Two-Dimensional Problem

Two-Dimensional Problem

 

a type of problem in mathematical physics. It arises when (1) the pattern of the phenomenon under study is the same in all planes parallel to a given plane or (2) as a result of disregarding one of three dimensions, a problem is reduced to a two-dimensional problem.

Areas where two-dimensional problems are encountered include the theory of elasticity, hydromechanics, aeromechanics, the theory of electricity, and the theory of heat conduction. In elasticity theory, for example, the two-dimensional problem arises when the lateral surface of an infinitely long cylinder is subjected to a load that is constant along each generatrix of the cylinder. To study phenomena inside the cylinder it is sufficient to study the phenomena in any of the planes perpendicular to its generatrices. If the phenomenon under study is steady-state— that is, if the pattern of the phenomenon does not vary with time —then the solution of the two-dimensional problem is in many cases associated with the theory of the functions of a complex variable and is carried out by the methods of conformal mapping. An example is the problem of the lines of flow around objects with different profiles in hydrodynamics and aerodynamics.

References in periodicals archive ?
The hypothesis that is used generally in current calculations of sustainability of gables is plane strain behavior, or in other words, a two-dimensional problem solution, there is a variety of three-dimensional soil behavior, and it is assumed that the two-dimensional problem does not lead to good solutions.
Let's accept additional notations and consider the purpose of simplification a two-dimensional problem only.
A two-dimensional problem can make many connections to other disciplines.
Web registration is essentially a planar or two-dimensional problem for a printer, but it becomes more complex when four colors are involved.
The solution of a two-dimensional problem with the holes and N = [1023.
An alternative preconditioner for Lagrange multipliers in two-dimensional problems based on the H(div)-inner product was studied in [25].
Focusing on two-dimensional problems utilizing linear elements, he explains the basic and essential aspects in CVFEM and basic constructions in the context of solving fundamental problems in both solids and fluids.
Table 3 presents the results obtained in solving three investigated two-dimensional problems.
For the two-dimensional problems presented, the SubDivNL algorithm was able to find simultaneously all the roots, from only one seek interval, without presenting convergence problems.
This visual strategy simplifies such tasks by turning them into two-dimensional problems, McBeath's group concludes.
5-7 Polynomial Solutions of Two-Dimensional Problems in Rectangular Cartesian Coordinates.
Papers on two-dimensional algorithms address such topics as elliptic barrier-type grid generators for problems with moving boundaries, a class of quasi-isometric grids, triangle distortions under quasi-isometries, grid optimization and adaptation, moving mesh calculations in unsteady two-dimensional problems, generation of curvilinear grids in multiply connected domains of complex topology.

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