Mesoscale simulations

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

Of all the topics discussed in this text, mesoscale simulations are probably at the most infantile stage of development. The idea of the mesoscale calculations is very attractive and physically reasonable. However, it is not as simple as one might expect. The choice of bead sizes and parameters is crucial to obtaining physically relevant results. More complex bead shapes are expected to be incorporated in future versions of these techniques. When using one simulation technique to derive parameters for another simulation, very small errors in a low-level calculation could result in large errors in the final stages. 

J. M. Yeomans, Mesoscale simulations lattice Boltzmann and particle algorithms, PhysicaA 369, 159 (2006). 

Gree-Kubo expression, 102-104 mesoscale simulation of complex systems basic princples, 90-92 real system simulations, 113-114 multicomponent systems, 96-97 nonideal fluids, 136-137 polymers, 122-128... 

Membrane simulations were performed with 2, = 4,9, and 15. The mesoscopic structure of the hydrated membrane is visualized in Figure 6.7, revealing a sponge-like structure similar to structures obtained by other mesoscale simulations.ii Together with hydrophilic beads of side chains, water beads... 

Mesoscale Simulations of Self-Organization in Catalyst Layers... 

The evolving structural characteristics of CLs are particularly important for further analysis of transport of protons, electrons, reactant molecules (O2), and water as well as for the distribution of electrocatalytic activity at Pt-water interfaces. In principle, the mesoscale simulations allow relating these properties to the choices of solvent, ionomer, carbon particles (sizes and wettability), catalyst loading, and hydration level. Explicit experimental data with which these results could be compared are still lacking. Versatile experimental techniques have to be employed to study particle-particle interactions, structural characteristics of phases and interfaces, and phase correlations of carbon, ionomer, and water in pores. 

Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

We think that judicious application of molecular simulation tools for the calculation of thermophysical and mechanical properties is a viable strategy for obtaining some of the information required as input to mesoscale equations of state. Given a validated potential-energy surface, simulations can serve as a complement to experimental data by extending intervals in pressure and temperature for which information is available. Furthermore, in many cases, simulations provide the only realistic means to obtain key properties e.g., for explosives that decompose upon melting, measurement of liquid-state properties is extremely difficult, if not impossible, due to extremely fast reaction rates, which nevertheless correspond to time scales that must be resolved in mesoscale simulations of explosive shock initiation. By contrast, molecular dynamics simulations can provide converged values for those properties on time scales below the chemical reaction induction times. Finally,... 

Bowman C, Newell AC (1998) Natural patterns and wavelets. Rev Modem Phys 70 289-301 Broughton JQ, Abraham FF, Bernstein N, Kaxiras E (1999) Concurrent eoupling of length scales Methodology and application. Phys Rev B 60 2391-2403 Bulatov V, Abraham FF, Kubin L, Devincre B, Yip S (1998) Connecting atomistic and mesoscale simulations of crystal plasticity. Nature 391 669-672... 

The SM2-U model (Dupont and Mestayer, 2004 [158] Dupont et al., 2005 [160]) is based on the force-restore model of Noilhan and Planton 1989 [469] for the transfers between the atmosphere, one vegetation layer, and three soil layers in its most recent version, ISBA-3L (Boone et al., 1999 [66]). It keeps the principal characteristics of this soil model and was developed as a pre-processor for fine resolution sub-mesoscale simulations. The surface dynamic influence is represented through roughness lengths... 

MM5 is a multiscale (10-1000 km) weather prediction system consisting of data analysis and initialization, dynamical prediction, and postprediction diagnosis and verification codes. The MM5 model (Grell et al. 1994) system source codes and documentation are in the public domain (i.e., the Internet) for use by any person. The MM5 model has demonstrated high skill in mesoscale simulation of tropical cyclone-orography interaction (Wu et al. 1999) as well as various mesoscale... 

