Coarse-graining the electrostatic potential via distributed multipole expansions

Multipole expansions offer a natural path to coarse-graining the electrostatic potential. However, the validity of the expansion is restricted to regions outside a spherical enclosure of the distribution of charge and, therefore, not suitable for most applications that demand accurate representation at arbitrary positions around the molecule. We propose and demonstrate a distributed multipole expansion approach that resolves this limitation. We also provide a practical algorithm for the computational implementation of this approach. The method allows the partitioning of the charge distribution into subsystems so that the multipole expansion of each component of the partition, and therefore of their superposition, is valid outside an enclosing surface of the molecule of arbitrary shape. The complexity of the resulting coarse-grained model of electrostatic potential is dictated by the area of the molecular surface and therefore, for a typical three-dimensional molecule, it scale as N2/3 with N, the number of charges in the system. This makes the method especially useful for coarse-grained studies of biological systems consisting of many large macromolecules provided that the configuration of the individual molecules can be approximated as fixed.     

Assessment of atomistic coarse-graining methods

This paper reviews classical theories of coarse-graining and gives a short introduction to representative coarse-grained atomistic models that were developed based on structure reduction, an assumption of homogenous deformation, and field representation. The applicability and limitations of these coarse-grained models are analyzed on the basis of their theoretical frameworks as well as the coarse-graining methods they employ.     

Molecular dynamics study of the mechanical properties of polydisperse pressure-sensitive adhesives

Amorphous polymers are one of the primary materials used in pressure sensitive adhesives (PSAs). Their design can be aided by a better understanding of the mechanisms governing the molecular and mesoscopic scale behavior. This work presents a molecular dynamics study of the toughness and failure modes of a coarse-grained polydisperse PSA model in probe peel tests, achieved by varying the crosslinking density and locations. Generally, the toughness of polydisperse PSAs increases at a crosslinking density of 0.5%, compared to the non-crosslinked structure, and declines at higher crosslinking densities, which also changes the failure mode from cohesive to adhesive. The performance is affected by the length of the polymer chains that form crosslinks, although high crosslinking densities make the system less sensitive to effects related to its polydispersity. The results herewith presented display an optimal performance when 35–45% of the particles in the system belong to the giant component of the PSA network. This is achieved at crosslinking densities of 0.5–1.0%, depending on the length of the chains that are allowed to crosslink.     

Coupling resolved and coarse-grain DEM models

The discrete element method (DEM) is a well-established approach to study granular flows in numerous fields of application; however, the DEM is a computationally demanding method. Thus, simulations of industrial scale systems are hardly feasible on today’s hardware. This situation is typically resolved by limiting the simulation domain or introducing a coarse-grain model. While the former approach does not provide information of the full system, the latter is especially problematic in systems, where geometric restrictions are in the range of particle size, so both are insufficient to adequately describe large-scale processes. To overcome this problem, we propose a novel technique that efficiently combines resolved and coarse-grain DEM models. The method is designed to capture the details of the granular system in spatially confined regions of interest while retaining the benefits of the coarse-grain model where a lower resolution is sufficient. To this end, our method establishes two-way coupling between resolved and coarse-grain parts by volumetric passing of boundary conditions.     

Influence of model particle size and spatial resolution in coarse-graining DEM-CFD simulation

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is a powerful tool for exploring the detailed behaviors of dense particle–fluid interaction problems such as fluidized beds. Coarse-graining models have been proposed to decrease the computational cost by increasing the model particle size. In this study, we examine the influence of the model particle size and the spatial resolution on the average size and number of bubbles in coarse-graining DEM-CFD calculations of bubbling fluidized beds. Calculation results indicate that the bubble size is scaled by the model particle size if parameters are following similarity laws defined in a particle scale, as well as the geometric similarity of the whole system is maintained. The usage of coarse spatial resolution increases the bubble size and decreases the number of bubbles. The countervailing influence of the model particle size and the spatial resolution in a practical coarse-graining scenario results in nearly the same bubble size.     

Effect of solvent model when probing protein dynamics with molecular dynamics

We probe the dynamics of the Bpti and Galectin-3 proteins using molecular dynamics simulations employing three water models at different levels of resolution, viz. the atomistic TIP4P-Ewald, the coarse-grained Elba and an implicit generalised Born model. The dynamics are quantified indirectly by model-free order parameters, S² of the backbone NH and selected side-chain bond vectors, which also have been determined experimentally through NMR relaxation measurements. For the backbone, the order parameters produced with the three solvent models agree to a large extent with experiments, giving average unsigned deviations between 0.03 and 0.06. For the side-chains, for which the experimental data is incomplete, the deviations are considerably larger with mean deviations between 0.13 and 0.17. However, for both backbone and side-chains, it is difficult to pick a winner, as all models perform equally well overall. For a more complete set of side-chain vectors, we resort to analysing the variation among the estimates from different solvent models. Unfortunately, the variations are found to be sizeable with mean deviations between 0.11 and 0.15. Implications for computational assessment of protein dynamics are discussed.     

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ-leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ-leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption–desorption, surface diffusion, and phase transitions.     

A coarse-grained parcel method for heat and mass transfer simulations of spray coating processes

The Discrete Element Method (DEM) is commonly used for modeling the flow of particulate materials. Unfortunately, such detailed simulations are computationally very demanding, restricting its use for industrially-scaled processes. The number of particles in a simulation can be reduced by introducing parcels (i.e., “coarse graining”), which – in essence – relies on the increase of the particle diameter for interaction calculations. However, sophisticated models are necessary to preserve the original behavior of the material when using such an approach. Our present contribution extends available coarse-graining concepts by introducing models for (i) particle–fluid mass transfer and (ii) the deposition rate of spray droplets on particles. Our mass transfer model is based on an existing model for heat transfer. For the spray deposition model, we introduce an effective particle diameter to compute the correct amount of droplets that impact particles. We show that these models can be used with confidence up to a coarse-graining level of 5, which we demonstrate for a simple-shaped fluidized bed. The models proposed by us are critical for detailed simulations of spray coating processes since they enable precise particle-droplet-air interaction modeling at low computational cost.