# Need a force-like unit for classical particle system simulation

iteratee
TL;DR Summary
How to deal with "non-compressible" fluids?
I am doing a learning project by writing a simulation that includes capacitance and current flow amongst capacitors that may potentially be in parallel. I don't care about certain details yet - dissipation factor, frequency dependent effects, temperature. Tiny capacitences within diode junctions and (importantly) FET gates are the relevant charge storage elements.

A pretty fundamental sub-problem eventually arises: what unit would one substitute for the Newton to describe the magnitude of interaction between motionless and effectively mass-less particles in a classical field simulation? I want to "simplify" the system so that my particles are essentially a non-compressible fluid, with the obvious immediate implication being that Newton's first law effectively goes away. Intuitively I need some kind of unit that works independently of acceleration, (and some googleable terms or else I just get pointed to a pile of "what is force?" articles.)

Are there methods for starting from a "fictitious shove magnitude" as a force surrogate for establishing initial conditions that later convert to back into conventional units for currents and voltages etc? I have looked at how spice handles operating point analysis with its initial conditions approximation, but I'm investigating alternatives.

Clues greatly appreciated! Mentor
Summary:: How to deal with "non-compressible" fluids?

I am doing a learning project by writing a simulation that includes capacitance and current flow amongst capacitors that may potentially be in parallel. I don't care about certain details yet - dissipation factor, frequency dependent effects, temperature. Tiny capacitences within diode junctions and (importantly) FET gates are the relevant charge storage elements.

A pretty fundamental sub-problem eventually arises: what unit would one substitute for the Newton to describe the magnitude of interaction between motionless and effectively mass-less particles in a classical field simulation? I want to "simplify" the system so that my particles are essentially a non-compressible fluid, with the obvious immediate implication being that Newton's first law effectively goes away. Intuitively I need some kind of unit that works independently of acceleration, (and some googleable terms or else I just get pointed to a pile of "what is force?" articles.)

Are there methods for starting from a "fictitious shove magnitude" as a force surrogate for establishing initial conditions that later convert to back into conventional units for currents and voltages etc? I have looked at how spice handles operating point analysis with its initial conditions approximation, but I'm investigating alternatives.

Clues greatly appreciated! What is your math background so far? Does it include Calculus, Differential Equations and Linear Algebra (matrices)?

Do you have experience with SPICE already? That is the gold standard for circuit simulations. If you do, have you done these simulations in SPICE and are now wanting to get into more of a FEA-type of analysis? If so, trying to model current flow with fluid mechanics is probably the wrong way to go. You should be using Fermi surfaces and solid state Physics equations to try to model current flow at an atomic level, IMO.

iteratee
What is your math background so far? Does it include Calculus, Differential Equations and Linear Algebra (matrices)?

Ha well I'm a self-taught computer science guy with my day-to-day being predictably irrelevant discrete math, logic, type-theory sorts of things. Learning the linear algebra necessary for solving matrices for circuit simulation looks pretty "within reach". I should do that. I have no formal math education.

Do you have experience with SPICE already? That is the gold standard for circuit simulations. If you do, have you done these simulations in SPICE and are now wanting to get into more of a FEA-type of analysis?

I've had a couple years playing around with ngspice, ltspice, and have done some reverse-engineering / modifying of old opamp macromodels to understand their workings. I'm kind of curious about trying my hand at writing xspice libraries and also in the methods underlying tools like fastcap that sort of compile a field simulation down into an equivalent netlist (kind of a hack but interesting nonetheless).

If so, trying to model current flow with fluid mechanics is probably the wrong way to go. You should be using Fermi surfaces and solid state Physics equations to try to model current flow at an atomic level, IMO.

Drats, OK somewhat expected answer. Modeling fermi-dirac distribution is a little "lower level" than I was thinking. I'll have to learn some prerequisites clearly, but I knew that. If I were really hardcore about proper semiconductor simulation I'd use the existing models for starters.

• berkeman
Mentor
I've had a couple years playing around with ngspice, ltspice, and have done some reverse-engineering / modifying of old opamp macromodels to understand their workings. I'm kind of curious about trying my hand at writing xspice libraries and also in the methods underlying tools like fastcap that sort of compile a field simulation down into an equivalent netlist
I think that's a great next step for you. Learn to write code that simulates circuits using the same equations that SPICE simulators use. There are lots of examples out there, and it's pretty easy to see if your simulation is correct for simpler circuits. Post some of your time domain transient results for us to check! • sophiecentaur and iteratee
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