# Representing charges in computer programming

I'm preparing for a thesis in computer science on calculations based on concepts from Neuroelectrodynamics.

In short this theory states, that information transfer is not done by spike time coding, but by movement of electric charges. Also this charges affect (and get affected by) proteins in the brain cells, so the cells can act as a kind of memory

How can electric charges be represented in terms of programming? Do you have to simulate each and every ion or are there overall principles so you can calculate with "whole" charges? I could imagine Circuit simulations already implement some calculations with electrodynamics.

I assume there are already computation systems, but I didn't know what to look for.

Also, I'm quite new to the field of electrodynamic. Which book can you recommend on this topic?

• is there a pre-existing model you're looking to implement, or are you developing a model of your own? certainly if you want to model ions/charges moving around, there must be some kind of structural constraints. the particulars of that structure may steer your implementation one way or another. (the maxwells-equations tag seems like a shot in the dark) – JustJeff Dec 16 '11 at 0:45
• No, not really. I want to take a look at particle swarm optimization and see if I can modify it for my purposes. My ultimate goal would be to prove that a computational unit based on the new findings outperforms Integrate&Fire + STDP – user390 Dec 16 '11 at 19:39

As a general rule, when dealing with "big" things like cells, you shouldn't simulate the individual charged particles. A useful abstraction is charge density, the charge per unit volume, usually denoted $\rho$. The equations of electrodynamics can be formulated in terms of this charge density $\rho$ and the current density ${\bf J}$.

Electrodynamics is a big topic, and it can take a while to learn. If you want to study electrodynamics at an undergraduate level, you could try Griffiths. At a graduate level, Jackson's book is the standard. However, if you're unfamiliar with charge density, you might want to look at a freshman-level calculus-based physics book like Serway or Halliday, Resnick and Walker.

• Thanks, I notice that I definitely need some stronger background on that topic, so I'll stick with your recommendations. – user390 Dec 15 '11 at 23:40
• Could you add links for the books? I presume you mean Griffiths and Jackson etc.? – Mark Booth Dec 16 '11 at 13:03
• For the "introductory level" book, I'd recommend Halliday, Resnick, and Krane over Halliday, Resnick, and Walker. – aeismail Dec 16 '11 at 15:39
• @aeismail: I'm unfamiliar with Haliday, Resnick and Krane. What makes it different from Haliday, Resnick and Walker? – Dan Dec 16 '11 at 17:44
• HRK—"Physics"—is more mathematically rigorous and provides more details than HRW—"Fundamentals of Physics." I would argue HRK is more appropriate for physical scientists and engineers as a reference than HRW. – aeismail Dec 16 '11 at 20:20

The answer depends on what you're actually dealing with. If you're studying transport of ions in channels, then a "charge-by-charge" view might be appropriate. However, if you're operating at a systems level, then you'd want to express your model according to conservation principles. There's no easy way to answer this without having a better sense of what it is you want to do.