In this approach one sets up the dimensional equation and solves it as far as one can.
2.
Other much studied periodic one-dimensional equations are the Kronig Penney model and Mathieu's equation.
3.
We now have four fundamental parameters, and one dimensionless constant, so that the dimensional equation may be written:
4.
ZOOMQ3D takes a simplifying approach to the solution of the three-dimensional equation by recognising that in many aquifers it is possible to identify a layered structure.
5.
A dimensional equation can have the dimensions reduced or eliminated through nondimensionalization, which begins with dimensional analysis, and involves scaling quantities by characteristic units of a system or natural units of nature.
6.
Any one-dimensional equation of order n is equivalent to an n-dimensional first-order system ( as described in Ordinary differential equation # Reduction to a first order system ), but not necessarily vice versa.
7.
If the layers are aligned parallel to the horizontal coordinate axes, then the three-dimensional equation can be integrated vertically across the layer to produce an equation which describes the flow within a layer and its interactions with adjacent layers.
8.
In this case, a properly conditioned one-dimensional equation may fully describe the system . ( It is more likely that spherical coordinates are used, rather than " sheets " or " lines ", which would be reduced-dimension Cartesian coordinates ).
9.
The three-dimensional equation f = ma does hold in the lab frame in this situation, with m being object 2's relativistic mass, which implies that object 2's acceleration is smaller as measured in the lab frame than in the objects'rest frame by a factor of 1 / ? 2.
10.
There are three fundamental variables so the above five equations will yield two dimensionless variables which we may take to be \ pi _ 1 = \ dot { m } / \ eta r and \ pi _ 2 = p _ \ mathrm { x } \ rho r ^ 5 / \ dot { m } ^ 2 and we may express the dimensional equation as
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