Grain boundaryIn materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep.
Grain growthIn materials science, grain growth is the increase in size of grains (crystallites) in a material at high temperature. This occurs when recovery and recrystallisation are complete and further reduction in the internal energy can only be achieved by reducing the total area of grain boundary. The term is commonly used in metallurgy but is also used in reference to ceramics and minerals. The behaviors of grain growth is analogous to the coarsening behaviors of grains, which implied that both of grain growth and coarsening may be dominated by the same physical mechanism.
Abnormal grain growthAbnormal or discontinuous grain growth, also referred to as exaggerated or secondary recrystallisation grain growth, is a grain growth phenomenon through which certain energetically favorable grains (crystallites) grow rapidly in a matrix of finer grains resulting in a bimodal grain size distribution. In ceramic materials this phenomenon can result in the formation of elongated prismatic, acicular (needle-like) grains in a densified matrix with implications for improved fracture toughness through the impedance of crack propagation.
PolygonIn geometry, a polygon (ˈpɒlɪɡɒn) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain.
Convex polytopeA convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue.
Gibbs free energyIn thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy.
Monotone polygonIn geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects the boundary of P at most twice. Similarly, a polygonal chain C is called monotone with respect to a straight line L, if every line orthogonal to L intersects C at most once. For many practical purposes this definition may be extended to allow cases when some edges of P are orthogonal to L, and a simple polygon may be called monotone if a line segment that connects two points in P and is orthogonal to L lies completely in P.
SimulationA simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.
Harmonic oscillatorIn classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
Computer simulationComputer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.
Polygon partitionIn geometry, a partition of a polygon is a set of primitive units (e.g. squares), which do not overlap and whose union equals the polygon. A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example a partition with a smallest number of units or with units of smallest total side-length. Polygon partitioning is an important class of problems in computational geometry. There are many different polygon partition problems, depending on the type of polygon being partitioned and on the types of units allowed in the partition.
PolyhedronIn geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions.
OscillationOscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.
Convex hullIn geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact.
Thermodynamic free energyIn thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system (the others being internal energy, enthalpy, entropy, etc.). The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point.
Polygon triangulationIn computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs. Over time, a number of algorithms have been proposed to triangulate a polygon.
Helmholtz free energyIn thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.
Recrystallization (metallurgy)In materials science, recrystallization is a process by which deformed grains are replaced by a new set of defect-free grains that nucleate and grow until the original grains have been entirely consumed. Recrystallization is usually accompanied by a reduction in the strength and hardness of a material and a simultaneous increase in the ductility. Thus, the process may be introduced as a deliberate step in metals processing or may be an undesirable byproduct of another processing step.
DampingDamping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag (a liquid's viscosity can hinder an oscillatory system, causing it to slow down; see viscous damping) in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators.
Training simulationIn business, training simulation is a virtual medium through which various types of skills can be acquired. Training simulations can be used in a variety of genres; however they are most commonly used in corporate situations to improve business awareness and management skills. They are also common in academic environments as an integrated part of a business or management course. The word simulation implies an imitation of a real-life process, usually via a computer or other technological device, in order to provide a lifelike experience.
