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Akano's Blog



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WIRELESS WIZARD!

Posted by Akano Toa of Electricity , in D&D Feb 25 2014 · 128 views
Fad, Wizard, Lightning Bolt!
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.

 
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Physics Conference

Posted by Akano Toa of Electricity , in Math/Physics Feb 24 2014 · 78 views
Physics
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.

 

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A quarter century

Posted by Akano Toa of Electricity , in Life Feb 22 2014 · 118 views

That's how old I am now.

Wat.

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Sleep

Posted by Akano Toa of Electricity , in Music Feb 19 2014 · 75 views

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.

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Love this theme

Posted by Akano Toa of Electricity , in Music Feb 17 2014 · 85 views
Doctor Who




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Equation of the Day #8: Bessel functions

Posted by Akano Toa of Electricity , in Math/Physics Feb 15 2014 · 122 views
Equation of the Day
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,

 

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

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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,
 

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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.
 

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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() and cos() (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:
 

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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
 

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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:
 

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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 cool videos (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.

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Happy birthday, little bro

Posted by Akano Toa of Electricity , in Life Feb 14 2014 · 62 views
Birthday, Siblings, Aww, Shut up
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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Snow Days

Posted by Akano Toa of Electricity , in Life Feb 05 2014 · 66 views

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.

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I made some things

Posted by Akano Toa of Electricity , in Math/Physics Jan 31 2014 · 95 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.

8D

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Select Quotes From a Brilliant Man

Posted by Akano Toa of Electricity , in Math/Physics Jan 29 2014 · 111 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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About Me

Akano Toa of Electricity
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Premier Members
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Name: Akano
Real Name: Forever Shrouded in Mystery :P
Age: 25
Gender: Male
Likes: Science, Math, LEGO, Bionicle, Ponies, Comics, Yellow, Voice Acting
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Misses the 90's. A lot.
Twitter: @akanotoe

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