Dynamics tier models

We proposed a method for deriving nonlinear low-dimensional models for the dynamics in each time scale. Subsequently, we proposed a hierarchical controller design framework that takes advantage of the time-scale multiplicity, and relies on a multi-tiered structure of coordinated decentralized and supervisory controllers in order to address distributed and process-level control objectives. 

A dynamic 7-tier reverse logistics network design model for maximizing profits of a tmck tire-remanufacturing network [15]... 

It should be stressed that the wave-packet picture of photophysical relaxation and photochemical reaction dynamics described in this chapter is substantially different from the traditional concepts in this area. In contrast to the established picture of radiationless transitions in terms of interacting tiers of zero-order molecular eigenstates, the dynamics is rationalized in terms of local properties of PE surfaces such as slopes, barriers and surface intersections, a view which now becomes widely accepted in photochemistry. This picture is firmly based on ah initio electronic-structure theory, and the molecular relaxation d3mamics is described on the basis of quantum mechanics, replacing previously prevaUing kinetic models of electronic decay processes. Such a more detailed and rigorous description of elementary photochemical processes appears timely in view of the rich and specific information on ultrafast chemical processes which is provided by modern time-resolved spectroscopy. " ... 

Two-dimensional (2D) models represent a second tier of spatial complexity with respect to sediment transport models. Models in this class have become more prevalent during the last couple of decades due to advancements in computer hardware and software capabilities. Two-dimensional models typically solve the depth-averaged flow continuity and Navier-Stokes equations with respect to hydrodynamic behavior and mass balance equations with respect to sediment transport. Computational methods employed in 2D models include finite difference, finite element, and finite volume. Examples of 2D models include Environmental Eluid Dynamics Code (EFDC), SEDZLJ, SEDZL, USTARS, MIKE21, and Delft 2D. 

When bnilding a simnlation model of a supply chain, two considerations must be noted. First, the system mnst be a dynamic, multi-echelon system that brings together mnltiple tiers of snpphers and multiple tiers of customers (Fig. 7.2). Second, while the overall simnlation model deals with the entire supply chain, aity analysis of this data will tend to focns on the performance of only one node or entity in the model - the focns of interest (as shown in Fig. 7.2). While simulation does allow ns to look at the performance at multiple points, typically, the question that we most often addressed takes the form of How does a supply chain disraption taking place at some upstream point in the supply chain affect the performance of this firm ... 

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