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The exact location that I went to was Santa Fe, New Mexico. I realize that the life outside New York City is completely different. Without a car, you can do nothing. When I planed to go there, I thought I could buy soap, shampoo blah blah blah there easily, just as in Manhattan. Oh my beloved Nature, that was completely wrong. The undergraduates there told me that I could get to the nearest CVS by walk in one hour. Fortunately the undergraduates were so kind that they drove me to CVS by car. The pace of life there is slower than in New York. People there are generally nicer and more polite than New Yorkers.

One thing that annoys me pretty much is that people there are quite religious. One can find churches everywhere. The buildings, streets are usually named as Saint XYZ. OK, that is just some names. Who care? Near Santa Fe, it is the Los Alamos National Lab (LANL). A cosmologist working at LANL told me that people in that town were pretty religious. As you may know, at LANL, some people are working on weapons of mass destruction. Those people are particularly religious. That seems to me pretty understandable. For atheists, we at most make fun of those religious people. But religion can drive people insane. They can do crazy things if they believe themselves to be messengers, disciples or whatever of the god, and they think you don’t believe in his god, or even worse believe in the wrong god.

Even within the participants in the workshop, they are more religious than my colleagues at NYU. One guy believes that god can change the laws of physics at will. Moses could violate the laws of physics when he separated the water in Red Sea. But he worked on dark matter observation. What if he observes is just some tricks played by god? Then his work is totally meaningless. I thing he should add in the paper that the phenomenon he observed can be an artifact due to god. What they work on and they believe are fundamentally inconsistent.

There are two possibilities for the higher percentage of “religiousness”. First simply people outside New York are more religious. Secondly, astronomers are more religious than physicists. For physicists, the laws of physicists are fundamental, it can’t be changed arbitrarily. I will never ever identify myself as an astronomer.

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Thank Keith for inviting me to blog about our recent paper. In this post I will briefly talk about the paper that Roman Scoccimarro and I just uploaded to the arXiv. I will keep it brief and elementary, so for more details, please refer to the original paper arXiv:0906.4548.

Here is the abstract

Large-Scale Structure in Brane-Induced Gravity II. Numerical Simulations

Authors: K. C. Chan, Roman Scoccimarro

(Submitted on 24 Jun 2009)

Abstract: We use N-body simulations to study the nonlinear structure formation in brane-induced gravity, developing a new method that requires alternate use of Fast Fourier Transforms and relaxation. This enables us to compute the nonlinear matter power spectrum and bispectrum, the halo mass function, and the halo bias. From the simulation results, we confirm the expectations based on analytic arguments that the Vainshtein mechanism does operate as anticipated, with the density power spectrum approaching that of standard gravity within a modified background evolution in the nonlinear regime. The transition is very broad and there is no well defined Vainshtein scale, but roughly this corresponds to k_*= 2 h/Mpc at redshift z=1 and k_*=1 h/Mpc$ at z=0. We checked that while extrinsic curvature fluctuations go nonlinear, and the dynamics of the brane-bending mode $C$ receives important nonlinear corrections, this mode does get suppressed compared to density perturbations, effectively decoupling from the standard gravity sector. At the same time, there is no violation of the weak field limit for metric perturbations associated with $C$. We find good agreement between our measurements and the predictions for the nonlinear power spectrum presented in paper I, that rely on a renormalization of the linear spectrum due to nonlinearities in the modified gravity sector. A similar prediction for the mass function shows the right trends but we were unable to test this accurately due to lack of simulation volume and mass resolution. Our simulations also confirm the induced change in the bispectrum configuration dependence predicted in paper I.

DGP model is an extra-dimension model, which has one co-dimension, and ordinary matter lives on the 3-brane. The graviton propagator is modified in the infrared. One of the interesting properties of this model is that it exhibits self-accelerating solution. The hope was that the recent observed cosmic acceleration may be due to modification of gravity rather than the mysterious dark energy. However, both theoretically and observationally, this model is proved to be unfavorable. However, this model has inspired a bunch of more sophisticated models such as degravitation, galleon. One of the serious problem in modification of gravity is that it induces new degrees of freedom. The theory can usually be approximated as a scalar-tensor theory. But any scalar degree of freedom is likely to be highly constrained by current solar system experiments. There are two nice ways have been put forward to evade this kind of constraints. One of them is chameleon mechanism, which has been realized in gravity. The other mechanism is called Vainshtein effect, which is incorporated in DGP and some massive gravity models. The scalar degree of freedom becomes strongly coupling and frozen because of the derivative self-interactions. The theory effectively becomes GR.

In this paper, using numerical simulations, we study this type of brane-induced gravity in the nonlinear regime, in particular the Vainshtein effect. We compute the cosmological observables: the power spectrum, bispectrum, mass function, and bias, which give us the signatures of the DGP model, and help us to differentiate modified gravity model from dark energy. In the companion paper arXiv:0906.4545 by Scoccimarro, the model is studied by perturbative calculations. Some of the results are checked against the numerical results in this work.

