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Thread: Imaginary part in the second Fick's low

  1. #1 Imaginary part in the second Fick's low 
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    Hello!

    Could anyone answer this question: https://physics.stackexchange.com/qu...-the-ficks-low
    I am sorry for such a form, but I don't know how to handle LaTeX here.

    Thank you for any help.
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  2. #2  
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    Quote Originally Posted by Boro View Post
    Hello!

    Could anyone answer this question: https://physics.stackexchange.com/qu...-the-ficks-low
    I am sorry for such a form, but I don't know how to handle LaTeX here.

    Thank you for any help.


    So, there will be two solutions, one dependent of and one dependent of
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  3. #3  
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    But what these solutions describes since there is only one diffusion process? Describes the magnetization vector in NMR and I want to get the signal attenuation due to diffusion. Under the standard asumption about gradient linearity, the imaginary part is equal to zero, but I wanted to calculate it for more genaral case. Can I just reject the imaginary part as devoided of the physical meaning?
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  4. #4  
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    Quote Originally Posted by Boro View Post
    But what these solutions describes since there is only one diffusion process? Describes the magnetization vector in NMR and I want to get the signal attenuation due to diffusion. Under the standard asumption about gradient linearity, the imaginary part is equal to zero, but I wanted to calculate it for more genaral case. Can I just reject the imaginary part as devoided of the physical meaning?
    No, you can't, because there are TWO solutions, both valid, not one.
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  5. #5  
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    Ok. But what is the physical meaning of the existence two solutions?
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  6. #6  
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    Quote Originally Posted by Boro View Post
    Ok. But what is the physical meaning of the existence two solutions?
    There are actually two equations, hence two solutions. One dependent on , the other dependent on , as already explained. Using complex functions simply reduces the two equations to solving one, it is a well known mathematical trick.
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  7. #7  
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    So, if the real part coresponds to x direction and the imaginary part to y direction on the plane on which the vector is spinning, there are separate solutions for x and y? It doesn't make sense for me. Thank you for answers anyway.
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  8. #8  
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    Quote Originally Posted by Boro View Post
    So, if the real part coresponds to x direction and the imaginary part to y direction
    This is not true (and it is not what I have been trying to explain).

    on the plane on which the vector is spinning, there are separate solutions for x and y? It doesn't make sense for me. Thank you for answers anyway.
    No, this is not what I meant. You need to study differential equations, this is not working, you lack the fundamentals.
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  9. #9  
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    I know that it is not what you meant, but it is true, because it is my assumption. I wrote: "Psi describes the magnetization vector in NMR". The vector is rotation on the xy plane and is given by the complex number. Perhaps I did not make it clear enough in the previous posts.
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