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I would like to know what is the definition of "front propagation" without using any equation ?

The answer should start by : Front propagation is ...

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You might like to read Front propagation: Theory and applications. You can click 'look inside' to see the first couple of pages. Regards –  Amzoti Jan 16 '13 at 16:01
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One meaning of this could be in the context of wave propagation. In physics it could come under Huygens Principle. Every point on the "front" becomes center of a semicircle of radius $c dt$ where $c$ is speed of propagation and $dt$ is the time laps. The envelope of these semi-circles becomes the new front and so the wave has propagated to time $t+dt$.

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