Time multiscale approach

Variations of the average size of cationic argon clusters excited by electron impact at t — 0, as predicted by a time multiscale approach combining non-adiabatic molecular dynamics trajectories until internal conversion to the ground electronic state is achieved, followed by classical MD up to 100 ps and finally a kinetic approach based on phase space theory for sequential monomer evaporation. The results of approximate treatments with harmonic densities of states, or with the neglect of the classical MD relaxation stage, are also shown. 

To achieve these new developments the approach cover a large domain of technical disciplines and also a multiscale approach in time and length. This new complexity require to increase the relative weight of modeling and scientific calculation in the process development. For exemple, CFD calculation is currently used for the development of reactor technologies and reactor internal, but most of the time it is difficult to couple hydrodynamic modelisation and reaction modelisation. A lot of improvement are expected by coupling these two approaches. 

One of the ultimate goals in modeling heterogeneous catalytic reaction systems would be the development of a multiscale approach that could simulate the myriad of atomic scale transformations that occur on the catalyst surface as they unfold as a function of time, processing conditions and catalyst structure and composition. The simulation would establish all of the elementary physicochemical paths available at a specific instant... 

Charpentier JC Among the trends for a modem chemical engineering, the third paradigm the time and length multiscale approach as an efficient tool for process intensification and product design and engineering, Chem Eng Res Des 88(3A) 248—254, 2010. 

Bridging the gap between the production and detection times thus requires using various computational strategies and connecting them carefully in suitable time domains. This chapter aims to present the time multiscale modeling approach in more details in the context of atomic and molecular... 

Our second application of the time multiscale modeling approach aims to describe the sequential emission of carbon dimers from a purely theoretical perspective, without any adjustment. Because the absolute dissociation rates... 

It has been shown that such electron dynamics can be performed in good agreement with time-resolved experiments for perylene-Ti02 interfaces with different anchor and spacer groups. In particular, the use of electronic structure information from previous atomistic quantum chemical calculations provides an illustration of a successful combination of different levels of theory into a first principles-based multiscale approach. Theoretical developments of such electron dynamics simulations have recently also included vibrational effects that can be incorporated from separate calculations of molecular vibrational modes. ... 

To account for the effect of a sufficiently broad, statistical distribution of heterogeneities on the overall transport, we can consider a probabilistic approach that will generate a probability density function in space (5) and time (t), /(i, t), describing key features of the transport. The effects of multiscale heterogeneities on contaminant transport patterns are significant, and consideration only of the mean transport behavior, such as the spatial moments of the concentration distribution, is not sufficient. The continuous time random walk (CTRW) approach is a physically based method that has been advanced recently as an effective means to quantify contaminant transport. The interested reader is referred to a detailed review of this approach (Berkowitz et al. 2006). 

Vora, N.P., Contou-Carrere, M.N., and Daoutidis, P. (2006). Model reduction of multiple time scale processes in non-standard singularly perturbed form. In A. N. Gorban, N. Kazantzis, I.G. Kevrekidis, H.C. Ottinger, and K. Theodor-opoulos, eds., Coarse Graining and Model Reduction Approaches for Multiscale Phenomena, pp. 99-116. Berlin Springer-Verlag. 

The review is organized as follows In Section 2 we present the multiscale equilibrium thermodynamics in the setting of contact geometry. The time evolution (multiscale nonequilibrium thermodynamics) representing approach of a mesoscopic level LmeSoi to the level of equilibrium thermodynamics Leth is discussed in Section 3. A generalization in which the level Leth is replaced by another mesoscopic level LmesoZ is considered in Section 4. The notion of multiscale thermodynamics of systems arises in the analysis of this type of time evolution. 

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