By Panagiotis D. Christofides, Antonios Armaou, Yiming Lou, Amit Varshney
Interest within the keep an eye on and optimization of multiscale procedure platforms has been caused through the necessity to in achieving tight suggestions keep an eye on and optimum operation of advanced methods, reminiscent of deposition and sputtering of skinny motion pictures in semiconductor production, that are characterised by means of hugely coupled macroscopic and microscopic phenomena. Drawing from fresh advances within the dynamics and keep watch over of allotted parameter strategies for which continuum legislation are appropriate in addition to stochastic modeling of phenomena at mesoscopic/microscopic size scales, keep an eye on and optimization of multiscale procedure platforms has advanced right into a very lively learn sector of platforms and regulate engineering.
This book—the first of its kind—presents basic equipment for suggestions controller synthesis and optimization of multiscale platforms, illustrating their program to thin-film development, sputtering tactics, and catalytic structures of commercial curiosity. starting with an creation to basic matters on keep an eye on and optimization of multiscale structures and a evaluation of past paintings during this quarter, the ebook discusses exact modeling ways for multiscale approaches with emphasis at the concept and implementation of kinetic Monte Carlo simulation, equipment for suggestions keep an eye on utilizing kinetic Monte Carlo types, stochastic version development and parameter estimation, predictive and covariance keep watch over utilizing stochastic partial differential equation versions, and either steady-state and dynamic optimization algorithms that successfully handle coupled macroscopic and microscopic targets.
Key good points of the paintings:
* Demonstrates the benefits of the tools offered for keep an eye on and optimization via large simulations.
* contains new ideas for suggestions controller layout and optimization of multiscale approach platforms that aren't incorporated in different books.
* Illustrates the appliance of controller layout and optimization the way to complicated multiscale strategies of commercial interest.
* features a wealthy number of new study themes and references to major fresh work.
The e-book calls for simple wisdom of differential equations, chance thought, and regulate idea, and is meant for researchers, graduate scholars, and approach keep an eye on engineers. during the publication, functional implementation concerns are addressed to aid researchers and engineers comprehend the improvement and alertness of the tools awarded in higher depth.
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Extra info for Control and Optimization of Multiscale Process Systems
Roughly speaking, the computational complexity of the algorithm we adopt in this work is O(N 4 ) and the magnitude of the fluctuation in the solution is O(1/N 2 ), where N is the size of the lattice. The fourth order dependence on computational complexity and the second order dependence of fluctuations on the size of the lattice leave room for reducing the solution time with a relatively small loss of accuracy. 2 Real-Time Estimation 29 open-loop operation obtained from kMC simulators using different lattice sizes.
Although there is no limitation on the initial surface configuration, in many applications, a perfect surface is assumed to start the simulation [97, 100, 155]. In computer memory, the surface configuration can be stored in the form of a 2D array S, whose size is equal to the size of the simulation lattice. Each element indicates the number of atoms on the corresponding surface site of the substrate. In this simulation, a 10 × 10 zero matrix can be used to represent the initial perfect surface of the 10 × 10 lattice (flat surface with no atoms).
The probability that the surface is in a possible configuration is described by the master equation of Eq. 11). However, due to the extremely high dimension of a master equation for any system of meaningful size, it is impossible to directly solve the master equation using numerical methods for integration of ordinary differential equations (such as Runge–Kutta). On the other hand, kinetic Monte Carlo (kMC) simulation methods provide a numerical solution to the master equation . The kMC simulation method can be used to predict average properties of the thin film (which are of interest from a control point of view; for example, surface roughness), by explicitly accounting for the microprocesses that directly shape the thin-film microstructure.