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Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
Although named for Edgar Buckingham, the π theorem was first proved by the French mathematician Joseph Bertrand in 1878. [1] Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains, in distinct terms, all the basic ideas of the modern proof of the theorem and clearly indicates the theorem's utility for modelling physical phenomena.
Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
Predictive analytics is a set of business intelligence (BI) technologies that uncovers relationships and patterns within large volumes of data that can be used to predict behavior and events. Unlike other BI technologies, predictive analytics is forward-looking, using past events to anticipate the future. [ 3 ]
In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as Voltage, voltage angles, real power and reactive power.
In computing, the star schema or star model is the simplest style of data mart schema and is the approach most widely used to develop data warehouses and dimensional data marts. [1]
Dissipative particle dynamics (DPD) is an off-lattice mesoscopic simulation technique [1] which involves a set of particles moving in continuous space and discrete time. . Particles represent whole molecules or fluid regions, rather than single atoms, and atomistic details are not considered relevant to the processes addr