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Akano

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Blog Entries posted by Akano

  2. 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.
     

  4. 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.
     

  5. 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.
     

  6. 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.
     



     

  8. 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.
     

  10. 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. 

  11. 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
     

  12. Akano

    Snow Days

    By Akano,

    So, today was the second day this week where classes have been cancelled for snow/winter weather. Today the cancellation occurred due to power outages and falling frozen tree branches.
     
    So, I'm now at home doing work since there's actually power here. So that's been fun.
     
    Outside looks especially pretty, though.
     

  13. 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
     

  14. Akano
    I have posted before about the genius of physicist David J. Griffiths. I thought I'd post a few quotes by him to share why I think he's awesome.
     
    "…You can always tell the particles apart, in principle—just paint one of them red and the other one blue, or stamp identification numbers on them, or hire private detectives to follow them around."
     
    "...And, of course, if you’re in a really bad mood you can create a state for which neither position nor momentum is well defined..."
     
    "It is traditional to write the Bohr radius with a subscript: a0. But this is cumbersome and unnecessary, so I prefer to leave the subscript off."
     
    "If you think this is starting to sound like a mystical numerology, I don’t blame you. We will not be using Clebsch-Gordan tables much in the rest of the book, but I wanted you to know where they fit into the scheme of things, in case you encounter them later on. In a mathematical sense this is all applied group theory—what we are talking about is the decomposition of the direct product of two irreducible representations of the rotation group into a direct sum of irreducible representation (you can quote that, to impress your friends)."
     
    "I’m not at all sure what I’m supposed to say today. Maybe you’re expecting a grand philosophy of education. But I learned very early as a parent that almost any philosophy of childrearing is worse than no philosophy at all, and I am inclined to think the same applies to teaching."
     
    "Personally, I never bring notes to a lecture unless I am egregiously ill-prepared, for they break a very delicate and important bond of trust with the listener: If B really follows from A, how come he has to refer to his notes?"
     
    "There are a thousand ways to get a problem wrong—not all of them bad—and many ways to get a problem right—not all of them good."
     
    "Above all, I think studying science—and especially physics—is a tremendously liberating experience. I don’t happen to know how a carburetor works; I’m not even sure what a carburetor does; let me be frank: I don’t know what a carburetor looks like. But I do know that the behavior of carburetors is perfectly rational; somebody understands them, and if I really wanted to I’m sure I could understand them too. For I have confidence, grounded in the study of physics, that the world is rationally intelligible, and this, to me, is the most important—and most profoundly liberating—idea in human experience. The universe is comprehensible..."
     
    "A colleague of mine in Chemistry likes to boast that ‘‘anyone can teach; the important thing is to attract good researchers.’’ I think it’s exactly the reverse: competent research physicists are a dime a dozen, but good teachers are few and far between. Please don’t misunderstand: I’ve got nothing against research—I do a certain amount of it myself, and I think it goes hand in hand with good teaching. But I regard myself as a professional teacher, and an amateur researcher, whereas most physicists are professional researchers but amateur teachers, and it shows. In my opinion by far the most effective thing we can do to improve the quality of physics instruction—much more important than modifications in teaching technique—is to hire, honor, and promote good teachers."
     
    There are many more wonderful quotes, but I don't remember them/don't have the sources on me. Perhaps I'll add to this in another blog entry.
     

  15. Akano

    Physics Jokes!

    By Akano,

    In no particular order, some fun physics jokes. Ready? GO!
    My friend was trying to talk to me about atoms, but I got Bohr'd.
    Did you hear that Albert Einstein developed a theory about space? It was about time, too.
    Never trust an atom; they make up everything.
    The oddly pleasant feeling of looking down on a physicist as they finish the last of their drink. The strange charm of a top-down bottoms-up.
    Why does hamburger have less energy than steak? It's in the ground state.
    Why are physics books always unhappy? Because they're full of problems.
    Neutrinos make the worst friends; they rarely interact with anyone.
    In a quantum finish!

