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At least 289 records · Page 16

Modular Approach for the Synthesis of Bottlebrush Diblock Copolymers from Poly(Glycidyl Methacrylate)-block-Poly(Vinyldimethylazlactone) Backbones

A strategy that enables the facile synthesis of bottlebrush block copolymers with flexible backbones was developed. A demonstration of the strategy’s utility was carried out by grafting end-functionalized polymethylmethacrylate (PMMA) and polystyrene (PS) to the dually reactive block copolymer, poly(glycidyl methacrylate)-block-poly(vinyldimethylazlactone) (PGMA-b-PVDMA). Five different bottlebrush diblock copolymers were investigated by size-exclusion chromatography (SEC), 1H NMR, Fourier transform infrared (FT-IR), differential scanning calorimetry (DSC), X-ray scattering methods, atomic force microscopy (AFM), rheology and computational simulations using molecular dynamics (MD), and self-consistent field theory (SCFT). A relationship between the glass transition temperature and the fraction of chain ends was demonstrated by DSC and highlights the potential of this synthetic method to tailor polymer properties. All five samples were found to be in a disordered phase exhibiting multiscale structures revealed by two broad peaks in small-angle X-ray scattering (SAXS) that can be attributed to graft-to-graft and backbone-to-backbone density correlations using MD simulations. The SCFT-based simulations justify the observation of a disordered phase due to its stabilization by the grafts. Additionally, this modular approach can be easily extended to other grafts, including responsive, conducting, and charged polymers with the prerequisite end groups. The versatility and ease of assembling these functional bottlebrushes constitute a powerful “toolbox” method for the rapid and scalable synthesis of novel bottlebrush block copolymers with desired properties.

36 MATERIALS SCIENCE↗

Computational and experimental study of different brines in temperature swing solvent extraction desalination with amine solvents

Rapid global urbanization and high-salinity wastewater disposal from industrial activities have exerted significant pressure on water resources. Over the past few years, temperature swing solvent extraction (TSSE) has been identified as a promising technique to desalinate hypersaline brines. Despite its potential, the TSSE desalination literature has been mainly based on empirical insights, and the limited molecular simulation studies have primarily focused on NaCl brines. Herein, we use molecular dynamics (MD) simulations to study the TSSE desalination of four different brines, namely, KCl, KBr, NaCl, and NaBr using diisopropylamine as the solvent. Based on both bulk and interfacial brine-diisopropylamine MD results, here we investigate the qualitative and quantitative performance of the simulations by benchmarking these results against our experimental evaluations of these same systems. MD results provide satisfactory qualitative agreement with the experimental data of water solubilization in the organic phase and amine solubilization in the aqueous phase for the KBr, KCl, and NaBr brines. Also, the molecular mechanism of solvation of ionic species by water molecules over diisopropylamine suggested by the MD simulations is in agreement with our experimental data. However, larger qualitative and quantitative deviations were observed for the NaCl brines, and this is likely due to polarization and charge transfer effects, as quantified by our quantum chemical calculations.

42 ENGINEERING↗

Effects of nanoconfinement and surface charge on iron adsorption on mesoporous silica

Here, we present a combined molecular dynamics (MD) simulation and X-ray absorption fine structure (XAFS) spectroscopic investigation of aqueous iron adsorption on nanoconfined amorphous silica surfaces. The simulation models examine the effects of pore size, pH (surface charge), iron valency, and counter-ion (chloride or hydroxide). The simulation methods were validated by comparing the coordination environment of adsorbed iron with coordination numbers and bond lengths derived from XAFS. In the MD models, nanoconfinement effects on local iron coordination were investigated by comparing results for unconfined silica surfaces and in confined domains within 2 nm, 4 nm, and 8 nm pores. Experimentally, coordination environments of iron adsorbed onto mesoporous silica with 4 nm and 8 nm pores at pH 7.5 were investigated. The effect of pH in the MD models was included by simulating Fe(II) adsorption onto negatively charged SiO 2 surfaces and Fe(III) adsorption on neutral surfaces. The simulation results show that iron adsorption depends significantly on silica surface charge, as expected based on electrostatic interactions. Adsorption on a negatively charged surface is an order of magnitude greater than on the neutral surface, and simulated surface coverages are consistent with experimental results. Pore size effects from the MD simulations were most notable in the adsorption of Fe(II) at deprotonated surface sites (SiO - ), but adsorption trends varied with concentration and aqueous Fe speciation. The coordination environment of adsorbed iron varied significantly with the type of anion. Considerable ion pairing with hydroxide anions led to the formation of oligomeric surface complexes and aqueous species, resulting in larger iron hydroxide clusters at higher surface loadings.

