Hence, the inflationary scalar potential
needs symmetries to protect it from dangerous quantum corrections.
The new total vector field is consistent with Helmholtz's theorem, which states that any physical vector field can be expressed as the sum of the gradient of a zero-rotational scalar potential
and the curl of a zero-divergence vector potential .
mu]-] = ([PSI] / c, -D) 4-potential of gravitational field which is described through scalar potential
f and vector potential D of this field,
c] together with scalar electric potential combined with the use of magnetic scalar potential
in the non-conducting area (Ciric, 2007).
In general, STG form a collection of theories which contain two functional degrees of freedom, a coupling function [omega]([PSI]), and a scalar potential
Different potentials have been used for the eddy current problem: a vector potential A for the magnetic field, a scalar potential
V for the electric field in the conducting domain, a scalar magnetic potential [psi] in dielectric domains, etc.
As they simultaneously cover a new computer-aided design technology and give applications, they describe hierarchical basis functions for triangles and tetrahedra, finite element formulations of electromagnetic BVPs, iterative methods, preconditioners, the multigrid, the nested multigrid preconditioner, the nested multigrid vector and scalar potential
preconditioner, hierarchical multilevel and hybrid potential preconditioners, Eigenvalue analysis (Krylov-subspace based, two-dimensional analysis of waveguides and three-dimensional analysis of resonators), model order reduction of electromagnetic systems, and finite element analysis of periodic structures.
where [phi] is the magnetic scalar potential
and [rho] = [square root of ([y.
e] = -GM/r is the gravitational scalar potential
in a spherically symmetric gravitational field, r > R, the radius of the homogeneous sphere, G is the universal gravitational constant, c is the speed of light in vacuum, [m.
This element is based on the electric scalar potential
formulation, and it is applicable to a 2D electrostatic and time-harmonic quasi-static electric field analyses.
where [PHI] = -GM/r is the gravitational scalar potential
in Schwarzschild's gravitational field.
where [PHI] is Newton's gravitational scalar potential
for the field under consideration.