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Akano

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Blog Entries posted by Akano

  2. Akano

    *Slow clap*

    By Akano,

    Well done, Alex Hirsch. Well done.
     
    The latest Gravity Falls episode was excellent. Totally squashed theories about the author of the journal and, while answering some questions, raised even more. Can't wait for the next episode...
     

  3. Akano
    Yet again, my brothers suggested I do something that they've done. This time it was "watch Gravity Falls," a show which I knew of but didn't know much about. I have now finished the first season, and I must say it's a brilliant, funny show. In no particular order, what makes it stand out is
    The humor - By and far an important aspect of any comedy, the humor of Gravity Falls resonates very well, from the lamest pun to the brilliant stuff they get past the censors (and, wow, do they get a lot past the censors. This is a Disney show, right?). Expertly crafted and leaving me wanting more in the best way possible.
    The story - while not the most story-heavy series (a lot of the episodes are very standalone and can be watched without missing much of previous episodes), the story that is ongoing is very engaging. Gravity Falls, OR is a place where weird, paranormal stuff happens. Our main characters want to know why, thus we want to know why, and their curiosity becomes ours in a genuine, unforced way.
    The relationships are believable - Dipper and Mabel, the two main protagonists, are twin siblings who are sent to their great uncle (or, you guessed it, Grunkle) Stan's tourist trap, the Mystery Shack, for the summer. And they have a relationship that is completely believable (and as a twin, I can fully attest to it). Even when they have a scuffle or conflict, at the end of they day they can hug it out and not hate each other, which is very refreshing in a kids show. Also, the characters are not just defined by single character traits; for instance, Mabel has a fantastically overactive imagination and looks at the world from a very different angle than most of the other characters, but she's never called stupid or foolish by the others. Soos, the Mystery Shack's general repair and groundskeeper guy, who is overweight and sometimes dull-witted, is not defined by these traits, nor is he mocked for them; everyone treats him as they do everyone else, which is also really refreshing to see in a kids show. As for romantic relationships,
     
    This show has provided me with a lot of laughs and a fun world of mystery, and I look forward to what else it has in store.
     

  4. Akano
    I have been up to lots of stuffs recently. Mostly of the electronic gaming variety.
     
    First off, I played Mega Man X for the first time courtesy of the Wii U Virtual Console (prompted by a fantastic video by Egoraptor). Fantastic game; the more I play SNES games, the more I regret not owning a SNES in childhood.
     
    After playing Fire Emblem (Rekka no Ken) and Sacred Stones, I finally caved into my roommate's demands that I play Awakening; OMG SO MUCH AWESOME! Probably one of my favorite games of all time, and definitely looking forward to playing it again.
     
    Right after completing Awakening, I received Professor Layton vs. Phoenix Wright: Ace Attorney in the mail. Another fantastic game; Layton puzzles and story combined with Phoenix Wright courtroom shenanigans made for an awesome crossover. I just wish Maya hadn't been given a valley girl accent. :/
     
    And, finally, my roommate got some 3DS Smash Bros codes, one of which he shared with me. I'm loving Mega Man so far; will definitely be playing as him once the Wii U version comes out (not getting the 3DS version; I'd like to spare my buttons of a painful death). I really wish the demo included Robin as a playable character, though; of the new roster, I'm looking forward to playing as him the most.
     
    On a more academic note, this Thursday is my Ph.D. preliminary exam oral defense, so that'll be fun. I've already worked through the problems that I will be asked about, and I think I've solved all of them. Hopefully all will go well.
     

  5. Akano
    Haldo, BZPeople!
     
    As you may have noticed, this summer the blogs were highly accented with my extreme absence since I took a trip to the northern UK. The reason for this absence is simple: I was studying for, and subsequently started taking, my preliminary examinations for continuation to my Ph.D. in physics. Last week for me was filled with three four-hour exams: one on Monday (Quantum Mechanics), one on Wednesday (Electromagnetism), and one on Friday (Classical, Special Relativity, and Statistical Mechanics grab bag). I am happy to say that I survived the initial onslaught of my prelims and am now in phase two: a twelve-hour take-home exam to be done over seventy-two hours (10 a.m. today to 10 a.m. Thursday). I have glanced at the problems but not worked on them yet, but I feel pretty good about the quantum section.
     
    In other news, the new school year is set to start in a week, but I have a class starting this Thursday. That'll be quite fun. 8D
     

  6. Akano
    While days 2-4 were relatively uneventful (mostly collaborating days, doing research) my last three days in Edinburgh were pretty cool.
     
