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An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3]
The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings. The Penrose tilings are a well-known example of aperiodic tilings. [1] [2]
A material is a substance or mixture of substances that constitutes an object.Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geological origin or biological function.
Trending cyclostationary processes have several applications in finance, engineering, economics, and environmental research. Trending cyclostationary processes are used in economics to predict the seasonality and trend of time series data that display both periodic and trending behavior, such as rail and air travel demand. [2]
Non-metallic inclusions are chemical compounds and nonmetals that are present in steel and other alloys.They are the product of chemical reactions, physical effects, and contamination that occurs during the melting and pouring process.
Nonmetallic material, or in nontechnical terms a nonmetal, refers to materials which are not metals. Depending upon context it is used in slightly different ways. In everyday life it would be a generic term for those materials such as plastics, wood or ceramics which are not typical metals such as the iron alloys used in bridges.