Partial Differential Equations!

[Katganistan]

Let's discuss Partial Differential Equations!

Laplace's equation is nice to work with because it is homogeneous and linear and hence always separable. It's solutions are many, but they are always of a polynomial or exponential nature. Physically, Laplace's equation usually implies some superposition of wave-like behavior in a scalar field.

The equation for a solenoidal vector field (that the vector field has zero divergence) is also very easy to solve and is always separable, but it also doesn't reveal the entire picture. It cannot tell you how the x component of the vector field depends on an additive term containing the y and z variables, for example. In order to figure out the full behavior of the vector field, you must know its curl field as well.

EDIT: I should correct myself. The solutions to Laplace's equation are always of a polynomial or exponential nature for coordinates in a holonomic basis.

[Yootopia]

What is there to discuss -_-

[Wilgrove]

You lost me...

[UnhealthyTruthseeker]

What is there to discuss -_-

Would you rather discuss abortion for the 3.34 x 10²⁸th time?

[Wilgrove]

What is there to discuss -_-

Would you rather discuss abortion for the 3.34 x 10²⁸th time?

Like being a good comedic, in order to make a good thread, your subject has to be universal. This subject is not universal.

[UnhealthyTruthseeker]

Like being a good comedic, in order to make a good thread, your subject has to be universal. This subject is not universal.

We've pretty much discussed every universal topic hundreds of times. Besides, aren't there comedians that joke about specific topics?

[Natapoc]

Let's discuss Partial Differential Equations!

Laplace's equation is nice to work with because it is homogeneous and linear and hence always separable. It's solutions are many, but they are always of a polynomial or exponential nature. Physically, Laplace's equation usually implies some superposition of wave-like behavior in a scalar field.

The equation for a solenoidal vector field (that the vector field has zero divergence) is also very easy to solve and is always separable, but it also doesn't reveal the entire picture. It cannot tell you how the x component of the vector field depends on an additive term containing the y and z variables, for example. In order to figure out the full behavior of the vector field, you must know its curl field as well.

EDIT: I should correct myself. The solutions to Laplace's equation are always of a polynomial or exponential nature for coordinates in a holonomic basis.

Given the set of solutions to all possible Laplace's equations do you think the number of such solutions that are polynomial are greater then, equal to, or less then the number that are exponential? And why?

[UnhealthyTruthseeker]

Given the set of solutions to all possible Laplace's equations do you think the number of such solutions that are polynomial are greater then, equal to, or less then the number that are exponential? And why?

I would say equal. Both are sets with a cardinality of the continuum.

Also, if you remember, exponentials (and yes, sinusoids are exponential functions) are really just polynomial functions of arbitrarily high degree. (Think about the Taylor series.)

[Niur]

oh god, what language are you speaking?! were not all mathmaticians here...

[UnhealthyTruthseeker]

oh god, what language are you speaking?! were not all mathmaticians here...

I'm not speaking any language. However, I am typing in English.

[Yootopia]

What is there to discuss -_-

Would you rather discuss abortion for the 3.34 x 10²⁸th time?

Aye aye aye discussing abortion is dull but couldn't you have picked a less utterly pish alternative?

[Natapoc]

Given the set of solutions to all possible Laplace's equations do you think the number of such solutions that are polynomial are greater then, equal to, or less then the number that are exponential? And why?

I would say equal. Both are sets with a cardinality of the continuum.

Also, if you remember, exponentials (and yes, sinusoids are exponential functions) are really just polynomial functions of arbitrarily high degree. (Think about the Taylor series.)

Oh yeah good point. I was not thinking about that. I can see that now. Hmm I'll try to contribute a better question

[UnhealthyTruthseeker]

Aye aye aye discussing abortion is dull but couldn't you have picked a less utterly pish alternative?

Pish as in pissy or as in absurd?

[Northern Delmarva]

[UnhealthyTruthseeker]

Oh yeah good point. I was not thinking about that. I can see that now. Hmm I'll try to contribute a better question

And if you look at the kind of exponential products that you get vs. the kind of polynomials you get, you will see that the kinds of polynomial solutions you get really just look like the products of portions of exponential polynomial series.

x³ + 3x²y - 3xy² - y³

Is one such example. Does that not look like the product of simpler polynomials of a certain kind?