  16. Akano

    Allons-y!

    By Akano,

    So, I may have just finished watching all six series of Doctor Who available on Netflix.
     
    And I'm quite glad I did. Awesome show. David Tennant is best pony Doctor.
     
    I want a sonic screwdriver.
     

  17. Akano

    Life Update: Winter 2014

    By Akano,

    When I visit home I tend to not do anything online. So, here's a basic rundown of my winter holidays:
    KK, Tekulo, and I are in the same house again. This changes tomorrow, as KK and I are going to a friend's house, then KK returns to school.
    Had a New Year's Eve celebration with friends from college. Had a blast.
    My Christmas gifts include Super Mario Bros. 3D World, the Winter Market LEGO set (which I may trade with KK for his Winter Village Cottage, which I like a lot), a Fluttershy (my third so far), the mini-VW camper LEGO set, and a ceramic Snoopy sitting on his doghouse. All in all, a good haul.
    I hope everyone has had a good winter holiday season. May 2014 bring you more joy and happiness.
     

  18. Akano
    This is one that I didn't really know much about until recently, so I thought I'd share it. Today's equation is known as the Virial theorem,
     



     
    or, in component form,
     



     
    The word "virial" comes from the Latin vis, which means "force" or "energy," and looking at the equation, it makes sense why it's called that. Here the big Σ means sum, the "k" index denotes the kth particle of a system of N particles, V is the potential energy function affecting the kth particle, T is the potential energy of all the particles in the system, and rk is the position of the kth particle. This essentially relates the kinetic energy of all the particles to the positions and forces exerted on each particle (since -grad V is the force when energy is conserved, which is an assumption we are making). The brackets 〈 〉 denote that we're taking an average, so 〈T〉 is the average kinetic energy, etc.
     
    Now, you may be thinking, "okay, that's a cute equation, I guess, but I don't see how it's particularly useful." Okay, here's where the usefulness comes in. Let's say I want to know the mass of some distant galaxy, but I don't have a good galaxy-weighing device on hand. We know that the gravitational potential energy of an object is given by
     



     
    where m is the mass of the star, M is the mass of the center of the galaxy, and r is the distance from the center of the galaxy. Taking the distance r and multiplying by the gradient of the potential yields...the potential again, with a negative sign out front. So, for gravity,
     



     
    Plugging this into the Virial theorem above and noting that 2T = mv^2 (where v is speed), we get that, for an object in the gravitational pull of an object of mass M,
     



     
    Thus, we have at our disposal a way of measuring the mass of something like a galaxy by measuring only the speeds of stars and their distance away from the center. That's pretty incredible.
     
    This actually is one of the ways scientists support the idea that there is dark matter in the universe; the Virial theorem gives an average of what speeds the stars in our galaxy should have based on their distance away from the center of the Milky Way, but what we actually observe is startlingly different. Thus, we can conclude that something is wrong with our knowledge of how gravity within a galaxy works. Based on this and other observations, the idea that there's extra stuff that can't be seen that adds to the gravitational force of a galaxy seems to be a reasonable idea.
     
    In my research on diatomic hydrogen (H2), the Virial theorem is used in a different capacity. When figuring out the potential energy of an electron (or two) around the two positively charged protons, the virial has the Coulomb force term (which is just -V, just like gravity) and an additional term that pops up from assuming that the electrons are keeping the protons at equilibrium. I won't go too much into the physics, but the final product is
     



     
    where E, T, and V are the total energy, kinetic energy, and potential energy of the electron(s), respectively, and R is the distance between the nuclei. This tells us something useful about the energy of the electrons; more specifically, it tells us about how the energy changes as you move the nuclei farther apart or closer together. In other words, since E = T + V,
     
     



     
    which is very useful when constructing potential energy curves for hydrogen.
     
    On a slightly related note, our lab's paper got published! Akano is now a for reals, published scientist! 8D
     

  19. Akano

    I Caught Some Shinies!

