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MODFLOW simulation. MODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation.The program is used by hydrogeologists to simulate the flow of groundwater through aquifers.
The above groundwater flow equations are valid for three dimensional flow. In unconfined aquifers, the solution to the 3D form of the equation is complicated by the presence of a free surface water table boundary condition: in addition to solving for the spatial distribution of heads, the location of this surface is also an unknown. This is a ...
Governing equations are used to mathematically define the behavior of the system. Algebraic equations are likely often used for simple systems, while ordinary and partial differential equations are often used for problems that change in space in time. Examples of governing equations include:
The Novak–Tyson Model is a non-linear dynamics framework developed in the context of cell-cycle control by Bela Novak and John J. Tyson. It is a prevalent theoretical model that describes a hysteretic , bistable bifurcation of which many biological systems have been shown to express.
This equation requires the system to be closed, and where it is not (for example when surface runoff contributes to a different basin), this must be taken into account. Extensive water balances are discussed in agricultural hydrology. A water balance can be used to help manage water supply and predict where there may be water shortages.
In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [ 1 ]
The McKendrick–von Foerster equation is a linear first-order partial differential equation encountered in several areas of mathematical biology – for example, demography [1] and cell proliferation modeling; it is applied when age structure is an important feature in the mathematical model. [2]
The eukaryotic cell cycle is very complex and is one of the most studied topics, since its misregulation leads to cancers. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups [1] [2] have produced several models of the cell cycle simulating several organisms. They ...