Recent content by grep6

Can anyone offer an explanation for the powers (6 and 12) used in the Lennard Jones potential? (other than simply saying weak attractive and strong repulsion forces) I am especially looking for short derivation that can be used to argue that the attractive potential falls off with the sixth...

It is a problem to take the exponential of a non-square matrix. How can you calculate A^n when you can't multiply a non-square matrix with itself, its non conformable.

Nonlinear equations are often solved by making a substitution that puts the equation in a linear form. For the first problem, try multiplying through by y and making the substitution v=y^2 to yield x v'(x) - 2v(x) = 8x^3 then solve, and substitute y back in. Looks like the second problem...

I got a slightly different answer than what you posted from the text y(x) = -\sqrt{\frac{1}{2}(x^2+1)} and mathematica agrees with me, so perhaps a typo? Anyway, it looks like your on the right track, although go back through the integration, I think you may be off by a factor. Then...

I am curious what the nonlinear bernoulli equation is used to model. Is there a certain topic or context where it shows up often? Can any suggest some references for more info? I am reviewing some ODE stuff for an upcoming exam and would really like an intuitive feel for the equation and its...