Scattering of Waves Formulation (moved to correct forum)

In summary: Your Name]In summary, the conversation discusses the boundary condition for soft scattering of plane waves incident upon an infinitely long cylinder of radius a. It is determined that the Neumann boundary condition applies to the circular end caps of the cylinder, while the side surface still has a Dirichlet boundary condition. This allows the incident waves to pass through without any reflection or absorption.
  • #1
splitringtail
58
0

Homework Statement



Consider plane waves incident upon an infinitely long cylinder of radius ,a, whose propagation is perpendicular to the axis of the cylinder.


Homework Equations



This is more of a conceptional question, since the solutions are already developed and just needs to be adapted to the problem.

The Attempt at a Solution



I am not sure what kind of boundary condition describes soft scattering. I want to say it is a Neumann boundary condition, since I remember in quantum mechanics doing hard sphere scattering where the boundary condition is a Dirichlet.
 
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  • #2
However, in this situation, the cylinder is infinitely long, so I am not sure if that changes anything.

Dear fellow scientist,

Thank you for bringing up this interesting question. In this situation, the boundary condition for soft scattering can indeed be described by a Neumann boundary condition. This is because the infinitely long cylinder acts as an open boundary, allowing the incident plane waves to pass through without any reflection or absorption.

However, it is important to note that the Neumann boundary condition only applies to the surface of the cylinder. In the case of an infinitely long cylinder, this would be the circular end caps of the cylinder. The side surface of the cylinder would still have a Dirichlet boundary condition, as there is no propagation in that direction.

I hope this helps clarify the concept of soft scattering in this scenario. Let me know if you have any further questions.
 

Q: What is the basic concept behind scattering of waves formulation?

The basic concept behind scattering of waves formulation is that when a wave encounters an obstacle or an inhomogeneous medium, it gets scattered in different directions. This scattering can be described mathematically by considering the incident wave, the scattering object, and the scattered wave.

Q: How is the scattering of waves formulated mathematically?

The scattering of waves can be formulated mathematically using the scattering amplitude, which is the ratio of the scattered wave to the incident wave at a given point. This amplitude can be calculated using the boundary conditions and the properties of the scattering object.

Q: What are some applications of scattering of waves formulation?

Scattering of waves formulation has many practical applications, such as in radar and sonar systems for detecting objects, in medical imaging techniques like ultrasound, and in material characterization for non-destructive testing.

Q: How does the size and shape of the scattering object affect the scattering of waves?

The size and shape of the scattering object play a significant role in the scattering of waves. Objects that are smaller than the wavelength of the incident wave tend to scatter in all directions, while larger objects tend to reflect the wave in a more directional manner. The shape of the object can also affect the scattering pattern and intensity.

Q: Can the scattering of waves be controlled or manipulated?

Yes, the scattering of waves can be controlled and manipulated through various techniques such as using metamaterials or designing specific shapes and sizes of the scattering object. This can be useful in applications such as cloaking devices or creating specific scattering patterns for desired outcomes.

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