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This was taken a few nights ago. I used mjpg-streamer over wireless at 10fps.

New Equations!

Homework for chapter 10 is done!

The follow equations were used, along with some for Dr. M. Smith, Professional Bad-Ass Calc professor.

Here is the rendering!



Here is the LaTeX.

\begin{enumerate}
\item $\psi (r,\theta, \phi) = \frac{1}{\sqrt{\pi}} \left ( {}\frac {1}{a_{0}} \right )^{3/2} e^{-r/a_{0}}$ \\
\item $\left | \psi (r) \right |^{2} 4\pi r^{2} dr$ \\
\item $P(r) = 4a_{0}^{-3}\int_{0}^{\infty} r^{2}e^{-2r/a_{0}}dr$ \\
\item $4 \pi r^{2}$ \\
\item $-\frac {\hbar ^{2}}{2m} \nabla^{2} \psi (\mathbf{r}) \hspace{6pt} + \hspace{6pt} U(\mathbf{r})\psi (\mathbf{r}) \hspace{pt6} = \hspace{6pt} E\psi(\mathbf{r})$ \\
\item $ -\frac {\hbar ^{2}}{2m} \nabla^{2} \psi (\mathbf{r}) \hspace{6pt} + \hspace{6pt} U(\mathbf{r})\psi (\mathbf{r}) \hspace{6pt} = \hspace{6pt} E\psi(\mathbf{r}) $ \\
\item $\nabla^{2} = \frac{\partial^2 }{\partial r^2} +\left ( \frac {2}{r} \right )\frac{\partial }{\partial r} +\frac{1}{r^{2}} \left [\frac{\partial^2 }{\partial \theta^2} +cot \theta \frac{\partial }{\partial
\theta}+ csc^{2}\theta \frac{\partial^2 }{\partial \phi^2} \right ] $ \\
\item $\nabla^{2} = \frac{\partial^2 }{\partial x^2} + \frac{\partial^2 }{\partial y^2} + \frac{\partial^2 }{\partial z^2} $ \\
\item $ \frac{\mathrm{d} }{\mathrm{d} v} n(v)dv = \frac{4\piN}{V}\left ( \frac{m}{2\pi K_{B}T} \right )^{\frac{3}{2}} \left \{ 2ve^ {\frac{-mv^{2}}{2K_{B}T}}+\frac{-2m}{2K_{B}T}v^{3}e^ {\frac{-mv^{2}}{2K_{B}T}}\right \}$ \\
\item $ $ \\
\item $ $ \\


\end{enumerate}

LaTeX Equations from tonight

The following images are LaTeX generated and I made them in the process of doing my homework. They serve here as a reminder of syntax, nostalgia-bait, and examples of the power/shortcomings of LaTeX. Also, check out SAGE.

Equations
Code:

\documentclass[a4paper,10pt]{scrartcl}
\usepackage[utf8x]{inputenc}

%opening
\title{10.8 Feb 4}
\author{Spencer Krum}

\begin{document}

\maketitle

\begin{abstract}

\end{abstract}

\section{Equations}
\begin{enumerate}
\item $v_{mp} = \sqrt{\frac{2k_{b}T}{m}}$
\item $n(v)dv = \frac{4 \pi N}{V}\left ( \frac{m}{2\pik_{b}T} \right )^{3/2}v^{2}e^{\frac{-mv^{2}}{2k_{b}T}}dv$
\item $-4 \, \frac{\pi N k m t x^{3} e^{\left(-\frac{1}{2} \, k m t x^{2}\right)}}{V} + 8 \, \frac{\pi N x e^{\left(-\frac{1}{2} \, k m t x^{2}\right)}}{V}$
\item $-c k m t x^{3} e^{\left(-\frac{1}{2} \, k m t x^{2}\right)} + 2 \, c x e^{\left(-\frac{1}{2} \, k m t x^{2}\right)}$

\end{enumerate}


\end{document}

Statistical Physics

There are 3 important distributions you should know about. This information may one day save your life.

1) Maxwell-Boltzman distribution.
2) Bose-Einstein distribution.
3) Fermi-Dirac Distribution.

You use these when you want to deal with an ensemble of particles. Not one electron around a hydrogen nucleus but moles of electrons on the surface of a conducting sphere. These distributions have differences in how and when you use them but the all do essentially the same thing for you: They describe the energy states of particles as a function of temperature. Do note the difference between temperature and heat as it is a significant one in thermodynamics.

Glass and plastic cups

At dinner at a nice but not very nice restaurant the cups could have been either thin light glass or a convincing plastic immitation. To determine which kind they were we tapped the cups with a metal knife. The cups chimed, therefore they were made of glass.

The best guess I have for this is that a glass cup is essentialy one cystal of silicon dioxide whereas a plastic cup is several long chain polymers linked together by strong intermolecular forces. The result is that when force is applied to the glass cup the force translates smoothly through the cup and at the opposite end of the cup the force reverses direction and travels back through the cup. Thus the resonance is the velocity of the comperssion wave through the cup divided by the length. A plastic cup doesn't resonate becuase it's non crystaline structure does not have enough uniformity for the pressure waves to bounce back and forth within it.


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White and Black

A simple idea: paint roofs, roads, and everything else white instead of black. The underlying idea is that the black color absorbs sunlight and converts it to heat energy while white color reflects the light back into space.

Energy Secretary Chu thinks

"making roads and roofs a paler color would be equivalent to taking all cars worldwide off the road for 11 years."

Chu, by the way, won the 1997 Nobel Prize in Physics. Read about it here.

Does the idea hold up?

The quote from Chu can be misleading. What is the equivalence? The most likely equivalence is that the CO2 emissions from all cars over 11 years will trap some amount of light energy here. That same amount of light energy will be reflected instead of absorbed by painting things white. Also, what roads? All roads everywhere? Or just in the United States?

Two processes will be discussed to help understand this ambitious plan. First the process by which light absorption increases temperature and second the nature of color in terms of absorption and reflection.

Think about a greenhouse in a garden. It's warm. It's warm because ultraviolet and visible light can penetrate the glass and are absorbed by objects inside the greenhouse. Once absorbed, some light energy is converted to heat, making the object warmer, and the rest is emitted as light of a lower wavelength. Light incident as visible and ultraviolet light is converted into infrared light by this process. Infrared light is unable to penetrate glass and so infrared light is trapped inside a greenhouse bouncing from object to object until it is entirely converted to heat energy.

A white object reflects all light and absorbs none. A red object is red because it reflects red light and absorbs other colors of light. A dark object reflects less of the light than it absorbs. A black object reflects no light and absorbs all of it. This is a physical interpretation of light and coupled with the above discussion it is plain to see what significance color has.

Painting surfaces white will reflect light back up into the atmosphere instead of converting it to heat. Much of this light will make it out into space.

The idea is scientifically sound, but practicality issues of course present themselves.

50% chance of rocks, folks.

Short summary: They found an exoplanet (that's a planet orbiting around a different star) that has regular rock precipitation. The day side of the planet is hot enough to vaporize minerals into the atmosphere, and the night side is cool enough to re-form them as mineral rain. Sweet.


http://www.examiner.com/examiner/x-1242-Science-News-Examiner~y2009m10d1-A-planet-that-rocks