By Leon Uris
Spanning the many years from global battle II to the 2008 presidential crusade, A God in Ruins is the riveting tale of Quinn Patrick O'Connell, a good, principled, and brave guy on the point of changing into the second one Irish Catholic President of the USA. yet Quinn is a guy with an explosive mystery that may shatter his political targets, threaten his existence, and tear the rustic apart--a mystery buried for over a part century--that even he doesn't know...
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38) shows that ∇ · (E × H) = H · (∇ × E) − E · (∇ × H). 108) into the right-hand side of the above identity and using A · A = A2 , yields −∇ · (E × H) = E · ∂B ∂D +H· + σE 2 + E · J + H · J m . 161) This may be integrated over a volume V bounded by a closed surface S. Applying the divergence theorem, we get (E × H)· dS = − S E· V ∂D ∂B +H· + σE 2 + E ·J +H·J m dV. 162) are the instantaneous or time-domain Poynting theorem in derivative form and in integral form, respectively. For non-dispersive isotropic media, D = E, B = µH, the permittivity and the permeability are constant scalars, independent of time t, we have ∂ E ·D 1 ∂D 1 ∂E 1 ∂ E 1 ∂E ∂D ∂E = E· + · D= E · + · E =E · =D· , ∂t 2 2 ∂t 2 ∂t 2 ∂t 2 ∂t ∂t ∂t 1 ∂B 1 ∂H 1 ∂µH 1 ∂H ∂B ∂H ∂ H·B = H· + ·B = H· + ·µH = H· = B· .
These differences will change the signs in some equations but will not affect the physical field. (2) Maxwell’s Equations in Complex Form The partial derivative of the sinusoidal field with respect to time can be expressed as follows, ∂ A(x, t) = ∂t A(x) ∂ jωt = e ∂t j ωA(x)e jωt . 64) V B · dS = 0, ∇ · B = 0. 65) S These are Maxwell’s equations in complex form or the so-called frequencydomain Maxwell equations. 67) ∇ · H = 0. 68) The equation of continuity in the complex form is J · dS = −j ω S ρdV, ∇ · J = −j ωρ.
152) become ∇2 E + k 2 E = 1 ∇ρ + j ωµJ , ∇2 H + k 2 H = −∇ × J . 155) In the source-free region, ρ = 0 and J = 0, they become homogeneous generalized complex wave equations ∇2 E + k 2 E = 0, 2 2 ∇ H + k H = 0. In low-conductivity media and in the high-frequency range, σ have k2 = ω2 µ . 157) are well known as Helmholtz’s equations. 159) k 2 = −j ωµσ. 157) become complex diffusion equations. It should be noted that the time-domain wave equations are suitable only for vacuum or non-dispersive media, but the frequency-domain complex wave equations are suitable for dispersive media, while the permittivity and the permeability are functions of frequency.
A God in Ruins by Leon Uris