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This paper focuses on the application of modal decomposition to a nonlinear convection-reaction-diffusion distributed parameter system (DPS).
Then, the employment of Prony's method enables the realization of the full modal decomposition to the acoustic field in the flow duct.
We have developed specific procedures that utilize the G-Scheme modal decomposition to carry out the sensitivity analysis along-with the numerical integration of chemical kinetics systems, so as to understand the roles of the most important reactions, and to identify the most important reaction paths of the processes.
Using modal decomposition to discretize the spatial coordinate, and the notions of spatial and modal controllability and observability, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in an abstract space, which is subsequently solved using standard search algorithms.
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We use a finite element method to solve the coupled wave propagation problem in underground porous media and a modal decomposition method to solve the dynamic ordinary differential equations given by the finite element method.
The objective of the modal decomposition is to generate, for control design, a discretized finite-dimensional model that contains the dominant modes of the process dynamics.
The new Green function is used together with a modal decomposition technique to remove the effect of source rotation, thereby allowing an estimation of the rotor-based source strengths in the rotating reference frame.
In that work, the bond graph formulation was used to model the system and the modal decomposition was limited to systems with proportional damping.
Among many forms of frequency domain system identification such as frequency response function analysis and modal decomposition, transmissibility (output-to-output relationship) estimation has been regarded as one of the most practical tools for its clear physical interpretation, its compatibility with output-only data, and its sensitivity to local changes of structural parameters.
First, modal decomposition is employed to rewrite the MIMO vibration control problem as a combination of individual SISO control problems in modal coordinates.
At the receiver, nointerferometric modal decomposition [61] is performed to demultiplex the modes before photodetection for each of the five wavelengths.
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