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Akano's Blog


I made some things

Posted by Akano , in Math/Physics Jan 31 2014 · 284 views

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.


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Select Quotes From a Brilliant Man

Posted by Akano , in Math/Physics Jan 29 2014 · 490 views
David Griffiths, quotes
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.

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Physics Jokes!

Posted by Akano , in Math/Physics Jan 20 2014 · 834 views

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!
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Equation of the Day # 7: The Virial Theorem

Posted by Akano , in Math/Physics Dec 10 2013 · 625 views
Equation, Virial
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,

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or, in component form,

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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

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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,

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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,

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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

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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,

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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

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The Quantum World

Posted by Akano , in Math/Physics Sep 11 2013 · 251 views
Quantum, Morgan Freeman, Feynman

Best Symphony of Science ever.

Also, how do I YouTube? Thanks, Xaeraz!

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First Intro Lab T.A.'ing of the semester

Posted by Akano , in Math/Physics Sep 10 2013 · 181 views


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Blog Statistics

Posted by Akano , in Math/Physics Aug 31 2013 · 433 views
stats, blag, math
I have absolutely no life to the point that I just spent the better part of my afternoon going back through my blog posts and recording the view count, reply count, and word count of all 185 entries I've made prior to this one. These are the results of my labor:

All time averages:
Views: 57.4 ± 45.8
Replies: 2.2 ± 2.6 (LOL)
Word Count: 176 ± 242 (BIGGER LOL)

Post-server upgrade averages:
Views: 79.9 ± 42.6
Replies: 2.58 ± 3.01 (LOL again)
Word Count: 198 ± 292 (BIGGER LOL again)

Largest stats:
Views: 266 (courtesy of "Ask Akano" blog entry; Fort Legoredo review got 265, a close second)
Replies: 24 (again, "Ask Akano")
Word Count: 1711 (Vampyre Castle review)

Here are the graphs for each stat.

What I learned from this experience:
  • Before the server upgrade, I made a lot of posts about how I'm a terrible blogger.
  • Among my most viewed posts were my set reviews.
  • My old text color is more painful to view since the background is now completely white.
  • Most of my blog posts have fewer than 50 words.
  • Most of my blog posts get zero replies.
  • Post-server upgrade, most of my entries get between 60-90 views. Pre-upgrade, they got between 10-20 views.
  • This is my 186th post.
I hope this was informative. I know I learned quite a bit from the experience.

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A GIF of a neutron bouncing on a table

Posted by Akano , in Math/Physics Aug 29 2013 · 319 views
Science, Quantum mechanics
I've blogged before about the physics of bouncing a particle like a neutron on a table or other similar surface. Well, someone at the University of Arkansas has made an animation of how the spread of said particle over space evolves in time if it starts out in a "Gaussian wavepacket," which is a fancy way of saying that the neutron starts out looking more like a particle than a wave by being localized in space. The animation is here, while the full page containing the full Quicktime movie is here.

The red dot is a classical bouncing ball evolving over time (it's pretty boring comparatively). On the left is a plot of the probability of finding the particle at a certain height (the vertical axis) at any given time of the movie. The quantum particle does sort of bounce, become kind of wavy and messy, and then bounces again, but out of phase with the classical ball.

TL;DR: Cool animation of doing mundane physics with a quantum system with results that are anything but mundane. Click the links to have your mind blown.

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A Year of Sky

Posted by Akano , in Math/Physics Jul 29 2013 · 352 views
Because awesome.

Click here.

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Life Updates

Posted by Akano , in Math/Physics, Life Jun 11 2013 · 531 views
Family, Research, Life

So, in the last few weeks, my family came to visit (including Tekulo and KK) and we spent the latter half of the week seeing sights and enjoying each other's company. My mom won a game of Trivial Pursuit on a category that was supposed to stump her. Story of my Trivial Pursuit life.

When they left, they abandoned KK with me, which has led to me stepping into the nerd realm of playing Dungeons & Dragons. We're doing a campaign in the land of Hyrule with the races of Hyrule being used as analogs of D&D races. We're currently in the Forest Temple seeking an herb to cure the Great Deku Tree's muteness.

I'm also working in a new physics lab where I'm studying the energy states of the hydrogen molecule (H2). I'm thoroughly enjoying it, since I'm learning computational stuffs and learning my way around Linux. (Emacs rules the school.) The program I'm working with is in Fortran, which is my native programming language but was written by someone else with a lot more skill than I possess.

And now I'm shoveling through a LOT of data.

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Oak Log Bans

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About Me

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Premier Members
Stone Champion Nuva
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1,500+ posts
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+2 for Premier Membership
+1 from Pohuaki for reporting various things in Artwork

Name: Akano
Real Name: Forever Shrouded in Mystery :P
Age: 29
Gender: Male
Likes: Science, Math, LEGO, Bionicle, Comics, Yellow, Voice Acting, Pixel Art, Video Games
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Twitter: @akanotoe

Equation of the Day

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My Lovely Topics

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Hieroglyphs And The Like

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