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When the scale factor is larger than 1, (uniform or non-uniform) scaling is sometimes also called dilation or enlargement. When the scale factor is a positive number smaller than 1, scaling is sometimes also called contraction or reduction. In the most general sense, a scaling includes the case in which the directions of scaling are not ...
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation).
Here is the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement if the scale factor exceeds 1. The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude.
Dilation (physics), size increase Thermal expansion of crystalline triglycerides is referred to as dilation; Scale invariance, a feature of objects or laws that do not change if length scales (or energy scales) are multiplied by a common factor
In a scale invariant quantum field theory, by definition each operator acquires under a dilation a factor , where is a number called the scaling dimension of . This implies in particular that the two point correlation function O ( x ) O ( 0 ) {\displaystyle \langle O(x)O(0)\rangle } depends on the distance as ( x 2 ) − Δ {\displaystyle (x^{2 ...
Dilation is commutative, also given by = =. If B has a center on the origin, then the dilation of A by B can be understood as the locus of the points covered by B when the center of B moves inside A. The dilation of a square of size 10, centered at the origin, by a disk of radius 2, also centered at the origin, is a square of side 14, with ...
Here the radial position has been decomposed into a time-dependent scale factor, (), and a comoving coordinate, . Inserting this metric into Einstein's field equations relate the evolution of this scale factor to the pressure and energy of the matter in the universe.
A scale factor of 1 ⁄ 10 cannot be used here, because scaling 160 by 1 ⁄ 10 gives 16, which is greater than the greatest value that can be stored in this fixed-point format. However, 1 ⁄ 11 will work as a scale factor, because the maximum scaled value, 160 ⁄ 11 = 14. 54, fits within this range. Given this set: