Is Modeling or Pure Mathematical Equations Better for Analyzing Capacitors?

[tommyers]

Hi,

When modelling something such as a capacitor using a method like Boundary Element Analysis (BEM) then this may lead you to a visual model i.e it shows you the charge across the plates or the density of the fringing field, rather than a method which uses a pure mathematics such as Gauss' law that lead you to an absolute answer i.e the charge at one point in more detail but with less visual information.

I guess what I am trying to get at is ... a modeling method is good for somethings, whilst a pure mathematical approach as other advantages - both are 'use-able' it just depends on what you are trying to achieve.

Regards

Tom

 

[PerennialII]

hi tommyers,

yep - one of the biggest problems of numerical methods like BEM is trying to really understand the underlying "physics" of the problem - what is really going on, to what is the 'system' responsing to, what are the important parameters, how will the system response differ if something is varied a somewhat, does the solution actually make any sense and so forth. As such, a whole lot of work is done with far simpler models than could be done in numerically, simply to get a better grip of the problem. And often you see approaches where a numerical solution is interpreted primarily on the basis of an analytical one (pure math as you said above), the numerical solution being used to investigate some limitation of the analytical approach or "inject" new information to it (such as nonlinearity, finite domains etc.). Although in many cases can investigate systems by doing a large number of numerical analyses, it is still somewhat difficult to understand the system behavior on the basis of limited numerical data sets, let alone improve the models without some analytical handiwork (at which point drawing a line between these 2 becomes obscure, and actually pretty much irrelevant).

 

[charng]

Hi Tom,

Thank you for bringing up the topic of modelling vs pure equations. I believe that both methods have their own strengths and can be useful in different situations.

Modelling, such as using BEM, can provide a visual representation of a system which can be helpful in understanding complex relationships and patterns. It allows us to see the behavior of a system in a more tangible way and can aid in making predictions or identifying potential issues. However, it is important to keep in mind that modelling is only as accurate as the assumptions and parameters used in the model, and it may not always provide an absolute answer.

On the other hand, pure equations, such as Gauss' law, can provide precise and exact solutions to problems. They rely on mathematical principles and can be used to derive relationships between variables in a system. However, they may not always be easy to visualize or understand without a strong mathematical background.

In my opinion, the choice between modelling and pure equations depends on the specific problem at hand. For some situations, a visual representation may be more useful, while for others, a precise mathematical solution may be necessary. As scientists, it is important to be familiar with both methods and to use them appropriately to achieve our research goals.

Thank you for bringing up this interesting topic for discussion.