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Here's my educated guess: The first step would be to model the sphere as some kind of filamentary or foamy network with ice filling the voids. In that case, ice would only sublimate from the outer surface, and gradually this frozen surface would shrink as more and more of the dried network would be exposed. Then there'd be three parts to the problem: ...


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This is explained in part II of my Phys.SE answer here, which shows that a 2D system always has a Hamiltonian description locally. It turns out, that before the non-canonical transformation $(x,y) \to (q,p)$, from the first pair of eoms (1) alone, the Hamiltonian and non-canonical Poisson bracket can be derived as $$H~=~\gamma \ln x -x +\ln y -y $$ and ...


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Maxwell equations read $$\nabla\cdot \vec E=\rho\tag1$$ $$\nabla\times \vec E = -\frac{\partial \vec B}{\partial t}\tag2$$ $$\nabla\cdot\vec B=0\tag3$$ $$\nabla\times\vec B=\vec j+\frac{\partial\vec E}{\partial t}\tag4$$ For the sake of simplicity, I assume $\vec{j}=0$. Equations (2) and (3) form a linear first order system $$D_x {\bf X}(t,x) = \partial_t ...


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The Maxwell's equations are the basics of EM phenomenon. Whatever be the fields you select, they shouldn't violate these fundamental 4 equations. Suppose we are provided a problem to find the electric and magnetic fields of an EM wave or a charge, or whatever be it. As you said, we have now a four component problem. But the degree of freedom is not 4 as each ...


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Lets look at the 4 equations in ED, $$\nabla\cdot \vec E=\rho\tag1$$ $$\nabla\times \vec E = -\frac{\partial \vec B}{\partial t}\tag2$$ $$\nabla\cdot\vec B=0\tag3$$ $$\nabla\times\vec B=\vec j+\frac{\partial\vec E}{\partial t}\tag4$$ which can ofcourse be written in a more compacted form, $$\partial_\mu F^{\mu\nu}=j^\nu \tag5$$ The $(2)$ and the $(3)$ ...



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