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)
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.
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.
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.
where T is the kinetic energy and V is the potential energy. Since the kinetic and potential energy, in general, depend on the coordinate position and velocity of the particle in question, as well as time, so too does the Lagrangian. You're probably thinking, "okay, what makes that so great?" Well, if we were to plot the Lagrangian and calculate the area under the curve with respect to time, we get a quantity known as the action of the particle.
where t1 and t2 are the starting and ending times of interest. Usually if the motion is periodic, the difference between these times is one period. Now, it turns out that for classical motion, the action is minimized with respect to a change in the path along which the particle moves for the physical path along which the particle actually moves. This sounds bizarre, but what it means is that there is only one path along which the particle can move while keeping the action minimized. Physicists call this the Principle of Least Action; I like to call it "the universe is inherently lazy" rule. When you do the math out, you can calculate an equation related to the Lagrangian for which the action is minimized. We call these the Euler-Lagrange Equations.
These are the equations of motion a particle with Lagrangian L in generalized coordinates qi with velocity components denoted by qi with a dot above the q (the dot denotes taking a time derivative, and the time derivative of a coordinate is the velocity in that coordinate's direction). This is one of the advantages of the Lagrangian formulation of mechanics; you can pick any coordinate system that is best-suited for the physical situation. If you have a spherically symmetric problem, you can use spherical coordinates (altitude, longitude, colatitude). If your problem works best on a rectangular grid, use Cartesian coordinates. You don't have to worry about sticking only with Cartesian (rectilinear) coordinates and then converting to something that makes more sense; you can just start out in the right coordinate system from the get go! Now, there are a couple of special attributes to point out here. First, the quantity within the time derivative is a familiar physical quantity, known as the conjugate momenta.
Note that these do not have to have units of linear momentum of [Force × time]. For instance, in spherical coordinates, the conjugate momentum of longitude is the angular momentum in the vertical direction, which has units of action, [Energy × time]. The Euler-Lagrange equations tell us to take the total time derivative of these momenta, i.e. figure out how they change in time. This gives us a sort of conjugate force, since Newton's second law reads that the change in momentum over time is force. The other quantity gives special significance when it equals zero,
This is just fancy math language for saying that if one of our generalized coordinates, qi, doesn't appear at all in our Lagrangian, then that quantity's conjugate momentum is conserved, and the coordinate is called "cyclic." In calculating the Kepler problem – the physical situation of two particles orbiting each other (like the Earth around the Sun) – the Lagrangian is
Note that the only coordinate that doesn't appear in the Lagrangian is ϕ, the longitude in spherical coordinates. Thus, the conjugate momentum of ϕ, which is the angular momentum pointing from the North pole vertically upwards, is a conserved quantity. This reveals a symmetry in the problem that would not be seen if we used the Lagrangian for the same problem in Cartesian coordinates:
That just looks ugly. Note that all three coordinates are present, so there are no cyclic coordinates in this system. In spherical coordinates, however, we see that there is a symmetry to the problem; the symmetry is that the situation is rotationally invariant under rotations about an axis perpendicular to the plane of orbit. No matter what angle you rotate the physical situation by about that axis, the physical situation remains unchanged.
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.)
So the next time you feel lazy loafing on your couch or computer chair, just remember that you are traveling at light speed, no matter how fast or slowly you move.
This entry brought to you by SCIENCE!
There's a conference that my adviser wants my lab group to go to in June. Understandable. What's not understandable is that the deadline for abstracts to present at said conference is tomorrow (it was originally Friday, but got bumped back over the weekend). This means, of course, that I have to have enough data to write an amazingly short paragraph about what I'd be presenting at the conference by tomorrow. At 5 p.m.
Now, I'm not one for stress. As my brothers and roommate can easily tell you, I take it rather easy and do not like to be rushed. This past week has been the exact opposite for me.
So, I'm slightly burned out, but I have some data that will hopefully be enough to make an abstract with. Huzzah...
On a more pleasant note, yesterday's Spike episode was good. I love Gummy. And Tank.
Oak Log Bans
Akano Toa of Electricity
Stone Champion Nuva
+2 for Premier Membership
+1 from Pohuaki for reporting various things in Artwork
Real Name: Forever Shrouded in Mystery
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.
Hieroglyphs And The Like
Just beat the original Legend of Zelda last nightAkano - Aug 26 2016 06:48 PM
Just beat the original Legend of Zelda last nightBaltarc - Aug 10 2016 07:55 AM
Just beat the original Legend of Zelda last nightAkano - Aug 09 2016 09:37 PM
Just beat the original Legend of Zelda last nightLyichir - Aug 09 2016 08:10 PM
Just beat the original Legend of Zelda last nightLapis Lazuli - Aug 09 2016 12:32 PM