tag:blogger.com,1999:blog-267456202024-02-03T10:15:36.098-06:00Astronomers. In the wild.The universe from a lightcone centered in Mexico. Astronomy, physics, science and math sprinkled with some humor and mundane stuff.Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.comBlogger80125tag:blogger.com,1999:blog-26745620.post-64661033146778542872011-07-25T03:36:00.003-05:002011-07-26T15:55:39.255-05:00News from the solar neighborhood<div style="text-align: justify;">
The past week was a remarkable one for planetary science. Not only we had a probe arriving to an asteroid but also the solar family welcomed a new member.</div>
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In one side we have that the probe <a href="http://dawn.jpl.nasa.gov/">Dawn</a> arrived to asteroid Vesta and is now in orbit around it. The story behind the whole mission is quite interesting. Actually the mission was cancelled many times and was only successful after the contractor (<a href="http://www.orbital.com/">Orbital Sciences Corporation</a>) offered to build the probe at cost. I certainly don't know of any other cases where the contractor ends up offering a whole probe at cost.</div>
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<a href="http://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Vesta_from_Dawn,_July_17.jpg/220px-Vesta_from_Dawn,_July_17.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Vesta_from_Dawn,_July_17.jpg/220px-Vesta_from_Dawn,_July_17.jpg" /></a></div>
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<i>Vesta as seen from Dawn after it entered orbit.</i></div>
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The scientific program of this probe is <i>quite</i> ambitious. It plans to visit two of the biggest members of the asteroid belt, Vesta and Ceres, which were chosen as representative of "young" and "evolved" asteroids. Additionally, Vesta is (allegedly) the source of many of the micrometeorites that produce shooting stars in the sky which made it a particularly attractive target of study. This is also the first time a probe enters around the orbit of two objects. In previous "tours" like the Voyager missions the observations were made during flyby's. A similar option was considered a few years ago for Cassini with a potential transfer to Uranus which would had required a 20+ year cruise time. Eventually, that option was discarded and it was decided to send Cassini in a collision route with Saturn.</div>
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In a different development, it turns out that Pluto (the good old planet, now dwarf planet) system has at least three moons. This was spotted with the Hubble Space Telescope and the new satellite will be most likely studied by the probe New Horizons during its expected flyby of the system. </div>
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<a href="http://news.bbcimg.co.uk/media/images/54184000/gif/_54184715_pluto.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="153" src="http://news.bbcimg.co.uk/media/images/54184000/gif/_54184715_pluto.gif" width="320" /></a></div>
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<i>The Pluto system as shown by latest Hubble observations.</i></div>
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<i><span class="Apple-style-span" style="font-style: normal;">If you add all this with the results that are being announced from EPS-HEP there is no doubt that the past week has been one of the most exciting in a long time.</span></i></div>
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Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com73tag:blogger.com,1999:blog-26745620.post-72182303825179215622011-07-15T21:52:00.004-05:002011-07-17T14:43:01.986-05:00What is the relevance of the JWST?<div style="text-align: justify;">
The James Web Space Telescope, the succesor of the Hubble Space Telescope is now under the very serious treat of termination due to budget cuts. The story goes like this: last week, the House Commerce, Justice, and Science Appropriations Subcommittee recommended the cancellation of the JWST project. This was followed when the full House Science, Space and Technology Committee approved the subcommittee's plan.</div>
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From a scientific standpoint this is a total disaster. We <i>need</i> the JWST if we are going to push the frontiers of current research to an epoch where the first stars and galaxies formed. The scientific case has already been <a href="http://blogs.discovermagazine.com/cosmicvariance/2011/07/07/why-we-need-the-james-webb-space-telescope/">well explained</a> by Julianne Dalcanton in Cosmic Variance so I don't need to repeat it again.</div>
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But, from the point of view of the average Joe in the street, what is the justification for pouring truckloads of money in the JWST? Maybe the most poetic justification reads something like it will enhance our comprehension of the origin of cosmos and the existence of life in it. But nonetheless, I find that, while completely true, this kind of answers are easy to dodge by any opportunistic politician who wants to present himself as the "hero of the community" by "saving the hard earned money of the community from falling into this resources swamp". </div>
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Well, this is utter nonsense. Let me tell you why. The principal outcome of massive scientific collaborations is not a stream of papers with the latest and greatest results about fundamental questions but <i>a stream of highly trained people who goes and contributes to the society in countless ways</i>. I can not really estimate how many people went on to get a PhD based on Hubble's data or research started by Hubble's observation and while a few of them remain in the academia most have gone into all other corners of life. Many of them have joined big corporations or started their own corporation and contributed to the development of many technologies that are now commercialized and now create jobs for the people producing and manufacturing them. That is not to mention the secondary sources of income that are created when this people go and spend their income. So please keep in mind that by shooting down the JWST you are not only shooting down the few professional astronomers in your district but actually the training of some of the most skilled people in the society, the kind of people who <i>will</i> later produce some of the best sources of income available in society.</div>
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<b>If you are in the USA, please take five minutes of your time and <a href="http://aas.org/policy/contact.php">contact your representative</a> to keep the JWST alive, the vote of the congress is still required to terminate this project. </b></div>
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If history can give us some clues as what can happen, let me mention the Superconducting Supercollider, the project that was supposed to lead experimental high energy in the late 20th and early 21st century. After its cancellation not only we as scientists remain with doubts about fundamental physics as the Higgs boson or superpartners but also the region of Texas where it was going to be built entered into a local recession and furthermore, now the advance of the field is led by the CERN in Europe, ending with decades of US dominance of the field. Please don't allow this to happen<i> again</i>.</div>
Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com14tag:blogger.com,1999:blog-26745620.post-10927870585268116142011-07-13T21:12:00.006-05:002011-07-18T13:36:28.188-05:00Blog v3<div style="text-align: justify;">
As anyone of you reading this has undoubtedly realized, the site has been completely overhauled. This is an attempt to bring it up to date in web standards. We now have an atom feed for updates, latex to mathml translation for maths and a new theme. You won't see it, but also the backend editor is new and is supposed to produce cleaner code. Let me know if you find any glitch with the new design.</div>
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On an unrelated thing. Neptune was discovered almost 165 years ago by John Galle who was looking for it after Adams and Le Verrier had predicted its existence based on the effect of Neptune on the orbit of Uranus. Since the orbital period of Neptune is 164.79 years we can say today that we are celebrating Neptune's first birthday!<br />
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<i>Happy "birthday" Neptune!</i></div>
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Interestingly enough, from his observational notebooks we know now that Galileo had observed Neptune in his telescope which was too rudimentary to actually show its disc and reveal it as a planet. Additionally, in a strike of bad luck he just happened to observe Neptune when its proper motion was less noticeable. Nonetheless, there is <a href="http://www.msnbc.msn.com/id/31835303">some evidence</a> that he was at least aware that it moved to respect the background stars. Unfortunately, bad weather prevented him to pursue this issue further. It is interesting how a small set of circumstances shapes history, not only of science.</div>
Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-42273085064442918372011-07-12T11:24:00.016-05:002011-07-24T23:28:23.813-05:00Linux kernel 2.38 and Ubuntu Natty: The devourer of laptops<div style="text-align: justify;">
Some of you have undoubtedly installed a Linux distribution featuring the kernel 2.38 (or a latter version). This kernel comes with Ubuntu 11.4 Natty Narwhal but also in Fedora 15 and some rolling release distributions like Arch or LMDE.</div>
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While installing a new fancy distro carries the advantage of bringing you with the latest packages including the new fool-proof desktop environments that have been recently in the spotlight (unity and gnome 3) it will also bring you to one of the most annoying bugs that I have dealt with.</div>
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All the Linux kernel versions starting with 2.38 made changes to the Active-State Power Management (ASPM) that have resulted in a <i>dramatic</i> power consumption increase. This might be not so evident for a desktop computer but can easily trounce the charge duration of a laptop by a third, not to mention the fact that it turns it into a portable pan.</div>
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To fix this we need to enable the <span class="Apple-style-span" style="font-family: monospace; font-size: 13px; line-height: 16px; white-space: pre;">pcie_aspm=force </span>option. The downside is that this might turn some systems unstable or even prevent them from booting. Use this at your own risk.</div>
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A simple way to see if this fix will work for your recently turned into pan laptop is to enable this option for a single boot. In Ubuntu you need to select your Ubuntu system and press <span class="Apple-style-span" style="font-family: monospace; font-size: 13px; line-height: 16px; white-space: pre;">e</span> in the menu that allows you to choose an operating system just after turning on your computer. This allows you to edit the boot options for this session. Locate something looking like <span class="Apple-style-span" style="font-family: monospace; font-size: 13px; line-height: 16px; white-space: pre;">quiet splash</span> and add <span class="Apple-style-span" style="font-family: monospace; font-size: 13px; line-height: 16px; white-space: pre;">pcie_aspm=force </span>inmediately next to it, separated by a space. If your computer boots and remains stable you will notice that it will heat considerably less and that battery life is extended.</div>
