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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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Computation of Mie derivatives.

Yang Li¹, Nicola Bowler

¹Department of Electrical and Computer Engineering and Center for Nondestructive Evaluation, Iowa State University, Ames, Iowa 50011, USA. 20002000.leon@gmail.com

|July 16, 2013

Summary

This summary is machine-generated.

This study derives accurate analytical and approximate expressions for Mie scattering coefficients, enhancing computational efficiency for spherical particles. These methods improve accuracy and speed for designing metamaterials and analyzing aerosol data.

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Area of Science:

Electromagnetics and Optics
Computational Physics
Materials Science

Background:

Mie scattering theory describes light interaction with spherical particles.
Calculating derivatives of Mie scattering coefficients is crucial for applications like metamaterial design and remote sensing.
Existing numerical methods can suffer from overflow and reduced accuracy.

Purpose of the Study:

To derive analytical and approximate expressions for Mie scattering coefficients' derivatives.
To enhance computational efficiency and accuracy in scattering calculations.
To provide tools for designing metamaterials and retrieving aerosol properties.

Main Methods:

Derivation of analytical expressions for Mie scattering coefficients' derivatives.
Development of approximate expressions using logarithmic derivatives of Riccati-Bessel functions to prevent numerical overflow.
Verification against Mathematica's analytical expressions and comparison with numerical derivatives.

Main Results:

Analytical and approximate expressions for derivatives were obtained.
The new expressions demonstrate higher accuracy and significantly improved speed (2.0x and 2.8x faster, respectively) compared to numerical methods for single spheres.
Approximate expressions maintain acceptable accuracy and computation time for a wide range of electrical radii and high orders.

Conclusions:

The derived analytical and approximate expressions offer a more efficient and accurate approach to Mie scattering calculations.
These methods are valuable for the design of nonmetallic metamaterials, including optical, all-dielectric, mu-negative types.
The findings support improved retrieval of aerosol properties from remote sensing data.