[Yootopia]

Aye aye aye discussing abortion is dull but couldn't you have picked a less utterly pish alternative?

Pish as in pissy or as in absurd?

"pish: urine; also denoting that something is bad, e.g. "thats pure pish" - http://www.gla.ac.uk/clubs/ski/weegie.html#pish

[UnhealthyTruthseeker]

"pish: urine; also denoting that something is bad, e.g. "thats pure pish" - http://www.gla.ac.uk/clubs/ski/weegie.html#pish

You know, you could model a stream of urine using a few partial differential equations. Navier-Stokes and the equation of continuity for mass come to mind.

Also, why is math pure piss?

[Yootopia]

"pish: urine; also denoting that something is bad, e.g. "thats pure pish" - http://www.gla.ac.uk/clubs/ski/weegie.html#pish

You know, you could model a stream of urine using a few partial differential equations. Navier-Stokes and the equation of continuity for mass come to mind.

Also, why is math pure piss?

Maths is alright but a poor topic when the OP is made up of declaratives.

[UnhealthyTruthseeker]

Maths is alright but a poor topic when the OP is made up of declaratives.

Would you have preferred that I phrase it as questions?

[Natapoc]

"pish: urine; also denoting that something is bad, e.g. "thats pure pish" - http://www.gla.ac.uk/clubs/ski/weegie.html#pish

You know, you could model a stream of urine using a few partial differential equations. Navier-Stokes and the equation of continuity for mass come to mind.

Also, why is math pure piss?

Hay that is a great point. Actually this is very important in the development of computer games. If the urine flow is not correctly modeled it could float all over the place and people would not play the game because they think it is to fake.

Want to try to come up with a simplistic model? What variables do you think are important enough to consider for an effective urine flow model?

edit: I need to get some pencil and paper out for this conversation

[New Kereptica]

"pish: urine; also denoting that something is bad, e.g. "thats pure pish" - http://www.gla.ac.uk/clubs/ski/weegie.html#pish

You know, you could model a stream of urine using a few partial differential equations. Navier-Stokes and the equation of continuity for mass come to mind.

Also, why is math pure piss?

Hay that is a great point. Actually this is very important in the development of computer games. If the urine flow is not correctly modeled it could float all over the place and people would not play the game because they think it is to fake.

Want to try to come up with a simplistic model? What variables do you think are important enough to consider for an effective urine flow model?

All of them. No concessions can be made when it comes to realistically modelling urine.

[UnhealthyTruthseeker]

Hay that is a great point. Actually this is very important in the development of computer games. If the urine flow is not correctly modeled it could float all over the place and people would not play the game because they think it is to fake.

Want to try to come up with a simplistic model? What variables do you think are important enough to consider for an effective urine flow model?

Well, it's better than another abortion thread I guess.

First, urine is very similar to water, so I would say the assumptions of Newtonian fluid and incompressible fluid would hold valid. Next, if you were to put the piss stream into a parabolic cylindrical system (parabolas along the direction of flow and compact [that is to say limited in size] cylinders around the direction of flow), you could model it as irrotational. Also, the parabolic axis would remove the need to take gravitation into account, as the flow solutions would be isoclines of the parabolic axis.

[Pevisopolis]

Let's discuss Partial Differential Equations!

Laplace's equation is nice to work with because it is homogeneous and linear and hence always separable. It's solutions are many, but they are always of a polynomial or exponential nature. Physically, Laplace's equation usually implies some superposition of wave-like behavior in a scalar field.

The equation for a solenoidal vector field (that the vector field has zero divergence) is also very easy to solve and is always separable, but it also doesn't reveal the entire picture. It cannot tell you how the x component of the vector field depends on an additive term containing the y and z variables, for example. In order to figure out the full behavior of the vector field, you must know its curl field as well.

EDIT: I should correct myself. The solutions to Laplace's equation are always of a polynomial or exponential nature for coordinates in a holonomic basis.

[UnhealthyTruthseeker]

Actually, there are some divide by zero issues when you put the Laplacian into cylindrical or spherical coordinates. Of course, they are removable singularities, because they don't exist in all coordinate systems, and the Laplacian is separable in all coordinates.

[Vetalia]

We should kill all nonwhites. That should spice things up.