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In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns ) obtained in X-ray , electron and neutron ...
In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization.
In the context to structural analysis, a structure refers to a body or system of connected parts used to support a load. Important examples related to Civil Engineering include buildings, bridges, and towers; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important.
In condensed matter physics, the dynamic structure factor (or dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space and time.
Static structure factor of the hard-spheres liquid in Percus–Yevick approximation at three different packing ratios. For hard spheres, the potential u(r) is either zero or infinite, and therefore the Boltzmann factor / is either one or zero, regardless of temperature T. Therefore structure of a hard-spheres fluid is temperature independent.
Atoms with low B-factors belong to a part of the structure that is well ordered. Atoms with large B-factors generally belong to part of the structure that is very flexible. Each ATOM record (PDB file format) of a crystal structure deposited with the Protein Data Bank contains a B-factor for that atom.
A clear distinction is made between the ultimate state (US) and the ultimate limit state (ULS). The Ultimate State is a physical situation that involves either excessive deformations leading and approaching collapse of the component under consideration or the structure as a whole, as relevant, or deformations exceeding pre-agreed values.
One can determine () indirectly (via its relation with the structure factor ()) using neutron scattering or x-ray scattering data. The technique can be used at very short length scales (down to the atomic level [ 10 ] ) but involves significant space and time averaging (over the sample size and the acquisition time, respectively).