Application of Conformal Mapping in Physics

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Conformal mapping in complex analysis is widely applicable in physics, particularly in heat transfer, fluid dynamics, and electrostatics. It is primarily used to solve planar potential flow problems, which are crucial for understanding various physical phenomena. The principles of conformal mappings can be extended to higher dimensions, although detailed applications in this area are less commonly discussed. The discussion highlights the importance of potentials in physics and the need for further exploration of higher-dimensional applications. Overall, conformal mapping remains a vital tool in both theoretical and applied physics.
hoalacanhdk
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Hi,
I'm studying about Conformal Mapping in Complex Analysis and see its applications in Heat transfer, Fluid and Static Eletrocity. But it is said that this subject is very useful in many branches of Physics.
Can you tell me about that?
Thanks.
 
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You have already mentioned some important applications. In general, complex analysis conformal mappings are used to find solutions to planar potential flows. (see http://brennen.caltech.edu/fluidboo...ialflow/complexvariables/conformalmapping.pdf )
Potentials are very important in physics.
The basic ideas of complex analysis conformal mappings are extended to higher dimensions and have more applications than just planar flows.
 
FactChecker said:
You have already mentioned some important applications. In general, complex analysis conformal mappings are used to find solutions to planar potential flows. (see http://brennen.caltech.edu/fluidboo...ialflow/complexvariables/conformalmapping.pdf )
Potentials are very important in physics.
The basic ideas of complex analysis conformal mappings are extended to higher dimensions and have more applications than just planar flows.
Can you tell more about applications to higher dimensions?
 
hoalacanhdk said:
Hi,
I'm studying about Conformal Mapping in Complex Analysis and see its applications in Heat transfer, Fluid and Static Eletrocity. But it is said that this subject is very useful in many branches of Physics.
Can you tell me about that?
Thanks.

http://www.southampton.ac.uk/~evans/TS/Toolbox/confrml_map.pdf

Zz.
 
hoalacanhdk said:
Can you tell more about applications to higher dimensions?
I'm afraid that I was sloppy and too ambitious in my answer. The basics of mappings that locally map Rn into another space, preserving the local angles, is what I was referring to. I really don't have enough expertise to say more.
 

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