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In hydrogeology, the superposition principle is applied to the drawdown of two or more water wells pumping in an ideal aquifer. This principle is used in the analytic element method to develop analytical elements capable of being combined in a single model. In process control, the superposition principle is used in model predictive control.
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position.
The superposition principle means that a linear combination of inputs to the system produces a linear combination of the individual zero-state outputs (that is, outputs setting the initial conditions to zero) corresponding to the individual inputs. [5] [6]
The WLF equation is a consequence of time–temperature superposition (TTSP), which mathematically is an application of Boltzmann's superposition principle. It is TTSP, not WLF, that allows the assembly of a compliance master curve that spans more time, or frequency, than afforded by the time available for experimentation or the frequency range ...
Block diagram illustrating the superposition principle and time invariance for a deterministic continuous-time single-input single-output system. The system satisfies the superposition principle and is time-invariant if and only if y 3 (t) = a 1 y 1 (t – t 0) + a 2 y 2 (t – t 0) for all time t, for all real constants a 1, a 2, t 0 and for all inputs x 1 (t), x 2 (t). [1]
The law of superposition is an axiom that forms one of the bases of the sciences of geology, archaeology, and other fields pertaining to geological stratigraphy.In its plainest form, it states that in undeformed stratigraphic sequences, the oldest strata will lie at the bottom of the sequence, while newer material stacks upon the surface to form new deposits over time.
The time–temperature superposition principle is a concept in polymer physics and in the physics of glass-forming liquids. [ 1 ] [ 2 ] [ 3 ] This superposition principle is used to determine temperature-dependent mechanical properties of linear viscoelastic materials from known properties at a reference temperature.
To further illustrate, Schrödinger described how one could, in principle, create a superposition in a large-scale system by making it dependent on a quantum particle that was in a superposition. He proposed a scenario with a cat in a closed steel chamber, wherein the cat's life or death depended on the state of a radioactive atom, whether it ...