Drip irrigationDrip irrigation or trickle irrigation is a type of micro-irrigation system that has the potential to save water and nutrients by allowing water to drip slowly to the roots of plants, either from above the soil surface or buried below the surface. The goal is to place water directly into the root zone and minimize evaporation. Drip irrigation systems distribute water through a network of valves, pipes, tubing, and emitters.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Joint (geology)A joint is a break (fracture) of natural origin in a layer or body of rock that lacks visible or measurable movement parallel to the surface (plane) of the fracture ("Mode 1" Fracture). Although joints can occur singly, they most frequently appear as joint sets and systems. A joint set is a family of parallel, evenly spaced joints that can be identified through mapping and analysis of their orientations, spacing, and physical properties. A joint system consists of two or more intersecting joint sets.
Laplace's equationIn mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as or where is the Laplace operator, is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function.
Flow netA flow net is a graphical representation of two-dimensional steady-state groundwater flow through aquifers. Construction of a flow net is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical. The method is often used in civil engineering, hydrogeology or soil mechanics as a first check for problems of flow under hydraulic structures like dams or sheet pile walls. As such, a grid obtained by drawing a series of equipotential lines is called a flow net.
Clique-widthIn graph theory, the clique-width of a graph G is a parameter that describes the structural complexity of the graph; it is closely related to treewidth, but unlike treewidth it can be small for dense graphs. It is defined as the minimum number of labels needed to construct G by means of the following 4 operations : Creation of a new vertex v with label i (denoted by i(v)) Disjoint union of two labeled graphs G and H (denoted by ) Joining by an edge every vertex labeled i to every vertex labeled j (denoted by η(i,j)), where i ≠ j Renaming label i to label j (denoted by ρ(i,j)) Graphs of bounded clique-width include the cographs and distance-hereditary graphs.
Euler–Lagrange equationIn the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it.
TreewidthIn graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests. The graphs with treewidth at most 2 are the series–parallel graphs. The maximal graphs with treewidth exactly k are called k-trees, and the graphs with treewidth at most k are called partial k-trees. Many other well-studied graph families also have bounded treewidth.
Plucking (glaciation)Plucking, also referred to as quarrying, is a glacial phenomenon that is responsible for the weathering and erosion of pieces of bedrock, especially large "joint blocks". This occurs in a type of glacier called a "valley glacier". As a glacier moves down a valley, friction causes the basal ice of the glacier to melt and infiltrate joints (cracks) in the bedrock. The freezing and thawing action of the ice enlarges, widens, or causes further cracks in the bedrock as it changes volume across the ice/water phase transition (a form of hydraulic wedging), gradually loosening the rock between the joints.
ScreeScree is a collection of broken rock fragments at the base of a cliff or other steep rocky mass that has accumulated through periodic rockfall. Landforms associated with these materials are often called talus deposits. Talus deposits typically have a concave upwards form, where the maximum inclination corresponds to the angle of repose of the mean debris particle size. The exact definition of scree in the primary literature is somewhat relaxed, and it often overlaps with both talus and colluvium.
