessert (I have gotten a variety of things such as fruit with pudding or a piece of pie), some cheese, and a roll or two of bread. I enjoy lunch very much and the food is subsidized for students so that all costs around 2.50 euros! It is cool how balanced the meals are here. You have a lot of small plates instead of just one large dish of food.
So thats about that. I haven't been sleeping too well so I should be getting to bed now. Yesterday, I stayed up late doing some GRE studying since I haven't been keeping up with my studying goals. I really felt it at work so I hope to get at least 7 hours of sleep tonight.
Just to summarize a few notable experiences,
Yesterday, I went with two other people on a "pasta-venture." My goal was to get a pan, pasta, and some toppings. We took the train and bus to a very large supermarket (called a hypermarche/). Carrefour is basically the French Walmart. It was a lot of fun to go around and see the all of the different food sections. There was a huge cheese section, a fish section, etc. Another cool area was the french book area. There were a lot of children's books. I spent about 15 minutes reading Winnie the Pooh (or Winnie l'Ourson). It was fun to read but I did not recognize some of the grammar structures. It was 10 euros so I didn't buy it but I do have fond memories of Winnie the Pooh from when I was younger! Another fun feature of the store is that they had moving walkways to go upstairs so you could take your shopping cart. The surrounding shopping center had these as well.
When I went to the checkout, apparently I almost bought a 50 euro pot. I also didn't weigh my bananas. So I was able to use my french to say no thanks. Apparently I misread the label for the pot and it actually cost 20 euros only if I bought 50 vignettes whatever that means. I was able to get another pot.
Another thing that I have been doing is that I have been trying different French cheeses. I have always eaten a lot of cheese and so it has been fun to explore different kinds. At my lunch, I have been getting a little cheese with each meal. I also bought some cheese from the store. So far, I have had Camembert, Brie, and Roquefort. The last cheese there is one of the moldy cheeses that is supposed to be quite strong but I thought it was tasty. Tomorrow, I hope to try Munster. I also bought "mimolette jeune". It looks like cheddar but I haven't tasted it yet. I hope to continue to try different french cheeses.
Tonight, I was successful in using my pot to cook pasta and I put some cheese on it (emmental). After looking this up, it is just what we refer to as Swiss cheese. I also got two other pasta sauces. One is a tomato sauce with Ricotta, and another is tomato sauce "basquaise" I just chose it randomly when I was there. Apparently it is a sauce with tomatoes and hot peppers. All in all, I am looking forward to making more pasta!
I have been trying to spend less money lately in general so I think that I will be doing well now that I am settled. For breakfast, I have a few cereal bars (they were quite cheap at that store), for lunch, it is subsidized so that is cheap, and dinner will be cheap with the pasta. I will go out occasionally but not everyday like I was doing at the start of the trip.
Also I am not sure if I have talked about the lunch at work. So basically, around 12, the whole lab moseys over to the lunch area. There is typically a long line so we talk a bit. When you are in line, you pick up a tray and put various dishes on your plate. A typical lunch for me includes: a hot plate with a meat and rice or pasta, a small salad, some fruit, a dessert (I have gotten a variety of things such as fruit with pudding or a piece of pie), some cheese, and a roll or two of bread. I enjoy lunch very much and the food is subsidized for students so that all costs around 2.50 euros! It is cool how balanced the meals are here. You have a lot of small plates instead of just one large dish of food.
So thats about that. I haven't been sleeping too well so I should be getting to bed now. Yesterday, I stayed up late doing some GRE studying since I haven't been keeping up with my studying goals. I really felt it at work so I hope to get at least 7 hours of sleep tonight.
Collecting thoughts on Research
My first attempt to calculate the phase from the simulated reflectivity data did not seem to work so I am going back and reading as much as I can. I am looking for ways to improve my calculation of phase.
I attempted to implement a method in matlab that integrated reflectivity data to get the phase but the results are not very good. (I took reflectivity data for every 0.1 eV (apparently this is typical for real data), created a function that interpolated those points into a smooth curve (I used a cubic spline), then I numerically integrated that using an adaptive simpson's rule routine. In order to handle the principal part integral, I removed a symmetric neighborhood of the singularity). For extrapolation, I assumed that the reflectivity was constant.