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Now, to make this change permanent we need to edit the bootloader. Open a terminal and enter:</div>
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which will ask you for privileges escalation (the password of the administrator). Then, look for this line</div>
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<span class="Apple-style-span" style="background-color: #ffe599; font-family: monospace; font-size: 13px; line-height: 16px; white-space: pre;">GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"</span></div>
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and change it to</div>
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<span class="Apple-style-span" style="background-color: #ffe599; font-family: monospace; font-size: 13px; line-height: 16px; white-space: pre;">GRUB_CMDLINE_LINUX_DEFAULT="quiet splash pcie_aspm=force"</span></div>
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Make sure that this is indeed how the line looks like, we don't want to screw the bootup. After that we need to update the bootloader:</div>
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And that's it, you have rescued your laptop from becoming your next broiler. Just reboot and the change must be there permanently.</div>
Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com16tag:blogger.com,1999:blog-26745620.post-71027725539041941122010-11-23T02:25:00.021-06:002011-07-15T21:56:04.941-05:00From the quantum world to the guy next door (part 1)<div style="text-align: justify;">
This post will be a little more technical than the usual ones. Nonetheless, I believe there ia "market" for it: students who are just learning quantum mechanics and might require to dispel much of the baloney that is told about the quantum weirdness. Recently I was discussing with one of the cobloggers of <i>astronomers in the wild</i> about some limerick from David Morin's <a href="http://www.amazon.com/Introduction-Classical-Mechanics-Problems-Solutions/dp/0521876222/ref=sr_1_1?ie=UTF8&qid=1290500985&sr=8-1">mechanics book</a>:</div>
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When walking, I know that my aim</div>
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And although I don't see</div>
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Where they walk next to me,</div>
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I know they're all there, just the same.</div>
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This is mentioned just as some side note when discussing the stationary action principle, specifically, in the context of learning if there is a deep reason behind it. The stationary action principle says that the quantity S, called the action and given by</div>
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\[ S= \int_{t_a}^{t_b} dt\ L(x,\dot{x};t) \]</div>
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should take a stationary value. That means that from all possible paths involved in getting from a to b, a classical particle will take the path in which the action takes a minimum value (well, actually a stationary one, usually the minimum). This is the principle behind classical mechanics. The motion of everything we can see around us, including the stars in the sky or matter around a black hole follow from this principle.</div>
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Hence, it would be great to know if there is a reason behind this principle. Well, yes, there is. It is deeply rooted in quantum mechanics and its essence is captured in above's limerick. </div>
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So, the purpose of the few next posts will be to see how we can pass from the quantum description of the world to the kind of phenomena we observe everyday when dealing with baseballs, pulleys and all that. </div>
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This is not a trivial question, every experiment has confirmed the validity of quantum mechanics as the correct description of our world but it is in stark contrast with the intuition we have all developed from observing microscopical objects all our life. Nonetheless, at first glance, both descriptions are radically different. To see how weird the quantum behavior is for us, macroscopic beings, let's consider one situation that shows most of the quantum subtleties: <i>the double slit experiment</i>.</div>
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Consider some particles source <i>S</i>, placed at a point <i>A.</i> In front of it, we place a screen <i>C</i> with two slits in it. Hence, we expect that any particle arriving to a screen at the point <i>B </i>where the arrival of electrons is measured must pass through one of the slits. This configurations is shown below.</div>
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<img alt="" border="0" id="BLOGGER_PHOTO_ID_5542666045663341170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhKylOty5CwXIYgvkM9EPxaPx9NASNYytFFOBQ4kgHNB-USO70tBVJkbbcTC8Pouerhco-KraJnjBQHMc5ZmKI9SHXPTrPqwcb68keS9vRwkjlNR6nwFUFm9zry-t4Du7HgbqF/s400/base.jpg" style="cursor: pointer; display: block; height: 396px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></div>
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Well, if we do this experiment with marbles, baseballs, grains of sand or any other classical object coming out of the source S, then the outcome will be just what we expect. Namely, if we shut one of the slits, then the distribution of arriving marbles at B will be peak just in front of the open slit. The resulting distribution of arriving marbles at B when both slits are open is just a sum of the peaks produced by the particles entering through each slit. This is shown below.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKPQ7jGjb2cW4JlL00OqWL2JImhgSLrNz1ZnwtOtdoIzYqBzP_LL4QOABy6XMq024zPZmUp1RPF6yCVy2uoxAbCXfqG1CIyXM8ST_InV5AySmTNsqPfPq9mdIGg_dIn3FPB8-e/s1600/particles.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5542667786625942274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKPQ7jGjb2cW4JlL00OqWL2JImhgSLrNz1ZnwtOtdoIzYqBzP_LL4QOABy6XMq024zPZmUp1RPF6yCVy2uoxAbCXfqG1CIyXM8ST_InV5AySmTNsqPfPq9mdIGg_dIn3FPB8-e/s400/particles.jpg" style="cursor: pointer; display: block; height: 396px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></a></div>
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<i>Here, the outcome of the double slit experiment with classical particles is shown. If we shut one slit, we get one sharp distribution (shown in blue). The outcome with both slits open is just the sum of the two peaks and it is shown in red.</i></div>
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There is a second classical object that we can throw against our screen at <i>C: waves</i>. So, lets imagine that we place the whole setup in a pool and the source at A stirs the water a little bit so it create waves. In a realist experiment, we should place <i>S</i> very far from <i>C</i> so we can have some nice plane waves arriving at <i>C</i>, but ignore such nuances for our purposes. When the incoming wave arrives to <i>C</i>, each slit will act as a new wavefront and produce an outgoing wave. Since we have two slits, the outgoing waves will be out of phase from some parts and in phase for others. This is better seen in the picture below.</div>
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<a href="http://www.webexhibits.org/causesofcolor/images/content/3doubleslit.jpg"><img alt="" border="0" src="http://www.webexhibits.org/causesofcolor/images/content/3doubleslit.jpg" style="cursor: pointer; display: block; height: 195px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 258px;" /></a><br />
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The darker zones correspond to places where destructive interference happens, namely where the waves are completely out of phase and cancel out. On the other hand, clear zones are where waves are in phase and constructive interference happens. The outcome of all this, is that the distribution at B will be different from the one we got using marbles as we now have some interference pattern, as shown below.</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXSardrcbqPfc6fr-6xyBtfDrd-I2IOE_vULJkRW5ohsSvEGAYIcoMm0FxbpYAiWNxVMhaWU0NV7GG4VdgBVSkqPjUTg-ms3c5zHsAxkaNznjXuLdHhwUTNGkqZpnp280qnPgj/s1600/waves.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5542670877057423346" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXSardrcbqPfc6fr-6xyBtfDrd-I2IOE_vULJkRW5ohsSvEGAYIcoMm0FxbpYAiWNxVMhaWU0NV7GG4VdgBVSkqPjUTg-ms3c5zHsAxkaNznjXuLdHhwUTNGkqZpnp280qnPgj/s400/waves.jpg" style="cursor: pointer; display: block; height: 396px; margin-bottom: 10px; margin-left: auto; margin-right: auto; margin-top: 0px; text-align: center; width: 400px;" /></a></div>
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As you can see, we now have many peaks and actually the biggest one is in front of a closed part of the screen <i>C </i>! This is just the result of the way waves behave: they can add or subtract from each other in stark contrast with marbles as we do not expect one marble to cancel another!</div>
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So, if an electron behaves exactly as a marble we expect that the chance of arrival at some point <i>x</i> of the target <i>B</i> will obey two simple rules:</div>
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I repeat, this is the case for classical particles. Even in classical mechanics we can get a different behavior by using waves, as illustrated above. Now, we use to imagine electrons as lil' charged things and with a big degree of naivety we would expect these two rules to extend to electrons. </div>
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Well, what happens when we use electrons? It turns out that <i>we get a distribution identical to the one we get from waves</i>! This is a good place to stop today, but nonetheless I should tease you a little. </div>
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The questions that arise immediately are:<i> is the electron a wave?</i> If so, <i>how can we reconcile that with our intuition that it should pass through one hole? how can we measure that? </i>As of now, we could actually say that the electron is indeed a wave. Nonetheless, that contradicts our experience of electric charge as a flow of electrons, which has proved to be extremely successful. Additionally, <i> </i>when using electrons to strip electrons from some metal the behavior is consistent with particles (its analog with photons is the well known <i>photoelectric effect</i>). Actually, all the subsequent discussion for the quantum case can be carried as well with photons. This kind of behavior with electrons behaving as confused teens not making their mind about being particles or waves is usually stated as the <i>wave/particle duality</i>. Hopefully, by the end of this series of posts you will agree with me that such duality is a rather childish way to describe things: electrons <i>are</i> particles, which get their peculiar behavior due to the way probabilities/amplitudes add. Furthermore, the mechanism to get the amplitude will lead us directly to the classical world with which we are all so familiar.</div>
