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


10 years ago

## Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
							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
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10 years ago
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