In mathematical models and computer simulations, periodic boundary conditions (PBC) are a set of boundary conditions that are often used to simulate a large system by modelling a small part that is far from its edge. Periodic boundary conditions resemble the topologies of some video games; a unit cell or simulation box of a geometry suitable for perfect three-dimensional tiling is defined, and when an object passes through one face of the unit cell, it reappears on the opposite face with the same velocity. The simulation is of an infinite perfect tiling of the system. In topological terms, the space can be thought of as being mapped onto a torus. The tiled copies of the unit cell are called images, of which there are infinitely many. During the simulation, only the properties of the unit cell need be recorded and propagated. The minimum-image convention is a common form of PBC particle bookkeeping in which each individual particle in the simulation interacts with the closest image of the remaining particles in the system.
An example occurs in molecular dynamics, where PBC are usually applied to simulate bulk gasses, liquids, crystals or mixtures. A common application uses PBCs to simulate solvated macromolecules in a bath of explicit solvent.
Read more about Periodic Boundary Conditions: PBC Requirements and Artifacts, Practical Implementation: Continuity and The Minimum Image Convention, Unit Cell Geometries, Conserved Properties
Famous quotes containing the words boundary conditions, periodic, boundary and/or conditions:
“The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience.”
—Willard Van Orman Quine (b. 1908)
“It can be demonstrated that the child’s contact with the real world is strengthened by his periodic excursions into fantasy. It becomes easier to tolerate the frustrations of the real world and to accede to the demands of reality if one can restore himself at intervals in a world where the deepest wishes can achieve imaginary gratification.”
—Selma H. Fraiberg (20th century)
“In the west, Apollo and Dionysus strive for victory. Apollo makes the boundary lines that are civilization but that lead to convention, constraint, oppression. Dionysus is energy unbound, mad, callous, destructive, wasteful. Apollo is law, history, tradition, the dignity and safety of custom and form. Dionysus is the new, exhilarating but rude, sweeping all away to begin again. Apollo is a tyrant, Dionysus is a vandal.”
—Camille Paglia (b. 1947)
“The strong sunlight, the wind from the sea,
all the conditions of its existence,
may have flaked off the paint, if ever it was painted,
and made it homelier than it was.”
—Elizabeth Bishop (1911–1979)