Divergence of dyadic product of a dyadic and vector

In summary, the speaker is asking for help in finding the exact expression for taking the divergence of a triadic expression involving a dyadic product and a vector. They mention being able to take the divergence of a dyadic and suggest breaking down the triadic into a product of a dyadic and a vector. They are seeking assistance with this problem.
  • #1
praban
13
0
I would like to take divergence of the following expression

∇.((xi × xj × xk)/r^3), which is a triadic.

here × denote a dyadic product and r=mod(r vector) and xi, xj and xk are the components of r vector. So, the above eq. can also be written as

∇.((xixjxk ei×ej×ek)/r^3), where ei, ej and ek are unit vectors in i, j and kth directions.

I know how to take divergence of a dyadic. I guess that we can write the triadic as a product of dyadic and vector and then proceed. I am looking for the exact expression of the divergence of dyadic product of a dyadic and a vector.

I would appreciate any help.

Praban
 
Physics news on Phys.org
  • #2
praban said:
I know how to take divergence of a dyadic.
Then you can simply iterate the procedure: ##a\otimes b \otimes c= (a\otimes b ) \otimes c##.
 

Related to Divergence of dyadic product of a dyadic and vector

What is the definition of "divergence of dyadic product of a dyadic and vector"?

The divergence of dyadic product of a dyadic and vector is a mathematical operation that involves taking the dot product of a dyadic (a tensor with two indices) and a vector, and then taking the divergence of the resulting vector. It is commonly used in vector calculus and electromagnetic theory.

How is the divergence of dyadic product of a dyadic and vector calculated?

To calculate the divergence of dyadic product of a dyadic and vector, first take the dot product of the dyadic and vector, which results in a vector. Then, take the divergence of this vector by applying the del operator (∇) to it. The result is a scalar quantity.

What is the physical significance of the divergence of dyadic product of a dyadic and vector?

The physical significance of the divergence of dyadic product of a dyadic and vector is that it represents the rate at which a vector field is spreading or diverging at a given point. This is important in understanding the behavior of electromagnetic fields and other physical phenomena.

Is the divergence of dyadic product of a dyadic and vector a scalar or a vector quantity?

The divergence of dyadic product of a dyadic and vector is a scalar quantity. This is because it is the result of taking the divergence (a scalar operation) of a vector, which is already the dot product of a dyadic (a tensor with two indices) and a vector.

In what fields of science is the divergence of dyadic product of a dyadic and vector commonly used?

The divergence of dyadic product of a dyadic and vector is commonly used in fields such as electromagnetics, fluid mechanics, and continuum mechanics. It is also used in mathematical physics and engineering to analyze and solve problems involving vector fields and their behavior.

Similar threads

  • Linear and Abstract Algebra
Replies
7
Views
677
Replies
2
Views
1K
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
974
  • Differential Geometry
Replies
18
Views
17K
  • Calculus and Beyond Homework Help
Replies
5
Views
507
Replies
3
Views
2K
Replies
14
Views
1K
  • Linear and Abstract Algebra
Replies
4
Views
1K
Back
Top