Scale concurrent modeling

In terms of numerical procedures for multiscale modeling, Fish and Shek [245] laid out a numerical technique for global and local interactions for composites. Later, Fish and Yu [246] in a three-scale concurrent multiscale methodology for composites analysis introduced a nonlocal damage model. 

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. 

The EMMS model was first proposed for the hydrodynamics of concurrent-up particle-fluid two-phase flow. Though it is based on a rather simplified physical picture of the complex system (Li, 1987 Li and Kwauk, 1994), it harnesses the most intrinsic complexity in the system, the meso-scale heterogeneity, and this is why it allows better predictions to the critical phenomena in the system which is obscured in other seemingly more comprehensive models. 

With the advent of nanomaterials, different types of polymer-based composites developed as multiple scale analysis down to the nanoscale became a trend for development of new materials with new properties. Multiscale materials modeling continue to play a role in these endeavors as well. For example, Qian et al. [257] developed multiscale, multiphysics numerical tools to address simulations of carbon nanotubes and their associated effects in composites, including the mechanical properties of Young s modulus, bending stiffness, buckling, and strength. Maiti [258] also used multiscale modeling of carbon nanotubes for microelectronics applications. Friesecke and James [259] developed a concurrent numerical scheme to evaluate nanotubes and nanorods in a continuum. 

Practically any experimental kinetic curve can be reproduced using a model with a few parallel (competitive) or consecutive surface reactions or a more complicated network of chemical reactions (Fig. 4.70) with properly fitted forward and backward rate constants. For example, Hachiya et al. used a model with two parallel reactions when they were unable to reproduce their experimental curves using a model with one reaction. In view of the discussed above results, such models are likely to represent the actual sorption mechanism on time scale of a fraction of one second (with exception of some adsorbates, e.g, Cr that exchange their ligands very slowly). Nevertheless, models based on kinetic equations of chemical reactions were also used to model slow processes. For example, the kinetic model proposed by Araacher et al. [768] for sorption of multivalent cations and anions by soils involves several types of surface sites, which differ in rate constants of forward and backward reaction. These hypothetical reactions are consecutive or concurrent, some reactions are also irreversible. Model parameters were calculated for two and three... 

A fluidized-bed MTG concept was concurrently developed by Mobil. The process research went through several stages involving bench-scale fixed fluidized-bed 4-bbl/day and 100-bbl/day cold-flow models, and a 100-bbI/day semiwork plant. 

Unfortunately, few of the published studies of extraction equilibria heve provided complete quantitative models that are useful for extrapolation of data or for predicting multiple metal distribution equilibria from single metal data. The chemical-reaction equilibrium formulation provides a framework for constructing such models. One of the drawbacks of purely empirical correlations of distribution coefficients is that pH has often been chosen as an independent variable. Such a choice is suggested by the form of Pigs. 8-3-5 and 8.3-8. Although pH is readily measured and contmlled on a laboratory scale, it is really a dependent variable, which is detenmined by mass belances and simultaneous reaction equilibria. An appropriate phare-equilibrium model should be able to predict equilibrium pH, at least within a moderate activity coefficient correction, concurrently with other species concemrations. 

The primary purpose of the meso-damage modelling is to describe failure as processes occurring at the yam scale. Compared to unidirectional laminated composites, damage accumulation in textile composite has some specific features (1) the early initiation of intra-yam cracking (0.1—0.3% of applied deformation), (2) the concurrent accumulation of crack density and incremental crack length growth. 

This review on concurrently operated multiphase packed bed reactors shows that much information on the behavior of these reactor types has been accumulated in the past, but we are still far from a complete elucidation. The difficulty still exists that not enough information is available on systems different from air/water nonporous packings to safely scale-up multiphase reactors using a sophisticated mathematical model. The fact that fluid-dynamics and thermal effects may be different in laboratory units from those in technical reactors restricts the usefulness of simplified, i.e. lumped, models in reactor scale-up. On the contrary, the different mechanisms acting in multiphase catalytic reactions have to be kept separated to a certain extent, thus enabling the correct inclusion of their probably changing amount of influence during scale-up. 

Service value networks offer a new business model and a new paradigm to service delivery mechanisms. They reconcile two conflicting, but concurrent, requirements of customers, namely to leverage economies of scale (from a diverse block of data storages), and to be able to deliver highly speciflc customized solutions (Brown Vashistha, 2002). This service value network pathway is being driven by ... 

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