Mie Scattering Theory for Phonon Transport in Particulate Media

2004 ◽  
Vol 126 (5) ◽  
pp. 793-804 ◽  
Author(s):  
Ravi S. Prasher
Keyword(s):  
Cross Section ◽  
Scattering Theory ◽  
Mode Conversion ◽  
Mie Scattering ◽  
Phonon Transport ◽  
Scattering Cross Section ◽  
Particulate Media ◽  
Scattering Cross ◽  
Transport Cross Section ◽  
Mie Scattering Theory

Scattering theory for the scattering of phonons by particulate scatterers is developed in this paper. Recently the author introduced the generalized equation of phonon radiative transport (GEPRT) in particulate media, which included a phase function to account for the anisotropic scattering of phonons by particulate scatterer. Solution of the GEPRT showed that scattering cross section is different from the thermal transport cross-section. In this paper formulations for the scattering and transport cross section for horizontally shear (SH) wave phonon or transverse wave phonon without mode conversion is developed. The development of the theory of scattering and the transport cross section is exactly analogous to the Mie scattering theory for photon transport in particulate media. Results show that transport cross section is very different from the scattering cross section. The theory of phonon scattering developed in this paper will be useful for the predictive modeling of thermal conductivity of practical systems, such as nanocomposites, nano-micro-particle-laden systems, etc.

Scattering of Phonons by Nano and Micro Particles

2004 ◽  
Author(s):  
Ravi S. Prasher
Keyword(s):  
Cross Section ◽  
Scattering Theory ◽  
Phonon Scattering ◽  
Mode Conversion ◽  
Mie Scattering ◽  
Scattering Cross Section ◽  
Particulate Media ◽  
Scattering Cross ◽  
Transport Cross Section ◽  
Micro Particles

Scattering theory for the scattering of phonons by particulate scatterers is developed in this paper. Recently the author introduced the generalized equation of phonon radiative transport (GEPRT) in particulate media which included a phase function to account for the anisotropic scattering of phonons by particulate scatterer. Solution of the GEPRT showed that scattering cross section is different than the thermal transport cross section. In this paper formulations for the scattering and transport cross section for horizontally shear (SH) wave phonon or transverse wave phonon without mode conversion is developed. The development of the theory of scattering and the transport cross section is exactly analogous to the Mie scattering theory for photon transport in particulate media. Results show that transport cross section is very different than the scattering cross section. It is also shown that for SH (horizontally shear) phonons the scattering and transport cross sections are proportional to ω8 rather than the well accepted value of ω4 in the Rayleigh regime where ω is the frequency of the SH phonons. The theory of phonon scattering developed in this paper will be useful for the predictive modeling of thermal conductivity of practical systems such as nano composites, nano-micro particle laden systems and etc.

Phonon Transport in Anisotropic Scattering Particulate Media

2003 ◽  
Vol 125 (6) ◽  
pp. 1156-1162 ◽  
Author(s):  
Ravi Prasher
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Transport Theory ◽  
Mode Conversion ◽  
Anisotropic Scattering ◽  
Phonon Transport ◽  
Isotropic Scattering ◽  
Radiative Transport ◽  
Particulate Media ◽  
Transport Cross Section

Equation of phonon radiative transport (EPRT) is rewritten to include anisotropic scattering by a particulate media by including an acoustic phase function and an inscattering term which makes EPRT exactly same as equation of radiative transport (ERT). This formulation of EPRT is called generalized EPRT (GEPRT). It is shown that GEPRT reduces to EPRT for isotropic scattering and is totally consistent with phonon transport theory, showing that transport cross section is different from the scattering cross section. GEPRT leads to same formulation for transport cross section as given by phonon transport theory. However GEPRT shows that transport cross section formulations as described by phonon transport theory are only valid for acoustically thick medium. Transport cross section is different for the acoustically thin medium leading to the conclusion that mean free path (m.f.p) is size dependant. Finally calculations are performed for two types of scatterers for acoustic waves without mode conversion: (1) acoustically hard Rayleigh sphere; and (2) large sphere in the geometrical scattering regime. Results show that the scattering from these particles is highly anisotropic. It is also shown that for geometrical scattering case isotropic scattering leads to the conclusion of total internal reflection at the particle/medium interface.

