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Akano's Blog



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Finite Difference, Y U NO WORK?!

Posted by Akano , in Math/Physics Dec 09 2012 · 466 views
E&M, FORTRAN, Programming
So, I'm working on a computer project for my Electrodynamics course. I'm using a computer method called the Relaxation or Finite Difference Method. It basically takes a physical scenario, divides the space of interest into a grid, and assigns voltages for each grid intersection. Then, using a computer language of choice (I'm using FORTRAN, like a boss), I make a program that essentially takes a weighted average of all the points whose voltages aren't fixed until the program doesn't change those voltages anymore. This gives a surprisingly good approximation for a physical system.

I'm basically modeling a system with two conducting cylindrical shells of equal radius separated by some height and which are at voltages +V0 and -V0. The problem is that my output graphs do not look physical; the voltage just drops to near zero rapidly for points outside and between the cylinders, whereas I expect that the graph should gradually drop.

Curse you, technology!

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Sleepless in Ponyville

Posted by Akano , in My Little Pony Dec 08 2012 · 377 views
Scootaloo, Luna
Heartwarming and cute. ^_^

Also,
Spoiler


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New Comic!

Posted by Akano , in Comics Dec 05 2012 · 297 views
Comic 130, New
And just before the apocalypse hits, too! :P Head on over here to read it!

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Equation of the Day #5: Cardioid

Posted by Akano , in Math/Physics Dec 02 2012 · 1,101 views
Math, Geometry, Cardioid, Heart and 1 more...
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I made it in GIMP. A cardioid is the envelope formed by a set of circles whose centers lie on a circle and which pass through one common point in space. This image shows the circle on which the centers of the circles in the above image lie. A cardioid is also the path traced by a point on a circle which is rolling along the surface of another circle when both circles have the same radius (here is a cool animation of that).

What is the cardioid's significance? Well, it looks like a heart, which is kind of cool. It's also the (2D) pickup pattern of certain microphones (I have a cardioid microphone). If a sound is produced at a given point in space, the pickup pattern shows an equal intensity curve. So, if I place a microphone at the intersection point of all those circles, the outside boundary is where a speaker producing, say, a 440 Hz tone would have to be to be heard at a given intensity. So, the best place to put it would be on the side where the curve is most round (the bottom in this picture) without being too far away from the microphone.

Another interesting fact about the cardioid is that it is the reflection of a parabola through the unit circle (r = 1. Here's what I mean). In polar coordinates, the equation of the above cardioid is given by
 
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where a is a scaling factor, and theta is the angle relative to the positive x-axis. The origin is at the intersection of the circles. The equation of a parabola opening upwards and whose focus is at the origin in polar coordinates is just

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which is an inversion of the cardioid equation through r = 1, or the unit circle.



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Magic Duel

Posted by Akano , in My Little Pony Dec 02 2012 · 446 views
Trixie
I was pleasantly surprised.

I loved when Fluttershy found the book with the amulet in it. Adorable. ^_^

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New Avatar and Banner

Posted by Akano , Dec 01 2012 · 287 views

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Not even remotely Fall-related.

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Pokédex 3D Pro

Posted by Akano , in Pokémon Nov 30 2012 · 530 views

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.

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Babs Seed

Posted by Akano , in My Little Pony Nov 29 2012 · 543 views

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. :unsure:

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Lunar Eclipse!

Posted by Akano , in Math/Physics Nov 28 2012 · 329 views
SCIENCE!
In, like, ten minutes several hours.

GO LOOK AT IT, WEST COAST BZPers! :P

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Equation of the Day #4: Measurement Standards

Posted by Akano , in Math/Physics Nov 25 2012 · 410 views
Standard, Meter, Pendulum
If you're building something and want to tell other people how to build it, it's useful to show the dimensions of said something (how big it is) relative to other things that people are familiar with. However, there are very few things in this world that are exactly the same size as other similar things (e.g. not all apples weigh the same or have the same volume). So, some smart people once upon a time decided to make standards of measurement for various properties of matter (which I think we can all agree was a smart decision). I wanted to talk about one of these today: the meter.

The word meter (or metre for those who live across the pond/in Canada) comes from the word for "measure" in Greek/Latin (e.g. speedometers measure speed, pedometers measure steps, &c.), but the meter I'm talking about is the International System (SI) unit of distance. The original definition of the meter was one ten-millionth of the distance from the Earth's equator to the North Pole at sea level (not through the Earth). The first person to measure the circumference of the Earth was the Greek mathematician/astronomer/geographer Eratosthenes (and he was accurate to within 2% of today's known value) circa 240 B.C., so this value was readily calculable in 1791 when this standard was accepted.

In 1668, an alternative standard for the meter was suggested. The meter was suggested to be the length a pendulum needed to be to have a half-period of one second; in other words, the time it took for the pendulum to sweep its full arc from one side to the other had to be one second. The full period of a pendulum is

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So, when L = 1 m and T = 2 sec, we get what the acceleration due to gravity, g, should be in meters per second per second (according to this standard of the meter). It turns out that g = pi2 meters per second per second, which is about 9.8696 m/s2. This is very close to the current value, g = 9.80665 m/s2 which are both fairly close to 10. In fact, for quick approximations, physicists will use a g value of ten to get a close guess as to the order of magnitude of some situation.

So, you may be wondering, why is it different nowadays? Well, among a few other changes in the standard meter including using a platinum-iridium alloy bar, we have a new definition of the meter: the speed of light. Since the speed of light in a vacuum is a universal constant (meaning it is the same no matter where you are in the universe, unlike the acceleration due to gravity at a point in space), they decided to make the distance light travels in one second a set number of meters and adjust the meter accordingly. Since the speed of light is 299,792,458 meters per second exactly, this means that we have defined the meter as the distance light travels in 1/299,792,458th of a second.

This is all nice, but it's not a very intuitive number to work with. After all, we humans like multiples of ten (due to having ten fingers and ten toes), so why not make a length measurement of the distance light travels in one billionth (1/1,000,000,000th) of a second (a.k.a. nanosecond)? That seems a bit more intuitive, don't you think? It turns out that a light-nanosecond is about 11.8 inches, or about 1.6% off of the current definition of a foot. In fact, one physicist, David Mermin, suggests redefining the foot to the "phoot," or one light-nanosecond, since it's based off of a universal constant while the current foot is based off the meter by some odd, nonsensical ratio.

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Oak Log Bans

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About Me

Akano
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Premier Members
Stone Champion Nuva
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1,500+ posts
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Proto
+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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