    Day 5: I climbed Arthur's Seat for a second time; it was sunny, so the view was even better than on Sunday when my advisor and I climbed it together. I also got proof That I made it to the summit. 8D
     
    Day 6: I went to Edinburgh Castle and walked around the former residence of the Scottish royal family. There were a few museums that were mainly dedicated to the history of Scottish military. I also saw the Scottish crown jewels, but was not allowed to take photos (and didn't realize I wasn't allowed until a lady yelled at me for taking out my phone).
     
    Day 7: I journeyed to Pencaitland, which is about 12 miles outside of Edinburgh, for a tour of the Glenkinchie distillery. However, I was late for my booked tour, as the bus didn't take me the whole way to the distillery, and it was a 2 mile walk to the distillery from the bus stop. I literally was walking, in the middle of Scottish farmland, following signs that I hoped were telling me the truth and leading me in the right direction. I eventually got there, however, unharmed but late. The lady at the front desk was very accommodating, though, and fit me into the next tour. It was quite lovely, and we got to see all the steps of brewing whiskey followed by a tasting session. After tasting, I picked up a bottle for my dad and a smaller bottle for me (if they sold 50 cl bottles, they would have been the same size, but, alas, they only had them in 20 and 70 cl sizes). I tried to get on the distillery's shuttle back to Edinburgh, but unfortunately I had asked to join it after it had left; they told me not to worry, though, as there was a local barman who would come and pick me up with two other women who also took the bus and take us to his pub, which was a few seconds' walk from the bus stop. The three of us had a drink at his pub (his only request in exchange for picking us up, which was completely fair in my opinion) and we got to talking. The one lady was around my age and still in college, while the older woman was her aunt and was retired. We got to talking about math and science, since the aunt had studied nutrition science for her job and enjoyed talking about science. We also discussed beer, the tour, and previous and future travels we were planning to take. All in all, it was a lovely afternoon, and we sat together on the bus back to Edinburgh and talked some more. Once we were back in the city, we said our goodbyes and were very glad to have met each other.
     
    Then, this morning, I boarded my flight back to the states, and now I am quite tired, as it is (as I'm typing this) around 1:30 a.m. back in Edinburgh, and my body wants to be very well asleep. I am happy to say, though, that it was a fruitful trip, both for research and fun, as now my code that I've been working on for nearly a year finally works and has reproduced the results of the paper we modeled it off of! Now, we get to push it into new parameter space to aid us in our spectroscopic analysis.
     
    Well, that's all for now. I'm going to go eat some cookies with my friends.
     

  7. Akano

    I'm in Scotland

    By Akano,

    So, I'm currently in Edinburgh, UK for official Hogwarts business doing research with a collaborator at the local university. Things I have done include
    Vaguely losing consciousness on the plane ride over the Atlantic to adjust to new time zone. Would not qualify it as sleeping.
    Instead of checking into the hotel (which didn't allow checkins until 2 p.m. local time), climbing Arthur's Seat to the summit with my advisor like a boss.
    Enjoyed a Guinness. (Not Scottish, I know, but arguably fresher than those sold in the US.)
    Things I have not yet done include
    Tossing a caber.
    Wearing a kilt.
    Playing bagpipes.
    Trying haggis. (Will probably do this at breakfast tomorrow, though.)
    So far so fun. Also I've done research. Totally why I'm here.
     

  8. Akano
    I like triangles. I like numbers. So what could possibly be better than having BOTH AT THE SAME TIME?! The answer is nothing! 8D
     
    The triangular numbers are the numbers of objects one can use to form an equilateral triangle.
     

    Anyone up for billiards? Or bowling? (Image: Wikimedia Commons)


     
    Pretty straightforward, right? To get the number, we just add up the total number of things, which is equal to adding up the number of objects in each row. For a triangle with n rows, this is equivalent to
     



     
    This means that the triangular numbers are just sums from 1 to some number n. This gives us a good definition, but is rather impractical for a quick calculation. How do we get a nice, shorthand formula? Well, let's first add sequential triangular numbers together. If we add the first two triangular numbers together, we get 1 + 3 = 4. The next two triangular numbers are 3 + 6 = 9. The next pair is 6 + 10 = 16. Do you see the pattern? These sums are all square numbers. We can see this visually using our triangles of objects.
     

