Electromagnetics in deterministic and stochastic bianisotropic media
Electromagnetics in deterministic and stochastic bianisotropic media
Electromagnetics in deterministic and stochastic bianisotropic media
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Determ<strong>in</strong>istic problems: Modell<strong>in</strong>g<br />
From (1) <strong>and</strong> (2) we wish to determ<strong>in</strong>e the quadruplet (B, D, E, H),<br />
assum<strong>in</strong>g that the vector J <strong>and</strong> the scalar ρ are known.<br />
Need to calculate 12 scalar functions from a system of 8 scalar equations.<br />
So, constitutive relations must be <strong>in</strong>troduced<br />
D = D(E, H) , B = B(E, H) . (5)<br />
It can be seen that we may consider as “the Maxwell system” the set of<br />
equations (1) (curlH = ∂tD + J <strong>and</strong> curlE = −∂tB), plus the constitutive<br />
relations (5), plus the equation of cont<strong>in</strong>uity<br />
∂tρ + divJ = 0. (6)<br />
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 12 / 95
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