Fluid dynamicsIn physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
Monteggia fractureThe Monteggia fracture is a fracture of the proximal third of the ulna with dislocation of the proximal head of the radius. It is named after Giovanni Battista Monteggia. Mechanisms include: Fall outstretched hand with the forearm in excessive pronation (hyper-pronation injury). The ulna fractures in the proximal one-third of the shaft due to extreme dislocation. Depending on the impact and forces applied in each direction, degree of energy absorption determines pattern, involvement of the radial head and whether or not open soft tissue occurs.
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.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Incompressible flowIn fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent). Incompressible flow does not imply that the fluid itself is incompressible.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Hair cellHair cells are the sensory receptors of both the auditory system and the vestibular system in the ears of all vertebrates, and in the lateral line organ of fishes. Through mechanotransduction, hair cells detect movement in their environment. In mammals, the auditory hair cells are located within the spiral organ of Corti on the thin basilar membrane in the cochlea of the inner ear. They derive their name from the tufts of stereocilia called hair bundles that protrude from the apical surface of the cell into the fluid-filled cochlear duct.
Stress fractureA stress fracture is a fatigue-induced bone fracture caused by repeated stress over time. Instead of resulting from a single severe impact, stress fractures are the result of accumulated injury from repeated submaximal loading, such as running or jumping. Because of this mechanism, stress fractures are common overuse injuries in athletes. Stress fractures can be described as small cracks in the bone, or hairline fractures. Stress fractures of the foot are sometimes called "march fractures" because of the injury's prevalence among heavily marching soldiers.
Navier–Stokes equationsThe Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