The method developed in this book is also used to provide input parameters for composite models which can be used to predict the thermoelastic and transport properties of multiphase materials. The prediction of the morphologies and properties of such materials is a very active area of research at the frontiers of materials modeling. The prediction of morphology will be discussed in Chapter 19, with emphasis on the rapidly improving advanced methods to predict thermodynamic equilibrium phase diagrams (such as self-consistent mean field theory) and to predict the dynamic pathway by which the morphology evolves (such as mesoscale simulation methods). Chapter 20 will focus on both analytical (closed-form) equations and numerical simulation methods to predict the thermoelastic properties, mechanical properties under large deformation, and transport properties of multiphase polymeric systems. 

See also Nicolaides [13] and Spyriouni and Vergelati [14], for examples of the estimation of % by the method developed in this book, and by atomistic simulations, respectively, to be used as an input parameter in mesoscale simulations of the dynamics of multiphase materials. 

New and physically robust mesoscale simulation methods are being improved and used increasingly more often in the dynamic modeling of the interfacial and phasic behavior of... 

Mesoscale simulation methods [34] bridge between the short length and time scales typically probed by atomistic and coarse-grained simulations at a higher computational cost and the larger scales typically probed by continuum simulations of bulk material behavior. Figure 7.4 is a schematic illustration of length and time scales, adapted from Shelley and Shelley [35]. 

Mesoscale simulations of various types also provide the ability to estimate the interfacial tension as a function of time in an evolving system, as summarized below. 

Mesoscale simulation methods will also be discussed further in Section 19.C, in the broader contexts of multiscale modeling and of predicting the morphologies of multiphase polymeric systems. Many additional examples will be given in that discussion of their utilization in addressing technologically important problems. 

The methods developed in this book can also provide input parameters for calculations using techniques such as mean field theory and mesoscale simulations to predict the morphologies of multiphase materials (Chapter 19), and to calculations based on composite theory to predict the thermoelastic and transport properties of such materials in terms of material properties and phase morphology (Chapter 20). Material properties calculated by the correlations presented in this book can also be used as input parameters in computationally-intensive continuum mechanical simulations (for example, by finite element analysis) for the properties of composite materials and/or of finished parts with diverse sizes, shapes and configurations. The work presented in this book therefore constitutes a "bridge" from the molecular structure and fundamental material properties to the performance of finished parts. 

D. Moldovan, D. Wolf, S. R. PhiUpot, and A. J. Haslam. Role of grain rotation during grain growth in a columnar microstructure by mesoscale simulation. Acta Materialia, 50 3397-3414, 2002... 

E Loix, P. Badel, L. Orgeas, C. Geindreau, and P. Boisse, Woven fabric permeability from textile deformation to fluid flow mesoscale simulations. Compos. Sci. Technol. 68, 1624-1630 (2008). 

The top bourrdary eorrditiorrs are sirtrilar to the lateral bormdary condition arrd mrrst be accrrrately represerrted. Most mesoscale models exterrd into the stratosphere in order to minimize the effect of the model top on the mesoscale simulation. Damping zones at the model top (referred to as an absorbing layer) are ustrally inserted so that upward-propagating model-simulated gravity waves do not erroneously reflect from the artificial model top. 

This chapter is organized as follows. In section 1.1, we introduce our notation and present the details of the molecular and mesoscale simulations the expanded ensemble-density of states Monte Carlo method,and the evolution equation for the tensor order parameter [5]. The results of both approaches are presented and compared in section 1.2 for the cases of one or two nanoscopic colloids immersed in a confined liquid crystal. Here the emphasis is on the calculation of the effective interaction (i.e. potential of mean force) for the nanoparticles, and also in assessing the agreement between the defect structures found by the two approaches. In section 1.3 we apply the mesoscopic theory to a model LC-based sensor and analyze the domain coarsening process by monitoring the equal-time correlation function for the tensor order parameter, as a function of the concentration of adsorbed nanocolloids. We present our conclusions in Section 1.4. 

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