    By Akano,

    Over the past week I caught a shiny Remoraid (evolved it and gave it to Tekulo), shiny Octillery, and shiny Clauncher (traded from Tekulo's X version).
     
    I have become a consecutive fishing master! I want to get a shiny Corsola next.
     
    Also, I had a very enjoyable Thanksgiving with my family and our friends. Tomorrow I head back to my apartment, and then Monday is school as usual.
     

  20. Akano
    So, I've been doing various things in the world of Pokémon recently. I obtained a Squirtle on Wonder Trade (that was awesome), a Froakie from Spain, various forms of Vivillon, a Riolu from Japan (リオル), and a Rotom (8D) from Japan (ロトム). I'm hoping to try the Masuda method to get a shiny Riolu, because shiny Lucario is awesome (and yellow).
     
    Also, I caught a shiny Ditto in Pokémon Village. Luckiest chain ever (I definitely did not get a chain of 40...).
     

  21. Akano

    Recent updates

    By Akano,

    Due to the combination of the servers being taken offline and me being in school, it's been a while since my last entry. I managed to find most of my entries from Google's cache (Aug 26 - now), so they've been posted as though I had posted them on their original entry days, but the comments have disappeared into the aether.
     
    On a more jubilant note, I've been playing Pokémon Y and Ace Attorney: Dual Destinies recently (this is in no way like Tekulo's recent entry). I'm on the first part of case three of the latter, and I have to say that case two was very enjoyable. The twist was really good, and all the crazy weirdness of the people in that case now makes sense (it kind of reminds me of Turnabout Big Top from Justice for All).
     
    In Pokémon Y, I have gotten through Victory Road and am now ready to face the Pokémon League:
     







    Also, I think it's fantastic that I can customize my character with a yellow hoodie and well-matching fedora.
     



     
    My party currently consists of Keaton (Delphox), Anubis (Lucario), Lapras, Sylveon, Snorlax, and my HM user (a linear combination of Machoke, Talonflame, Pansage in near equal probability). I absolutely love the fact that the Fennekin family is based on mages, and Sylveon is absolutely fantastic. Since evolving it, I don't think I've had it faint once.
     

  22. Akano

    Visiting KK

    By Akano,

    So, it's currently my fall break, and I decided the best way to spend that time would be to visit my brother, KopakaKurahk. I arrived Saturday evening and enjoyed a fun day yesterday of meeting people at his grad school, checking out his lab, and enjoying some relaxation (also watching JonTron and MentalFloss and discussing physics and geology).
     
    Good times.
     
    EDIT: Also, apparently this is my 200th entry! This is a milestone for some reason!
     

  24. Akano

    My semester thus far

    By Akano,

    Hi, all!
     
    As you may have noticed, I've been kinda away from BZP recently due to the wonder that is me being in grad school. Last month began my third year into the foray of graduate studentdom, and since then I've been up to the following:
    Taking Thermodynamics/Statistical Mechanics (four lectures a week spread across Thursday and Friday)
    T.A.'ing three sections of introductory physics lab
    Doing research (My group recently submitted a paper which we have gotten back with editing suggestions. We're going to resubmit tomorrow and hopefully get published! I'm going to be a for-reals published scientist!)
    Buying a Wii U bundled with The Legend of Zelda: Wind Waker HD (Pictures of the awesome GamePad will follow. As of this writing, I have just beaten Gohdan)
    Finding out exactly what a true Hufflepuff is, anyways.
    Pertaining to Wind Waker HD, they made many great improvements to the game. For one, Carlov will make as many figurines in one day as you give him, which is really fantastic. Also, you get the deluxe Picto Box much earlier (when you complete Lenzo's tasks for him), so you can get figurines much earlier. The Picto Box also holds 12 pictures now, and thanks to the Tingle Bottle, you can use pictographs sent to you from random people on Miiverse.
     
    I'm very happy with the improvements made in the game. If only there weren't so much BLOOM (it's not that bad, though).
     

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