Electronics!

Even though I was an Electrical Engineer, I never was one for electronics.  But since I’ve been in a lab, and needing it to run experiments, I’ve become a recent convert.  I blame Cornell’s ECE 210/215.  Those classes (when I took them) were more about “what’s the voltage here” and “the current there,” rather than developing electronics to do things.

For example, in this lab, I needed a PID controller for Laser frequency stabilization.  Basically, the frequency of the laser drifts, and we need to control it, using a feedback loop.  Basically, the PID controller adds a correction to the current in the laser diode (which determines the frequency of the laser) .  This correction is a sum of a proportional signal (i.e. what’s going on right now—are we too high? or too low?), an integral signal (in the long-term, what’s its tendency to do?), and a derivative signal (right now, are we drifting away from where want to be? or towards?).

This provides an actual purpose to the circuit.  Can I build a proportional signal?—yes, that’s just an amplifier with adjustable gain.  I can build an integrating circuit, and a differentiating circuit as well.  But before, I never had any reason to build them.  They were just simple circuits that did what they did, and that was that.

That’s what was missing in my intro circuits class.  I never felt that the circuits we made were to do things.  We made circuits, and tested to see how they behaved.  Which, quite frankly, didn’t interest me at all.

A new year…

A new year, a new look, and now using WordPress.  My resolution will be to keep this blog updated.

Judge Ito Strikes!

Well, not really. I’ve been trying to learn some Ito calculus, and damn, it is hard. I’ve never been good at probability—especially given my terrible, terrible education in it at Cornell. I’ve gotten a decent handle on some of it via quantum theory, as well as the stochastic processes course I took. But nothing like this.

Suppose we had this function W(t) that took on a random value at each time t. How the hell do you integrate it? Does this make any sense to anyone? Supposing we understood this in a ‘classical’ sense. What does it mean if we consider quantum stochastic processes? ahhh!!!! my brain’s about to explode!

Mr. Wolfram’s crazy Ising model

A few years back, I went to see Steve Wolfram talk at Cornell about his crazy theory of Cellular Autonoma being “A new kind of Science.” The basic gist of his theory is something like this.

Suppose we had an array of cells, being either black or white. Given a certain set of rules, a cell will change it’s color from black to white (or vice versa). The rules are simple; a cell will flip based on the current colors of itself and it’s nearest neighbors. Mr. Wolfram noticed that surprisingly simple rules with a simple initial condition can generate chaotic patterns:

To me, this seems like he’s simply been performing a one-dimensional simulation of the Ising Model. This models magnetic domains in solids. Particles have a property called spin that is related to its magnetic moment. The one-dimensional version of this model is as such:

Suppose we had an array of particles whose spin can either be up or down. The ground state of this array is the configuration that minimizes the energy. The energy is determined by the spins of the nearest neighbors in the array. In a sense, the spin of a particle will flip depending on its nearest neighbors.

This is an interesting thought, but I have no mathematical ‘proof’ of this idea. Thoughts?

Mr. Wolfram’s crazy Ising model

A few years back, I went to see Steve Wolfram talk at Cornell about his crazy theory of Cellular Autonoma being “A new kind of Science.” The basic gist of his theory is something like this.

Suppose we had an array of cells, being either black or white. Given a certain set of rules, a cell will change it’s color from black to white (or vice versa). The rules are simple; a cell will flip based on the current colors of itself and it’s nearest neighbors. Mr. Wolfram noticed that surprisingly simple rules with a simple initial condition can generate chaotic patterns:

To me, this seems like he’s simply been performing a one-dimensional simulation of the Ising Model. This models magnetic domains in solids. Particles have a property called spin that is related to its magnetic moment. The one-dimensional version of this model is as such:

Suppose we had an array of particles whose spin can either be up or down. The ground state of this array is the configuration that minimizes the energy. The energy is determined by the spins of the nearest neighbors in the array. In a sense, the spin of a particle will flip depending on its nearest neighbors.

This is an interesting thought, but I have no mathematical ‘proof’ of this idea. Thoughts?