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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 ).

Grade:11

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

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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