Aeolian processesAeolian processes, also spelled eolian, pertain to wind activity in the study of geology and weather and specifically to the wind's ability to shape the surface of the Earth (or other planets). Winds may erode, transport, and deposit materials and are effective agents in regions with sparse vegetation, a lack of soil moisture and a large supply of unconsolidated sediments. Although water is a much more powerful eroding force than wind, aeolian processes are important in arid environments such as deserts.
Boundary value problemIn the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.
Neumann boundary conditionIn mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.
Headward erosionHeadward erosion is erosion at the origin of a stream channel, which causes the origin to move back away from the direction of the stream flow, lengthening the stream channel. It can also refer to the widening of a canyon by erosion along its very top edge, when sheets of water first enter the canyon from a more roughly planar surface above it, such as at Canyonlands National Park in Utah. When sheets of water on a roughly planar surface first enter a depression in it, this erodes the top edge of the depression.
Cauchy boundary conditionIn mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.
Mixed boundary conditionIn mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.
Fractal dimensionIn mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.
Erosion and tectonicsThe interaction between erosion and tectonics has been a topic of debate since the early 1990s. While the tectonic effects on surface processes such as erosion have long been recognized (for example, river formation as a result of tectonic uplift), the opposite (erosional effects on tectonic activity) has only recently been addressed. The primary questions surrounding this topic are what types of interactions exist between erosion and tectonics and what are the implications of these interactions.
Fluvial processesIn geography and geology, fluvial processes are associated with rivers and streams and the deposits and landforms created by them. When the stream or rivers are associated with glaciers, ice sheets, or ice caps, the term glaciofluvial or fluvioglacial is used. Fluvial processes include the motion of sediment and erosion or deposition on the river bed. The movement of water across the stream bed exerts a shear stress directly onto the bed.
Drainage system (agriculture)An agricultural drainage system is a system by which water is drained on or in the soil to enhance agricultural production of crops. It may involve any combination of stormwater control, erosion control, and watertable control. While there are more than two types of drainage systems employed in agriculture, there are two main types: (1) surface drainage and (2) sub-surface drainage. Figure 1 classifies the various types of drainage systems. It shows the field (or internal) and the main (or external) systems.
