# Monthly Archives: June 2010

## Schrodinger’s kit: Tools that are in two places at once – physics-math – 28 June 2010 – New Scientist

Filed under Articles

## Reading Material

Filed under Side Projects

## Mirrors, concave and convex.

In class today we were going over how mirrors and lens work. It reminded me of this very neat toy I saw, a Parabolic Mirror Wok, that projects a real image on the items in side up outward.

I wonder what would happen if you had a little screen in the bottom projecting an image?

Filed under Side Projects

## Quama, Laser TV and Liquid Helium

So I downloaded this new tool to let me blog remotely more easily. Hopefully it will be very helpful! To test it out here is a list of recent articles which have caught my eye.

Laser Phosphor Display (LPD) television – it’s all done with mirrors

(PhysOrg.com) — Californian company Prysm has unveiled a high definition television with a “laser phosphor display” based on their patented method of using lasers reflected off a bank of mirrors to excite pixels on the television screen in a similar way to cathode ray tubes.

*This is the first time I’ve heard of a TV using lasers. The video link in the article is very cool*

*This is a neat video on Liquid Helium. We were studying Temperature in class, the book mentioned superfluids and this is a neat video I found on superfluids.*

And to see how Quama handles images, here is a recent photo of me from the webcam in my Airie.

Oh Yeah, I’ve also figured out I can learn Chemistry through MIT Opencourseware. So I’ve been working through 5.111 Principles of Chemical Science As taught in: Fall 2008. There is a full video lecture series and the professor teaching it is awesome! I’m very happy to be learning from her.

I would like to see if my LaTeX editor can pick up things. Lets give it a try…

[math]!(a+b)^2[/math]

If it works I’ve got to track down my lost post on how to write LaTeX again.

Filed under Side Projects

## Quantum Cascade Surface-Emitting Photonic Crystal Laser

We combine photonic and electronic band structure engineering to create a surface-emitting quantum cascade microcavity laser. A high-index contrast two-dimensional photonic crystal is used to form a micro-resonator that simultaneously provides feedback for laser action and diffracts light vertically from the surface of the semiconductor surface. A top metallic contact allows electrical current injection and provides vertical optical confinement through

a bound surface plasmon wave. The miniaturization and tailorable emission properties of this design are potentially important for sensing applications, while electrical pumping can allow new studies of photonic crystal and surface plasmon structures in nonlinear and near-field optics.

http://iqse.harvard.edu/research/docs/science_2003-302-1374.pdf

Filed under Articles

## Entangled photons available on tap – physics-math – 02 June 2010 – New Scientist

Filed under Side Projects

## Bursting bubbles beget tiny copies of themselves – physics-math – 09 June 2010 – New Scientist

Filed under Side Projects

## Bursting bubbles beget tiny copies of themselves – physics-math – 09 June 2010 – New Scientist

Filed under Uncategorized

## Fluids – Chapter Notes

The Density (rho) is mass per unit volume, the unit is kg/m^{3}.

[math]displaystyle rho = frac{m}{V}[/math]

rho equals m over V

[math] m = rho V[/math]

m equals rho V

**Specific Gravity** is ratio of the density of the substance to the density of water at 4C.

Pressure is force per unit area, when the force is magnitude acting perpendicular to the surface area **A**.

[math]displaystyle P = frac {F}{A}[/Math]

Pressure is a scalar with the unit name Pascal, which is N/m^{2}.

Pressure due to liquid is , remember the funny looking p is “rho” aka DENSITY.

As the pressure increases, density increases as well though so for cases with gas, pressure is

[math] displaystyle frac{dP}{dy} = -rho g[/math].

Another way to express is equation is

[math] displaystyle P_2 – P_1 = -int_{y_1}^{y_2} rho g dy [/Math]

If you can ignore variations in density this can be expressed as:

[math] P_2 – P_1 = – rho g(y_2 – y_1) [/math]

For an open contain of liquid, you simply add the pressure from the atmosphere

[Math] P = P_0 + rho gh[/math]

**Pressure head:** Sometimes the h in *Rho g h* is called the pressure head.

Atmospheric Pressure is 101.3 kPa for 14.7lb/in^{2}. sometimes we use bars, which are 10,000 N/m2.

Pressure gauges register gauge pressure. This does not include the atmospheric pressure, so we need to add it in, by adding the pressure of the atmosphere to the gauge.

Pascal’s Principle states *“If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount”*

[Math] P_{out} = P_{in}[/math]

[math] displaystyle frac{F_{out}}{A_{out}} = frac{F_{In}}{A_{In}}[/math]

[math] displaystyle frac{F_{out}}{F_{in}} = frac{A_{out}}{A_{In}}[/math]

This ratio gives mechanical advantage, F_{out}/F_{in}.

The buoyant force occur’s because pressure on the bottom surface of a submerged object is greater than the downward pressure on the top of the object. It is equal to the weight of fluid displaced by the object.

[math]F_b = m’g = rho Vg[/math] where m’g is the weight of the body of fluid equal to the volume of the original submerged object. When an objects float F_{b}=mg in general. When an object is partially submerged.

[math] displaystyle frac{V_{displaced}}{V_0} = frac {rho_0}{rho_{final}}[/math]

**Tools**

Hydrometer – measured specific gravity of a liquid

**Fluid Dynamics (Hydrodynamics)**

Streamline (laminar flow)

Turbulent flow

Mass flow rate equals change in mass over change in time.

[math]rho_1A_1v_1 = rho_2A_2v_2[/math] This is the equation of continuity. It reads *“initial Density times Area times Velocity equals final Density times Area times Velocity”*.

If density is constant, The equation of continuity can be written as

[math]A_1v_1 = A_2v_2[/math]

Bernoulli’s Principle “Where the velocity of a fluid is high, the pressure is low, and where the velocity is low, the pressure is high” Bernoulli’s Equation:

[math] displaystyle P_1 + frac{1}{2}rho v_1^2 + rho gy_1 = P_2 + frac{1}{2} rho v_2^2+ rho gy_2[/math]

or in other words

[math] displaystyle P + frac{1}{2}rho v^2 + rho gy[/math] is constant

and for both, **y** is the height of the center of the tube above a fixed reference level.

Liquid leaves a spigot with the same speed a freely falling object would attain if dropped from the same height.

[math] v_1 = sqrt{2g(y_2 – y_1)}[/math]

And if you want to use Bernoulli’s principle in the case where there is no significant change in height:

[math]displaystyle P_1 + frac{1}{2} rho v_1^2 = P_2 + frac{1}{2} rho v_2^2 [/math]

Filed under PHY 126

## How to use LaTeX

**Greek letters**

pi for lowercase

Pi for uppercase

No command for $Alpha$ – just use A

[Math]pi[/Math]

[Math]pi[/Math]

[Math]A[/Math]

**Fractions **

frac{numerator}{denominator}

[Math]displaystyle frac{F}{a}[/Math]

**Superscript **

x^2

[Math]x^2[/math]

**Subscript**

x_2

[Math]x_2[/Math]

**Using Curly Braces to make groups**

x_{F_2}

x_{min}

[Math]x_{F_2}[/Math]

[Math]x_{min}[/Math]

**Super and Sub**

x_F^3

[Math]x_F^3[/math]

**Limits and Integrals**

displaystyle lim_{x to infty} 3x

displaystyle int_0^2 x dx

[Math]displaystyle lim_{x to infty} 3x [/Math]

[Math] displaystyle int_0^2 x dx [/Math]

Filed under Side Projects