A new homogenization method approximates one-dimensional heterogeneous diffusion with an advection-diffusion equation whose effective diffusivity and velocity are fitted to match integral averages of the heterogeneous solution, reducing error in numerical tests.
Homogenization of Maxwell's equations in layered system beyond static approximation
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abstract
The propagation of electromagnetic waves through disordered layered system is considered in the paradigm of Maxwell's equations homogenization. In spite of the impossibility to describe the system in terms of effective dielectric permittivity and/or magnetic permeability the unified way to describe the propagation and Anderson localization of electromagnetic waves is proposed in terms of the introduced effective wave vector (effective refractive index). It is demonstrated that both real and imaginary parts of the effective wave vector (contrary to effective dielectric permittivity and/or magnetic permeability) are the self-averaging quantities at any frequency. The introduced effective wave vector is analytical function of frequency; corresponding Kramers-Kronig relation generalizes the Jones-Herbert-Thouless formula.
fields
physics.comp-ph 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Advection improves homogenized models of continuum diffusion in one-dimensional heterogeneous media
A new homogenization method approximates one-dimensional heterogeneous diffusion with an advection-diffusion equation whose effective diffusivity and velocity are fitted to match integral averages of the heterogeneous solution, reducing error in numerical tests.