Team:SEU/Model

Model

Computation method

Addition: \(A_1 \xrightarrow{k_1} O,\quad A_2 \xrightarrow{k_2} O\)

Proof: \(\dfrac{d A_i}{d t}=-k_i[A_i](t) \Rightarrow [A_i](t)=[A_i](0)e^{-k_it} \Rightarrow \dfrac{d O}{d t}=\sum_{i=1}^2 k_i[A_i](t) \Rightarrow [O](\infty)= [A_1](0)/k_1+[A_2](0)/k_2.\) If \(k_1\approx k_2\), then addition is successfully implemented.

Subtraction: \(A+B \xrightarrow{k_1} \phi\)

Multiplication: \(\alpha \xrightarrow{k} \phi, A+B+\alpha \xrightarrow{k} A+B+\alpha+C\)