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It was originally used by Onuki in 1989: Onuki, Akira. "Long-range interactions through elastic fields in phase-separating solids." Journal of the Physical Society of Japan 58.9 (1989): 3069-3072. Later on adopted by many authors: Ohta, T. "Interface dynamics under the elastic field." Journal...

I am trying to reproduce the results of a thesis that is 22 years old and I'm a bit stuck at solving the differential equations. Let's say you have the following equation $$\frac{\partial{\phi}}{\partial{t}}=f(\phi(r))\frac{{\nabla_x}^2{\nabla_y}^2}{{\nabla}^2}g(\phi(r))$$ where ##\phi,g,f## are...

Thank you. You've helped plenty.

Maybe, but after integrating over dr'', you essentially lose the second green function and are left with G(r,r')g(r')f(r') where f(r') is the result of the integral over dr''. I don't see how any property of Green's function will do anything about that! But my main concern was that is my way of...

##{u_{ij}}^2## is the square of the element ##u_{ij}##. Afterwards one sums over i and j. In physics, this would give (along with some additional unimportant terms) the free energy contribution of pure shear on a material.

Let's say you have a tensor u with the following components: $$u_{ij}=\nabla_i\nabla_j\int_{r'}G(r,r')g(r')dr'$$ Where G is a Green function, and g is just a normal well behaved function. My question is what is the square of this component? is it...

If they are connected by a massless rope, then surely the dynamics reduces to a 1 degree of freedom system. ##\theta_1=\theta_2##.

You're correct, my bad, I've made a couple of mistakes. Firstly, ##\beta## isn't the phase angle itself, but it's related to it by $$\tan{\omega\beta}=m\omega\frac {q_o}{p_o}$$ so obviously, it has units of time. Also, in the ##\alpha'## and ##\beta'## equations, there is a factor of ##\frac...

No I didn't, but that's what I was looking for! thanks!

Replacing ##w_1=nw## in the equation of ##\alpha'##, and then averaging over the period T of the natural oscillator gives: ##<\alpha'>=2mw^2p_oa\frac 1 T\int_{0}^T cos(nwt)cos(wt)\sim\delta_{n1}## By orthogonality of the cosine function over the interval [0,T]. P.s., i could not find the...

Homework Statement A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to ##z=a\cos(w_1t)##. By treating a as a small quantity, obtain a first-order solution to the motion of m in time...