# Scalar Field

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## scalar field

[′skā·lər ′fēld]
(mathematics)
The field consisting of the scalars of a vector space.
A function on a vector space into the scalars of the vector space.
(physics)
A field which is characterized by a function of position and time whose value at each point is a scalar.

## Scalar Field

a region with each of whose points P there is associated a number a(P) called a scalar. Mathematically, a scalar field can be defined in a given region G by specifying a scalar function a(P) of each point P of the region. Examples of scalar fields are the temperature field in a body and a density field. The methods of vector analysis are used to study scalar fields.

References in periodicals archive ?
In this paper, we will further analytically demonstrate that the vacuum polarization by the scalar field dark energy of 5D gravity can increase the relative optical path length (i.
n] (n = 1,2,3,4) are scalar fields that can, in general, be functions of Z.
So, in general terms the limit V [right arrow] [infinity] renders the system singular, and also 2[omega] + 3 [right] 0 implies [absolute value of H] [right arrow] [infinity] with the same conclusion that passing through [omega]([PSI]) = - 3/2 (corresponding to the change of the sign of the scalar field kinetic term in the Einstein frame action) would entail a space-time singularity and is impossible.
Choptuik M (1993) Universality and scaling in gravitational collapse of a massless scalar field, Phys.
The smooth paint in special room of valve has made without mass loss, divergence of scalar field, named solenoid being zero.
S] into a massive dark matter field and the scalar field [LAMBDA], and we have a compression factor which derivative is H c applied on any piece of the matter field [M.
The material time derivative of the scalar field f (r,t) [member of] R is its substantial derivative
Efficient methods for determining this scalar field are part of the paper.
Another 20 poster papers consider such topics as constraints on inflationary features in the primordial power spectrum with the Planck data, modeling the hierarchical evolution of galaxy clusters, future constraints on scalar field driven dark energy coupled with electromagnetism, looking for primordial non-Gaussianity using Minkowski functionals and neural networks, new constraints on interacting dark energy from Planck experiments, and a new geometrical approach to void statistics.
Recently, the author has developed a new mechanism for supernova explosion caused by gravitational field shielding [18], in accordance with his five-dimensional (5D) fully covariant Kaluza-Klein theory with a scalar field [8,19,20].
The second way that has also been comprehensively studied is the scalar-tensor (S-T) theory, which introduces a scalar field [phi], usually time-dependent, to the action of spacetime ([S.

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