memrister fundamentals

The memrister is the fourth fundamental electronic device, next to resistors, capacitors, and inductors
OR It’s the fourth basic element of circuits. Can you name the other three? Resistor, capacitor, and inductor. HP has produced a new device called the memrister. It’s memory that does not require refreshes and in fact retains information after being switched off. It could allow computers to be instantly turned on or off.
A memristor is a type of resistor in which the flow of electrical current in an electronic circuit is determined by the amount of charge that has previously flowed through it.
Together, capacitors, inductors and resistors form the three basic circuit elements. The reason that the memristor is so different from the other three basic circuit elements is that, unlike them, it retains memory without power. In layman’s terms, this means that if you did a hard shutdown on your computer and then restarted it, all the applications and documents you had open before you shut down would still be right there on your screen when you restarted. That’s an effect that can’t be duplicated by any circuit combination of resistors, capacitors and inductors today, which is why researchers feel the memristor qualifies as a fourth fundamental circuit element.
In 2008, scientists at HP Labs built the first working memristor. The original idea for a memristor is credited to Leon Chua, a professor in the Electrical Engineering and Computer Sciences Department of the University of California at Berkeley.
The memristor is formally defined[6] as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device. Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.
M(q)=frac{mathrm dPhi_m}{mathrm dq}
Noting from Faraday’s law of induction that magnetic flux is simply the time integral of voltage , and charge is the time integral of current, we may write the more convenient form
M(q)=frac{mathrm dPhi_m/mathrm dt}{mathrm dq/mathrm dt}=frac{V}{I}
It can be inferred from this that memristance is simply charge-dependent resistance. If M(q) is a constant, then we obtain Ohm’s Law R = V/I. If M(q) is nontrivial, however, the equation is not equivalent because q and M(q) will vary with time. Solving for voltage as a function of time we obtain