Description
Wave Scattering by Many Small Particles is an advanced research monograph that presents an asymptotically exact solution to the many-body scattering problem under the condition:
a≪d≪λa \ll d \ll \lambda
where:
- a is the characteristic size of a small particle,
- d is the minimum distance between particles, and
- λ is the wavelength in the surrounding medium.
This rigorous mathematical framework provides a comprehensive treatment of scattering phenomena involving large collections of small particles and offers important theoretical and practical insights into modern materials science and wave engineering.
The book investigates both scalar wave scattering and electromagnetic wave scattering, while also developing theories of heat transfer in media containing numerous small bodies. In addition, it constructs a quantum-mechanical theory of scattering by multiple potentials with small support, extending the analysis to quantum systems.
Key Topics Covered
- Many-body scattering theory
- Asymptotically exact solutions for wave scattering
- Scalar wave scattering
- Electromagnetic wave scattering
- Heat transfer in media containing many small particles
- Quantum-mechanical scattering theory
- Scattering by multiple small-support potentials
- Mathematical methods in wave propagation
- Inverse scattering problems
- Wave-material interactions
Major Applications
The theoretical results presented in the book lead to several important applications, including:
Materials with Desired Refraction Properties
The book introduces methods for designing and creating materials with a specified or engineered refractive index, enabling the development of advanced optical and electromagnetic materials.
Wave-Focusing Materials
A novel approach is presented for constructing materials capable of focusing waves in desired ways, with potential applications in optics, acoustics, imaging, and communications.
Advanced Material Engineering
The text discusses practical and technological challenges that must be overcome to implement these theoretical findings in real-world applications
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