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<i></i> Besides, now that we can not use the two rules stated above<i>, what rules should we use to calculate the distribution at B?</i> This last question is essential: the big difference between the classical and quantum world is in the way we calculate probabilities. That is the topic for the next post. Meanwhile, you can read what happened when this experiment was performed in 1998 by <a href="http://www.weizmann.ac.il/condmat/heiblum/papers/391871a0.pdf">E. Buks et al</a>.<br />
<br />
<b>For all you able to read spanish, I decided to continue this "story" in my spanish website: <a href="http://sanchezluis.x10.mx/personal">sinédoque</a>. This was due to the capabilities of blogger which were too meager at the time, specially regarding mathematical expressions. I have just implemented a new system on this blog so maybe some more "math heavy" posts will appear here in the future. <i>Keep tuned.</i></b></div>
Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com1tag:blogger.com,1999:blog-26745620.post-81816246350763612432010-02-15T09:56:00.007-06:002010-10-05T14:41:06.899-05:00The Towers of HanoiI don't know why but I recently came back to this old, interesting little problem. For those not familiar with the puzzle, here's an excerpt from Wikipedia:<br /><blockquote>[The Towers of Hanoi puzzle] consist of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. <p>The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:</p> <ul><li>Only one disk may be moved at a time.</li><li>Each move consists of taking the upper disk from one of the rods and sliding it onto another rod, on top of the other disks that may already be present on that rod.</li><li>No disk may be placed on top of a smaller disk.</li></ul></blockquote>Here's an image of how the initial configuration looks like with 8 disks (also from Wikipedia):<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7mlYDiJy1kXZqpQ1Yjh2JOZ2_NVAB7JlwNcAwrnXuBjsIloiHHnWq2fTpQINoTimfILT72JELhTgdxaGz2H04LXkCpg__vcGJ9nyPnOMbaVW2H2LfpKrXGxtTPw-kZplCy2HfMA/s1600-h/Tower_of_Hanoi_sm.jpeg"><img style="cursor: pointer; width: 320px; height: 141px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7mlYDiJy1kXZqpQ1Yjh2JOZ2_NVAB7JlwNcAwrnXuBjsIloiHHnWq2fTpQINoTimfILT72JELhTgdxaGz2H04LXkCpg__vcGJ9nyPnOMbaVW2H2LfpKrXGxtTPw-kZplCy2HfMA/s320/Tower_of_Hanoi_sm.jpeg" alt="" id="BLOGGER_PHOTO_ID_5438501565497666194" border="0" /></a><br /></div><br />Also, here's an applet of the puzzle so you can try to solve it yourself: <a href="http://www.mazeworks.com/hanoi/index.htm">MazeWorks - Tower of Hanoi</a>. Try with 3, 4 and maybe 5 disks, and see if you can solve it with the fewest number of moves.<br /><br />You'll notice that, according to that applet, the minimum number of moves for the puzzle with N disks seems to be <b>2^N-1</b>. The other day it occurred to me that this can be proven by mathematical induction easily, and that the procedure for doing so is actually the recipe for a recursive algorithm to solve the problem. I'll talk about these two items separately.<br /><br /><span style="font-size:130%;"><span style="font-weight: bold;">Proof that it takes 2^N-1 moves to solve the puzzle.</span></span><br /><br />We want to prove that a solution to the Towers of Hanoi problem requires 2^N-1 moves, where N>=1 is the number of disks to move. Let's proceed by mathematical induction.<br /><br /><span style="font-weight: bold;">1) Base case: we prove the claim is valid for N=1.</span><br /><br />If there is one only disk, moving it to the correct peg requires (trivially) a single move. And 2^1 - 1 = 1, which show what we want to prove is true for the base case.<br /><br /><span style="font-weight: bold;">2) Induction Hypothesis: we </span><span style="font-style: italic; font-weight: bold;">assume </span><span style="font-weight: bold;">the claim is valid for N=k, where k >= 1 is some number.</span><br /><br />This assumes that the solution to the k-disk problem takes 2^k - 1 moves. That is, we assume it takes 2^k - 1 moves to transfer k disks from one peg to an empty peg, using a third empty peg as auxiliary. Note that because of the rules, an "empty peg" is equivalent to "a peg containing one or more disks that are all larger than the disks we're moving".<br /><br /><span style="font-weight: bold;">3) Prove the claim holds for (k+1) disks: we must show that </span><span style="font-style: italic; font-weight: bold;">if</span><span style="font-weight: bold;"> the induction hypothesis is true, then we can prove that the claim is true for the (k+1)-disk problem as well.</span><br /><br />In other words, we want to show that if it's true that the k-disk problem requires 2^k-1 moves to solve, then the (k+1)-disk problem requires 2^(k+1)-1 moves to solve.<br /><br />So we want to solve the (k+1)-disk problem. Let's call the peg on which the disks initially reside the S (source) peg, the peg to which we want to transfer all the disks the D (destination) peg, and the third peg the I (intermediary) peg, which we'll use as auxiliary peg during the process. Then, we proceed as follows:<br /><ol><li>Move the upper k disks from the S peg to the I peg. This is possible since we assumed it in the induction hypothesis, which also establishes doing so takes 2^k - 1 moves. This leaves the largest disk alone on the S peg. </li><li>Now that it's possible, move the largest disk from the S peg to the D peg. The disk is now in its final position, so we don't have to move it again. This takes 1 move.</li><li>Move the k disks that were on the I peg to the D peg. Again, by induction hypothesis, this takes 2^k - 1 moves. It doesn't matter we're moving the disks to a non-empty peg, since the disk on the D peg is larger than any disk we're moving, and hence doesn't interfere with the task. The S peg is used as auxiliary peg in this process. After this, the problem is solved, for all disks lie on the D peg.</li></ol>So what was the total move count? In step i), we used 2^k-1 moves, in step ii) a single move, and in step iii) 2^k-1 moves again. The total:<br /><br />Moves = (2^k-1) + (1) + (2^k-1) = 2*(2^k) + (1-1-1) = 2^(k+1) - 1<br /><br />And so, we have proved that if it takes 2^k-1 moves to solve the k-disk problem, then it takes 2^(k+1)-1 moves to solve the (k+1)-disk problem. This, together with the base case whose validity we verified in the first step, makes the claim valid for all N. Q.E.D.<br /><br /><span style="font-weight: bold;">Optimality</span><br /><br />Note, however, that at first this proof does not guarantee this is the optimal number of moves needed to solve the problem, only that the N-disk problem can be solved with 2^N-1 moves. Luckily, it seems I can justify the optimality of the solution formally.<br /><br />Consider the following modified proposition, which we'll prove by induction too: "It takes 2^N-1 moves to solve the N-disk problem, and this is the minimum number of moves of any solution". This is trivially true for the base case (N=1).<br /><br />To prove the induction step, consider the following argument. We want to show that solving the (k+1)-disk problem requires a minimum of 2^(k+1)-1 moves.<br /><br />But consider that no matter how you solve the problem, at one point you'll need to move the largest disk to the D peg. Since the largest disk cannot be placed on top of any other disk, this means that the remaining k disks must be on the I peg when this happens. There is no other way this could be. So any solution strategy, no matter what is is, must pass through this common state.<br /><br />Now, by the (modified) induction hypothesis, moving k disks from one peg to another is done <i>optimally</i> in 2^k-1 moves. So putting the puzzle in the configuration required to move the largest disk to the D peg requires a minimum of 2^k-1 steps. Similarly, after the largest disk is moved to the D peg, transferring the remaining k disks to the D peg also requires a minimum of 2^k-1 steps.<br /><br />Finally, the middle step, moving the largest disk to the D peg, is trivially optimal, since we're moving a single disk.<br /><br />With this, we prove that if the solution of the k-disk problem requires a minimum of 2^k-1 moves, then the solution of the (k+1)-disk problem requires 2^(k+1)-1 moves, and that it is also the minimum number of moves.<br /><br />The uniqueness of the optimal solution is also proved with the same argument, since moving a single disk (both in the base case and in moving the largest disk to the D peg) is both optimal and the unique way to do it.<br /><br /><span style="font-size:130%;"><span style="font-weight: bold;">Solution Algorithm</span></span><br /><br />A nice thing of this proof by induction is that it naturally produces a recursive solution algorithm. Basically, we define a function, let's it call it Solve(n, A, B, C), that moves n disks from peg A to peg C, using peg B as intermediary. The function is defined recursively following the logic of the proof above (Python pseudocode):<br /><br /><code> def Solve(n, A, B, C):<br /> if (n==1):<br /> A.transferTo(C)<br /> else:<br /> Solve(n-1, A, C, B)<br /> A.transferTo(C)<br /> Solve(n-1, B, A, C) </code><br /><br />This is almost full Python code; it's only missing the data structure definitions needed to handle the disks and pegs. But it shows the heart of the algorithm. Note how the function calls itself recursively twice: first in a series needed to move the (n-1) disks to the intermediate peg, then in a second series to move the (n-1) disks onto the final peg. In each call, the peg order is changed to reflect which pegs are source, destination and intermediate.<br /><br />You can get the full Python code <a href="http://meithan.exofire.net/other/Hanoi.py">here</a>.Meithan Westhttp://www.blogger.com/profile/11188867674657701972noreply@blogger.com4tag:blogger.com,1999:blog-26745620.post-74994405044552257222010-01-11T10:01:00.004-06:002010-01-11T18:34:14.644-06:00LHC alarmism debunked<div style="text-align: justify;">I just attended a seminar by Michelangelo Mangano titled "<span style="font-style: italic;">Black holes at the LHC: safety and society</span>". While of course the bottom line was that there is no real risk of the LHC destroying the universe it is still worthwhile to discuss it a little bit.<br /><br />So, a little compendium of why you shouldn't be scared of LHC produced black holes:<br /><br /></div><ul style="text-align: justify;"><li>LHC is almost surely not likely to produce black holes, simple as that, most of the models predicting such scenarios work with additional dimensions and require a higher center of mass energy than would be available at LHC. Anyway, there are indeed some scenarios where black holes can indeed produced at LHC, they are not very plausible but a case can be surely made from them.<br /></li><li><span style="font-style: italic; font-weight: bold;">Black holes are unstable</span>: Black holes decay via Hawking radiation. Particles can be created out of "nowhere" in the vacuum, a rather sloppy argument essentially says that the uncertainty principle allows particles to pop out of nowhere as long as the energy loan required to create them is payed really fast. Now, consider one of this virtual particles being created just outside the black hole and the other one just inside of the black hole. The net effect for an observer outside the black hole is that black hole is radiating, in the process the black hole is loosing mass that is just escaping in this radiation. This radiation is not only electromagnetic, in principle a black hole can radiate anything.