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Curve of the variation of a T as a function of T for a reference temperature T 0. [ 9 ] The empirical relationship of Williams-Landel- Ferry , [ 10 ] combined with the principle of time-temperature superposition, can account for variations in the intrinsic viscosity η 0 of amorphous polymers as a function of temperature, for temperatures near ...
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function – for example creep of a turbine blade could cause ...
Thermoelectric sorting functions similarly to a thermocouple but involves an unknown material instead of an unknown temperature: a metallic probe of known composition is kept at a constant known temperature and held in contact with the unknown sample that is locally heated to the probe temperature, thereby providing an approximate measurement ...
The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well. The heat equation implies that peaks ( local maxima ) of u {\displaystyle u} will be gradually eroded down, while depressions ( local minima ...
The law holds well for forced air and pumped liquid cooling, where the fluid velocity does not rise with increasing temperature difference. Newton's law is most closely obeyed in purely conduction-type cooling. However, the heat transfer coefficient is a function of the temperature difference in natural convective (buoyancy driven) heat transfer.
For the high-temperature limit and series expansions of the hyperbolic functions, the above is simplified as α S,vib = (ΔS vib /q) = (k B /q)Σ i (-Δω i /ω i). The Seebeck coefficient derived in the above Onsager formulation is the mixing component α S,mix , which dominates in most semiconductors.
The explicit term on the right-hand side is the leading order term of a Volterra expansion for the full nonlinear response. If the system in question is highly non-linear, higher order terms in the expansion, denoted by the dots, become important and the signal transducer cannot adequately be described just by its linear response function.