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In mathematics and physics, the Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the product integral solution of a first-order homogeneous linear differential equation for a linear operator.
single-expansion ramp nozzle (SERN), a linear expansion nozzle, where the gas pressure transfers work only on one side and which could be described as a single-sided aerospike nozzle. Each of these allows the supersonic flow to adapt to the ambient pressure by expanding or contracting, thereby changing the exit ratio so that it is at (or near ...
A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction".For example, the coefficient of thermal expansion of water drops to zero as it is cooled to 3.983 °C (39.169 °F) and then becomes negative below this temperature; this means that water has a maximum density at this temperature, and ...
Like other nickel/iron compositions, Invar is a solid solution; that is, it is a single-phase alloy.In one commercial grade called Invar 36 it consists of approximately 36% nickel and 64% iron, [4] has a melting point of 1427C, a density of 8.05 g/cm3 and a resistivity of 8.2 x 10-5 Ω·cm. [5] The invar range was described by Westinghouse scientists in 1961 as "30–45 atom per cent nickel".
Negative thermal expansion (NTE) is an unusual physicochemical process in which some materials contract upon heating, rather than expand as most other materials do. The most well-known material with NTE is water at 0 to 3.98 °C.
The application of linear algebra in this context is vital for the design and operation of modern power systems, including renewable energy sources and smart grids. Overall, the application of linear algebra in fluid mechanics, fluid dynamics, and thermal energy systems is an example of the profound interconnection between mathematics and ...
The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems , linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems . [ 1 ]
In physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves: = = (+) (^ ^), where i is the imaginary unit , k is a wave vector of length k ,