Potential energyIn physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to the ancient Greek philosopher Aristotle's concept of potentiality. Common types of potential energy include the gravitational potential energy of an object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field.
Gravitational energyGravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (converted into kinetic energy) when the objects fall towards each other. Gravitational potential energy increases when two objects are brought further apart. For two pairwise interacting point particles, the gravitational potential energy is given by where and are the masses of the two particles, is the distance between them, and is the gravitational constant.
Planar graphIn graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.
Gravitational potentialIn classical mechanics, the gravitational potential at a point in space is equal to the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point. It is analogous to the electric potential with mass playing the role of charge. The reference point, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance.
Elastic energyElastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. (Note however, the work done by a stretched rubber band is not an example of elastic energy. It is an example of entropic elasticity.
Electric potential energyElectric potential energy is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may be said to have electric potential energy by virtue of either its own electric charge or its relative position to other electrically charged objects. The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields.
Bipartite graphIn the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in red, each edge has endpoints of differing colors, as is required in the graph coloring problem.
Elastic modulusAn elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form: where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter.
Line graphIn the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.
Gravitational redshiftIn physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known more generally as a redshift. The opposite effect, in which photons (seem to) gain energy when travelling into a gravitational well, is known as a gravitational blueshift (a type of blueshift).
List of graphsThis partial list of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see . Some of the finite structures considered in graph theory have names, sometimes inspired by the graph's topology, and sometimes after their discoverer.
Elasticity (physics)In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.
Gravitational fieldIn physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenomena, and is measured in newtons per kilogram (N/kg). Equivalently, it is measured in meters per second squared (m/s2). In its original concept, gravity was a force between point masses.
Graph isomorphismIn graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection. If an isomorphism exists between two graphs, then the graphs are called isomorphic and denoted as . In the case when the bijection is a mapping of a graph onto itself, i.
Chordal graphIn the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree.
Petersen graphIn the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by .
ForceIn physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. It is measured in the SI unit of newton (N) and often represented by the symbol F.
Graph operationsIn the mathematical field of graph theory, graph operations are operations which produce new graphs from initial ones. They include both unary (one input) and binary (two input) operations. Unary operations create a new graph from a single initial graph. Elementary operations or editing operations, which are also known as graph edit operations, create a new graph from one initial one by a simple local change, such as addition or deletion of a vertex or of an edge, merging and splitting of vertices, edge contraction, etc.
Linear elasticityLinear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.
Chemical potentialIn thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system.
