astroverted

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14 years, 223 days

A childhood interest in telescopes and astronomy started me on a somewhat non-Euclidean path towards a career in optical engineering and lens design.  Eventual completion of a master of science revealed both gaps and uncharted waters in mathematical understanding  that I (am still) continuing to develop by  a process of self-education. 

While I am still very much in the "learning curve" with MAPLE, I can already sense that the core emphasis on symbolic solving and rich heritage in mathematical education will mesh quite well with my desire to expand my mathematical modeling skills through self-study.  I look forward to integrating the MAPLE toolset into my daily work designing and analyzing optical imaging systems.

MaplePrimes Activity


These are questions asked by astroverted

Dill_ABC_Model_PDE_System_Solution.mw

The attached Maple 2019  document attempts to solve a non-linear system of two coupled, time-dependent first-order PDE's, given a list of initial and boundary conditions.  The system models the optical transmittance through a thin photoresist layer whose transmittance changes upon exposure to the incident exposure energy, and hence, the cumulative transmittance through the layer is itself a function of both the exposure time and the distance traveled through the resist layer.  The list of fixed parameters, P, defines the characteristics of a particular photoresist (hereafter "pr") and an assumed exposure irradiance.

My first attempt towards a general solution without initial or boundary conditions (hereafter "ics" & "bcs") apparently "succeeds" (in that no error messages are thrown), however, the form of the solution is quite complicated and difficult (for me at least) to interpret.  I think I understand that the _Cn are undefined constants that require supplying ics & bcs to determine the solutions for the transmitted intensity I(z,t) & the normalized molar fraction of the photo-active component in the pr, M(z,t).  However I do not understand what the symbol _f refers to in the returned solutions.

I make a second attempt to solve the system numerically, supplying a list of the [ics,bcs] as arguments to Pdesolve, however the error message "Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {Iota(0, t), Iota(z, 0), Mu(0, t), Mu(z, 0)}" raises the question of whether I have misunderstood the required syntax in using Pdesolve or that the system as posed is in fact insoluble by Maple.

I would appreciate any insights that readers of this post can contribute, as my experience using Maple and PDesolve in particular must be considered embryonic at best.

Scott Milligan

God forgive me, I know this is a bad way to start asking for help, but it is such a PITA to figure out how to get WYSIWYG representation of even simple Maple worksheets onto this forum.  I searched the catacombs of Rome looking for a simple way to attach a couple of (very small) Maple & Matlab files relevent to my current angst, but to no avail; the dragon of legacy unix protocol has slain its latest unsuspecting victim.

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