Six Passive Circuit Elements

 I was watching a video from 7 years ago about memory resistors (memristors), and about using them to create synapse like circuits (Alex Nugent, Knowm). That got me thinking about memristors and how they are the 4th passive circuit element. 

I found the name, Leon Chua, (googled, and google gave me me a pdf of the article: Memristor: The Fourth Fundamental Passive Circuit Element)

So, my thought was that we don't really have a final four, we have six, but in pairs: memory resistor (memristor), memory capacitor(memcapir?), and memory inducer(memducer?).  I don't know how to type the nomenclature.. I know there is MathML and other syntax markers, and if I revisit this I'll mark it all up. So resistor R would have an equivalent memory based component, Rm. 

So the six elements would be R Rm, C Cm, I Im. The R value of the resistor and memrister at initial state would have the same R, measured in ohms. The Rm would probably need to have a known Min and Max (thinking of the analogies with resistors and their color coding. The resistor has known and marked physical properties, and thinking about what extra properties would want to be known for that component, and how they would be marked, I digress).

So we have a way of denoting a complex component with as a single symbol for abstraction. The more concrete example I've been thinking as I try to understand how it would works is ionic flow. Let's say we have a pipe, 4 cells in the pipe, high sodium concentration in water on one side (ratio of ionic concentration external, number 1(Rx1)), and high chloride concentration on the other (Rx2). Each of the cells in the pipe have eight ion channels (four input, four output(which is which would depend on the direction of the current)).

Anyway, the cell would only be able to take in four ions per time it takes for the ion to clear the channel, and it would only be able to hold on to a certain number of ions. Those internal ions are the memory, or buffer in the cell. If you had all + ions in memory (in the cell), and the inputs were all + , and the concentration on the outside of my outputs was -, then I would pass all four + ions and pick up another 4, and usually not take in any - ions. It's easier to imagine the polarity reversing making a difference if we had four cells in the pipe. All four cells have + ions. If the polarity reversed, and I had all + ions, that there would be a period of time where the ions mingled, so the resistance would go up sharply for the amount of time it took for the ions to revers direction. This would illustrate the memory (the ions inside the cell), has an effect of its resistance to the flow of ions from input to output. 

There's also some curve that shows a figure eight when measuring the capacitance and resistance when switching polarity. the figure eight, that crossing point, shows that there is a period of total resistance (no flow) when changing polarity.  

I don't know how the others would work well enough because I don't fully understand them. The memcapir would behave something like an electrical synapse where the capacitance and timing would be effected by the stored memory (its internal ions). The memducer would be an ion generator and/or distributor; it would hold a concentration of a particular ion, and so its flow would be dependent on its memory.

Cell:

Starting ions (4Na+)

Ion capacity (4 ions)

Number of input chanels

Number of output channels