PseudoelasticityPseudoelasticity, sometimes called superelasticity, is an elastic (reversible) response to an applied stress, caused by a phase transformation between the austenitic and martensitic phases of a crystal. It is exhibited in shape-memory alloys. Pseudoelasticity is from the reversible motion of domain boundaries during the phase transformation, rather than just bond stretching or the introduction of defects in the crystal lattice (thus it is not true superelasticity but rather pseudoelasticity).
Nearest neighbor searchNearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth in vol.
Icosahedral twinsAn icosahedral twin is a nanostructure appearing in atomic clusters and also nanoparticles with some thousands of atoms. These clusters are twenty-faced, with twenty interlinked tetrahedral crystals joined along triangular (e.g. cubic-(111)) faces having three-fold symmetry. A related, more common structure has five units similarly arranged with twinning, which were known as "fivelings" in the 19th century, more recently as "decahedral multiply twinned particles", "pentagonal particles" or "star particles".
Aperiodic tilingAn 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. In March 2023, four researchers, David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, announced the proof that the tile discovered by David Smith is an aperiodic monotile, i.
PentagonIn geometry, a pentagon (from the Greek πέντε pente meaning five and γωνία gonia meaning angle) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram. A regular pentagon has Schläfli symbol {5} and interior angles of 108°. A regular pentagon has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°).