One problem: I am getting high reflectivity in regions where we wouldn't normally measure the reflectivity. I am looking at an aperiodic mirror from "Aperiodic multilayer mirrors for efficient broadband reflection
in the extreme ultraviolet". So there is reflectivity of about 0.15 in a wide region (30-80 eV) where the mirror was optimized, but there is also another peak near 10 to 20 eV. I am not sure if this is due to bad optical constants, or if this is just how their calculation worked out. Anyways this may be causing problems in my integration (and my way of extrapolating the reflectivity to low frequencies is not going to work)
So I looked at a lot of papers today. There is a ton of work that has been done in the area of using the KK relations. Here is a summary of things to do / things that I am thinking about:
1. learn more optics
a. how is the reflection coefficient derived from known constants for a multi-layer (maybe this would help me understand where the zero reflectivity points are)
b. does the reflectivity coefficient have zeros in the complex frequency plane (how can I predict their position... eg. the dielectric function for a semi-infinite substrate has its only zeros on the imaginary axis)
c. qualitatively, what is the reflectivity of a multilayer for high frequency/low frequency (so I can extrapolate correctly)
d. what effect does polarization, angle of incidence have on the calculations that I am doing?
e. is there a relationship between the complex reflectivity coefficient and the complex dielectric function
2. Kramers-Kronig relationship
a. which representation should I be using
i. real and imaginary part of a boundary condition for an analytic function are related by the Hilbert transform
ii. the transformation can be done as two Fourier transforms
b. zeros of reflectivity (for complex frequency) give rise to singularities in the integral above and result in extra terms being needed in the transformation
c. how is this derived? how can one use causality to show that reflectivity as a function of a complex variable is analytic?
3. Using matlab to do the hilbert transform numerically (there are MANY papers on this subject)
a. use of gaussian quadrature method (write integral as INT w(x) p(x) where w(x) is the weight function log x^(-1)... this may require a different program as you need high precision arithmetic for large numbers of sample points
b. write the transform of a sequence of fourier transforms and approximate as a discrete fourier transform (cooley-turkey algorithm?)
c. look into algorithms that allow one to isolate the zeros of the reflectivity as a function of a complex variable (eg. find the blaschke factors that are needed to recover a function that has singularities when it is fourier transformed...one paper suggests using transmission data?)
d. look into methods that acceleration of convergence of the integral by knowing the phase (eg. multiply subtractive KK method)
Anyways, I feel like there is SO much that I can do at the moment.
I attempted to implement a method in matlab that integrated reflectivity data to get the phase but the results are not very good. (I took reflectivity data for every 0.1 eV (apparently this is typical for real data), created a function that interpolated those points into a smooth curve (I used a cubic spline), then I numerically integrated that using an adaptive simpson's rule routine. In order to handle the principal part integral, I removed a symmetric neighborhood of the singularity). For extrapolation, I assumed that the reflectivity was constant.
One problem: I am getting high reflectivity in regions where we wouldn't normally measure the reflectivity. I am looking at an aperiodic mirror from "Aperiodic multilayer mirrors for efficient broadband reflection
in the extreme ultraviolet". So there is reflectivity of about 0.15 in a wide region (30-80 eV) where the mirror was optimized, but there is also another peak near 10 to 20 eV. I am not sure if this is due to bad optical constants, or if this is just how their calculation worked out. Anyways this may be causing problems in my integration (and my way of extrapolating the reflectivity to low frequencies is not going to work)
So I looked at a lot of papers today. There is a ton of work that has been done in the area of using the KK relations. Here is a summary of things to do / things that I am thinking about:
1. learn more optics
a. how is the reflection coefficient derived from known constants for a multi-layer (maybe this would help me understand where the zero reflectivity points are)
b. does the reflectivity coefficient have zeros in the complex frequency plane (how can I predict their position... eg. the dielectric function for a semi-infinite substrate has its only zeros on the imaginary axis)
c. qualitatively, what is the reflectivity of a multilayer for high frequency/low frequency (so I can extrapolate correctly)
d. what effect does polarization, angle of incidence have on the calculations that I am doing?
e. is there a relationship between the complex reflectivity coefficient and the complex dielectric function
2. Kramers-Kronig relationship
a. which representation should I be using
i. real and imaginary part of a boundary condition for an analytic function are related by the Hilbert transform
ii. the transformation can be done as two Fourier transforms
b. zeros of reflectivity (for complex frequency) give rise to singularities in the integral above and result in extra terms being needed in the transformation
c. how is this derived? how can one use causality to show that reflectivity as a function of a complex variable is analytic?
