Q:What is the analogue of the excitation vector in the case of mass density?

In summary, there is a 2-form, known as "excitation" (D), that is equivalent to the electric charge density 3-form. This is described by the Gauss-law equation, one of Maxwell's equations. In fluid-dynamics, there must also be a counterpart to this equation involving the mass density. Similarly, there is a counterpart to the Oersted-Ampere law in fluid-dynamics, which is derived from the continuity equation and the Gauss-law. Both of these equations involve the magnetic excitation field (H), which is a 1-form field. These equations and quantities are used in both electrodynamics and fluid-dynamics.
  • #1
mma
245
1
Mass density is a 3-form, just like electric charge density. Hence it's exterior derivative is 0. This implies that there is a 2-form whose exterior derivative is the density 3-form. If this density is the electric charge density, then the name of this 2-form is "excitation" (D). But what is the name of it in the case when we speak about mass density instead off electric charge density? And where is it used?
 
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  • #2
Of course the above mentioned D excitation is the electric excitation (other name of it is electric displacement field). The equation which states that the exterior derivative of the electric excitation is the electric charge density is the so-called Gauss-law, and this is one of 4 the Maxwell's equations. And this equation must have a counterpart in fluid-dynamics, where the mass density plays the role of the electric charge density in this equation.

Moreover, there is another Maxwell's equation what must have a counterpart in fluid-dynamic. This is the Oersted-Ampere law. This equation follows directly from the continuity equation and from the Gauss-law. Regarding that both equations are valid not only in electrodynamics but in fluid-dynamics also, there must be a corresponding equation in fluid-dynamics, i.e. there must be a counterpart of the magnetic excitation field (H) also (this is an 1-form field).

Does anybody use these equations and quantities in fluid-dynamics?
 
  • #3
I mean eqations (3.1) and (3.2) in http://arxiv.org/abs/physics/0005084"
 
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Related to Q:What is the analogue of the excitation vector in the case of mass density?

What is the analogue of the excitation vector in the case of mass density?

The analogue of the excitation vector in the case of mass density is the displacement vector, which describes the change in position of a particle or medium in response to a force or disturbance.

How is the displacement vector related to mass density?

The displacement vector is directly related to mass density through the equation ρ = m/V, where ρ is the mass density, m is the mass of the particle or medium, and V is the volume. This means that the greater the mass density, the larger the displacement vector will be in response to a force.

What is the significance of the displacement vector in the study of mass density?

The displacement vector is significant in the study of mass density because it allows us to understand how a material or medium responds to external forces. It helps us quantify the amount of displacement that occurs, which can provide insights into the material's physical properties and behavior.

How is the displacement vector measured?

The displacement vector can be measured in various ways, depending on the specific situation. In some cases, it can be measured directly using instruments such as displacement sensors or accelerometers. In other cases, it can be calculated using mathematical formulas based on known values of force and mass density.

Can the displacement vector be used to determine the mass density of a material?

Yes, the displacement vector can be used to determine the mass density of a material by rearranging the equation ρ = m/V to solve for m. This can be done by measuring the displacement vector and the volume of the material and then plugging those values into the equation. However, it is important to note that this method may not be accurate for materials with varying densities or complex structures.

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