<br />This makes the black hole to "evaporate" as it looses mass via radiation, it turns out that the lifetime of a black hole is proportional to its mass. For black holes with really small mass, like the ones speculated to be produced at LHC this yields out such a short lifetime that there is not a reason to worry at all.<br />We can now be cynical and say that QFT in curved spacetime (the fancy name for the framework used to calculate this kind of things) is not really experimentally established, maybe there is something wrong with it and black holes could be stable, then you should consider that...</li><li><span style="font-weight: bold; font-style: italic;">Black holes produced in particle collisions are charged: </span>Collisions at hadron colliders happen between the <span style="font-style: italic;">charged </span>components of protons and conservation of charge requires that the final product (in this case a black hole) remains charged. Any charged particle, even a microscopic black hole interacts with matter in a way that has being throughly studied and is summarized in the so called Bethe-Bloch equation for the range of energies likely involved in the LHC. The result is that the black hole will just radiate all its energy away in a short distance. But hey, what if we are somehow missing something in the creation of microscopic black holes and it is possible to produce stable and neutral black holes? This looks extremely unlikely but lets go ahead and see what can happen if they are indeed produced.</li><li><span style="font-weight: bold; font-style: italic;">Accretion rates from microscopic black holes are negligible: </span>Lets say we have a slow moving, stable and neutral black hole. Can it eat the Earth and cause all other kinds of havoc? Well, if we model mass infall into a black hole via Bondi accretion (a fancy name for spherical accretion) it turns out that to gain a considerable mass, say 1 ton, a huge amount of time is required. Right now I don't remember now the exact number but it was of the order of a thousand millions of years. If a predator capable of running at most a 1mm per year is chasing you with bad intentions you wouldn't be scared, would you?</li></ul><div style="text-align: justify;">Well, despite this arguments there is still people around trying to halt LHC and the issue has even been brought to court, where it has always been dismissed based on technicalities, mostly because the LHC is out of jurisdiction of the court.<br /><br />So, why I am telling you all this? Well, wait for tomorrow...</div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-58488444654077284902010-01-01T11:19:00.012-06:002011-07-13T19:59:46.848-05:00Create wallpaper slideshow in Ubuntu 9.10First of all, happy new year! Nothing like the morning of a new year to be messing around with Linux and Python!<br /><br />One of the new things in Ubuntu 9.10 is that you can now use a wallpaper slideshow for your desktop, which will cycle your desktop wallpaper at regular intervals from a selected pool of wallpapers. The default Ubuntu 9.10 comes with a space-themed wallpaper slideshow, but there is apparently no option to create your own ones. However, the configuration is stored in plaintext XML files, one in /usr/share/gnome-background-properties and the other in the corresponding directory where the images are stored, in /usr/share/backgrounds.<br /><br />The following Python script will automatically create these two XML files so that you can set a wallpaper slideshow with the images of your preferences.<br /><br /><div><a href="http://meithan.x10hosting.com/other/SlideshowBuilder.py">Slideshow Builder script</a><br />(Right-click and select "Save Link As..", or the equivalent in your browser).<br /><br />Here's the instructions. You will need root access since the directory where you're doing the operations, /usr/share/, is owned by root. Simply use sudo (or sudo -i if you're lazy).<br /><br />1) Create a directory in /usr/share/backgrounds with the name of your slideshow. For instance, if the desired name is 'space', the dir should be called '/usr/share/backgrounds/space/'.<br /><br />2) Copy all the wallpaper images to that folder. The supported formats are jpg, png, gif and bmp.<br /><br />3) Run the Python script in the images directory. This will automatically create two xml files: one in the (current) images directory, and another one in /usr/share/gnome-background-properties.<br /><br />4) That's all! You can now select the slideshow in the Gnome wallpaper selection interface.<br /><br />A sample usage of the script is shown in the following image:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga_i_Qh3O33F0VfPn-oqaaLrc1d7zcruRYpW3afyMErlK53viPqQ1v64mfB7E2sklehwqYwyqGguF4dylifTA2rWcWBiEsiC83kJlj6cS3iZj6EBt89ynhd4mb5Cci_qz_YF8j1A/s1600-h/sample.png"><img style="cursor: pointer; width: 320px; height: 210px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga_i_Qh3O33F0VfPn-oqaaLrc1d7zcruRYpW3afyMErlK53viPqQ1v64mfB7E2sklehwqYwyqGguF4dylifTA2rWcWBiEsiC83kJlj6cS3iZj6EBt89ynhd4mb5Cci_qz_YF8j1A/s320/sample.png" alt="" id="BLOGGER_PHOTO_ID_5421831209334925634" border="0" /></a><br /><br />And the slideshow now appears in the desktop Background selection screen:<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoD8FuOPXVjkGYzX62CTg0p7odn8wbXoxPFBTn2lz3uF4qvQNrNbiKCTbAQEZ6aWDPQJRR6MWBRyRYTQMgJfvFCD4BdItBB4HH0qbAlUvlRw5hrgscIOhEfCjQuhtIFGe5I_wE6A/s1600-h/sample1.png"><img style="cursor: pointer; width: 320px; height: 270px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoD8FuOPXVjkGYzX62CTg0p7odn8wbXoxPFBTn2lz3uF4qvQNrNbiKCTbAQEZ6aWDPQJRR6MWBRyRYTQMgJfvFCD4BdItBB4HH0qbAlUvlRw5hrgscIOhEfCjQuhtIFGe5I_wE6A/s320/sample1.png" alt="" id="BLOGGER_PHOTO_ID_5421831379560374210" border="0" /></a></div><br /><br /><b>Update: </b> I've fixed the dead link to the script.Meithan Westhttp://www.blogger.com/profile/11188867674657701972noreply@blogger.com69tag:blogger.com,1999:blog-26745620.post-11460777215825183982009-12-18T06:44:00.003-06:002009-12-18T11:26:07.077-06:00No dark matter, yet...So, what happened with all this CDMS fuzz? The collaboration reports 3 events out of a expected background of 0.5. Nonetheless, one of the events was out of the "box", so lets forget about it. So, with 2 events we have a 1.06 sigma signal and with 3 events we have a 1.7 sigma signal. <br /><br />It is just a ridiculously low signal, and by no means can be considered a discover. Nonetheless, it is rather interesting and intriguing. Experiments using liquid targets have a significantly bigger mass and can catch up this signal in one, maybe two years to a level where it can actually be considered a detection, but, until then, the coin is still in the air regarding dark matter.Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com3tag:blogger.com,1999:blog-26745620.post-77009117854155456622009-12-17T13:36:00.002-06:002009-12-17T13:47:11.784-06:00CDMS results in a few hours!As most of you know, there is a rumor about CDMS getting some of sort of signal from its dark matter search. Well, in a few hours we will know if all the fuzz around it was justified.<br /><br />CDMS stands for cryogenic dark matter search. It is a solid state detector designed to "listen" the sound made by dark matter particles when they interact with the nucleus of the atoms in the detector. These interactions cause the nucleus to recoil, as a result of that the atoms in the detector (which are arranged in a lattice) vibrate and produce phonons (some sort of quanta of sound). This signal can be measured and used to detect the interactions of weak interacting particles.<br /><br />Now, this is only a very simplified description of the experiment. The practical difficulties are huge. First of all, random thermal vibrations can wash away very easily any signal, so the detector must be kept at really low temperatures. Then, collisions with cosmic rays will also spark the detector as fireworks, for this reason the detector is located underground in a deep mine in Minessota. But, how about other "backgrounds" like nuclear decay of particles in the rocks surrounding the detector? Well, the study of systematic backgrounds is really an art. One way to calibrate the detector is to place it close to some radioactive source and use the signal gathered this way to callibrate the detector.<br /><br />Early in the year, I saw the results of the CDMS collaboration and there was no signal (or hint of it), so it is hard to think that the results that are about to be announced will have 5-sigma signal (the usual threshold accepted as a detection), but maybe they got some sort of provocative signal at a smaller sigma level. Or maybe all the fuzz was just that, fuzz. <br /><br />Anyway, we will know the answer in a few hours!Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com2tag:blogger.com,1999:blog-26745620.post-79997941581896517652009-09-23T08:53:00.007-05:002011-07-14T12:53:34.882-05:00Fixing unrecognized File Type extensions in UbuntuI've had a little 'bug' in my Ubuntu for the past month that was annoying me a bit. I use TeXmacs for creating/editing small LaTeX documents. The problem is that Nautilus was incorrectly detecting the file type of .tm files, thinking they were plain text documents (see image below). The consequence is that TeXmacs files would be opened in gedit (or the default text editor) when opening them through the Nautilus file browser.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4CaJw5aVNDaOdTzWRJYke7hpEPw3CGYkKkfElhZfvMBVtgQUv56xrBQn_qb4UwGMD9VhgqtsZBJr3RI42YbDvtwkeAB_yFm6WWcGZYjBmXSIcR2JwJcTXbFNPXuGdIKYRWlv_7A/s1600-h/BadFileType.png" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5384665655675432802" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4CaJw5aVNDaOdTzWRJYke7hpEPw3CGYkKkfElhZfvMBVtgQUv56xrBQn_qb4UwGMD9VhgqtsZBJr3RI42YbDvtwkeAB_yFm6WWcGZYjBmXSIcR2JwJcTXbFNPXuGdIKYRWlv_7A/s320/BadFileType.png" style="cursor: pointer; height: 320px; width: 311px;" /></a><br />
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The first solution attempt was right-clicking a .tm file, going to "Properties -> Open With" and changing the default application to GNU TeXmacs. This was a disaster, since now *all* plain text files would be opened in GNU TeXmacs, since Nautilus genuinely believed a .tm to be the same as a .txt and thus changed the default application for all text files.<br />
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My second attempt at a solution (after googling a bit) was checking the MIME file type associations, which is the way Ubuntu associates an extension to a file type. The info is all in the file /etc/mime.types. However, to my disappointment, this file already contained a mime type for TeXmacs documents, indicated by the entry<br />
"text/texmacs tm ts". So even though the mime type was correctly recognized, it seems Nautilus wasn't picking it up. This could be further deduced from the fact that running the command <span style="font-style: italic;">file</span> on a .tm document in the terminal returned the correct mime type.<br />
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After more googling, I finally discovered that this is in fact a bug and found a fix for it:<br />
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<a href="http://savannah.gnu.org/bugs/?25938#discussion">http://savannah.gnu.org/bugs/?25938#discussion</a><br />
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Essentially, you manually create an xml file describing the TeXmacs mime type to <span id="hidsubpartcontentdiscussion" style="display: inline;">/usr/share/mime/packages and then manually update the mime database of the system (setting an icon for the file type is optional, but may be useful).</span> <span style="font-weight: bold;"><br /><br />NOTE:</span> the original poster of the above bug fix made a small typo: an extra semicolon (;) at the end of the line containing "<span style="font-style: italic;">mime-info xmlns=</span>" Remove it before trying to update the mime database.<br />