    (Image: Wikimedia Commons)


     
    You can do this for any two sequential triangular numbers. This gives us the formula
     



     
    We also know that two sequential triangular numbers differ by a new row, or n. Using this information, we get that
     



     
    Now we finally have an equation to quickly calculate any triangular number. The far right of the final line is known as a binomial coefficient, read "n plus one choose two." It is defined as the number of ways to pick two objects out of a group of n + 1 objects.
     
    For example, what is the 100th triangular number? Well, we just plug in n = 100.
     

    T100 = (100)(101)/2 = 10100/2 = 5050


     
    We just summed up all the numbers from 1 to 100 without breaking a sweat. You may be thinking, "Well, that's cool and all, but are there any applications of this?" Well, yes, there are. The triangular numbers give us a way of figuring out how many elements are in each row of the periodic table. Each row is determined by what is called the principal quantum number, which is called n. This number can be any integer from 1 to infinity. The energy corresponding to n has n angular momentum values which the electron can possess, and each of these angular momentum quanta have 2n - 1 orbitals for an electron to inhabit, and two electrons can inhabit a given orbital. Summing up all the places an electron can be in for a given n involves summing up all these possible orbitals, which takes on the form of a triangular number.
     



     
    The end result of this calculation is that there are n2 orbitals for a given n, and two electrons can occupy each orbital; this leads to each row of the periodic table having 2⌈(n+1)/2⌉2elements in the nth row, where ⌈x⌉ is the ceiling function. They also crop up in quantum mechanics again in the quantization of angular momentum for a spherically symmetric potential (a potential that is determined only by the distance between two objects). The total angular momentum for such a particle is given by
     



     
    What I find fascinating is that this connection is almost never mentioned in physics courses on quantum mechanics, and I find that kind of sad. The mathematical significance of the triangular numbers in quantum mechanics is, at the very least, cute, and I wish it would just be mentioned in passing for those of us who enjoy these little hidden mathematical gems.
     
    There are more cool properties of triangular numbers, which I encourage you to read about, and other so-called "figurate numbers," like hexagonal numbers, tetrahedral numbers, pyramidal numbers, and so on, which have really cool properties as well.
     

  9. Akano
    It's finals week at my grad school, but since I didn't take any classes this semester, I have no exams to study for (except my prelims, which are at the end of the summer ). I am, however, holding office hours for my students before they take their exams, so I'm not without stuff to do.
     
    I also went to Philly BrickFest two weekends ago, but I was only there for a couple hours since I had to leave for choir rehearsal. I did snap some pics, which will hopefully end up on my Brickshelf at some point. Maybe.
     
    In other news, I'm still obsessed with quantum mechanics and have been playing around with various mathematical things associated with it, like deriving the ladder operators and matrix elements for the quantum harmonic oscillator, deriving formulas for coherent states, and trying to find out what a true Hufflepuff is, anyway deriving coordinate transformations to the center of mass frame of two particles. Fun fun.
     
    (This is the part where you all look at me like I'm mad, and I reply with an expression like this: 8D)
     
    So, not too much going on with me right now, but I can't complain.
     

  10. Akano
    Today I want to talk about mass. Sometimes you'll hear it defined loosely as "the amount of stuff in an object." There are, however, two separate definitions of mass in classical physics. The first definition comes from Newton's second law.




     
    This mass is known as the inertial mass. The larger an object's inertial mass, the more it resists being accelerated by a given force. The second definition of mass also comes from Newton, but it is instead determined by his law of gravitation.
     



     
    The mass here determines how much two massive objects attract one another; this is known as the gravitational mass. But here's the interesting thing about these two masses: there is no law of physics that says these masses are one and the same. Such a notion is known in physics as the equivalence principle. The weak equivalence principle was discovered by Galileo; he noticed that objects with different masses fall at the same rate. Einstein came up with the strong equivalence principle, which discusses how a uniform force and a gravitational field are indistinguishable when you look at a small enough portion of spacetime. The only reason we believe these two masses are equivalent is because experiments show that they are equal to within the precision of the instruments with which we measure them, and there are ongoing experiments trying to narrow down that precision to determine if there is any difference between the two.
     

  11. Akano
    You've probably heard of the Uncertainty Principle before. In words, it says "you cannot simultaneously measure the position and the momentum of a particle to arbitrary precision." In equation form, it looks like this:
     



     
    What this says is that the product of the uncertainty of a measurement of a particle's position multiplied by the uncertainty of a measurement of a particle's momentum has to be greater than a constant (given by the reduced Planck constant, h over τ = 2π). This has nothing to do with the tools with which we measure particle; this is a fundamental statement about the way our universe behaves. Fortunately, this uncertainty product is very small, since ħ is around 1.05457 × 10-34 J s. The real question to ask is, "Why do particles have this uncertainty associated with them in the first place? Where does it come from?" Interestingly, it comes from wave theory.
     




