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This therefore proves that the velocity distribution at theta of 0 and 120 degrees are the same. If we denote theta_1 to represent one of the periodic boundaries for the 1/3 domain and theta_2 being the other boundary, then  

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{latex}$\vec{v}^{\,}(r_i,\theta_1)=\vec{v}^{\,}(r_i,\theta_2)${latex}
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The boundary conditions on the fluid domain are as follow:

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