3. Using matlab to do the hilbert transform numerically (there are MANY papers on this subject)
a. use of gaussian quadrature method (write integral as INT w(x) p(x) where w(x) is the weight function log x^(-1)... this may require a different program as you need high precision arithmetic for large numbers of sample points
b. write the transform of a sequence of fourier transforms and approximate as a discrete fourier transform (cooley-turkey algorithm?)
c. look into algorithms that allow one to isolate the zeros of the reflectivity as a function of a complex variable (eg. find the blaschke factors that are needed to recover a function that has singularities when it is fourier transformed...one paper suggests using transmission data?)
d. look into methods that acceleration of convergence of the integral by knowing the phase (eg. multiply subtractive KK method)
Anyways, I feel like there is SO much that I can do at the moment.
Monday, June 6, 2011
matlab fatlab?
So I am at work again and I am going to write a few thoughts: Phase can be calculated from reflectivity using the the integral
phi(E)= -1/pi int 0 to infinity ln R(X/E) / (X^2 -1) dX (this is understood to be a principal part integral)
So the main issues for me are as follows:
1. We only know the function R for a limited range so we need to extrapolate it for other values of energy (frequency). For the moment, I am just assuming that R is constant outside that range. I do not know if this a reasonable assumption or how to go about saying what the reflectivity is for large frequencies.
For large frequency, I get the error as Log(R_infinity)/(2 Pi) Log | ( Emax-E)/(Emax+E) |
For small frequency, Log(R_0)/(2 Pi) Log | (E-Emin)/(E+Emin)|
R_infinity = R(E_max)
R_0=R(E_min)
2. I have to find an appropriate method of discretizing the integral that takes into account that we need to take a principal part integral.
2a. For the moment, I am using a right-side riemann sum. Perhaps I will implement simpson's rule. The disadvantage of the latter method is that it assumes equal spacing so I cannot see if the large spacing is the issue.
2b. Say we want to estimate the phase for a frequency omega. Then we need to know the reflectivity very precisely near omega. However, from what I hear from the lab, the reflectivity is measured every 0.2 eV, which I do not think is accurate enough.
Anyways, so I spent most of today trying to get the phase to predict more accurately. I had an idea that would let me integrate over the singularity. Basically, I just wanted to subtract the singularity out around a small symmetric neighborhood. This contributes nothing to the principal part integral but removes the singularity. This seemed fine but when I went to try and integrate this new function, I spent probably 3 hours trying to figure out how to get matlab to integrate this. This was pretty frustrating for me because I could have done this in 15 mins in mathematica but my lab does not use that program. I understand that this is just something that I will learn in time but I don't like having work go so slowly like this. I eventually asked one of the guys that I work with a few questions that I was able to figure it out. The main idea is that many functions need to be able to handle a vector input. I also didn't realize that when you write equations, you need to allow for vectors to work as well.
phi(E)= -1/pi int 0 to infinity ln R(X/E) / (X^2 -1) dX (this is understood to be a principal part integral)
So the main issues for me are as follows:
1. We only know the function R for a limited range so we need to extrapolate it for other values of energy (frequency). For the moment, I am just assuming that R is constant outside that range. I do not know if this a reasonable assumption or how to go about saying what the reflectivity is for large frequencies.
For large frequency, I get the error as Log(R_infinity)/(2 Pi) Log | ( Emax-E)/(Emax+E) |
For small frequency, Log(R_0)/(2 Pi) Log | (E-Emin)/(E+Emin)|
R_infinity = R(E_max)
R_0=R(E_min)
2. I have to find an appropriate method of discretizing the integral that takes into account that we need to take a principal part integral.
2a. For the moment, I am using a right-side riemann sum. Perhaps I will implement simpson's rule. The disadvantage of the latter method is that it assumes equal spacing so I cannot see if the large spacing is the issue.
2b. Say we want to estimate the phase for a frequency omega. Then we need to know the reflectivity very precisely near omega. However, from what I hear from the lab, the reflectivity is measured every 0.2 eV, which I do not think is accurate enough.
Anyways, so I spent most of today trying to get the phase to predict more accurately. I had an idea that would let me integrate over the singularity. Basically, I just wanted to subtract the singularity out around a small symmetric neighborhood. This contributes nothing to the principal part integral but removes the singularity. This seemed fine but when I went to try and integrate this new function, I spent probably 3 hours trying to figure out how to get matlab to integrate this. This was pretty frustrating for me because I could have done this in 15 mins in mathematica but my lab does not use that program. I understand that this is just something that I will learn in time but I don't like having work go so slowly like this. I eventually asked one of the guys that I work with a few questions that I was able to figure it out. The main idea is that many functions need to be able to handle a vector input. I also didn't realize that when you write equations, you need to allow for vectors to work as well.