     
     




     
     
    Take the two waves above. The one on top is very localized, meaning its position is well-defined. But what is its wavelength? For photons, wavelength determines momentum, so here we see a localized wave doesn't really have a well-defined wavelength, thus an ill-defined momentum. In fact, the wavelength of this pulse is smeared over a continuous spectrum of momenta (much like how the "color" of white light is smeared over the colors of the rainbow). The second wave has a pretty well-defined wavelength, but where is it? It's not really localized, so you could say it lies smeared over a set of points, but it isn't really in one place. This is the heart of the uncertainty principle. Because waves exhibit this phenomenon – and quantum particles behave like waves – quantum particles also have an uncertainty principle associated with them.
     
    However, this is arguably not the most bizarre thing about the uncertainty principle. There is another facet of the uncertainty principle that says that the shorter the lifetime of a particle (how long the particle exists before it decays), the less you can know about its energy. Since mass and energy are equivalent via Einstein's E = mc2, this means that particles that "live" for very short times don't have a well-defined mass. It also means that, if you pulse a laser over a short enough time, the light that comes out will not have a well-defined energy, which means that it will have a spread of colors (our eyes can't see this spread, of course, but it means a big deal when you want to use very precise wavelengths of light in your experiment and short pulses at the same time). In my lab, we use this so-called "energy-time" uncertainty to determine whether certain configurations of the hydrogen molecule, H2, are long-lived or short lived; the longer-lived states have thinner spectral lines, and the short-lived states have wider spectral lines.
     
    So while we can't simultaneously measure the position and momentum of a particle to arbitrary certainty, we can definitely still use it to glean information about the world of the very, very small.
     

  13. Akano

    Together, We Ride

    By Akano,

    So, my roommate finally coaxed me into playing the first Fire Emblem (actually the seventh, but the first one released in the US) for GBA, and I'm loving it. After finishing it, I'm definitely looking forward to playing Fire Emblem: Awakening, because I've heard nothing but good things about it.
     
    The music is great in that awesome nostalgic way, the characters are fun and memorable, the magic wielders are freakin' awesome, and the gameplay is fantastic – in order to keep all your troops alive, obtain everything worth getting in each level, recruiting all new troops, and beating the levels is a fun challenge.
     
    Other things I've done in the past week or so include:
    Finishing MetalBeard's Sea Cow (Awesome!)
    Learning how to derive the formula for the volume of an n-dimensional sphere (really clever trick!)
    Drinking lots of tea.


  15. Akano

    My Weekend

    By Akano,

    So this weekend two of my friends and I journeyed to the New England city known as Boston. We didn't actually do anything downtown, but we did get to see some history in Concord, such as the Old North Bridge (site of the fabled "shot heard 'round the world") and walked past Sleepy Hollow Cemetery (we didn't have time to walk through it, unfortunately), and went to a birthday party for a friend of a friend. We also saw one of my grad school professors who left my school due to his wife and him getting a job somewhere that didn't involve one of them taking a nearly three hour commute to work, and there was Indian food.
     
    All in all, a good weekend with good company. Now I'm just relaxing and recovering from the drive, and will soon get to go home and build a pirate ship.
     
    My body is ready.
     

  17. Akano
    Today I want to talk about something awesome: Special Relativity. It's a theory that was developed by this guy you may have heard of, Albert Einstein, and it's from this theory that arguably the most famous equation in physics, E = mc2, comes from. I'm not going to talk about E = mc2 today (in fact, I've already talked about it, but it's not the whole story!), but I wanted to talk about two other cool consequences of Special Relativity (SR), time dilation and length contraction.
     
    First and foremost, the main fact from which the rest of SR falls out is the fact that the speed of light is the same for all observers moving with constant velocity, regardless of what those velocities may be. Running at 5 m/s? You see light traveling at the same speed as someone traveling 99% the speed of light.
     
    Wait, how can that be? This idea originally came from Maxwell's equations, which govern electromagnetism. When you solve these equations, you can put them into a form that results in a wave equation, and the speed of those waves is equal to that of light. This finding brought on the realization that light is an electromagnetic wave! But here's the interesting thing: Maxwell's equations do not assume any particular frame of reference, so the speed of the waves governed by Maxwell's equations have the same speed in all reference frames. Thus, it makes sense from an electromagnetic point of view that the speed of light shouldn't depend on how fast someone is traveling!
     
