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The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 2).
The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.
Examples of graded potentials. Graded potentials are changes in membrane potential that vary according to the size of the stimulus, as opposed to being all-or-none.They include diverse potentials such as receptor potentials, electrotonic potentials, subthreshold membrane potential oscillations, slow-wave potential, pacemaker potentials, and synaptic potentials.
In materials science Functionally Graded Materials (FGMs) may be characterized by the variation in composition and structure gradually over volume, resulting in corresponding changes in the properties of the material. The materials can be designed for specific function and applications.
The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of potential are mixed under Lorentz transformations. Practically, the electric potential is a continuous function in all space, because a spatial derivative of a discontinuous electric potential yields an electric field of impossibly ...
Because the atmospheric electric field is negatively directed (meaning toward the ground) in fair weather, the convention is to refer to the potential gradient, which has the opposite sign (meaning the electrical potential increases with distance from the ground) and is about 100 V/m at the surface, at a distance from thunderstorms. [6]
The potential has units of energy per mass, e.g., J/kg in the MKS system. By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero. The gravitational field, and thus the acceleration of a small body in the space around the massive object, is the negative gradient of the gravitational potential ...
For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.