Normalization Method

Guanchu Cheng's picture

Is it possible to define a dimensionless number being capable of characterizing the two effects with totally opposite direction?

1. assuming to exist a PDE describing an equilibrium along one direction (e.g., postive direction along X coordinate), A+B=0;

2. after normalization process to the above PDE, we got, A*+(C)B*=0;

3. (C)=B/A, is the dimensionless number, and obviously, (C) implicits that both two effects arising from A and B are the same in the direction, i.e., along the X positive coordanate;

 4. so my concern is that: is it possbile to define a dimensionless number (C) that can be able to characterize the two effects with different directions, i.e., A could be along the X postive cooridinate, whereas B could be along the X negative cooridinate???

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