gradient

(noun)

The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.

Related Terms

Examples of gradient in the following topics:

  • Electric Field and Changing Electric Potential

    • Electric field is the gradient of potential, which depends inversely upon distance of a given point of interest from a charge.
    • Electric field is the gradient of potential, which depends inversely upon distance of a given point of interest from a charge.
    • The relationship between potential and field (E) is a differential: electric field is the gradient of potential (V) in the x direction.

  • Vertical Structure

    • The pressure gradient in the disk must resist the vertical component of gravity.
    • We can do a bit better than this by calculating the temperature gradient through the disk.

  • Kelvin-Helmholtzor Shearing Instability

    • These pressure gradient causes the wrinkle to grow.

  • Diffusion

    • However, diffusion can still occur in the absence of a concentration gradient.

  • Electromagnetic Potentials

    • Only the electric and magnetic fields are measurable so we can make any change to the potentials ${\bf A}$ and $\phi$ that we want as long at ${\bf E}$ and $\bf B$ remain unchanged.Because ${\bf B} = \nabla \times {\bf A}$ we can add the gradient of any function $\psi$ to ${\bf A}$ without changing ${\bf B}$ (the curl of a gradient of a function is zero).
    • However, if we add a gradient of function to ${\bf A}$ the value of ${\bf E}$ is affected,

  • Other Geophysical Applications

    • The pressure-gradient force is represented by blue arrows and the Coriolis acceleration (always perpendicular to the velocity) by red arrows

  • Angular Momentum Transport

    • The viscous stress is proportional to the viscosity and the angular velocity gradient,

  • Tides

    • Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).
    • On average, the solar gravitational force on the Earth is 179 times stronger than the lunar, but because the sun is on average 389 times farther from the Earth its field gradient is weaker.

  • Heat Pumps and Refrigerators

    • A heat pump is a device that transfers heat energy from a heat source to a heat sink against a temperature gradient.

  • The Coriolois Force

    • This low-pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force.