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After this is done, logout / re-log (or simply kill / restart nautilus from the terminal) and the new file extension should now be recognized:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPaGaeK9SOZaQK25IfdP77jL043JF-6uFxunM8O1igB_16W-cPAflh2QKTYkhyYxx3xu8jdeD-rUwW7JUHpwQDPc3bD4Ux5EKIrJHZMhe5wcFsRncYzQOZT7ZEtEZ80vNBvYGChQ/s1600-h/FixedFileType.png" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5384667435898739906" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPaGaeK9SOZaQK25IfdP77jL043JF-6uFxunM8O1igB_16W-cPAflh2QKTYkhyYxx3xu8jdeD-rUwW7JUHpwQDPc3bD4Ux5EKIrJHZMhe5wcFsRncYzQOZT7ZEtEZ80vNBvYGChQ/s320/FixedFileType.png" style="cursor: pointer; height: 320px; width: 312px;" /></a><br />
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The nice thing about this is that it should conceivably work for any other file type that has a correct mime type in /etc/mime.types but is not being recognized by Nautilus.<br />
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Hope this was helpful ;).Meithan Westhttp://www.blogger.com/profile/11188867674657701972noreply@blogger.com12tag:blogger.com,1999:blog-26745620.post-82592886871899480372009-09-18T10:04:00.004-05:002010-01-01T12:26:01.013-06:00Goodbye MP3s!The story - skip to the end if you only want the scripts and could spare my self-righteous opinion.<br /><br />I've used MP3 as my music compression format for years, as I'm sure most people have, without thinking too much about it. But my relatively recent ascension into Free Software has changed my perspective on many things related to software. Especially, it has given me the awareness that, in general, as a user I am the one in charge and I have the power to choose what I want to use and how I use it - or at least I should.<br /><br />MP3 entered the equation when I learned that Apple iPods do not play any other music format except WAV, MP3 and ACC related codecs (such as M4A). The reason for this is simple: these are patented, proprietary compression formats that Apple supports in order to introduce DRM (copy protection), using iTunes as a centralizing vehicle. While I can't deny their right to do so, I do believe this sort of policies go against the realization I exposed in the previous paragraph.<br /><br />I don't own an iPod. I have this small, very practical, albeit ugly, 2GB iBit music player that I bought at Sam's Club for under $80 that will play MP3, M4A, FLAC, OGG and pretty much any format I've thrown at it. Why would this small company support OGG while Apple does not? Would Apple lose business if they did?<br /><br />So, exercising my right of decision, I've abandoned the MP3 format in favor of free alternatives: OGG for standard music compression and FLAC if I ever need lossless compression. Converting all my music to OGG is no easy task, however, mainly due to the size of my music collection. In Windows, I'd probably have to find a small utility that can do the batch conversion, and it probably would cost me something.<br /><br />Fortunately, Linux is rooted at the most fundamental level on the basic premise that the power belongs to the user (as opposed to Apple's diametrically opposed mindset), and it provides countless tools that allow you to perform complex tasks with a minimum effort. So I took this as an opportunity to learn a bit about bash scripting and wrote a small script to handle the conversion for me.<br /><br /><span style="font-weight: bold;font-size:130%;" >The script</span><br /><br />Here's the link to the source code. Copy/paste to your favorite text editor, save and set execute permission (<span style="font-style: italic;">chmod +x mpeg2ogg.sh</span>).<br /><br /><a href="http://code.google.com/p/hydrodynamics/source/browse/trunk/scripts/mpeg2ogg.sh"><span style="text-decoration: underline;">mpeg2ogg.sh</span></a><br /><br />The script assumes you have two programs installed in your system: <span style="font-weight: bold;">mpg321 </span>and <span style="font-weight: bold;">oggenc</span>. The former handles MP3 decoding and the latter compression to OGG. If you don't have them, you can most certainly get them through your favorite package manager (in Debian/Ubuntu, all you need to do is a <span style="font-style: italic;">sudo apt-get install mpg321 vorbis-tools</span>).<br /><br />Using the script is simple. Navigate to the root directory of your music library (in my case this was /home/meithan/Music), copy the script there (or put it in a dir in your path), and run it . It will find all MP3s in the directory tree rooted in the current directory, and convert them all to OGG. The script builds a list of all the files that it finds and uses it as a queue: every time a file is converted, it removes that entry from the list. Thus, you can stop the script whenever you want, and just run it again at a later time and it will resume where it had stopped (reading from the file list.txt).<br /><br />A note: since I still don't trust my bashing abilities enough, the script won't delete your original MP3 files. You should first try the OGG files first, and then, if you're confident the conversion was successful, manually delete your old MP3s. Now, since "manually" means something completely different in Linux, here's a minimal script that will batch remove all MP3s in the current directory and its subdirectories:<br /><br /><a href="http://code.google.com/p/hydrodynamics/source/browse/trunk/scripts/mp3del.sh">mp3del.sh</a><br /><br />Hope my ranting and/or bash hacking are useful to someone.Meithan Westhttp://www.blogger.com/profile/11188867674657701972noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-16512756875896807192009-02-25T11:21:00.004-06:002011-07-14T15:28:05.741-05:00Coolest fish ever<div style="text-align: justify;">
The world is full of surprises and this amazing fish is certainly one of them. This 6 inch wonder is called Macropinna microstoma and features a transparent head!</div>
<br />
The fish, discovered alive in the deep water off California's central coast by the Monterey Bay Aquarium Research Institute (<a href="http://www.mbari.org/">MBARI</a>), is the first specimen of its kind to be found with its soft transparent dome intact.<br />
<h1>
<a href="http://i333.photobucket.com/albums/m400/mmagnum/Feb%202009/barreleyes.jpg" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" src="http://i333.photobucket.com/albums/m400/mmagnum/Feb%202009/barreleyes.jpg" style="cursor: pointer; display: block; height: 248px; margin: 0px auto 10px; text-align: center; width: 350px;" /></a></h1>
<div style="text-align: justify;">
Now, that small orifices in the front of the fish are <span style="font-style: italic;">not</span> its eyes but a smelling organ. The barrel eyes are inside the green barrels and can be rotated inside the transparent head, giving this fish a quite wide visual range.</div>
<h1>
<a href="http://news.nationalgeographic.com/news/2009/02/photogalleries/fish-transparent-head-barreleye-picture/images/primary/090223-02-fish-transparent-head-barreleye-pictures_big.jpg" onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}"><img alt="" border="0" src="http://news.nationalgeographic.com/news/2009/02/photogalleries/fish-transparent-head-barreleye-picture/images/primary/090223-02-fish-transparent-head-barreleye-pictures_big.jpg" style="cursor: pointer; display: block; height: 276px; margin: 0px auto 10px; text-align: center; width: 346px;" /></a></h1>
<div style="text-align: justify;">
The barreleye lives about 2000 feet under the surface, where it just stays floating with the eyes looking upward, when a prey arrives they usually have to steal it from siphonophores (jellies that can grow to more than 33 feet). To make this feat it rotate its eyes and goes straight for its prey! Quite amazing.<br />
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<br /></div>
Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com14tag:blogger.com,1999:blog-26745620.post-11740052177292393612009-02-09T20:22:00.002-06:002009-02-09T20:29:22.385-06:00The universe, yours to discover<div style="text-align: justify;">As probably all of you know by now, 2009 is the "year of astronomy", a sort of celebration of the 400th anniversary of the first astronomical observations using a telescope by Galileo (of course it is arguable if he was the first to do it, nevermind).<br /><br />Of course this blog will join this, so you may expect more posts here, it has been rather complicated posting to this site, it is always hard to grab some time specially since many posts that are intended to be just "quick posts" end up consuming a significant amount of time. It also seems to me that you can do lots of nice posts that will be quickly erased of everyones mind but you are always dangerously close to make some comment that might annoy someone, of course that will change when I get tenure!<br /><br />Anyway, lets see how this year unfolds!<br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-9713882034067651902008-06-22T21:24:00.003-05:002008-06-22T21:35:50.040-05:00Summer time<div style="text-align: justify;">The semester has ended and it's time for the summer adventures, certainly this summer promises to be loaded of adventure for me. Hopefully the posting frequency will increase, which is quite a good thing as this blog has been rather inactive lately.<br /><br />Right now I have just arrived to <a href="http://www.astrosmo.unam.mx/">CRyA</a> (Center for radioastronomy and astrophysics) to continue a collaboration on hypercompact HII regions (this regions are where massive star formation takes place, more on that on a some near post). The cab driver as soon as he heard I was an astrophysicist (student, of course) instantly replied: "<span style="font-style: italic;">but that's just an awful lot of f.....n maths</span>", and proceeded to tell me the stories of "all those crazy geniuses" like Dali, Einstein, Newton and that "nut economist" (don't ask me who that nut economist is), at the end of the trip I guess he had the impression that he thought I'm every bit as crazy as them (but way <span style="font-style: italic;">dumber </span>than them), which is fine, at least I'm in good company.<br /><br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-28644262404235512162008-04-21T22:27:00.008-05:002008-04-22T17:20:59.641-05:00Join the PAM!<div style="text-align: justify;">There is a nice project started by Julien Girard called <a href="http://pam.astroscu.unam.mx/mediawiki/index.php/Portada">wikiPAM</a>, the idea behind this project is creating a wiki for the mexican astronomical community (the name comes from Proyectos Astronómicos Mexicanos, or Mexican Astronomical Projects). Anyone doing any sort of research in astronomy with a mexican group can get an account there and post their work.<br /></div><div style="text-align: justify;"><br /></div><div><div style="text-align: justify;">This portal has a lot of potential, you can post your code (or modifications to it), your data, an announcement for your future projects... It seems to me like a wonderful tool for a grad student looking for a thesis project.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">As far as I know it is possible to post there information only accessible to people in the same research group, so you can also use it to share confidential information to the rest of your group without anyone else seeing the data before it is made public.