If $\Delta p = p_1 - p_2$, is $\Delta^2 p$ defined as $(p_1-p_2)^2$ or should I be using $(\Delta p)^2$ to get $(p_1-p_2)^2$?
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$\begingroup$It is possible that the gradient be squared in a differential equation involving space and time ( predominantly addressed in engineering calculations). I am not sure if you are asking for the result of rate of change of gradient which is given by differentiating the gradient one more time. Both of them are defined and are of commonplace in depicting physical processes. I hope I answered your question.
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