Phonon Transport in Anisotropic Scattering Particulate Media

2003 ◽  
Author(s):  
Ravi S. Prasher
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Transport Theory ◽  
Mode Conversion ◽  
Anisotropic Scattering ◽  
Phonon Transport ◽  
Isotropic Scattering ◽  
Radiative Transport ◽  
Particulate Media ◽  
Transport Cross Section

Equation of phonon radiative transport (EPRT) is rewritten to include anisotropic scattering by a particulate media by including an acoustic phase function and an in-scattering term which makes EPRT exactly same as equation of radiative transport (ERT). This formulation of EPRT is called generalized EPRT (GEPRT). It is shown that GEPRT reduces to EPRT for isotropic scattering and is totally consistent with phonon transport theory, showing that transport cross section is different from the scattering cross section. GEPRT leads to same formulation for transport cross section as given by phonon transport theory. However GEPRT shows that transport cross section formulations as described by phonon transport theory are only valid for acoustically thick medium. Transport cross section is different for the acoustically thin medium leading to the conclusion that mean free path (m.f.p) is size dependant. Finally calculations are performed for two types of scatterers for acoustic waves without mode conversion: 1) Acoustically hard Rayleigh sphere 2) large sphere in the geometrical scattering regime. Results show that the scattering from these particles is highly anisotropic. It is also shown that for geometrical scattering case isotropic scattering leads to the conclusion of total internal reflection at the particle/medium interface.

A Mode-Resolved Continuum Mechanics Model of Acoustic Wave Scattering From Embedded Cylinders

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Vineet Unni ◽  
Joseph P. Feser
Keyword(s):  
Elastic Wave ◽  
Cross Section ◽  
Continuum Mechanics ◽  
Wave Scattering ◽  
Rayleigh Scattering ◽  
Mie Scattering ◽  
Scattering Cross Section ◽  
Density Contrast ◽  
Continuum Approximation ◽  
Scattering Cross

In this paper, we use continuum mechanics to develop an analytic treatment of elastic wave scattering from an embedded cylinder and show that a classic treatise on the subject contains important errors for oblique angles of incidence, which we correct. We also develop missing equations for the scattering cross section at oblique angles and study the sensitivity of the scattering cross section as a function of elastodynamic contrast mechanisms. We find that in the Mie scattering regime for oblique angles of incidence, both elastic and density contrast are important mechanisms by which scattering can be controlled, but that their effects can offset one another, similar to the theory of reflection at flat interfaces. In comparison, we find that in the Rayleigh scattering regime, elastic and density contrast are always complimentary toward increasing scattering cross section, but for sufficiently high density contrast, the scattering cross section for incident compressional and y-transverse modes is nearly independent of elastic contrast. The solution developed captures the scattering physics for all possible incident elastic wave orientations, polarizations, and wavelengths including the transition from Rayleigh to geometric scattering regimes, so long as the continuum approximation holds. The method could, for example, enable calculation of the thermal conductivity tensor from microscopic principles which requires knowledge of the scattering cross section spanning all possible incident elastic wave orientations and polarizations at thermally excited wavelengths.

Magnetically controlled multifrequency invisibility cloak with a single shell of ferrite material

2015 ◽  
Vol 29 (04) ◽  
pp. 1550007 ◽  
Author(s):  
Xiaohua Wang ◽  
Youwen Liu
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Scattering Theory ◽  
Mie Scattering ◽  
Ferrite Material ◽  
Invisibility Cloak ◽  
Total Scattering Cross Section ◽  
Multiple Frequencies ◽  
Mie Scattering Theory ◽  
Single Shell

A magnetically controlled multifrequency invisibility cloak with a single shell of the isotropic and homogeneous ferrite material has been investigated based on the scattering cancellation method from the Mie scattering theory. The analytical and simulated results have demonstrated that such this shell can drastically reduce the total scattering cross-section of this cloaking system at multiple frequencies. These multiple cloaking frequencies of this shell can be externally controlled since the magnetic permeability of ferrites is well tuned by the applied magnetic field. This may provide a potential way to design a tunable multifrequency invisibility cloak with considerable flexibility.

Mass Determination by Direct Measurement of Electron Scattering

1975 ◽  
Vol 33 ◽  
pp. 240-241
Author(s):  
M. K. Lamvik ◽  
A. V. Crewe
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Mass Density ◽  
Variable Mass ◽  
Scattering Cross Section ◽  
Mass Determination ◽  
Number Density ◽  
Cross Sectional ◽  
Thin Slice ◽  
Scattering Cross

If a molecule or atom of material has molecular weight A, the number density of such units is given by n=Nρ/A, where N is Avogadro's number and ρ is the mass density of the material. The amount of scattering from each unit can be written by assigning an imaginary cross-sectional area σ to each unit. If the current I0 is incident on a thin slice of material of thickness z and the current I remains unscattered, then the scattering cross-section σ is defined by I=IOnσz. For a specimen that is not thin, the definition must be applied to each imaginary thin slice and the result I/I0 =exp(-nσz) is obtained by integrating over the whole thickness. It is useful to separate the variable mass-thickness w=ρz from the other factors to yield I/I0 =exp(-sw), where s=Nσ/A is the scattering cross-section per unit mass.

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