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-   -   Are Lagrangian simulations 100% accurate ? (http://mymathforum.com/computer-science/340200-lagrangian-simulations-100-accurate.html)

InkSprite April 25th, 2017 07:53 AM

Are Lagrangian simulations 100% accurate ?
 
Are Lagrangian simulations 100% accurate algebraically?

When programming in a Lagrangian function for determining the position of objects in a system, are previous point values used when calculating new points?

I am still struggling with lagrangian mathematics. I may need to step back to calculous.

Joppy April 26th, 2017 03:37 AM

I think in most practical cases your results are going to be approximate, otherwise we wouldn't bother with numerics. But likely there are contrived examples.

And yes, it is typically the case that after a phase or state space is established (i.e., the system of equations governing the system), the 'future' values, depend on the previous values, along with some scaling factors and so on.

InkSprite April 29th, 2017 07:47 AM

Damn. So I can't reverse a system and get the initial state.

Joppy April 29th, 2017 06:47 PM

Umm. Depends on the system. What are you modelling ?

InkSprite April 30th, 2017 09:41 AM

1000's of particles.
They can pass through each other. They are just points that pull on each other.

Joppy April 30th, 2017 06:35 PM

Is energy conserved in the system (do the particles undergo elastic collisions or exchange heat)?

For nonequilibrium dynamics problems (NEMD), I think running backwards would be troublesome due to stability in your error.

InkSprite May 1st, 2017 06:59 AM

Quote:

Originally Posted by Joppy (Post 568764)
Is energy conserved in the system (do the particles undergo elastic collisions or exchange heat)?

For nonequilibrium dynamics problems (NEMD), I think running backwards would be troublesome due to stability in your error.

energy is conserved in the system. There is no heat exchanged. No elastic collisions. Is that like two rubber balls bouncing? no, none of that; not brick, or metal or anything. It's all just fields acting on points.

...
At some point int he simulation, energy may be added. From user input.

Joppy May 1st, 2017 07:10 AM

Quote:

Originally Posted by InkSprite (Post 568802)
energy is conserved in the system. There is no heat exchanged. No elastic collisions. Is that like two rubber balls bouncing? no, none of that; not brick, or metal or anything. It's all just fields acting on points.

...
At some point int he simulation, energy may be added. From user input.



Yes sometimes we have a constant field applied to the system for various reasons.

It's not always useful to think of physical examples when modelling abstract things, they tend to give the wrong impression.
There is no ball that will mimic your reductionist model of interacting particles.


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InkSprite May 1st, 2017 09:44 AM

Okay. I'm not trying to make a ball. I just didn't know what you meant by "elastic" collisions. Like classical physics at the human scale?

I'm just trying to simulate pseudo particles.

Quote:

Yes sometimes we have a constant field applied to the system for various reasons.
What about multiple moving fields?

Joppy May 23rd, 2017 05:52 AM

Yes pseudo particles would likely collide elastically in your simulation. This is a fairly unrealistic situation in the real world (except for the refraction of light maybe). But it stands as a good starting point.

The 'fields' i was referring to could be thought of as a gradient which causes items in your simulation to have foccussing/defocussing effects. In that sense, they are 'moving'. However i assume you mean that these gradients could change with time or as specified by some function.


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