# Articles by kariefury

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## 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

## Fluids – Chapter Notes

The Density (rho) is mass per unit volume, the unit is kg/m3.
$\displaystyle \rho = \frac{m}{V}$
rho equals m over V
$m = \rho V$
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.
$\displaystyle P = \frac {F}{A}$
Pressure is a scalar with the unit name Pascal, which is N/m2.
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
$\displaystyle \frac{dP}{dy} = -\rho g$.
Another way to express is equation is
$\displaystyle P_2 - P_1 = -\int_{y_1}^{y_2} \rho g \ dy$
If you can ignore variations in density this can be expressed as:
$P_2 - P_1 = - \rho g(y_2 - y_1)$
For an open contain of liquid, you simply add the pressure from the atmosphere
$P = P_0 + \rho gh$
Pressure head: Sometimes the h in Rho g h is called the pressure head.
Atmospheric Pressure is 101.3 kPa for 14.7lb/in2. 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”
$P_{out} = P_{in}$
$\displaystyle \frac{F_{out}}{A_{out}} = \frac{F_{In}}{A_{In}}$
$\displaystyle \frac{F_{out}}{F_{in}} = \frac{A_{out}}{A_{In}}$
This ratio gives mechanical advantage, Fout/Fin.
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.
$F_b = m'g = \rho Vg$ where m’g is the weight of the body of fluid equal to the volume of the original submerged object. When an objects float Fb=mg in general. When an object is partially submerged.
$\displaystyle \frac{V_{displaced}}{V_0} = \frac {\rho_0}{\rho_{final}}$

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.
$\rho_1A_1v_1 = \rho_2A_2v_2$ 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
$A_1v_1 = A_2v_2$
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:
$\displaystyle P_1 + \frac{1}{2}\rho v_1^2 + \rho gy_1 = P_2 + \frac{1}{2} \rho v_2^2+ \rho gy_2$
or in other words
$\displaystyle P + \frac{1}{2}\rho v^2 + \rho gy$ 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.
$v_1 = \sqrt{2g(y_2 - y_1)}$

And if you want to use Bernoulli’s principle in the case where there is no significant change in height:
$\displaystyle P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2$

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## How to use LaTeX

Greek letters
\pi for lowercase
\Pi for uppercase
No command for $\Alpha$ – just use A
$\pi$
$\pi$
$A$

Fractions
\frac{numerator}{denominator}
$\displaystyle \frac{F}{a}$

Superscript
x^2
$x^2$

Subscript
x_2
$x_2$

Using Curly Braces to make groups
x_{F_2}
x_{min}
$x_{F_2}$
$x_{min}$

Super and Sub
x_F^3
$x_F^3$

Limits and Integrals
\displaystyle \lim_{x \to \infty} 3x
\displaystyle \int_0^2 x\ dx
$\displaystyle \lim_{x \to \infty} 3x$

$\displaystyle \int_0^2 x\ dx$

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## Research Paper website

arXiv.org – Open access to 606,688 e-prints in Physics, Mathematics, Computer Science, Quantitative Biology, Quantitative Finance and Statistics

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## Articles of Interest: Quantum Laser, Quantum Amplifier, Light Activated Nanoshell, Optical Circuits

Applied physicists create building blocks for a new class of optical circuits

Imagine creating novel devices with amazing and exotic optical properties not found in Nature — by simply evaporating a droplet of particles on a surface.

Nanoshell structures: Self-assembly method yields materials with unique optical properties

Scientists from four U.S. universities have created a way to use Rice University’s light-activated nanoshells as building blocks for 2-D and 3-D structures that could find use in chemical sensors, nanolasers and bizarre light-absorbing metamaterials. Much as a child might use Lego blocks to build 3-D models of complex buildings or vehicles, the scientists are using the new chemical self-assembly method to build complex structures that can trap, store and bend light.

Physicists build quantum amplifier with single artificial atom

(PhysOrg.com) — By demonstrating how a single artificial atom can be used to amplify electromagnetic waves, physicists from Japan are opening up new possibilities for quantum amplifiers, which can be used in a variety of electronic and optical applications.

