Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell. PBCs are often used in computer simulations and mathematical models. The topology of two-dimensional PBC is equal to that of a world map of some video games; the geometry of the unit cell satisfies perfect two-dimensional tiling, and when an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by two-dimensional PBCs can be thought of as being mapped onto a torus (compactification). The large systems approximated by PBCs consist of an infinite number of unit cells. In computer simulations, one of these is the original simulation box, and others are copies called images. During the simulation, only the properties of the original simulation box need to 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.
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator.
To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.
NHSE can occur in different spatial dimensions and is closely related to the system's open boundary conditions (OBC) ... In 1D, NHSE arises from point gaps, where energy spectra under periodic boundary conditions form loops in the complex plane.
The SPF is a value similar to the coefficient of performance (COP), with the difference it is calculated over a longer period with varying boundary conditions ... “During the periods of high grid ...
list 3 of 4Australia use conditions and the toss to win World Cup, Indian legends say ...India’s boundary count ... However, Shreyas Iyer’s dismissal in the 11th over set off a boundary-less period of play that lasted more than an hour and 90 balls.
Due to the use of periodic boundary conditions in meta-atom design and aperiodic boundary conditions in the array simulation process, the mutual coupling between different meta-atoms causes unavoidable inaccuracy.
A little more bat on it and the ball would have headed to the boundary ...Root was surprised by the rising trajectory of the ball and was caught at mid-wicket, Stokes tried to dispatch Wagner to the boundary but was caught too.
Reconstructing Cretaceous conditions ... In all three cores, the researchers focused on sections from the mid-Cretaceous Period, just before the boundary of the Turonian and Cenomanian Ages, in order to reconstruct conditions leading up to OAE2.
The X-ray irradiation is expected to heat the companion star and change its effective surface boundary condition, which then attenuates the mass transfer rate of the binary system ... periodically.
... the boundary ... When choosing the open boundary condition and the periodic boundary condition in different directions, the system exhibits different kinds of PT symmetries for different kinds of edges.
