Jump to content

Akano

Premier Members
 View Profile  See their activity

  • Posts

    778

  • Joined

  • Last visited

  • Days Won

    1

 Content Type 

Blog Entries posted by Akano

  1. Akano

    Thesis Submitted

    By Akano,

    Six years, four papers, and 179 pages later, I have submitted my Ph.D. thesis.
     
    Now I have to defend it. But first, STRESS RELIEF VIA VIDEO GAMES!
     
     

  2. Akano

    Happy Halloween

    By Akano,

    (Click for larger image)


     
    The one on the left is my roommate's; the one on the right is mine.
     
    Happy Halloween, BZPower.
     
    (Also, check out my Haunted House review if you haven't already! It's full of awesome haunted house pictures!)
     

  3. Akano

    Babs Seed

    By Akano,

    SUCH A CATCHY SONG ZOMG!!
     
    Also, the CMC were very adorable in that episode.
     
    (I watched it the other day, but just listened to the song for about the fifth time.)
     
    EDIT: Also, apparently typing in darkgoldenrod as your font color doesn't work anymore.
     

  4. 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.
     

  6. Akano
    Yesterday, I obtained my 4-year…Norik head? Exactly what am I supposed to do with it? ~tries putting it on his face like a mask~
     
    You know, after one year, you can control time, after two years you get power over light, three years you get invisibility, but all I have now is a Rahkshi head?
     
    The fourth year stinks. XP
     

  7. Akano

    Pokédex 3D Pro

    By Akano,

    You look really cool, and I'm sure I'd enjoy your features and such, but you're $15. For a Pokédex.
     
    If you had 3D battling capabilities/games that would work in tandem with BW/B2W2, I'd probably get you, but you don't. Sorry.
     

  8. 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
     

  9. Akano
    The definition of a planet has been under scrutiny several times, and with New Horizon's recent visit to Pluto, the discussion of Pluto's demotion was on everyone's minds (at least, back in July). But I'm not going to talk about Pluto's demotion (though I think it was totally appropriate from a scientific perspective). Instead, I'm going to talk about the Moon.
     
    Should the Earth-Moon system be considered a binary planet? This sounds outlandish at first, since the Moon is a moon, obviously. It orbits the Earth as a natural satellite, just as the Galilean moons (Ganymede, Callisto, Io, and Europa) orbit Jupiter, Titan orbits Saturn, Triton orbits Neptune, and so on, right?
     
    The definition of a moon is vague, and thus there are multiple ways of determining whether or not a planet-moon system is really a binary planet. One way of drawing the line between the two descriptions is by finding the barycenter (or center-of-mass) of the system. The center of mass of a collection of N masses is given by
     



     
    where M is the total mass of the system, and mi and ri are the mass and position of the ith object, respectively. If the center of mass of a two-body system lies outside the larger object in that system, call it a binary planet. This makes sense, right? This means that the smaller body doesn't orbit the larger body, but instead they both orbit some point in space. For instance, the barycenter of the Pluto-Charon system lies outside Pluto (0.83 Pluto radii above Pluto's surface), the larger of the two bodies, while the Earth-Moon barycenter lies within the Earth (just under 3/4 of an Earth radius from the planet's center). By this definition, the Pluto-Charon system is a binary (dwarf) planet system, while the Earth-Moon system is is a planet-moon system. (Although, we are slowly losing our moon due to tidal acceleration. In a few billion years, the Moon will have drifted far enough away that the barycenter of the Earth-Moon system will leave the interior of our planet.) However, when you plug in values for the Sun-Jupiter system, you find that the center of mass lies outside the Sun! Indeed, Jupiter is the only natural satellite of the Sun for which this is true. (Does this mean Jupiter should have a different classification from the rest of the planets? Not really; the Sun is around 1000 times more massive than Jupiter, so the reason for this is that Jupiter is very distant from the Sun.)
     