From a classical laser to a ‘quantum laser’

Rainer Blatt’s and Piet Schmidt’s research team from the University of Innsbruck have successfully realized a single-atom laser, which shows the properties of a classical laser as well as quantum mechanical properties of the atom-photon interaction. The scientists have published their findings in the journal Nature Physics.

Yale scientists bring quantum optics to a microchip

A report in the journal Nature describes the first experiment in which a single photon is coherently coupled to a single superconducting qubit (quantum bit or “artificial atom”). This represents a new paradigm in which quantum optics experiments can be performed in a micro-chip electrical circuit using microwaves instead of visible photons and lasers. The work is a collaboration of the laboratory of Professor Robert Schoelkopf and the theory group of Professor Steven Girvin in the Departments of Applied Physics and Physics at Yale University.

Quantum leap: World’s smallest transistor built with just 7 atoms

(PhysOrg.com) — Scientists have literally taken a leap into a new era of computing power by making the world’s smallest precision-built transistor – a “quantum dot” of just seven atoms in a single silicon crystal. Despite its incredibly tiny size – a mere four billionths of a metre long – the quantum dot is a functioning electronic device, the world’s first created deliberately by placing individual atoms.

## Non-Equilibrium Statistical Mechanics talk

Today I attended a seminar on a Variational approach to Non-Equilibrium Statistical mechanics. (Maximum Caliber) It was quite a popular presentation. The speaker was talking about his new method for calculating small number problems, which are like when you are trying to find an average, so you look at the first case, and see it is one answer. So for that first case all you know is that the first case is one answer.

He briefly gave an example of a single cell about to evolve and choose the left path or the right path. It’s only a little length of the path, but the decision to go left or right makes a very big deal.

It touched on Risk Analysis for stocks too, just like the Barra system I’ve been using at work. If you think of your stocks as a horse race, at first all of the horses are in the gate, then the gate opens and the horses take off running. Some are a little behind and some are a little ahead.

It reminded me of the book I read about Evolution (well really it was on economics, but it was on the evolution of economic systems… I need to find the book again)

There was also talk of Maxwell’s Demon’s.

I was pondering why I seem to be writing more handwritten notes and why the difference between learning by hand and by machine. I tend to not need to think the speech in my head but as I write by hand but by keyboard the words are clearly visible. This same feature exists for writing in code and for writing by hand. But at times when writing by code on keyboards the thought are no longer in English. This is why when I write code by hand it is hard and sometimes when I write physics by computer it is harder. Because for code it goes to pure code when I am translating through a keyboard and for physics it goes to pure symbol when writing by hand.  And as always with any type of writing eventually it is no longer speech and I can transition to pure symbolic calculations. That’s when I’ve learned to do things “In my head”.

## Structures

Statics vars allow a var to retain value for multiple declarations, does not reinitialize each time.

Static & extern are auto initialized to 0

Structures (Structure Type)

possible to aggregate components into a single named variables

IE: Bank Account – Account #, balance, interest, name, address

Structure is user defined. You can declare an array of structures

struct account {
long number;
float balance;
float interestRate;
} accnt2, myAccounts[3];
struct account myAccount;

Members can be accessed using structure member operator “.”

myAccount.number = 1248609385;
myAccount.balance = 1004.005;
myAccount.interestRate = 0.18237672;

Can declare a structure and then declare the variables

struct fruit {
char name[15];
int calories;
}
typedef struct fruit fruits;
struct fruit lunch = {“plum”,150}; // order is important
fruits dinner = {.calories=150,.name=”peach”}; // order not important

you can copy structs of the same type to each other dinner = lunch

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## L’Hospitals Rule – Calculating Limits using Derivatives.

Use this for solving problem cases, where the limit on the right side exists or is +-infinity. These are problem Cases.

This is L’Hospital rule, used for the problem cases above.

This is how to rearrange your limits so you can use L’Hospital’s rule and still find the limit even though it has an indeterminate form. The situations are: Indeterminate quotient, Indeterminate product, Indeterminate difference and indeterminate powers.

Also, a note on derivatives and the chain rule. This is what you do with constants. Including e, which is a constant.

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