The method we used is the *N*-body simulation, which is largely similar to the standard gravity one. However, in GR, the field equation in the subhorizon, non-relativistic regime is just the Poisson equation, now we need to solve a fully nonlinear partial differential equation. Let me write down the equations although I am not attempting to explain it in details

The first equation is analogous to the Poisson equation, but now we have one more field *C*, whose equation of motion is given by the second one. The nonlocal term like can be easily handled in the Fourier space. The real headache comes from the nonlinear derivative terms and . One of the major achievement in this paper is that we developed a convergent method to solve this set of equations consistently. It involves alternate use of relaxation and Fast Fourier transform (so we call it FFT-relaxation method). Although that is a main result of the paper, I am not going to talk about it in details so as not to get too technical and dry. But interested readers are welcome to read the original paper.

Let me get to the results. As I have mentioned, from the simulations we have measured the power spectrum, bispectrum, mass function and bias. Here I only show the power spectrum.

In the first figure we show the power spectrum from three different models, which are the fully nonlinear DGP model (nlDGP), linearized DGP model (lDGP) and the GR with the same expansion history as the DGP model (GRH), which essentially is the GR limit. In order to see the difference more clearly, we have shown the ratios of power spectrum from various models, and in the lower figure. In the large scales (small k), the full nonlinear DGP model reduces to the linear one. More interestingly in the nonlinear regime (large k limit), the fully nonlinear DGP model approaches the GR with the same expansion history. This demonstrates that Vainshtein effect drives the model towards GR limit in the large k regime. The transition is broad and the limit is not yet fully attained in the range shown here.

OK, let me summarize some of the main results here. We have developed a convergent algorithm, FFT-relaxation method, to solve the fully nonlinear field equations in the DGP model. This enables to compute the observables like the power spectrum in the DGP model using numerical simulations. We have demonstrated the Vainshtein effect, and the Vainshtein radius at is about 1 h/Mpc. For more details, please refer to our original paper arXiv:0906.4548.

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When you put the modules on the table they glow and interact with each other to generate sound. You can either add more blocks to it and/or move the blocks to generate new effects. You can just create music by hands. I don’t know if you can program the interaction between the blocks yourself or not. It is cool, isn’t it? For more details see Reactable’s web site.

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The beggars people usually have in mind, at least I have in mind, are usually humble and pitiful. But this is not the case in New York. Beggars can be found everywhere here, particularly in the subway. I find it very annoying because I commute by subway everyday.

“Ladies and gentleman, sorry for disturbing you. My name is Peter. I am homeless, jobless. I am hungry. I have XYZ disease. Blah, blah, blah… I am grateful if you can give me some money or change.” Then the guy goes around the compartment to collect money when somebody is kind enough to give them money. The guy then goes to another compartment to continue his speech. The guy’s voice is loud and clear despite the fact that the guy claims himself to be “sick and hungry”. From the speech, I get the impression that the guy’s voice is energetic and confident, it sounds we have the responsibilities to pay him. Most of the time the beggars decently, sometimes they wear better than I do. In one occasion, the beggar wears a suit, isn’t it totally ridiculous? Should I call them gentlemen instead of beggars?

Most of the time I ignore them. But some people are “kind” enough to give them money. Let’s estimate how much money they make. From my observation, they get on average one dollar in each compartment in the train. Suppose this takes, say 5 minutes. So they make 12 dollars in one hour. Let’s assume they work 8 hours in one day. They make 96 dollars in one day. If somebody gets about 100 dollars a day, how likely that he suffers from hunger? That’s totally ridiculous. In fact, they make more money than I do! As a poor graduate student, I only get 70 dollars each day from the stipend. So I am poorer than a beggar!

So I will say those people who pay these beggars are not kind, but stupid. Almost all those people who ask for money are stronger and bigger than me, and have no apparent disabilities. OK, if they want to find a job in Wall Street, it can be difficult. I don’t think it is so difficult to get a job in McDonalds’ or in a pizzeria. They don’t do it because those stupid people keep on paying them money. This “job” as a beggar is easier and maybe more profitable than being a worker in a restaurant.

My observation is only limited to New York City. I don’t know if this is a local phenomenon, or it also occur in other parts of America. This is one of the ridiculous things I find in New York.

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Well, there is a rather interesting report appear in Nature, Entangled mechanical oscillators. You can you find it on arXiv 0901.4779.

You probably have heard of quantum entanglement many times, which means that the state is not factorizable. A famous example is the Schrdinger’s cat. Measurement causes the wave function to collapse. When you do measurement you either push the cat to the hell or drag it out of the hell. But this is still a thought experiment. Not just because physicists are kind to animals, but also it is impossible to do it on macroscopic scales because of decoherence. All the examples I heard of are limited to entanglement of spin or polarization. But in this the Nature report, a group of physicists at NIST have managed to convert spin entanglement to mechanical oscillations. The experimental details are technical, and I don’t really understand. In (and only in) simple terms, they first entangle the spin of two magnesium and two beryllium ions, and then separate them into two potential wells. In each well, there is one magnesium and one beryllium ion, which form an oscillator in the potential well. They then carry some measurements which create the motional entangle state. I don’t understand how they really do it. For those interested in, you should consult their paper.