Sunday, June 5, 2011
Visiting the Louvre and More Wanderings
The Louvre was AMAZING!! There is a seemingly endless collection of treasures. Further, the building that houses these masterpieces is equally as amazing. I wish that I know much more about the history. After going to the Centre Pompidou, it is so clear in my mind that modern art is nothing compared to the art here. There were so many sculptures and paintings that captured intensity and emotion. One of my favorite sculptures depicted a lion biting a man's leg. You could see the ferocity of the lion it his eyes and the fear in the man whose leg was getting devoured. Their entangled bodies captured the intensity of the fight. It is hard for me to see anything close to that in the art that I saw at the modern art museum.
It was impossible to appreciate everything at the Louvre. I hope to return sometime. Each tiny piece of art is the result of many hours or even years of careful craftsmanship. Further, there is a huge history behind all of the art. I was disappointed that all of the descriptions of the art were in French that was too complicated for me to understand.
This visit also makes me feel like it is somewhat pointless to visit a whole bunch of countries. There is so much to do in Paris. Seeing the details in the French culture is much more satisfying to me than rushing through a bunch of tourist attractions in other countries.
We decided to go to lunch outside the louvre to save some money. We ended up going to another street that was even move expensive. We looked at a BMW store and Louis Vuitton. The prices were so outrageous there. There was a not so fantastic looking handbag that was 25,000 euros!! I am really disgusted with anybody who buys things like that. There are so many other things that could use that kind of money. I tried to take pictures but they did not like that too much. After that, we came back to the Louvre but the line to get back in literally stretched a fourth of a mile. So we just wandered around for a bit.
It is hard to keep up with the blog because so much is going on. In other news, yesterday, I spent most of the day studying while the others went out. I felt pretty good about this because I got a fair amount done.
Also here are some pictures that I took at centre pompidou (modern art) and of cite universitaire (the place that I am living now).
Centre Pompidou and Cite Universitaire
http://www.facebook.com/media/set/?set=a.2159398021917.2101909.1155513641&l=c959a8756b
It was impossible to appreciate everything at the Louvre. I hope to return sometime. Each tiny piece of art is the result of many hours or even years of careful craftsmanship. Further, there is a huge history behind all of the art. I was disappointed that all of the descriptions of the art were in French that was too complicated for me to understand.
This visit also makes me feel like it is somewhat pointless to visit a whole bunch of countries. There is so much to do in Paris. Seeing the details in the French culture is much more satisfying to me than rushing through a bunch of tourist attractions in other countries.
Louvre (see picture descriptions for more detail about my day):
http://www.facebook.com/media/set/?set=a.2159452143270.2101910.1155513641&l=f431ca771c
We decided to go to lunch outside the louvre to save some money. We ended up going to another street that was even move expensive. We looked at a BMW store and Louis Vuitton. The prices were so outrageous there. There was a not so fantastic looking handbag that was 25,000 euros!! I am really disgusted with anybody who buys things like that. There are so many other things that could use that kind of money. I tried to take pictures but they did not like that too much. After that, we came back to the Louvre but the line to get back in literally stretched a fourth of a mile. So we just wandered around for a bit.
It is hard to keep up with the blog because so much is going on. In other news, yesterday, I spent most of the day studying while the others went out. I felt pretty good about this because I got a fair amount done.
Also here are some pictures that I took at centre pompidou (modern art) and of cite universitaire (the place that I am living now).
Centre Pompidou and Cite Universitaire
http://www.facebook.com/media/set/?set=a.2159398021917.2101909.1155513641&l=c959a8756b
Friday, June 3, 2011
Some feelings while in Paris
One thing that I wanted to blog a bit about was my mood. When we started the program, they showed us the happiness curve. It starts out erratic, then you go through a period of happiness due to being in new surroundings. Then there is a low when you start missing home and eventually, you get acclimated to the new country and it is similar to other places.
Anyways, I would say that I am in the erratic stage now. For the most part, I have been having a great time with seeing all that there is to see in France. I enjoy seeing the city but more importantly I have enjoyed interacting with French people. Too bad that I don't have time to do some type of French class. I feel like I am solidifying my French knowledge but I am not learning that many new things. But one thing that has been getting to me a bit is that I do feel like is that my social situation is unstable and that I have to put a lot of effort into that.
