Based on Multiscale Models

In this section, we give a brief overview of theoretical methods used to perform tribological simulations. We restrict the discussion to methods that are based on an atomic-level description of the system. We begin by discussing generic models, such as the Prandtl-Tomlinson model. Below we explore the use of force fields in MD simulations. Then we discuss the use of quantum chemical methods in tribological simulations. Finally, we briefly discuss multiscale methods that incorporate multiple levels of theory into a single calculation. 

Buehler et al. presented a preliminary study on formation of water from molecular oxygen and hydrogen using a series of atomistic simulations based on ReaxFF MD method.111 They described the dynamics of water formation at a Pt catalyst. By performing this series of studies, we obtain statistically meaningful trajectories that permit to derive the reaction rate constants of water formation. However, the method requires calibrations with either ab initio simulation results in order to correctly evaluate the energetics of OER on Pt. Thus, this method is system specific and less reliable than the ab initio methods and will not replace ab initio methods. Nevertheless, this work demonstrates that atomistic simulation to continuum description can be linked with the ReaxFF MD in a hierarchical multiscale model. 

Figure 3 Integrated, high fidelity, multiscale process modeling of C02 capture and storage. Modified based on Beyond the Molecular Frontier, NRC report (2003).

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

Many polymer blends or block polymer melts separate microscopically into complex meso-scale structures. It is a challenge to predict the multiscale structure of polymer systems including phase diagram, morphology evolution of micro-phase separation, density and composition profiles, and molecular conformations in the interfacial region between different phases. The formation mechanism of micro-phase structures for polymer blends or block copolymers essentially roots in a delicate balance between entropic and enthalpic contributions to the Helmholtz energy. Therefore, it is the key to establish a molecular thermodynamic model of the Helmholtz energy considered for those complex meso-scale structures. In this paper, we introduced a theoretical method based on a lattice model developed in this laboratory to study the multi-scale structure of polymer systems. First, a molecular thermodynamic model for uniform polymer system is presented. This model can... 

Concurrent multiscale methods have also been employed to address fatigue. Oskay and Fish [82] and Fish and Oskay [83] introduced a nonlocal temporal multiscale model for fatigue based upon homogenization theory. Although these formulations were focused on metals, Fish and Yu [84] and Gal et al. [85] used a similar concurrent multiscale method for analyzing fatigue of composite materials. 

Despite these obvious difficulties we decided to develop a model of the effects of DBS using a systems biology approach. Our aim is to propose a large scale and multiscale computational model of DBS effects in PD based on physiology of individual neurons, population of neurons, and interacting populations of neurons. 

Obviously, the spectrum of mesoscale, particle-based tools is too vast to be covered in a single paper. Therefore, in this and the subsequent sections, I mainly elaborate on MC methods to illustrate various aspects of multiscale modeling and simulation. Below, the modeling hierarchy for stochastic well-mixed chemically reacting systems is first outlined, followed by a brief introduction to MC methods. 

Doyle and co-workers have used sensitivity and identifiability analyses in a complex genetic regulatory network to determine practically identifiable parameters (Zak et al., 2003), i.e., parameters that can be extracted from experiments with a certain confidence interval, e.g., 95%. The data used for analyses were based on simulation of their genetic network. Different perturbations (e.g., step, pulse) were exploited, and an identifiability analysis was performed. An important outcome of their analysis is that the best type of perturbations for maximizing the information content from hybrid multiscale simulations differs from that of the deterministic, continuum counterpart model. The implication of this interesting finding is that noise may play a role in systems-level tasks. 

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