    Now, we're still in a bit of a pickle; if all observers see light traveling at the same speed, how do things other than light move? Think about it. If you're driving down the highway at 60 mph and the car next to you is driving 65 mph, they appear to be moving 5 mph faster than you, don't they? So why doesn't this work with light? If I'm traveling 5 mph, shouldn't I see light moving 5 mph slower than normal? No; the problem here isn't that the speed of light is the same for all observers, but the fact that we think relative velocities add up normally. In fact, this relative velocity addition is simply a very good approximation for objects that are much, much slower than light, but it is not complete.
     
    The answer to this conundrum is that
    . These two principles are governed by the equations 



     
    The first equation determines time dilation, and the second equation determines length contraction, when shifting from a frame moving at speed v to a frame moving at speed v' (β and γ are both physical parameters that depend on the velocity of the frame in question and the speed of light, c). From the first equation, we can see that the faster someone is moving in frame S (moving at speed v), the slower their clock ticks away the seconds in frame S' (moving at speed v') and the more squished they look (in the direction that they're traveling). These ideas are the basis for the famous "barn and pole" paradox. Suppose someone is holding a pole of length L and is running into a barn, which from door-to-door has a length slightly longer than L. If the person runs fast enough, an outside observer will see that the person running with the pole will completely disappear into the barn before emerging from the other side. But from the runner's frame of reference, the barn is what is moving really fast, and so the barn appears shorter than it did to the outside observer. This means that, in the runner's frame, a part of the pole is always outside of the barn, and thus he is always exposed.
     
    What if the observer outside the barn had the exit door closed and the entrance door open and rigs it such that when the runner is completely inside the barn, the entrance door closes and the exit door opens? Well, in the outside observer's frame, this is what happens; the entrance door closing and the exit door opening are simultaneous events. But in the runner's frame, there is no way for him to fit inside the barn, so does the door close on the pole? No, because the physics of what happens has to be the same in both frames; either the door shuts on the pole or it doesn't. So, in the runner's frame, the entrance door closing and the exit door opening are not simultaneous events! In fact, the exit door opens before the entrance door closes in the runner's frame. This is due to the time dilation effect of special relativity: simultaneous events in one reference frame need not be simultaneous in other frames!
     
    Special relativity is a very rich topic that I hope to delve into more in the future, but for now I'll leave you with this awesome bit of cool physics.
     

  18. Akano

    WIRELESS WIZARD!

    By Akano,

    Not sure what started this fad, but I'm okay with this.
     

    I Am A:
     
    True Neutral Human Wizard (3rd Level)


     
    Ability Scores:
    Strength- 9
    Dexterity- 12
    Constitution- 12
    Intelligence- 16
    Wisdom- 14
    Charisma- 12
     
    Alignment:
    True Neutral- A true neutral character does what seems to be a good idea. He doesn't feel strongly one way or the other when it comes to good vs. evil or law vs. chaos. Most true neutral characters exhibit a lack of conviction or bias rather than a commitment to neutrality. Such a character thinks of good as better than evil after all, he would rather have good neighbors and rulers than evil ones. Still, he's not personally committed to upholding good in any abstract or universal way. Some true neutral characters, on the other hand, commit themselves philosophically to neutrality. They see good, evil, law, and chaos as prejudices and dangerous extremes. They advocate the middle way of neutrality as the best, most balanced road in the long run. True neutral is the best alignment you can be because it means you act naturally, without prejudice or compulsion. However, true neutral can be a dangerous alignment when it represents apathy, indifference, and a lack of conviction.
     
    Race:
    Humans are the most adaptable of the common races. Short generations and a penchant for migration and conquest have made them physically diverse as well. Humans are often unorthodox in their dress, sporting unusual hairstyles, fanciful clothes, tattoos, and the like.
     
    Class:
    Wizards- Wizards are arcane spellcasters who depend on intensive study to create their magic. To wizards, magic is not a talent but a difficult, rewarding art. When they are prepared for battle, wizards can use their spells to devastating effect. When caught by surprise, they are vulnerable. The wizard's strength is her spells, everything else is secondary. She learns new spells as she experiments and grows in experience, and she can also learn them from other wizards. In addition, over time a wizard learns to manipulate her spells so they go farther, work better, or are improved in some other way. A wizard can call a familiar- a small, magical, animal companion that serves her. With a high Intelligence, wizards are capable of casting very high levels of spells.
     

