For the three-dimensional, incompressible Navier Stokes equation with periodic boundary conditions, if it has a global attractor, then this attractor will be of finite dimensions.
22.
The applications in specific areas of conjugate heat transfer at periodic boundary conditions and in exchanger ducts are considered in books [ 11 ] and [ 12 ], respectively.
23.
To achieve the desired normalization we pretend space is divided into cubes of volume " L " 3 } } and impose on the field the periodic boundary condition:
24.
The "'Car & ndash; Parrinello method "'is a type of molecular dynamics, usually employing periodic boundary conditions, planewave Dirac Medal by ICTP in 2009.
25.
These boundary conditions can represent real boundaries such as concrete walls or the surface of a pond, or can be used to represent an artificial infinite system using a periodic boundary condition.
26.
The compact dimension imposes specific boundary conditions on all fields, for example periodic boundary conditions in the case of a periodic dimension, and typically Neumann or Dirichlet boundary conditions in other cases.
27.
The Lax-Friedrichs solution at time t = 1 for the illustration problem in the Lax Friedrichs method article modified to have periodic boundary conditions with the discontinuous initial condition shown in the article.
28.
Applied to the illustration problem in the Lax Friedrichs method article modified to have periodic boundary conditions; if a = 1 the exact solution at time t = 1 is identical to this initial condition.
29.
When run on a finite array of cells with periodic boundary conditions, starting from a small seed of random cells centered within a larger empty neighborhood, it tends to fluctuate between ordered and chaotic states.
30.
The notation \ langle A ( \ mathbf { s } ) \ rangle indicates the expectation of the random variable in the infinite volume limit, after " periodic boundary conditions " have been imposed.
