Lattice in a sentence

This operation, understood as negation (¬), makes the lattice of subspaces a (possibly infinite ) orthocomplemented lattice (it is not a distributive lattice).

A diamond is a transparent crystal of tetrahedrally bonded carbon atoms in a covalent network lattice ( sp 3 ) that crystallizes into the diamond lattice which is a variation of the face centered cubic structure.

Another representation is obtained by noting that the image of any closure operator on a complete lattice is again a complete lattice (called its closure system).

Characteristics The three-dimensional crystal structure of H 2 O ice Ih (c) is composed of bases of H 2 O ice molecules (b) located on lattice points within the two-dimensional hexagonal space lattice (a).

Due to the face centered nature of the kamacite lattice and the body centered nature of the nickel lattice the two make intricate angles when they come in contact with each other.

First, although the subsets of a set form a set (as well as a lattice), in some classes it may not be possible to organize the subalgebras of an algebra as itself an algebra in that class, although they can always be organized as a lattice.

For instance, a lattice is a partially ordered set in which all finite subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum.

Garrett Birkhoff writes: "John von Neumann's brilliant mind blazed over lattice theory like a meteor". citation Von Neumann founded the field of continuous geometry based on lattice theoretic principles.

If the lattice Λ is related by multiplication by a non-zero complex number c to a lattice cΛ, then the corresponding curves are isomorphic.

In order that the quasicrystal itself be aperiodic, this slice must avoid any lattice plane of the higher-dimensional lattice.

In summary, one can say that every complete lattice is isomorphic to the image of a closure operator on a powerset lattice.

It has a face-centered cubic crystal lattice and no change in pressure can produce a lattice with a lower energy state.

Lattice QCD main A quark and an antiquark (red color) are glued together (green color) to form a meson (result of a lattice QCD simulation by M. Cardoso et al.

Now, the correlation length is the relevant length scale related to critical phenomena, so one can, e.g., surmise on "dimensional grounds" that the non-analytical part of the free energy per lattice site should be where is the dimension of the lattice.

Others make use of lattice field theory and call themselves lattice theorists.

Pythagorean triangles in a 2D lattice A 2D lattice is a regular array of isolated points where if any one point is chosen as the Cartesian origin (0, 0), then all the other points are at (x, y) where x and y range over all positive and negative integers.

Small amounts of defects or impurities (about one per million of lattice atoms) color diamond blue (boron), yellow (nitrogen), brown ( lattice defects ), green (radiation exposure), purple, pink, orange or red.

So the path-integral can be thought of as on a discrete square lattice, with lattice spacing and the limit should be taken carefully.

The lattice as a whole recoils but the recoil energy is negligible because the M in the above equation is the mass of the whole lattice.

This fact may be used to efficiently enumerate the simplex's face lattice, since more general face lattice enumeration algorithms are more computationally expensive.