Hierarchical multi-scale model

Different scales presented in Figure 3-1 are related to different approximation levels. For an overview of conventional molecular modelling methods, (see e.g.1-3). Bridging the above mentioned disparate time scales for the description of biologically relevant collective motions requires hierarchical, multi-scale approaches. In practice, to describe real complex (bio)molecular or material systems and processes various models have to be coupled to each other. Selected coupling mechanisms will be briefly reviewed. 

Multi-scale modeling provides a hierarchical computational approach to describe macroscopic catalytic processes. In this approach, atomistic methods (first principle quantum chemistry calculations and classical molecular dynamics) are used which reveal microscopic insight into the meehanisms and molecular-scale dynamics of reactions at electrode surfaces (for e.g. see [15,... 

At the same time computational methods based on the molecular mechanics, molecular dynamics (MD), Monte Carlo (MC) and ab initio methods evolved to the high level of predictive capability, accelerating development of new materials with designed properties. For the multicomponent and multiphase systems (e.g., nanocomposites, blends, composites with properties adjusted by incorporation of intercalants or compatibilizers) the most promising is the hierarchical multi-scale molecular modeling (MSMM). Thus, while such molecular simulations as MD or MC efficiently analyze the molecular structure at 0.1-10 nm, MSMM,... 

The alternative to the hierarchical modeling is known as concurrent modeling and consists of combining different numerical models that simultaneously describe different sub-domains. Each numerical model runs in its sub-domain and exchanges information with its parent/child sub-domain at defined boundaries. The critical issue here is to define the criteria and protocols in order to automate the application of more detailed numerical models in a simulation domain in time and realizing the so-called temporal multi-scale calculations or/ and space referred as spatial multi-scale ones. 

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. 

In this paper, we present a systematic approach for simultaneous optimisation of product portfolio and multi-site capacity planning in the face of clinical trials uncertainty while considering the trading structure of the company. A hierarchical algorithm is also proposed for the solution of the resulting large-scale MTT.P model. 

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