One example is that when we are in a group, I feel like I need to be loud otherwise my voice gets drowned out. In general, I am a person who likes to talk to people one on one. I feel like I have had good small group conversations with people but in the larger group I am sometimes quiet. This is not that different from other parts of my life but I do wish that I was more dynamic in a group setting at times. I remember one particular instance where some of us went out to rue de mouffetard and I was just quiet and I didn't feel like I had a good way to break into the conversation. For some reason, I was not in a very good mood.
One thing that is somewhat related is that I am not sleeping particularly well (I am averaging around 7 hours). I anticipated this earlier in the trip but now that it is happening, I am not sure that I am going to do much about it. When I am tired, I am less likely to speak up.
Looking at how I've been feeling, it is a bit strange that I have been so concerned with these small social issues. In the past, these things have not been on my mind. One aspect of it for me is that I feel like my relationships with the people on this trip are changing quickly (I know a few people that I have changed the way that I am acting around them a lot since the start of the trip). The main insecurity for me is that I don't want to feel like I don't have anybody to go around with.
In a related note, I have to be very careful with how I manage my time. I have been devoting a lot of time to social activities. I am taking the GRE general test on the 27th so I really do need to study for that more than I have been doing. I also feel that I haven't quite been doing as much as I could be on my research. One of the things that I have noticed is that it takes us a really long time to get dinner and I do not get that much done during the evenings. I think that until the 27th, I need to not be going out most of the time. I have some reservations about doing this because of the social issues that I mentioned above. I am glad that I chose that date though because I can then just be done with all of that and enjoy the rest of the summer.
In a bit unrelated note, I have noticed that I really do enjoy a bit of alone time. Tonight, I just sifted through my emails and watched a few starcraft videos. This was relaxing for me and I do like to have time with my thoughts. We are always running around and I think that it is great to have some personal relaxing time.
As always, there is way too much for me to talk about. Next time, I will talk more about my travels in the past few days and some things about research. Hopefully I get to do a practice GRE tomorrow morning...
Anyways, I would say that I am in the erratic stage now. For the most part, I have been having a great time with seeing all that there is to see in France. I enjoy seeing the city but more importantly I have enjoyed interacting with French people. Too bad that I don't have time to do some type of French class. I feel like I am solidifying my French knowledge but I am not learning that many new things. But one thing that has been getting to me a bit is that I do feel like is that my social situation is unstable and that I have to put a lot of effort into that.
One example is that when we are in a group, I feel like I need to be loud otherwise my voice gets drowned out. In general, I am a person who likes to talk to people one on one. I feel like I have had good small group conversations with people but in the larger group I am sometimes quiet. This is not that different from other parts of my life but I do wish that I was more dynamic in a group setting at times. I remember one particular instance where some of us went out to rue de mouffetard and I was just quiet and I didn't feel like I had a good way to break into the conversation. For some reason, I was not in a very good mood.
One thing that is somewhat related is that I am not sleeping particularly well (I am averaging around 7 hours). I anticipated this earlier in the trip but now that it is happening, I am not sure that I am going to do much about it. When I am tired, I am less likely to speak up.
Looking at how I've been feeling, it is a bit strange that I have been so concerned with these small social issues. In the past, these things have not been on my mind. One aspect of it for me is that I feel like my relationships with the people on this trip are changing quickly (I know a few people that I have changed the way that I am acting around them a lot since the start of the trip). The main insecurity for me is that I don't want to feel like I don't have anybody to go around with.
In a related note, I have to be very careful with how I manage my time. I have been devoting a lot of time to social activities. I am taking the GRE general test on the 27th so I really do need to study for that more than I have been doing. I also feel that I haven't quite been doing as much as I could be on my research. One of the things that I have noticed is that it takes us a really long time to get dinner and I do not get that much done during the evenings. I think that until the 27th, I need to not be going out most of the time. I have some reservations about doing this because of the social issues that I mentioned above. I am glad that I chose that date though because I can then just be done with all of that and enjoy the rest of the summer.
In a bit unrelated note, I have noticed that I really do enjoy a bit of alone time. Tonight, I just sifted through my emails and watched a few starcraft videos. This was relaxing for me and I do like to have time with my thoughts. We are always running around and I think that it is great to have some personal relaxing time.