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">There is also a portal for astronomical societies (i.e. amateur astronomers) in Mexico, it is called <a href="http://pam.astroscu.unam.mx/cosmowiki/index.php/Main_Page">Cosmowiki</a>. If you can read spanish look at <a href="http://pam.astroscu.unam.mx/cosmowiki/index.php/VER_COMPLETO">this interesting account</a> of the first mexican connection to internet that I found at cosmowiki, clearly showing its potential for outreach.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">I conclude this small post inviting <span class="Apple-style-span" style="font-style: italic;">you</span> to join this nice idea, you "only" need to be involved in research that somehow has the participation of the mexican astronomical community in it (for example having mexican astronomers in your group, or using mexican instrumentation like the <a href="http://www.lmtgtm.org/">LMT</a>).</div></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-1718280146407377052008-04-14T20:22:00.002-05:002008-04-14T20:26:11.175-05:00National astronomy meetingTomorrow starts the national astronomy meeting, this is the only event of the year when all the astronomical community meets in a single place and it's also a great occasion for seeing old friends from other institutions. I'll be participating with some of my work in regions of massive star formation.<div><br /></div><div>Hopefully I'll be posting soon about the interesting stuff that emerges there.</div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-74869952552787378972008-03-01T19:34:00.009-06:002008-03-02T11:12:22.757-06:00A new kind of supernova<div style="text-align: justify;">We are sure that at least two kinds of astrophysical black holes exist, one kind correspond to black holes of stellar mass (around 8 times the mass of the sun or bigger) and the black holes at the centers of galaxies with millions of solar masses. For some time there was speculation about the existence of some intermediate mass black holes with masses around few thousands the mass of the Sun, evidence from the rotation of stars in globular clusters gave the first evidence for the existence of intermediate mass black holes.<br /></div><div style="text-align: justify;"><br />Despite evidence from the rotation of stars around the centers of globular clusters, the case is far from closed, the centers of globular clusters are regions of high density, filled with degenerate stars (mostly <a href="http://en.wikipedia.org/wiki/White_dwarf">white dwarves</a>) and maybe the rotation speeds can be explained by an overabundance of stars. A new paper (<a href="http://www.faculty.iu-bremen.de/srosswog/RRH_2007.pdf">available here</a>) by Stephan Rosswog, Enrico Ramirez-Ruiz, and William R. Hix proposes a radically new method for searching this black holes.<br /><br />In close binary systems composed by a <a href="http://en.wikipedia.org/wiki/Red_giant">red giant</a> and a white dwarf, the white dwarf can steal some matter from the red giant star (which has a low surface gravity), matter falling into the white dwarf has angular momentum and as a result of that an <a href="http://en.wikipedia.org/wiki/Accretion_disk">accretion disk</a> is formed, white dwarves are supported against gravitational collapse by electron degeneracy (essentially if you try to pack electrons too closely they will start to move faster as a consequence of the uncertainty principle), this degeneracy can only support a mass of about 1.4 solar masses (otherwise the electrons would move faster than light), this is known as the <a href="http://en.wikipedia.org/wiki/Chandrasekar_limit">Chandrasekhar limit</a>, so when the white dwarf has "stealed" enough mass from its companion it will eventually surpass this limit, in this case the star is reignited by a mechanism known as <a href="http://en.wikipedia.org/wiki/Carbon_detonation">carbon deflagration</a>, creating a supernova explosion of the IA type.<br /><br />Now, enter intermediate mass black holes. Computer simulations including gravity, hydrodynamics and nuclear physics show the effects of a close interaction between a white dwarf and an intermediate mass black holes. The star is heavily disrupted by tidal effects and acquires a pancake-like form, as the star is squeezed there is a dramatic increase in pressure and the star is reignited and creates a new kind of supernova, around half of the mass is ejected and the other half falls into the black hole creating an accretion disk that should emit x-rays.<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.ucsc.edu/news_events/img/2008/01/coldens-350.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 342px; height: 503px;" src="http://www.ucsc.edu/news_events/img/2008/01/coldens-350.jpg" alt="" border="0" /></a><span style="font-style: italic;">This image shows the interaction of a white dwarf and a black hole, the star is heavily deformed in the first two frame, in the intermediate frames the star reignites and explodes, the "bubble" is the ejected material and at the bottom left corner an accretion disk is formed, the last two frames follow the evolution of this disk.<br /></span></div><br /><div style="text-align: justify;">While this supernovas should be much scarcer than usual IA supernovas, new surveys like the <a href="http://www.lsst.org/lsst_home.shtml">LSST</a> should detect enough supernovae to have a good chance of detecting this events, and x-ray emission should be detectable by the Chandra Space Telescope. The light curve should be different, although I haven't seen any detailed model. Considering that globular clusters are composed mostly of old stars and large populations of white dwarves this events should be happening relatively frequently around the universe and might give us unequivocal evidence of intermediate mass black holes.<br /></div></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-87887440465735582662008-02-17T18:07:00.004-06:002008-02-17T18:26:13.709-06:00Back to classes<div style="text-align: justify;">This weeks have been a bit hectic, the new semester has started and I have been busy handling endless tasks (which is why I haven't posted much in these days).<br /><br />This semester I will lecture for half of the general astronomy course, mostly about celestial mechanics (Keppler's laws, tides, Roche lobe and Lagrange points) and some practical optics (mostly the types of telescopes and the effect of diffraction on a telescope's resolution). The later half of the course is about stars and galaxies but I won't be lucky enough to lecture about <span style="font-style: italic;">that</span>.<br /><br />This seems to be a good place to hear your opinions/ideas about this kind of courses, I have always believed that these courses should be accessible to sophomores (or even freshmen), and with an emphasis on stars, galaxies and the universe more than an "applied physics" course (specially with central forces being discussed in most classical mechanics courses and the Rayleigh limit in optic courses), this could serve the double purpose of exposing students to the wonderful ideas of astronomy even if they lack a strong physics background and help to lure students in to the more advanced astronomy courses. What do you think?<br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-50582414278696404122008-01-25T13:29:00.001-06:002008-01-25T23:15:16.938-06:00Star formation 101. Part 1<div style="text-align: justify;">The time has come to pay one of the old debts of this blog: A mini-course on star formation. The night sky is full of little twinkling stars, but despite their obvious abundance its formation is still far from being a closed case.<br /><br />Gravitational collapse (a cloud of interstellar gas collapses and produces stars) is the obvious way to produce stars , but it leaves us with a startling question, we can estimate the time of this collapse using the expression:<br /><br /><div style="text-align: center;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?t_%7Bff%7D%20%5Csim%20%5Cfrac%7B1%7D%7B%5Csqrt%7BG%20%5Crho%7D%7D" alt="" align="middle" border="0" /><br /></div><br />which is called the free fall time and as you can see it only depends on the density of the cloud and not of its size, for a typical cold cloud this time is around one million years, this is obviously problematic because we know galaxies are much older than that and we can observe star formation in practically every spiral or irregular galaxy.<br /><br />This indicates us that other forces are acting on molecular clouds, slowing the process of gravitational collapse. There are four hurdles that star formation has to overcome, as we will see in this star formation series it is surprising that even a single star can overcome this hurdles! This hurdles are:<br /><br /><ul><li><span style="font-weight: bold;">The pressure hurdle: </span>A homogeneous, spherical gas cloud is stabilized against collapse by its own pressure gradient. This means that the temperature of the cloud despite being small still implies enough energy for the particles in the cloud to overcome their own gravitational attraction. We can estimate the size at which the cloud is doomed to collapse, this is called the Jeans radius and is given by<br /><br /><div style="text-align: center;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?r_J=%5Csqrt%7B3kT/4%20%5Cpi%20G%20m%5E2%20n%7D" alt="" align="middle" border="0" /><br /></div><br />where <span style="font-style: italic;">k</span> is Boltzmann's constant, <span style="font-style: italic;">T</span> the temperature of the cloud, <span style="font-style: italic;">m</span> the mass of the particles and <span style="font-style: italic;">n</span> the numerical density of particles. The Jeans mass is simply <img src="http://www.forkosh.dreamhost.com/mimetex.cgi?m_J=%284%5Cpi/3%29%5Crho%20r_J%5E3" alt="" align="middle" border="0" /> , when we plug numbers into it we realize that stars similar to our Sun require cooler and/or denser regions than the average of the interstellar medium. This regions are the molecular clouds.</li><li><span style="font-weight: bold;">The dynamical hurdle:</span> As the cloud collapses it is heated, the energy required to heat the cloud comes from its own gravitational potential and it eventually reaches an equilibrium state when<br /><br /><div style="text-align: center;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?2K+V=0" alt="" align="middle" border="0" /><br /></div><br />where <span style="font-style: italic;">K</span> is the kinetic energy and <span style="font-style: italic;">V</span> the potential energy, when this condition is satisfied we say that the cloud is <span style="font-style: italic;">virialized</span>. So we can see that star formation requires <span style="font-style: italic;">cooling</span>, otherwise the cloud will get virialized and reach a stable configuration halting the collapse. Thermal conduction and convection are remarkably ineffective in this regions and most of the cooling is radiative.</li><li><span style="font-weight: bold;">The angular momentum hurdle: </span>As gravitational collapse shrinks the cloud, angular momentum conservation amplifies any initial angular momentum (which is usually of the same magnitude of galactic rotation) by an enormous amount, the spin frequency is amplified by around 10¹⁶, this is such an spectacular increase in the spin that the cloud should be teared apart by the centrifugal effects. Dissipation is required to get rid of this excess of angular momentum, it is thought that this excess leads to proto-stellar disks.