  19. Akano

    Physics Conference

    By Akano,

    As the fates would have it, the day after my birthday I hopped on a plane and went to a physics conference. I'm now sitting here in my lovely hotel room waiting for today's poster session at which I am presenting a poster on my research thus far. It involves stuff from my first published paper and some current "in the works" calculations that I'm doing to help our analysis along.
     
    The talks up to this point have completely left me in the dust, so I'm hoping there will be discussion during the poster session that's more to my level of understanding on the various topics I've been exposed to.
     
    Also the food is quite good.
     



     

  21. Akano

    Sleep

    By Akano,

    http://youtu.be/bxjWNJU8rNE

    When I was in college I had the privilege of performing many beautiful pieces in both choir and band. While I got to sing Eric Whitacre's "Hope, Faith, Life, Love" and play trumpet in his instrumental piece "October," I never did get to sing this beautiful piece.
     
    I absolutely love his suspensions and cluster chords. They give it a real ethereal quality, and it's beautiful.
     

  23. Akano
    My very first Equation of the Day was about the wave equation, a differential equation that governs wave behavior. It doesn't matter whether you have linear waves (sine and cosine functions), cylindrical waves, or spherical waves, the wave equation governs them. Today I will focus on the second, the so-called cylindrical harmonics, or Bessel functions.
     
    A harmonic function is defined as one that satisfies Laplace's equation,
     



     
    For cylindrical symmetry, the Laplacian (the operator represented by the top-heavy triangle squared) takes the following form:
     



     
    This is where a neat trick is used. We make an assumption that the amplitude of the wave, denoted here by ψ, can be represented as a product of three separate functions which each only depend on one coordinate. To be more explicit,
     



     
    This technique is known as "separation of variables." We claim that the function, ψ, can be separated into a product of functions each with their own unique variable. The results of this mathematical magic are astounding, since it greatly simplifies the problem at hand. When you go through the rigamarole of plugging this separated function back in, you get three simpler equations, each with its own variable.
     



     
    Notice that the partial derivatives have become total derivatives, since these functions only depend on one variable. These are well-known differential equations in the mathematical world; the Φ function is a linear combination of sin(nϕ) and cos(nϕ) (this azimuthal angle, ϕ, goes from 0 to 2π and cycles, so this isn't terribly surprising) with n being an integer, and the Z function is a linear combination of cosh(kz) and sinh(kz), which are the hyperbolic functions. These equations are not what I want to focus on; what we've really been working so hard to get is the radial equation:
     



     
    This is Bessel's differential equation. The solutions to this equation are transcendental (meaning that you can't write them as a finite sum of polynomials; the sine and cosine functions are also transcendental). We write them as
     



     
    The Jn are finite at the origin (J0 is 1 at the origin, all other Jn are 0), and the Yn are singular (undefined) at the origin. They look something like this:
     







     
    The Jn are much more common to work with because they don't have infinities going on, but the Yn are used when the origin is inaccessible (like a drum head that has a hole cut in the middle). These harmonic functions are used to model (but are not limited to)
    Vibrational resonances of a circular drum head
    Radial wave functions for potentials with cylindrical symmetry in quantum mechanics
    Heat conduction in a cylindrical object
    Light traveling in a cylindrical waveguide

    Note that, while they kinda look sinusoidal, they don't have a set period, so the places where they cross the x-axis are have different intervals and are irrational; thus, they must be computed. This results in some weird harmonic series for instruments like xylophones, drums, timpani, and so on. I got into them because I'm a trumpet player, and the resonances of the surface of the bell of a trumpet are related to the Bessel functions.
     
    There are some
    (this one has a strobe effect during it) showing them in action. There are also some cool Mathematica Demonstrations related to them as well. There are also orthogonality relationships with them, but I'll save that for another day. 

  24. Akano

    I made some things

    By Akano,

    I made these two images in Mathematica and tidied them up in Photoshop.
     
    They're graphs in the complex plane. The color indicates the phase, or argument, of the complex number, and for this function, curves of equal phase are hyperbolas. To animate it, all I did was let the phase vary linearly in time.
     
    8D
     

  25. Akano

    Happy birthday, little bro

    By Akano,

    So, today is Tekulo's birthday. Since his birthday also happens to be Valentine's Day, and his job is baking, he's quite busy making pastries and other flour and sugar-based products for happy couples and families. And for himself, by the looks of it.
     
    Happy birthday, Tekky. I hope you have some part of the weekend off to make up for your busy day today.
     
    P.S. Go over here to wish Tekulo a happy birthday yourself! 8D
     

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