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For many years the lack of well-warranted covering laws seemed to be the chief difficulty with this conception of historical explanation, but chaos theory has recently raised another problem: the boundary conditions cannot be exactly specified.
As unpredictable processing and boundary conditions cannot be simulated in the process planning phase, a process parallel simulation of the workpiece temperature is required to observe and compensate thermal effects.
The series solution obtained in this way converges rapidly and provides practically acceptable results even in cases with one or more free edges, where the boundary conditions cannot be strictly satisfied.
First, it is shown herein that if one adopts the classical thin plate theory and the Galerkin's method with commonly used modal functions consisting of the products of free free beam modes, the natural boundary conditions cannot be satisfied at the free edges and the shear forces are completely erroneous, even when the eigenvalues have already converged.
In general, the framework of linear boundary conditions cannot be directly translated to this new situation.
In the case of short slopes for which boundary conditions cannot be ignored.
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As the ABLs develop over a no-flat terrain with heterogeneous roughness elements, standard ABL-LES with cyclic boundary condition cannot be used.
Control conditions cannot be selected arbitrarily.
The equation is degenerate on the boundary, accordingly, the usual boundary value condition cannot be imposed in Dirichlet's way.
Thus, if one wants to prove the uniqueness or the stability of the weak solutions, the boundary value condition cannot be used in the usual way.
Future directions of research will take into account that the approximation of periodic boundary conditions cannot easily be maintained for the modeling of dilute defects embedded in a regular crystalline environment.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com