What mathematical symbol is this?

[Ricochet J]

Hi,

What mathematical symbol is the one where it has a cross in a circle?

Is it just multiplication? I've never seen it before. It's not in the list of nomenclature in the original document.

Thanks

 

[Cheetah Designs]

Cross Product?

EDIT: This is a complete guess btw.

 

[Cosimo]

Tensor Product:

http://en.wikipedia.org/wiki/Tensor_product

http://planetmath.org/TensorProduct.html

 

[Judgeneo]

As above, it's a representation of the "outer tensor product" in this case (although I have seen that symbol used plenty of times to represent a general, non-specific, mathematical operator).

In this case, it's telling you that the two vectors multiply to create a second-rank tensor (i.e. a matrix) with components A_ij = (u_i)*(u_j)

This kind of notation is really not seen very often... It's far more convenient and efficient to use tensor notation (... with the Einstein summation convection).

Basically, the result of that operator (div (u X u) ) is the standard "(u.grad)u" term that appears in the momentum equation for all viscous fluids. incidentally, this term is the source of non-linenarity in the Navier-Stokes (and similar) equations, and is the reason we observe complex flow features like turbulence.

My work here is done.

 

[RomanNose]

 

[[FnG]magnolia]

The Operator Symbol.

 

[Duff-Man]

As above, it's a representation of the "outer tensor product" in this case (although I have seen that symbol used plenty of times to represent a general, non-specific, mathematical operator).

In this case, it's telling you that the two vectors multiply to create a second-rank tensor (i.e. a matrix) with components A_ij = (u_i)*(u_j)

This kind of notation is really not seen very often... It's far more convenient and efficient to use tensor notation (... with the Einstein summation convection).

Basically, the result of that operator (div (u X u) ) is the standard "(u.grad)u" term that appears in the momentum equation for all viscous fluids. incidentally, this term is the source of non-linenarity in the Navier-Stokes (and similar) equations, and is the reason we observe complex flow features like turbulence.

 

[Ricochet J]

Thanks all.

Snip

Being a CFD man you might think it looks familiar - it's from the Ansys theory guide!

 

[Alex74]

(although I have seen that symbol used plenty of times to represent a general, non-specific, mathematical operator)

Yea it's a bit odd how this and the direct sum operator seem to just find use in many different contexts meaning very different things. Quite annoying actually . Mainly i find it's computer scientists trying to find some nice notation for their compound binary operations

But in the context of set theory it does sorta still work out intuitively I guess..

...This kind of notation is really not seen very often...

Unfortunately manifolds arent always very nice about their coordinate frames. I wish this statement were true in general but not in my world..


/tangent..

 

[RichIbizaSport]

Just burst out laughing at the dinosaur picture, I love his little top hat. Thank you for brightening up my Friday afternoon

 

[gjrc]

this

 

[Duff-Man]

Unfortunately manifolds arent always very nice about their coordinate frames. I wish this statement were true in general but not in my world..

Manifolds and set theory? That's like... REAL maths... Dirty, dirty stuff

I'll stick to vector calculus and other engineering related guff thanks! I'm glad to have left pure maths behind at undergrad level (I never had much talent for it either).


... and yes - the dinosaur picture is awesome. The top hat and monocle are what make it.

 

[Morbius]

Being a CFD man you might think it looks familiar - it's from the Ansys theory guide!

As soon as I saw the equations I thought, "Someone's doing some fluid dynamics."

I did a lot of fluid dynamics for my maths degree, it's difficult to forget.

 

[Dave]

This kind of notation is really not seen very often... It's far more convenient and efficient to use tensor notation (... with the Einstein summation convection).

I use Einstein summation when I'm looking at the equations myself, and then full hardcore vector notation (complete with tensor product) when explaining to others as 1) it looks impressive and 2) it frightens undergrads

OP - I'm going to be a complete pedant here and say that in the manual when it says "total energy equation" I believe that it should be "total enthalpy equation" - I always presumed that total energy would be tracking the time rate of change of the internal + kinetic energy. This does change the energy equation a little, although I suppose if you're using commercial codes then you're not really too fussed. Just as an FYI, I think that the FLUENT manual is generally a more "readable" source for things like this, indeed I think that it uses standard summation notation for the governing equations. Future useful reference for maths symbols: Wiki list of symbols.

 

[Alex74]

I use Einstein summation when I'm looking at the equations myself, and then full hardcore vector notation (complete with tensor product) when explaining to others as 1) it looks impressive and 2) it frightens undergrads ...

Oh you are the worst sort of person

Manifolds and set theory? That's like... REAL maths... Dirty, dirty stuff

I'll stick to vector calculus and other engineering related guff thanks! I'm glad to have left pure maths behind at undergrad level (I never had much talent for it either)..

Haha fair enough. It is all pretty beautiful once it all coalesces though

 

[andy_mk3]

It's a light bulb

 

[DrunkRufie]

I would have said it's a button from a playstation controller

 

[SoundsGood]

Radioactive waste

 

[Reaper 392]

in signal processing its either:
convolution
correlation
cross correlation
autocorrelation

i forget which one though... which isnt great considering i have an exam on this stuff on wednesday

*edit*
its convolution

 

[ince]

Times