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A flow is a process in which the points of a space continuously change their locations or properties over time. More specifically, in a one-dimensional geometric flow such as the curve-shortening flow, the points undergoing the flow belong to a curve, and what changes is the shape of the curve, its embedding into the Euclidean plane determined by the locations of each of its points. [2]
As such, parabolic LCSs are composed of shrink lines and stretch lines that represent geodesics of the Lorentzian metric tensor. In contrast to hyperbolic LCSs, however, parabolic LCSs satisfy more robust boundary conditions: they remain stationary curves of the material-line-averaged shear functional even under variations to their endpoints.
An example is the linear map that takes any point with coordinates (,) to the point (+,). In this case, the displacement is horizontal by a factor of 2 where the fixed line is the x-axis, and the signed distance is the y-coordinate. Note that points on opposite sides of the reference line are displaced in opposite directions.
Horizontal deformation in mid-latitude cyclones concentrates temperature gradients—cold air from the poles and warm air from the equator.. Horizontal shear has two effects on an air parcel; it tends to rotate the parcel (think of placing a wheel at a point in space and as the wind blows, the wheel rotates) and deform the parcel through stretching and shrinking.
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).
By convention, the strain is set to the horizontal axis and stress is set to vertical axis. Note that for engineering purposes we often assume the cross-section area of the material does not change during the whole deformation process. This is not true since the actual area will decrease while deforming due to elastic and plastic deformation.
Researchers have produced conflicting results when it comes to the best pre-workout stretch. For example, a well-cited August 2003 study showed evidence of static stretching for warm-ups worsening ...
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...