</li><li><span style="font-weight: bold;">The magnetic flux hurdle:</span> Lorentz force implies that charged particles are free to move in the direction of the magnetic field but have a hard time moving perpendicularly to it, so the magnetic field behaves as a spring refusing to compression. Collisions between the charged particles and the neutral ones eventually transfer this "springy behavior" to the rest of the cloud. A process known as <span style="font-style: italic;">ambipolar diffusion</span> eventually allows the neutral component to fall through the ionized component.</li></ul>The current state of star formation is centered around two paradigms: The "standard model" based on the collapse of isothermal clouds under ambipolar diffusion and the "turbulent model" based on the redistribution of energy at diverse scales of the cloud, making some "lumps" where star formation takes place.<br /><br />In future post I expect to explain you how each of this hurdles can be overcome and give an overview of this two paradigms.<br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com1tag:blogger.com,1999:blog-26745620.post-68369917223279984392008-01-10T18:58:00.000-06:002008-01-11T18:48:19.801-06:00No asteroid impact on Mars<div style="text-align: justify;">We ended last year commenting the possibility of an asteroid impact on Mars, this asteroid (2007 WD5) had rather small change of crashing on Mars.<br /><br />The latest data has ruled out this possibility, the use of archival photos and observations from the German-Spanish Astronomical Center, Calar Alto, Spain; the Multi-Mirror Telescope, Mt. Hopkins, Arizona; and the University of Hawaii telescope, Mauna Kea, Hawaii yielded and impact probability of cero.<br /><br />We will need to wait for this kind of serious fireworks in the future!<span style="font-family:verdana;"></span><span style=";font-family:verdana;font-size:85%;" > </span></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0tag:blogger.com,1999:blog-26745620.post-6859921271476024732008-01-06T18:25:00.000-06:002008-01-09T20:29:40.818-06:00Milkomeda<div style="text-align: justify;">The local group of galaxies consists of two big spiral galaxies: our own <a href="http://seds.lpl.arizona.edu/Messier/more/mw.html">Milky Way</a> and <a href="http://www.solstation.com/x-objects/andromeda.htm">Andromeda</a>, and a rather small spiral galaxy known as the <a href="http://en.wikipedia.org/wiki/Triangulum_Galaxy">Triangulum</a> and about 40 small galaxies of varied morphology.<br /></div><div style="text-align: justify;"><br />Unlike most galaxies which are redshifted due to the expansion of the universe, Andromeda is blueshifted meaning that it is moving <span style="font-style: italic;">towards</span> us. Eventually the Milky Way and Andromeda will collide, this is a bit uncertain because the only way to know for sure if the local group is bound we need to measure the <span style="font-style: italic;">radial</span> and<span style="font-style: italic;"> transverse</span> velocities of its members, we can measure the radial speed from the redshift but transverse speeds are quite complicated to measure. Despite that, the measurements of the radial velocity of Andromeda are of 120 km s-¹ towards us and a transversal velocity of around 100 km s-¹ and it is certainly smaller than 200 km s-¹ (<span style="font-weight: bold;">Loeb A., Reid M. J., Brunthaler A., Falcke H., 2005, ApJ,633, 894</span>). Using this values we can conclude that the system is indeed bounded and that the merger is quite likely to happen.<br /></div><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.deepfly.org/TheNeighborhood/LocalGroup.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 511px; height: 375px;" src="http://www.deepfly.org/TheNeighborhood/LocalGroup.jpg" alt="" border="0" /></a><span style="font-style: italic;">The galaxies of the local group. Andromeda is clearly the biggest member (this doesn't means it is the most massive, we have reasons to believe that the Milky Way has more dark matter and is more massive). The only other major galaxy is Triangulum which is significantly smaller. The rest of galaxies are small and many of them have irregular morphologies like the Small Magellanic Cloud.</span><br /></div><br /><div style="text-align: justify;">Kahn and Woltjer pioneered the study of the dynamics of the local group (<span style="font-weight: bold;">Kahn F. D., Woltjer L., 1959, ApJ, 130, 705</span>), they argued that Andromeda and the Milky Way formed quite closely and then separated with the expansion of the universe, then started to approach each other due to their gravitational attraction. From this suppositions they were able to estimate the mass of the local group and the size of the orbit.<br /><br />A detailed simulation of this merger has been produced by T.J. Cox and Abraham Loeb (<span style="font-weight: bold;">arxiv:</span><a style="font-weight: bold;" href="http://xxx.lanl.gov/abs/0705.1170">0705.1170v1</a>). They used a model of the local group proposed by Kyplin et al (<span style="font-weight: bold;">Klypin A., Zhao H., Somerville R. S., 2002, ApJ, 573, 597</span>) which has as much as 20 times more dark matter than baryonic matter. The diffuse intragroup medium was supposed to have a mass comparable to the mass of the galaxies. The simulations were carried with the <a href="http://www.mpa-garching.mpg.de/gadget/">GADGET 2</a> code (if you are computer and astro savvy, you can download this code and run your own simulations of astrophysical phenomena in your computer).<br /><br />In this simulation we have the first detailed scenario for the Sun as the merger happens. This merger will start in less than 2 Gyr, first with tidal interactions that will create a stream of matter between the MW and Andromeda. As we mentioned in a <a href="http://sanchezluis.blogspot.com/2007/12/doomsday.html">previous post</a>, the Earth will be out of the habitable zone in about 1.1 Gyr, unless some advanced civilization enlarges the radius of Earths orbit (<span style="font-weight: bold;">Korycansky D. G., Laughlin G., Adams F. C., 2001,Ap&SS, 275, 349)</span>. Despite that, let's continue to discuss the fate of the solar system.<br /><br />During the first close encounter, there is a 12% chance that the Sun will be pulled out of it's current position in the outer arms of the MW and reside in the extended tidal material between the MW and Andromeda, during this phase we expect a burst of star formation. After the second encounter the chance of residing in the tidal material rises to 30% and a more interesting outcome arises, there is a 2.7 % chance that the Sun will be captured by Andromeda. In this scenario any astronomer in the Earth will be able to see the MW (or rather its remains) from Andromeda in the night sky.<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6GxnmJ42uZfLHgXadZyXDOWsS7z8i2F4caZFhoy3p6lOlIBrOdbcoK-VPgXvX666QxwynIJgYUZ2JM3ggf99Yj4oI5wV0rpsB1ZFZMAqU0l1fQiqOHSGouAYErT9FHiX54WhO/s1600-h/milkomeda.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 347px; height: 445px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6GxnmJ42uZfLHgXadZyXDOWsS7z8i2F4caZFhoy3p6lOlIBrOdbcoK-VPgXvX666QxwynIJgYUZ2JM3ggf99Yj4oI5wV0rpsB1ZFZMAqU0l1fQiqOHSGouAYErT9FHiX54WhO/s400/milkomeda.jpg" alt="" id="BLOGGER_PHOTO_ID_5152536953941370018" border="0" /></a><span style="font-style: italic;">This is the simulation by Loeb et al. You can see that the collision won't be a head-on merger, but rather the two galaxies will spiral into each other, the final result of the merger is an elliptical galaxy.</span><br /></div><br />After the merger is completed, the simulation suggests that the Sun will habit in the outer halo of a massive elliptic galaxy, which Cox and Loeb call <span style="font-style: italic;">Milkomeda</span>. This is only a possible scenario using realistic assumptions about the local group, in their paper Cox and Loeb report a dozen of additional runs with different values of the density of the intragroup medium and the transverse medium and find that the outcome is esentially the same. The resulting galaxy has the R^(1/4) brightness distribution that is typical of elliptical galaxies, so our own local group will act as a prototype of the late forming elliptical galaxies.<br /><br />Tomorrow the AAS anual reunion starts, so we can expect some nice news in astronomy for the next week!<br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com18tag:blogger.com,1999:blog-26745620.post-63436913046178314862007-12-26T13:10:00.000-06:002008-01-05T21:56:53.527-06:00Life and death of interstellar dust<div style="text-align: justify;">In this part of the "dusty posts program" we will talk about formation and destruction of dust in the interstellar medium. Before we embark on this questions we need to know at least two things about dust: its size and composition.<br /></div><div style="text-align: justify;"><br />As we mentioned in the last post, the dust betrays its presence by absorbing light, the absorption efficiency at some wavelength depends on the size of dust grains. Absorption is a rather complicated phenomenon because there are many physical processes that can cause absorption in our sightline, light might be literally absorbed by the dust grain or it might be scattered out of our sightline. Scattering is also dependent on the ratio between the wavelength of the scattered light and the dust grain diameter. If this ratio is small we talk of <a href="http://en.wikipedia.org/wiki/Rayleigh_scattering">Rayleight scattering</a>, otherwise the process is known as <a href="http://en.wikipedia.org/wiki/Mie_scattering">Mie scattering</a>.<br /><br />Detailed analysis of absorption curves leads us to believe that scattering is caused by small solid solid particles which have a diameter comparable to the wavelengths of visible light (this explains the 1/lambda behavior in the visible part of the spectrum), nonetheless we still need other components to explain some features of the absorption curve.<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.shodor.org/refdesk/Resources/Activities/InterstellarExtinction/aiec.gif"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 320px;" src="http://www.shodor.org/refdesk/Resources/Activities/InterstellarExtinction/aiec.gif" alt="" border="0" /></a><br /><div style="text-align: center;"><span style="font-style: italic;">An average absorption curve, the far infrared is on the left and the ultraviolet on the right. There are some variations in different zones of the galaxy, but the shape of the curve is usually quite similar. We can see the peak of absorption are at 200 nm (or 1/lambda = 4.6 ). </span><br /></div><br />Now let's move to the composition of dust. The Sun being so close to Earth is readily observed and we (somehow naively) assume that it is a typical star and its composition is assumed to be fairly typical of the Galaxy. We can then use the Sun abundance of elements as a guide for relative abundances between it and the interstellar medium.<br /><br />We know that the relative abundances of the Sun and the interstellar medium are different. The main difference is that some elements have an underabundance of elements compared to the Sun. This elements are usually refractory, meaning that this elements can survive high temperatures without being sublimated, this directly points us to dust, as this elements can condense in dust grains that can survive in the vicinity of stars. Depletion is defined as<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK0Tfzm_55og4UVvmkapQg52KvEmYnub2NnReOAsb3T9Ec4l7eRS_AAu8vQFcj2D_DV2KoUlakID2SAQR6i3P8dr0DdKEgNHd9z5zWRGXPmRBnCw3F5naFc_Q-5gHj1BIe3YSS/s1600-h/depl.gif"><span style="font-style: italic;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cmathrm%7Bdepletion%7D=%5Clog%28N/H%29-%5Clog%28N/H%29_%7B%5Codot%7D" /></span></a><br /></div><br />and as we can see below, this elements are among others Cr, Fe, Ni, Co, Ti. Despite that, the bulk of a grain is quite similar in composition to the dust you can find in your backyard and is mostly divied in to <a href="http://en.wikipedia.org/wiki/Graphite">graphites</a>, <a href="http://en.wikipedia.org/wiki/Silicates">silicates</a> and <a href="http://en.wikipedia.org/wiki/Olivine">olivines</a>.