    Maybe a different definition is needed to distinguish planet-moons from binary planets, then, since the Sun-Jupiter system is not a binary star (Jupiter is slightly too small to generate nuclear fusion). Another proposition is to look at the so-called tug-of-war value of a body. The tug-of-war value of a moon determines which Solar System object has a stronger gravitational hold, the Sun or the moon's "primary" (the Earth is the Moon's primary). Using Newton's law of gravitation
     



     
    we can take a ratio of the Sun's pull on a satellite to the primary's pull. The result is the tug-of-war value, proposed by Isaac Asimov.
     



     
    Here the subscripts s and p refer to the Sun and the primary, respectively; m is the mass of the body referred to by the subscript; and d is the distance between the moon and the body referred to by the subscript. If the tug-of-war value is larger than 1, then the primary has a larger hold on the moon than the Sun, whereas if it's less than 1, the Sun's gravity dominates. For the Earth-Moon system, it turns out this number is 0.46, which means that the Sun pulls on the Moon with more than twice the force of Earth's pull. This is an oddity among moons, but is not unique. It does mean, though, that the Moon, when viewed from the Sun, never undergoes retrograde motion; it moves across the solar sky without changing direction. Another way to put this is that the Moon is always falling toward the Sun (like the planets), and never in its orbit does it fall away from the Sun (unlike most moons). If you look at the orbits of the Earth and Moon from the point of view of the Sun, they dance around each other in careful step, which is unlike most other moons in the Solar System. For Asimov, this was reason enough to consider the Earth and Moon as a binary planet system.
     
    This tug-of-war value does not, however, classify Pluto and Charon as a binary dwarf planet system (they're too far from the Sun for their tug-of-war value to be less than 1). Perhaps the definition of a binary planet is a difficult one to pin down.
     
    Should the Moon be promoted to planet, just as Pluto was renamed as a dwarf planet? I don't know, but it gives us something to think about as we look up at the starry night, watching the dance of all the chunks of rock and gas hurtling through space in our sky, to music written by nature and heard through science.
     

  10. Akano
    When I first came to this site, I was very much a lurker. My brothers and I had gotten into BIONICLE from its beginning in 2001, and we eventually stumbled on this site in the early, awkward days of the World Wide Web. It was here that I saw the creative output of the fandom – sprite comics, artwork, MOCs, comedies, epics, and much more.
     
    Fourteen years ago, I became a part of that creative output with the premiere of Akano's Comics.
     
    It's been six years since I made a comic (sorry, everyone, grad school happened; I do want to make more, though!), but my creative outputs didn't stop. I made set reviews and Equation of the Day (which I'm still working on, I promise!).
     
    Thank you, everyone, for being my first audience. Now that I'm a professor, I'll have many, many more, but you were the first to truly see the crazy inner workings of my mind. Thanks for sticking with me, and thanks for helping me improve. You guys helped someone who stumbled to craft paragraphs become an author. You helped someone who enjoyed comedy but couldn't quite formulate a joke become a half-decent comedian.
     
    Here's to more creative output.
     

  11. Akano

    New Comic and Such

    By Akano,

    Hey, guys! Come over here and see the new comic this random yellow guy just posted! It's sure to make you LOL (or at least facepalm).
     
    Also, my Halloween Accessory Set review is feeling rather unloved. Pay it a visit, won't you?
     

  13. Akano

    Pokémon White 2: Postgame

    By Akano,

    While I technically beat the Elite Four on Tuesday, I thought I'd share my team here.

    Anubis (Lucario)
    Tornadus-T
    Vanessa (Emboar)
    Zoroark
    Tesla (Magnezone)
    Golduck - HM slave

     
    I couldn't nickname Zoroark due to it being N's originally, and Tornadus I just never got around to nicknaming after I got him from Dream Radar. This was actually the first time I've ever raised any of these Pokémon for a team, so it was a very different game experience this time around. I wish Lucario were just a bit bulkier, because he can dole out punishment but can't really take it. I love Zoroark's speed, but man is he frail. Emboar was all right, but I definitely prefer Samurott. Magnezone was pretty awesome, too; his Special Attack is beastly.
     
