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Updated: Oct 14, 2025

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Free boundary methods and non-scattering phenomena.

Mikko Salo¹, Henrik Shahgholian²

¹Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland.

Research in the Mathematical Sciences

|November 1, 2021

Summary

This summary is machine-generated.

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Certain penetrable obstacles can avoid scattering incident waves. This study proves that real-analytic boundaries always admit non-scattering waves, and explores conditions for obstacles with inward cusps.

Area of Science:

Mathematical Physics
Inverse Scattering Theory
Partial Differential Equations

Background:

Investigates the existence of incident waves that do not scatter from penetrable obstacles, a key problem in inverse scattering.
Examines the properties of obstacles and their boundaries in relation to wave propagation and scattering phenomena.

Purpose of the Study:

To determine if specific types of penetrable obstacles admit incident waves that do not scatter.
To analyze the conditions under which such non-scattering waves exist and the characteristics of the corresponding obstacles.

Main Methods:

Utilizes concepts from inverse scattering theory and the theory of free boundary problems.
Employs quadrature domains to analyze the zero-frequency case for obstacles with inward cusps.

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Last Updated: Oct 14, 2025

Scattering And Absorption of Light in Planetary Regoliths

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Published on: July 1, 2019

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Applies mathematical analysis to study the properties of boundary points under specific incident wave conditions.

Main Results:

Demonstrates that all penetrable obstacles with real-analytic boundaries admit non-scattering incident waves.
Shows that obstacles with inward cusps can also possess this non-scattering property at zero frequency.
Establishes a dichotomy for boundary points: either the boundary is regular, or the obstacle's complement is extremely thin.

Conclusions:

Confirms the existence of non-scattering incident waves for a broad class of penetrable obstacles.
Provides insights into the geometric conditions of obstacles that allow for the absence of scattering.
Highlights the interplay between boundary regularity and the thinness of the obstacle's complement in free boundary problems.