<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK0Tfzm_55og4UVvmkapQg52KvEmYnub2NnReOAsb3T9Ec4l7eRS_AAu8vQFcj2D_DV2KoUlakID2SAQR6i3P8dr0DdKEgNHd9z5zWRGXPmRBnCw3F5naFc_Q-5gHj1BIe3YSS/s1600-h/depl.gif"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK0Tfzm_55og4UVvmkapQg52KvEmYnub2NnReOAsb3T9Ec4l7eRS_AAu8vQFcj2D_DV2KoUlakID2SAQR6i3P8dr0DdKEgNHd9z5zWRGXPmRBnCw3F5naFc_Q-5gHj1BIe3YSS/s400/depl.gif" alt="" id="BLOGGER_PHOTO_ID_5148364002371282066" border="0" /></a><br /><div style="text-align: center;"><span style="font-style: italic;">Interstellar elemental abundances compared relative to hydrogen compared with the Sun. We can see that refractory elements are heavily depleted. The depletion is a logarithmic quantity defined, meaning that some elements like Ti are depleted by three orders of magnitude.<br /></span></div><br />So, how are dust grains formed? The first idea is to think that they grow slowly in the interstellar medium. The problem with this idea is that actual calculations show that this will take too much time, suppose that at time <span style="font-style: italic;">t=0 </span>the grain has a radius <span style="font-style: italic;">r(0)</span>, if we suppose the grain grows by addition of species <span style="font-style: italic;">i</span> with mass <span style="font-style: italic;">m_i</span> moving at a mean thermal speed <span style="font-style: italic;">v_i</span> then the radius at a later time t will be<br /><br /><div style="text-align: center;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?r%28t%29=r%280%29+%5Cfrac%7B%5Cepsilon%20n_i%20m_i%20%5Coverline%7Bv_i%7D%7D%7B4s%7Dt" /><br /></div><br />where epsilon is a "sticky coefficient" that meassures the probability that the <span style="font-style: italic;">m_i </span>will remain attached to the grain and <span style="font-style: italic;">s</span> is the density of the solid grain. Using the typical values for interstellar medium we find that for a typical grain (about the size of visible wavelengths) the time required is<br /><br /><div style="text-align: center;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?t=%5Cfrac%7B3%20%5Ctimes%2010%5E9%7D%7B%5Cepsilon%7D%5Cmathrm%7Byr%7D" /><br /><div style="text-align: justify;"><br />which is too much time if we consider that the value of epsilon is smaller than one, and that the age of the universe is around 13 Gyr.<br /><br />The solution comes from considering denser regions, in particular the atmospheres of cool stars. The material in stars is originally so hot that it did not contain any solids, but as it outflows in later phases of the life of the star it starts to cool with much higher densities than the interstellar medium and the atoms can arrange themselves in to the most stable molecules at that temperature (usually around 10³ K). When this outer layers are ejected in stellar winds the dust goes in to the interstellar medium. There is some controversy about the formation of dust in the early life of the universe, the most accepted view is that this dust was formed around active galactic nuclei.<br /><br />Now let's move to grains destruction. The simplest way to destroy a grain is to heat it enough so it sublimates. That indeed happens in the vicinities of young, hot stars. The sublimation temperatures depend on the composition and size of the grain, this results in a stratification of the dust with large graphites closer to the star, followed by smaller graphites and large silicates, at larger distances from the star we can find smaller silicates, olivines, fused quartz and silicates with ice mantles.<br /></div></div><br />A more interesting mechanism comes from accumulation of electric charges in the surface of the dust, if the grain is spherical with a radius <span style="font-style: italic;">a</span> and is carrying a charge of <span style="font-style: italic;">Z</span> electrons then the electrons capture cross section if the speed of the electrons is u_e is given by<br /><br /><div style="text-align: center;"><img src="http://www.forkosh.dreamhost.com/mimetex.cgi?%5Csigma_e%20=%20%5Cpi%20a%5E2%20%5Cleft%28%201+%20%5Cfrac%7B2%20Z%20e%5E2%7D%7B4%20%5Cpi%20%5Cepsilon_0%20a%20m_e%20u_e%5E2%7D%20%5Cright%29" /><br /></div><br />When enough electric charge accumulates on the surface the stress it causes on the grain as it tries to redistribute, causes the grain to literally explode! Quite an interesting consequence for the well known fact that charges redistributes on a surface!<br /><br />It actually results that the capture of species by dust grains has a crucial importance in astrobiology, keep tuned!<br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com1tag:blogger.com,1999:blog-26745620.post-13615803255106726192007-12-24T19:53:00.000-06:002007-12-30T13:12:41.269-06:00Merry Christmas<div style="text-align: justify;">Today it's Christmas eve. Receive the warmest regards from the "staff" of this blog. On this day, 39 years ago the crew of <a href="http://en.wikipedia.org/wiki/Apollo_8">Apollo 8</a> entered into orbit around Moon, so this is also an special day for space exploration. Not only that, maybe there is a quite special gift under the tree this year: 2007 WD5.<br /></div><div style="text-align: justify;"><div style="text-align: justify;"><br />2007 WD5 is an asteroid that will cross Mars orbital path in January 30. There is some chance (around 1 in 75) that it will impact Mars! This asteroid is around 50 meters wide and might create a half-mile wide impact crater. Despite this event is rather unlikely it will cast some serious fireworks in case it happens.<br /></div><br /><div style="text-align: justify;">You can read the <a href="http://www.jpl.nasa.gov/news/news.cfm?release=2007-152">JPL official press release here</a>.<br /></div></div><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.jpl.nasa.gov/images/mars/asteroid/wd5_orb-browse.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 400px;" src="http://www.jpl.nasa.gov/images/mars/asteroid/wd5_orb-browse.jpg" alt="" border="0" /></a><span style="font-style: italic;">This is the orbital path of 2007 WD5, you can clearly see that it intercepts Mars orbit. The uncertainties in the measurement of 2007 WD5 path don't allow us to assure a collision will happen, actually it's quite unlikely it will occur. In a few days we will have more data.</span><span><br /><br /></span><div style="text-align: justify;"><span style="font-size:130%;"><span style="font-weight: bold;">Update: </span></span>This asteroid has been recently identified in archival imagery, this has allowed astronomers to refine the orbital parameters, now the odds of a collision are of 1 in 25! Still a rather meager chance (4%), but we still need more data for a more accurate prediction.<br /></div></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com2tag:blogger.com,1999:blog-26745620.post-4993214393095944972007-12-17T13:30:00.001-06:002007-12-17T20:34:29.777-06:00Dust in the interstellar medium<div style="text-align: justify;">Today I will give you a brief overview of a topic that's quite close to me: the effects of <a href="http://en.wikipedia.org/wiki/Interstellar_dust"><span>dust in interstellar medium</span></a>. There are some regions in the sky that seem to be almost magically depleted of stars, even in very dense regions. The classical example of this "dark nebulae" is the <a href="http://www.seds.org/messier/Xtra/ngc/coalsack.html">coalsack</a> in the Crux constellation.<br /></div><div style="text-align: justify;"><br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://upload.wikimedia.org/wikipedia/commons/5/5d/Coal.sack.nebula.arp.300pix.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 320px;" src="http://upload.wikimedia.org/wikipedia/commons/5/5d/Coal.sack.nebula.arp.300pix.jpg" alt="" border="0" /></a><span style="font-style: italic;">The coalsack dark nebula is the best known region where interstellar dust is so dense that it blocks all the light (in the visible frequencies) in it's sightline.</span><br /></div><br /><div style="text-align: justify;">This regions are <span style="font-style: italic;">not</span> depleted of stars, but rather the light of the stars in the sightline is absorbed by dust. This is far from obvious, after all there is no <span style="font-style: italic;">a priori</span> reason to discard the idea that this regions simply lack any stars.<br /><br />The first conclusive evidence of light absorption in the <a href="http://en.wikipedia.org/wiki/Interstellar_medium">interstellar medium</a> came from the work of Robert Trumpler who measured the angular sizes of <a href="http://seds.org/messier/glob.html">globular clusters</a> trying to calculate its distance from Earth. The idea was simple, let's assume that globular clusters are roughly the same size, then the smaller a particular cluster seems to us, the farther it is. When Trumpler carried on this plan he realized that the there was a linear relation between the size and the distance, i.e. the clusters were bigger as the distance to them increased. This was quite unexpected and also seemed to point to the rather disturbing conclusion that Earth is located in a special place where globular clusters are smaller.<br /><br />Rather than that, Trumpler realized that the distance was systematically overestimated (so the clusters weren't that big, after all). Then he assummed that the reason for this bias was extinction in the interstellar medium, meaning that something (presumably dust) was absorbing light on its way to Earth.<br /><br />Further evidence for dust comes from <a href="http://en.wikipedia.org/wiki/Polarization_in_astronomy">light polarization</a>. When light is reflected from a dust grain it is polarized depending on the alignement of the grain, if the grains are aligned with Milky Way's magnetic field, we can then use the dust polarization as a measure of the direction of the magnetic field.<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://www.planck.fr/IMG/jpg/fig_fosalba.jpg"><img style="margin: 0px auto 10px; display: block; text-align: center; cursor: pointer; width: 320px;" src="http://www.planck.fr/IMG/jpg/fig_fosalba.jpg" alt="" border="0" /></a><span style="font-style: italic;">Measurements of <a href="http://www.planck.fr/article263.html">dust polarization</a>, this measurements show that optical polarization is aligned with the magnetic field.</span><br /></div><br />What is the composition of this dust? This depends on many factors. Nonetheless the most important one is the distance to a star, particullary to hot, young stars. This stars (known as early spectral type) are so hot that that dust sublimates in its vecinity. The grains composed of carbonites are more resistent (and bigger grains have a better chance of survival), then the silicates enter the stage. In colder enviroments larger molecules appear on the surface of the grains.<br /><br />How are this grains formed? Why is dust relevant for astrobiology? Which are the effects of dust on ionized regions? Keep tuned for later posts!<br /></div>Luis Sanchezhttp://www.blogger.com/profile/08968074398416860883noreply@blogger.com0