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In most projections, scale varies with latitude, so on small scale maps, covering large areas and a wide range of latitudes, the linear scale must show the scale for the range of latitudes covered by the map. One of these is shown below. Since most nautical charts are constructed using the Mercator projection whose scale varies substantially ...
The Wiener process is scale-invariant. 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).
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right). In science and engineering , a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes.
Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
Scale analysis is very useful and widely used tool for solving problems in the area of heat transfer and fluid mechanics, pressure-driven wall jet, separating flows behind backward-facing steps, jet diffusion flames, study of linear and non-linear dynamics.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
For example, in D = 4, only g 4 is classically dimensionless, and so the only classically scale-invariant scalar field theory in D = 4 is the massless φ 4 theory. Classical scale invariance, however, normally does not imply quantum scale invariance, because of the renormalization group involved – see the discussion of the beta function below.