    I should raise a Chandelure when I replay through White. He looks pretty awesome...
     

  14. Akano

    Science Journals

    By Akano,

    So, in an earlier blog entry I talked about a journal article one of our professors presented at our department's journal club discussing neutrons in a purely gravitational potential well. Well, I decided to read it and am going to present it to the math and science grad students on Friday because I think it's pretty dang awesome.
     
    Related: Airy functions are weird. And cool. Perhaps I'll discuss them later...
     
    Also, tomorrow spring is here! (If it weren't for ponies, I would not say that with so much excitement.)
     
    `
  17. Akano

    My morning

    By Akano,

    I'd like to describe to you all the most memorable scene from my morning walk into school.
     
    I emerged from the tunnel under the train tracks and headed towards the last intersection on my walk on my way to school. In the bare bushes of one of the office buildings on the street twittered a bunch of small sparrows, not a care in the world. I watched them as they chattered, when all of a sudden a brown blur appeared in my periphery. A hawk (I believe a broad-winged hawk) was in a dive, ready to snatch up a meal from the group of sparrows. It swooped, then crashed into the bare branches of the bushes. I could tell immediately after it crashed that it was unsuccessful in its quest, and as it looked around during its shocked stupor, I could see in its face the expression of "Well, this is just great." The poor thing sat there for a moment and eventually freed itself, its ego more bruised than its body, as it flew atop the building and reconsidered what its next move was.
     
    All in all, it was really cool, and I'm glad I got to witness it.
     

  19. Akano

    Merry Christmas, Everyone

    By Akano,

    I'm at home enjoying the holiday with my family. I hope all of you have the pleasure of doing the same or similar.
     
    For those who don't celebrate Christmas, may you have a wonderful holiday season!
     

  21. Akano

    Neutrons Bouncing on Glass

    By Akano,

    Yes, you read that right.
     
    So, today our physics department had our Journal Club, where one of the professors/grad students get to share a journal article or two that they found in the vast amount of physics literature available to academia. Today our resident dark matter-seeking professor gave the talk, and boy was it awesome.
     
    The researchers whose papers he found were bouncing neutrons on glass and looking at their quantum states due solely to the potential energy caused by gravity. Quantum mechanics with gravity.
     
    For those of you who don't understand how ridiculously awesome this is, let me put it in terms of Classical Mechanics: when a classical object is under the influence of a uniform gravitational potential (like that near Earth's surface), it follows parabolic trajectories. Imagine a ball bouncing on a table; it forms a series of parabolic bounces, each one smaller than the last due to friction and lost energy due to sound and such. This is essentially what this group did, but with neutrons and glass.
     
    However, because neutrons are not classical particles and instead behave quantum mechanically, they don't bounce in parabolic trajectories. Instead, they abide by the laws of quantum mechanics, which means that there are only certain heights above the table at which they are likely to be found and certain heights that they cannot be found. So, a neutron in the ground (lowest) state of this system is most likely to be found at about 10 microns (thousandths of a millimeter) above the glass.
     
    Also, when this was published back in 2005, it was the first time quantized energy levels due to Earth's gravitational potential alone were ever observed experimentally; the theory has been known for a while, but this is the first time anyone has in any way verified it.
     
    Now, this group is attempting to test the properties of the force of gravity using this apparatus and their neutrons. HOW AWESOME IS THAT?!
     
    This blog entry brought to you by SCIENCE!
     

  22. Akano

    It's All Relative

    By Akano,

    Being a physics grad student has seen me be in quite the scientific mood lately, hasn't it? Well, unfortunately, I still don't have a new comic made (I'm sorry, everyone! ><), but I do have another idea for a blog entry. Last week, Pi day (March 14) marked Einstein's 133rd birthday, and since my Classical Mechanics course is covering the Special Theory of Relativity, I thought I'd try to cover the basic ideas in blog form.
     
    According to the laws of physics laid down by Sir Isaac Newton, all non-accelerating observers witness the same laws of physics. This included an idea of spontaneity, the idea that someone traveling on the highway at 60 mph would witness an event occur at the exact same time as someone who was just sitting on the side of the highway at rest. The transformation from a reference frame in motion to one at rest for Newtonian physics is known as a Galilean transformation, where x is shifted by -vt, or minus the velocity times time. Under such transformations, laws of physics (like Newton's second law, F = ma, remain invariant (don't change).
     
    However, during the 19th century, a man by the name James Clerk Maxwell formulated a handful of equations, known now as Maxwell's equations, that outline a theory known as electromagnetic theory. Of the many new insights this theory gleaned (among these the ability to generate electricity for power which every BZP member uses) one was that light is composed of oscillating electric and magnetic fields; light is an electromagnetic wave. By using his newly invented equations, Maxwell discovered what the speed of light was by formulating a wave equation. When his equations are used to describe electromagnetism, the speed of light is shown to be the same regardless of reference frame; in other words, someone traveling near the speed of light (as long as they weren't accelerating) would see light travel at the same speed as someone who was at rest. According to Newton's laws, this didn't make sense! If you're in your car on the highway and traveling at 60 mph while another car in the lane next to you is traveling at 65 mph, you don't see the other car moving at 65 mph; relative to you, the other car moves at 5 mph. The reason that light is different is because a different theory governs its physics.
     
    This brought about a dilemma: is Maxwell's new electromagnetic theory wrong? Or does Newtonian mechanics need some slight revision? This is where Einstein comes in. He noticed the work of another physicist, Lorentz, who had worked on some new transformations that not only caused space to shift based on reference frames moving relative to each other, but also shifted time. Einstein realized that if light had the same speed in all non-accelerating reference frames, then objects moving faster experienced time differently than those that moved slower. This would come to be known as the Special Theory of Relativity.
     
    How does this make sense? Well, if you have some speed that must remain constant no matter how fast one is traveling, you need time to shift in addition to shifting space to convert between both reference frames, since speed is the change in distance over the amount of time that displacement took place. If you have two reference frames with some relative speed between them, the only way to shift your coordinates from one to another and preserve the speed of light is if both frames experience their positions and times differently. This means that, if something moves fast enough, a journey will take less time in one frame than the other. Special relativity says that moving clocks progress more slowly than clocks at rest, so someone traveling in a rocket at a speed comparable to the speed of light will find that the journey took less time than someone who had been anticipating his arrival at rest. This also means that if someone left Earth in a rocket traveling near the speed of light and came back ten years later would not have aged ten years, but would be younger than someone who was his/her age before his journey took place. Weird, huh?
     
    If you think this is crazy or impossible, there have been experiments done (and are still going) to try to confirm/reject the ideas of special relativity, and they all seem to support it. There's another relativity at play as well known as general relativity, which states that gravitational fields affect spacetime (the combination of space and time into one geometry). General relativity says that the higher up you are in a gravitational field, the faster clocks run (time speeds up). A proof of this theory is GPS; the satellites that help find your position by GPS are all higher up in Earth's gravitational field than we are, and thus their clocks run faster than those on Earth's surface. If general relativity weren't considered in the calculations to figure out where you are on Earth, your GPS would be off by miles.
     

  23. Akano

    Tekulo's birthday entry

    By Akano,

    I was going to make this a topic when it happened, but unfortunately the forums were offline, so I'll make an entry for it instead. My younger brother, Tekulo, turned 21 this past Thursday, Valentine's Day, so go ahead and wish him a belated happy birthday!
     

  25. Akano

    Ponies Premiere

    By Akano,

    These villains are getting less and less backstory development as we go, huh? In terms of development:
     

    Sombra < Chrysalis < Discord / Nightmare Moon


     
    That said, though, I enjoyed the episode quite a bit. The songs were okay, but I've only listened to them once, really. However, it was nice for Spike to get a role as Twilight's supporting vocals. Cathy Weseluck amazes me.
     
    I did think Rainbow Dash was a bit over the top, but I enjoyed everyone else.
     
    También, sombra = shadow en español, por tu información.
     

×
×
  • Create New...