Search results
Results from the WOW.Com Content Network
A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.
The translation in the language of neighborhoods of the (,)-definition of continuity leads to the following definition of the continuity at a point: A function f : X → Y {\displaystyle f:X\to Y} is continuous at a point x ∈ X {\displaystyle x\in X} if and only if for any neighborhood V of f ( x ) {\displaystyle f(x)} in Y , there is a ...
The definition of probability current and Schrödinger's equation can be used to derive the continuity equation, which has exactly the same forms as those for hydrodynamics and electromagnetism. [6] For some wave function Ψ, let:
This equation is called the mass continuity equation, or simply the continuity equation. This equation generally accompanies the Navier–Stokes equation. In the case of an incompressible fluid, Dρ / Dt = 0 (the density following the path of a fluid element is constant) and the equation reduces to:
Continuity (fiction), consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun) Continuity (setting) , one of several similar but distinct fictional universes in a broad franchise of related works (this is a count noun)
If electromagnetic energy is not gained from or lost to other forms of energy within some region (e.g., mechanical energy, or heat), then electromagnetic energy is locally conserved within that region, yielding a continuity equation as a special case of Poynting's theorem: = where is the energy density of the electromagnetic field. This ...
The velocity satisfies the continuity equation for incompressible flow: ∇ ⋅ u = 0. {\displaystyle \quad \nabla \cdot \mathbf {u} =0.} Although in principle the stream function doesn't require the use of a particular coordinate system, for convenience the description presented here uses a right-handed Cartesian coordinate system with ...
This is called the charge density continuity equation + = The term on the left is the rate of change of the charge density ρ at a point. The term on the right is the divergence of the current density J at the same point. The equation equates these two factors, which says that the only way for the charge density at a point to change is for a ...