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In mathematics and physics, a global mode … In mathematics and physics, a global mode of a system is one in which the system executes coherent oscillations in time. Suppose a quantity which depends on space and time is governed by some partial differential equation which does not have an explicit dependence on . Then a global mode is a solution of this PDE of the form , for some frequency . If is complex, then the imaginary part corresponds to the mode exhibiting exponential growth or exponential decay. The concept of a global mode can be compared to that of a normal mode; the PDE may be thought of as a dynamical system of infinitely many equations coupled together. Global modes are used in the stability analysis of hydrodynamical systems. Philip Drazin introduced the concept of a global mode in his 1974 paper, and gave a technique for finding the normal modes of a linear PDE problem in which the coefficients or geometry vary slowly in . This technique is based on the WKBJ approximation, which is a special case of multiple-scale analysis. His method extends the Briggs–Bers technique, which gives a stability analysis for linear PDEs with constant coefficients.or linear PDEs with constant coefficients.
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| rdfs:comment |
In mathematics and physics, a global mode … In mathematics and physics, a global mode of a system is one in which the system executes coherent oscillations in time. Suppose a quantity which depends on space and time is governed by some partial differential equation which does not have an explicit dependence on . Then a global mode is a solution of this PDE of the form , for some frequency . If is complex, then the imaginary part corresponds to the mode exhibiting exponential growth or exponential decay.g exponential growth or exponential decay.
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| rdfs:label |
Global mode
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