Electromagnetics in deterministic and stochastic bianisotropic media

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Time-harmonic Problems – The Interior Problem Periodic structures, gratings: Ammari, Bao / Zhang, Ma. Quaternionic methods: Kravchenko. Inverse scattering problems: Athanasiadis, S / Boutet de Monvel, Shepelsky / Gao, Ma, Zhang / Gerlach / Heumann / Li / Mc Dowall / Rikte, Sauviac, Kristensson, Mariotte. I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 30 / 95
Time-harmonic Problems – The Interior Problem The Bohren decomposition – Beltrami fields In view of the DBF constitutive relations, the Maxwell equations can be written as � � curl E = curl H γ2 k2 � βk 2 i ϖµ −i ϖε βk 2 � � � E . (24) H Diagonalising the matrix in (24), we obtain � � curl (i η−1E + H) = curl (E + i η H) � k 1−kβ 0 0 − k 1+kβ � �i � η−1 E + H , (25) E + i η H where η = µ 1/2 ε −1/2 is the intrinsic impedance of the medium. I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 31 / 95
Page 1 and 2: Electromagnetics in deterministic a
Page 3 and 4: Some remarks on the history of the
Page 11 and 12: Deterministic problems: Modelling I
Page 13 and 14: Deterministic problems: Modelling T
Page 15 and 16: Postulates Deterministic problems:
Page 19 and 20: Assumptions Assumption (A or) Deter
Page 21 and 22: Assumptions Assumption ( � A or)
Page 25 and 26: Time-harmonic Problems - The Interi
Page 29: Time-harmonic Problems - The Interi
Page 35 and 36: Time-domain problems The choice of
Page 37 and 38: Time-domain problems Other constitu
Page 39 and 40: Time-domain problems We now assume
Page 41 and 42: Homogenisation Homogenisation (dete
Page 43 and 44: Homogenisation (deterministic media
Page 51 and 52: Theorem (continued) Homogenisation
Page 61 and 62: Nonlinear problems Nonlinear media
Page 63 and 64: Assumption Nonlinear media 1 B AN(u
Page 65 and 66: Nonlinear media Nonlinear systems p
Page 67 and 68: Stochastic problems The constitutiv
Page 69 and 70: The Maxwell system The integral for
Page 71 and 72: Stochastic problems The Wiener chao
Page 73 and 74: Homogenisation (random media) Homog
Page 75 and 76: Homogenisation (random media) Self-
Page 77 and 78: Homogenisation (random media) The p
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Homogenisation (random media) The c
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Homogenisation (random media) This
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Homogenisation (random media) Well
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Assumption (A eℓ ) Homogenisation
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Homogenisation (random media) Defin
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Homogenisation (random media) Consi
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Homogenisation (random media) Homog
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Homogenisation (random media) We no
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Electromagnetics in deterministic and stochastic bianisotropic media

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