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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.
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 tilings obtained from an aperiodic set of tiles are often called aperiodic tilings , though strictly speaking it is the tiles themselves that are ...
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]
Benign: present in some organisms, sometimes bioaccumulating, but generally having no apparent effects (except possible harmful effects, notes "a" or "b"). 1 Extremely rare on the Earth's surface (less than 1×10 −7 %, i.e. less than 1/10 as common as the least common essential element, selenium), thus has low potential for any kind of ...
Biotic material, natural material, or natural product, a material produced by a living organism; Biomass, living or dead biological matter, often plants grown as fuel; Biomass (ecology), the total mass of living matter in a given environment, or of a given species; Body fluid, any liquid originating from inside the bodies of living people
The history of aperiodic crystals can be traced back to the early 20th century, when the science of X-ray crystallography was in its infancy. At that time, it was generally accepted that the ground state of matter was always an ideal crystal with three-dimensional space group symmetry, or lattice periodicity.
A trace element is a chemical element of a minute quantity, a trace amount, especially used in referring to a micronutrient, [1] [2] but is also used to refer to minor elements in the composition of a rock, or other chemical substance.
Metal ions in biology were studied in various specializations. In nutrition , it was to define the essentials for life; in toxicology , to define how the adverse effects of certain metal ions in biological systems and in pharmacology for their therapeutic effects. [ 2 ]