As always, there is way too much for me to talk about. Next time, I will talk more about my travels in the past few days and some things about research. Hopefully I get to do a practice GRE tomorrow morning...
More Paris
So there are just way too many things to talk about so I will try to be brief. We moved into our new living area, "Cite universitaire". The goal of this place is to house international students studying in Paris. Most of the major countries have a house. We live in the German house. The room is somewhat bare bones. We have to walk down the hallway to go to the bathroom and shower. I have never lived in dorm like this but it will not be that big a deal. Honestly, I hope to spend as little time as possible in the room. The cite universitaire campus is really nice. I have taken a lot of pictures of the different buildings. There is also a lot of open space for relaxing or playing sports.
Yesterday, we went to centre pompidou. I am not a big fan of modern art but it was fun to see. One trend that seemed new to me is that the modern art pieces included sound as well as visuals. One of my favorite pieces involved a bunch of mirrors hanging down from the wall and the way that they were situated allowed for you to see multiple images of yourself. I enjoyed reading some of the descriptions of the art work. One of the funniest was something along the lines of: this artist's trademark is to paint alternating white and colored stripes that are approximately 8.7 cm. Then the piece of art was just a wall painted in stripes. But I suppose if this guy can tell a good enough story to sell his art, good for him.
Another cool thing that I did was that I played some frisbee with french people at Cite. They were very nice to me and allowed me to play. They didn't speak very much english but we got along fine. They invited me to play with them again (they play every thursday evening). In the near future, I hope to go around and talk to more people at Cite. The people there are especially friendly.
Another interesting thing is that Thursday was a holiday so most French people take Friday off as well. There are not that many people in the lab and most of the eateries in the area where I work were closed.
Anyways, onto research:
I feel a bit intimidated by my project because I feel that there has been a lot of work done on it already. However, I know that isn't the correct attitude so I will continue to read more papers. Even if I don't get any results, I think that I will learn how to make progress on a difficult problem. For now, I am playing around with matlab because I want to use some simulated data. I prefer using mathematica but knowing how to use matlab would be a good skill for me to have. I have spent most of the day wrestling with matlab. At the moment, my goal is to write matlab code that allows me to convert simulated reflectivity data into phase data. I can compare this phase data with simulated phase data. So far, my results are not that good but that is not much of a surprise.
Yesterday, we went to centre pompidou. I am not a big fan of modern art but it was fun to see. One trend that seemed new to me is that the modern art pieces included sound as well as visuals. One of my favorite pieces involved a bunch of mirrors hanging down from the wall and the way that they were situated allowed for you to see multiple images of yourself. I enjoyed reading some of the descriptions of the art work. One of the funniest was something along the lines of: this artist's trademark is to paint alternating white and colored stripes that are approximately 8.7 cm. Then the piece of art was just a wall painted in stripes. But I suppose if this guy can tell a good enough story to sell his art, good for him.
Another cool thing that I did was that I played some frisbee with french people at Cite. They were very nice to me and allowed me to play. They didn't speak very much english but we got along fine. They invited me to play with them again (they play every thursday evening). In the near future, I hope to go around and talk to more people at Cite. The people there are especially friendly.
Another interesting thing is that Thursday was a holiday so most French people take Friday off as well. There are not that many people in the lab and most of the eateries in the area where I work were closed.
Anyways, onto research:
I feel a bit intimidated by my project because I feel that there has been a lot of work done on it already. However, I know that isn't the correct attitude so I will continue to read more papers. Even if I don't get any results, I think that I will learn how to make progress on a difficult problem. For now, I am playing around with matlab because I want to use some simulated data. I prefer using mathematica but knowing how to use matlab would be a good skill for me to have. I have spent most of the day wrestling with matlab. At the moment, my goal is to write matlab code that allows me to convert simulated reflectivity data into phase data. I can compare this phase data with simulated phase data. So far, my results are not that good but that is not much of a surprise.
Wednesday, June 1, 2011
Another Day of Research
So I am really getting started on my research. I am pleased that I will be doing a challenging project. To review, there is a mathematical relationship between the reflectivity and the delay (phase delay) of a mirror. Strictly speaking, this relationship requires that we know the reflectivity for all frequencies in order to determine the phase for a particular frequency. As it is not practical to measure the reflectivity for all phases, I am looking to approximate that relation so that the reflectivity only needs to be measured over a band. Also our lab builds mirrors by making layers of different metals. The lab uses a matlab program to optimize the depths of the layers. I am interested in learning how this program works.