The significance of this paper is they have for the first time created mechanical entangled states. This is one important step towards Schrdinger. But, cats, no panic, there may be still 500 steps away.

Incidentally, there is an article in Science describing this paper. The article is fine. But don’t read the comments if you don’t know much about this subject. I find them dubious, if not totally ridiculous. You may want to check it against John Baez’s crackpot index.

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Recently nongaussianity is rather popular topic in cosmology. The primordial density fluctuations in the early universe is very Gaussian. What I mean is that one can think of the density fluctuations drawn from a Gaussian distribution. The Gaussian field is completely characterized by its 2-point correlation function (or power spectrum in Fourier space.) Inflation, at least in simple models, predicts that the fluctuations are highly Gaussian. Because of the nonlinearity of gravity, a small amount of nongaussianity is generated. But the amount is not possible to detect in foreseeable observations (although some claim that 21 cm may do it). The common parametrization for nongaussianity is , where is the Gaussian potential. That is the nongaussianity is generated by the nonlinear in . This is a phenomenological expansion in , and you can add more terms if you like. The current observational efforts are to constrain the value of .

There are two kind of observations that allow people to probe nongaussianity. They are cosmic microwave background and large scale structure. Gaussian field has zero 3-pt function (or bispectrum in Fourier space). So people look for bispectrum in these observations. So far the best limit on is from WMAP data, but obtained by a group other than the WMAP team. The limit is (95% confidence level). It will be really interesting if the future data exclude 0.

I may talk about nongaussianity more in future if I run out of stuffs to say.

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So far I only use Google as a search engine. In fact I realized I use more than that, e.g. Youtube, maybe more. I still refuse to use Gmail although most of my colleagues use it now. The reason that I worry that Google has really a lot of momentum. In last few years or so, Google has released new products that kick other competitors’ ass. Google’s products are dominant in the market, everybody search using Google, email using Gmail, look for directions in Google map, watch videos on Youtube … It has the potential to eliminate all the competitors and take over the world.

But I now hesitate. Well, Google just makes our life easier. What do you want? The reason that everybody uses it simply because it is free and of high performance. This is just a demonstration of the survival of the fittest. The latest product Google wave is good for scientific collaboration. After all, Google seems very friendly to science so far. Google supports open software, which I personally admire.

Now I begin to question am I simply stupid pig headed, and making fuzz out of nothing? If Google is going to take over the world, the world may be of better shape than it present form.

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There are many plotting softwares available. However, I am a fan of the open software, and try my best not to use the commercial softwares, like Matlab and Origin, in plotting. Besides saving money, I admire the cause of open softwares. So far I can limit myself to using only open softwares happily (except Mathematica). So I will only talk about the open softwares only.

So far, I only need to plot not-so-fancy 2D graphs. I have tried several free plotting softwares, including xmgr, gnuplot and matplotlib.

xmgr is a graphical (GUI) plotting tool. Since it is GUI, it is relatively easy to start with. The quality is also good, as far as I remember. For those who used to use GUI, this is a good choice. But somehow I stop using it because it is not installed on the Linux system here at NYU. (Is it xmgr less popular than two other plotting tools? Is it not a routine part of the Linux distribution?)

Both gnuplot and matplotlib are script plotting tools. I think it is harder to begin with, in particular for people still live in the Windows world. If you use Linux or Mac, you probably are familiar with terminal and command-line approach already. I used to use Windows, and I found it pretty hard to accept the command-line softwares at that time. After quitting Windows, I am quite comfortable with scripts now. Of course, you don’t type the scripts every time. The first plot may be painful and time-consuming as you need to find out the appropriate commands to polish your graph. The second plot is going to be similar so you just need to copy from your old scripts. In the long run, the time required should be similar to, if not less than, the GUI plotting tool. I believe that the real master would use the scripts.

gnuplot is a sole plotting tool. The basic commands are easy to find online. I have been using it for some time. However, I (and some of my colleagues) find that the graphs from gnuplot still fall short of the publishing standard. Below I show the same data plotted using gnuplot and matplotlib respectively. Which one looks nicer?

I find the second one looks better, and it is plotted by matplotlib. If you think otherwise, I have nothing to say. matplotlib starts its life as a mimick of matlab, and it is a library in python. As you may know, python is a rather popular scripting language. To use it you have to import the matplotlib library in python. However to install the library may not be so easy, depending on your system. If you use Windows or Mac, you can install it easily using the Enthought Python Distribution, which is free for educational purpose. Certainly I satisfy this condition. I heard that installing it on Linux is pretty tricky. On one hand since it is just a library in python, you need to know the language python a little bit also, the potential barrier to overcome is higher than that for gnuplot. For example, I need to plot some graph using the columns of data in an ASCII file, I find it ridiculously complicated to do. It took me quite some time to google how to do it. On the other hand, as it is just a library in python, learning how to plot a graph using matplotlib you in fact have also started learning the python language. Isn’t it one stone two birds?

So what’s the conclusion? Which one is better? There is no conclusion. It is up to you to decide. I will use both gnuplot and matplotlib whenver convenient.

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