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Published equation contexts

M(q)=dφdq,v(t)=M(q(t)) i(t)M(q) = \frac{d\varphi}{dq}, \qquad v(t) = M\big(q(t)\big)\, i(t)

Why this formula appears here

In 1971, Leon Chua published “Memristor — The Missing Circuit Element” in IEEE Transactions on Circuit Theory . His argument was one of pure symmetry, not empirical discovery. Circuit theory recognizes four fundamental variables — charge, current, voltage, and magnetic flux linkage — and, in 1971, three of the six possible pairwise relationships among them were already embodied in named components: the resistor relates voltage and current, the capacitor relates charge and voltage, the inductor relates flux linkage and current. Chua noticed that the sixth relationship, between charge and flux linkage, had no corresponding physical device, and reasoned from the completeness of the other five…

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qq

Symbol q

q occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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M(q)=dφdq,v(t)=M(q(t)) i(t)M(q) = \frac{d\varphi}{dq}, \qquad v(t) = M\big(q(t)\big)\, i(t)

Equation 1 · Future Hardware

From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

In 1971, Leon Chua published “Memristor — The Missing Circuit Element” in IEEE Transactions on Circuit Theory . His argument was one of pure symmetry, not empirical discovery. Circuit theory recognizes four fundamental variables — charge, current, voltage, and magnetic flux linkage — and, in 1971, three of the six possible pairwise relationships among them were already embodied in named components: the resistor relates voltage and current, the capacitor relates charge and voltage, the inductor relates flux linkage and current. Chua noticed that the sixth relationship, between charge and flux linkage, had no corresponding physical device, and reasoned from the completeness of the other five…

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