# Re: Drift Diffusion Equation Setup

Great, that makes a lot of sense!

I've tried to define the current density as a CellVariable with the value J_n
as I've seen you describe in the mailing list before.  But, I keep
encountering the error "ValueError: could not broadcast input array from
shape (135) into shape (134)" with my mesh defined as length of 134.

I believe this is caused by the harmonicFaceValue, though I am not sure?

Would the following definition for current density also work:  J_p.value =
-mu_p * p * psi.arithmeticFaceValue.divergence + Dn *
p.aritmeticFaceValue.divergence

I apologize for the multiple questions and I'm very grateful for your help!
Justin

On Thu, Jul 25, 2019 at 10:55 AM Guyer, Jonathan E. Dr. (Fed) via fipy <
fipy@nist.gov> wrote:

> Justin -
>
> I would define a function that takes an argument x for each of your
> analytical expressions, e.g.,
>
> 
> def y01(x):
>     """Initial positive ion charge density"""
>     return
> pini*((special.gamma(k1+p1))/(special.gamma(k1)*special.gamma(p1))*((x/l)**(k1-1))*(1-(x/l))**(p1-1))/7.3572
>
> def y02(x):
>     """"Initial negative ion charge density"""
>     return
> nini*((special.gamma(k2+p2))/(special.gamma(k2)*special.gamma(p2))*((x/l)**(k2-1))*(1-(x/l))**(p2-1))/7.3572
>
> def y03(x):
>     """Initial potential"""
>     return a1*np.sin(b1*x+c1) + a2*np.sin(b2*x+c2)
> 
>
> Then you can invoke these functions with either the linspace to generate
> plots like you have, or with the mesh positions, to set the initial
> conditions:
>
> 
> Pion.value = y01(mesh.x)
> Nion.value = y02(mesh.x)
> potential.value = y03(mesh.x)
> 
>
> - Jon
>
> > On Jul 24, 2019, at 1:23 PM, Justin Pothoof <jpoth...@uw.edu> wrote:
> >
> > Thank you Jon,
> >
> > I will try writing it in one equation as you suggested.  Regarding the
> experimental data, I have an initial potential curve described by a sum of
> sines fit as well as initial positive/negative charge density curves
> described by a specific equation I'll show in a file.
> >
> > Thanks for the help!
> > Justin
> >
> > On Wed, Jul 24, 2019 at 6:06 AM Guyer, Jonathan E. Dr. (Fed) via fipy <
> fipy@nist.gov> wrote:
> > Justin -
> >
> > What that error means is that if you write 'var=' for any Term, then you
> must write 'var=' for every Term.
> >
> >
> > 
> > Pion.equation = TransientTerm() + k_rec * Pion * Nion +
> ConvectionTerm(coeff=1 / q, var=Jp) == 0
> > Nion.equation = TransientTerm() + k_rec * Pion * Nion +
> ConvectionTerm(coeff=-1 / q, var=Jn) == 0
> > potential.equation = DiffusionTerm(1 / q * epsilon) + Pion * Nion == 0
> > Jp.equation = ImplicitSourceTerm() + ConvectionTerm(coeff=-q * mu_p *
> Pion, var=potential) + ConvectionTerm(coeff=-q * Dp, var=Pion) == 0
> > Jn.equation = ImplicitSourceTerm() + ConvectionTerm(coeff=-q * mu_n *
> Nion, var=potential) + ConvectionTerm(coeff=q * Dn, var=Nion) == 0
> > 
> > FiPy does not know what Variable TransientTerm() applies to in
> Pion.equation and Nion.equation, DiffusionTerm() in potential.equation, nor
> ImplicitSourceTerm() in Jp.equation and Jn.equation.
> >
> > As a further point, you should not solve Pion.equation and Jp.equation
> separately nor Nion.equation/Jn.equation. Combine them for a single, second
> order PDE each for n and for p. You will want to take care that, e.g., the
> equation should not be taking the gradient (\nabla) of a vector (Jn), which
> would give you a tensor; rather, the expression should be divergence
> (\nabla\cdot) of a vector (Jn), giving a scalar.
> >
> > As to comparing to your experimental data, I'd need to know what form it
> >
> > - Jon
> >
> > > On Jul 23, 2019, at 9:09 PM, Justin Pothoof <jpoth...@uw.edu> wrote:
> > >
> > > Hello,
> > >
> > > I understand that modeling the drift diffusion equations are very
> challenging, but I'm having issues actually writing the equations.  I keep
> encountering the error: "fipy.terms.ExplicitVariableError: Terms with
> explicit Variables cannot mix with Terms with implicit Variables."
> > >
> > > Additionally, I have fitted experimental data that describes what the
> initial conditions for my system should be, but I don't know how to include
> that into FiPy.  I would appreciate any guidance that you can offer.  I
> will include a pdf of what the equations I'm trying to write are as well as
> the file I have written thus far.
> > >
> > > Thank you,
> > > Justin
> > > <FiPy
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> >
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>
>
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