Why Does Sigma(s) Cause Complex Roots in My Equation?

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the challenges of rearranging an equation involving sigma(s) that results in complex roots. Participants explore the implications of the equation's structure and the conditions under which real solutions may exist, focusing on theoretical and experimental aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant expresses difficulty in rearranging an equation due to sigma(s) appearing twice, leading to complex roots instead of a single equation for sigma(s).
  • Another participant suggests that the expression for sigma(s) is inherently multi-valued and may only yield real values under specific conditions related to theta and sigma(l).
  • A participant conducting a lab experiment indicates uncertainty about how to proceed if the equation cannot be solved for sigma(s).
  • In response, another participant asserts that the equation can indeed be solved numerically, provided the parameters are within the correct range, and suggests that there may be physical constraints to consider that could help eliminate complex solutions.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are competing views regarding the solvability of the equation and the nature of the roots. Some believe real solutions are possible under certain conditions, while others highlight the multi-valued nature of the expression.

Contextual Notes

There are unresolved assumptions regarding the parameters involved and the specific conditions under which real roots may be found. The discussion does not clarify the mathematical steps necessary to isolate sigma(s) or the implications of complex roots.

dscot
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Hi,

I've been having some problems trying to re-arrange this equation for a few days now, the problem is that sigma(s) appears twice in the equation: http://screencast.com/t/dlDwH4eIcp

The problem seems to be that I always end up with complex roots rather than a single equation for sigma(s).

Note the exponential should not be under the square root.

Thank you :)
 
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Not sure what you are trying to do...

It is pretty obvious from looking at the equation, that an expression for sigma_s will be multi-valued, and will only be real for certain values of theta and sigma_l.
 
Hi f95toli,

Thank you for taking the time to respond to my question.

Thats what I was afraid, I'm basically carrying out this experiment in the lab and have all the other values but couldn't get this equation solved for sigma(s).

I'm not too sure what to do if there's no way the equation can be solved?
 
Of course it can be solved. Assuming the other parameters are in the right range you can easily find the real roots by solving it numerically (I am here assuming that there are physical reasons for why sigma_s can't be complex).

Perhaps there are other constraints that will allow you to discard one of the solutions?
 

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