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				   Pls Can anyone explain the concept of homogenization of straight lines (as soon as possible ).


6 years ago

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										Dear student,
athematical homogenization theory dates back to the French, Russian and Italian schools. The method of asymptotic homogenization proceeds by introducing the fast variable ξ = x / ε and posing a formal expansion in ε:
$u(x) = u(x,\xi) = u_0(x,\xi)+\epsilon u_1(x,\xi)+\epsilon^2 u_2(x,\xi)+O(\epsilon^3)\,$
which generates a hierarchy of problems. The homogenized equation is  obtained and the effective coefficients are determined by solving the  so-called "cell problems" for the function u1(x,x / ε).

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Sagar Singh
B.Tech, IIT Delhi
sagarsingh24.iitd@gmail.com


6 years ago

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