Things to do:
1. continue to try to understand papers given to me and look at other papers that I have found on this subject
2. understand the matlab code used to simulate the reflectivity (this is more of a personal goal)
2a. learn about the simulated annealing algorithm
3. use simulated reflectivity data to estimate phase
3a. understand better what typical reflectivity data looks like for multilayer mirrors and see where the major contributions come from in terms of the
Today, I continued to read over the papers that one of the professors gave me. Now I am going to be more specific. So given a mirror, we can define a complex number called reflectivity, r(omega). This is a function of frequency. The magnitude of this complex number is the amplitude of the reflected wave divided by the input amplitude. The phase of this complex number is equal to the phase delay of the pulse after it is reflected. So it turns out that defining a complex reflectivity in this way has a number of nice properties. This is somewhat obvious, but if we write the input pulse in complex number form, then to transform that pulse (in the frequency domain), we just multiply by the reflectivity. So if we have a pulse in the time domain, we just Fourier transform it, multiply by the reflectivity, and then inverse fourier transform.
The other property that is really nice is that r(omega) is an analytic function (we extend omega to allow for complex frequencies) except at isolated points for Im(omega)>0. I am not quite sure why this is so. It may be arguable due to "causality arguments" but I am not sure. Anyways, experimentally, it is relatively easy to calculate R(omega) := |r|^2. So we know the magnitude but not the phase. We do a bit of a trick, we note that f(w) = ln r(w) = (1/2) ln R(w)+i phi(w) where phi(w) denotes the phase as a function of frequency. Since r is an analytic function, so is its logarithm. Now we know that the real an imaginary parts of a complex analytic function are related. This relation involves an integral from w=0 to infinity.
The formula that lets us calculate the imaginary from the real part requires that the real part be well behaved. In general, this is not a valid assumption so we need to do some normalization procedures in order to make the integral converge. As far as I can see, doing this requires some general knowledge of the function. Ex. for a semi infinite medium, the reflectivity for large frequencies is a real constant. Here, the integral diverges as ln(constant not equal to 1) is nonzero. So we divide out this constant and use that normalized reflectance to calculate the phase. I will write more about this when I get to it.
Things to do:
1. continue to try to understand papers given to me and look at other papers that I have found on this subject
2. understand the matlab code used to simulate the reflectivity (this is more of a personal goal)
2a. learn about the simulated annealing algorithm
3. use simulated reflectivity data to estimate phase
3a. understand better what typical reflectivity data looks like for multilayer mirrors and see where the major contributions come from in terms of the
Today, I continued to read over the papers that one of the professors gave me. Now I am going to be more specific. So given a mirror, we can define a complex number called reflectivity, r(omega). This is a function of frequency. The magnitude of this complex number is the amplitude of the reflected wave divided by the input amplitude. The phase of this complex number is equal to the phase delay of the pulse after it is reflected. So it turns out that defining a complex reflectivity in this way has a number of nice properties. This is somewhat obvious, but if we write the input pulse in complex number form, then to transform that pulse (in the frequency domain), we just multiply by the reflectivity. So if we have a pulse in the time domain, we just Fourier transform it, multiply by the reflectivity, and then inverse fourier transform.
The other property that is really nice is that r(omega) is an analytic function (we extend omega to allow for complex frequencies) except at isolated points for Im(omega)>0. I am not quite sure why this is so. It may be arguable due to "causality arguments" but I am not sure. Anyways, experimentally, it is relatively easy to calculate R(omega) := |r|^2. So we know the magnitude but not the phase. We do a bit of a trick, we note that f(w) = ln r(w) = (1/2) ln R(w)+i phi(w) where phi(w) denotes the phase as a function of frequency. Since r is an analytic function, so is its logarithm. Now we know that the real an imaginary parts of a complex analytic function are related. This relation involves an integral from w=0 to infinity.
The formula that lets us calculate the imaginary from the real part requires that the real part be well behaved. In general, this is not a valid assumption so we need to do some normalization procedures in order to make the integral converge. As far as I can see, doing this requires some general knowledge of the function. Ex. for a semi infinite medium, the reflectivity for large frequencies is a real constant. Here, the integral diverges as ln(constant not equal to 1) is nonzero. So we divide out this constant and use that normalized reflectance to calculate the phase. I will write more about this when I get to it.
Subscribe to:
Posts (Atom)