54 ENVIRONMENTAL SCIENCES↗

Deep potential molecular dynamics simulations of low-temperature plasma-surface interactions

Machine learning approaches to potential generation for molecular dynamics (MD) simulations of low-temperature plasma-surface interactions could greatly extend the range of chemical systems that can be modeled. Empirical potentials are difficult to generalize to complex combinations of multiple elements with interactions that might include covalent, ionic, and metallic bonds. This work demonstrates that a specific machine learning approach, Deep Potential Molecular Dynamics (DeepMD), can generate potentials that provide a good model of plasma etching in the Si-Cl-Ar system. Comparisons are made between MD results using DeepMD models and empirical potentials, as well as experimental measurements. Pure Si properties predicted by the DeepMD model are in reasonable agreement with experimental results. Simulations of Si bombardment by Ar + ions demonstrate the ability of the DeepMD method to predict sputtering yields as well as the depth of the amorphous-crystalline interface. Etch yields as a function of flux ratio and ion energy for simultaneous Cl 2 and Ar + impacts are in good agreement with previous simulation results and experiment. Predictions of etch yields and etch products during plasma-assisted atomic layer etching of Si-Cl 2 -Ar are shown to be in good agreement with MD predictions using empirical potentials and with experiment. Finally, good agreement was also seen with measurements for the spontaneous etching of Si by Cl atoms at 300 K. Further, the demonstration that DeepMD can reproduce results from MD simulations using empirical potentials is a necessary condition to future efforts to extend the method to a much wider range of systems for which empirical potentials may be difficult or impossible to obtain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exceptionally high spallation strength for a high-entropy alloy demonstrated by experiments and simulations

High-entropy alloys are materials with an increasing number of technological applications. Amongst them, the Cantor alloy, FeMnCoCrNi, shows desirable mechanical properties at normal loading conditions. In this study we focus on the performance of the Cantor alloy at the ultra-high deformation rates of shock waves. We study shock-induced spallation using both experiments and atomistic simulations. Experimental loading is achieved using high power laser, with VISAR to obtain velocity profiles and spall strength, followed by transmission electron microscopy of the recovered samples. Molecular Dynamics (MD) simulations of shock-induced spallation are compared with experiments. Both experiments and simulations show a high spall strength which would be beneficial for certain applications, with experiments giving ~8 GPa at ~10 7 s -1 and MD giving almost ~30 GPa at ~10 9 s -1 . The difference between experiments and simulations can be explained by the difference in strain rate. Post-mortem analysis of the experimental samples shows nanotwins near the spall plane, while MD simulations show a highly disordered region giving rise to void nucleation and spall during loading.

36 MATERIALS SCIENCE↗

Challenges of conventional iterative all-atom and coarse-grained multiscale molecular dynamics

In this work, we evaluate the biomolecular dynamics behaviors when conventionally iterating between all-atom (AA) and coarse-grained (CG) molecular dynamics (MD) simulations over multiple cycles. We implemented the workflow to iterate between AA and CG in OpenMM, namely the iterative multiscale MD (iMMD) simulation workflow. In particular, we aim to identify practical applications for iterating between AA and CG simulations in a conventional manner without any constraints or model modifications. We evaluate the iMMD workflow on four representative systems, spanning folding of two soluble proteins and protein-protein as well as protein-lipid interactions of two membrane proteins. We observe that iteration between AA and CG representations could help the soluble proteins exit undesirable metastable states to fold, resulting from random protein structural distortions due to cycling. Consequently, the most reliable use of iterative AA and CG simulations appears to be to accelerating complex lipid mixing for membrane-bound protein systems rather than sampling protein conformational space. Our work explores the practical usages and limitations for iterative AA and CG simulations using readily available AA and CG force fields. The evaluated iMMD workflow in OpenMM is made available at https://github.com/lanl/iMMD.

59 BASIC BIOLOGICAL SCIENCES↗

Determination of Interfacial Energy for Solid-State Precipitation

Precipitation of strengthening phases from solid state is a critical process for many materials. For example, the high-temperature creep resistance of Ni-based superalloys is governed by ’ precipitates. However, the interfacial energy which controls the precipitation is expensive to determine experimentally. For simulations, the atomic nature of precipitation events necessitates using Molecular Dynamics (MD) so relying on fitting to a-priori experimental behavior is not required. However, the solid-state precipitation takes orders of magnitude longer time than is accessible for traditional MD simulation. Taking inspiration from Kinetic Monte-Carlo (KMC) methods for simulating diffusion on a rigid lattice, we have developed a hybrid KMC-MD approach to enable simulation of solid-state precipitation (and determination of the interfacial energy). Implementing these methods in LAMMPS, we calculated the interfacial energy for the ’ precipitation out of a super-saturated  phase in Ni-based superalloys. The resulting interfacial energy value for the Ni-Al system is well within the accuracy of experimental values, demonstrating the capability of this method. Enabling the calculation of the interfacial energy without a-priori experimental knowledge of the precipitation unlocks a more efficient ICME-based approach for guiding annealing protocols in Ni-based superalloys and other solid-state precipitation systems.

Precipitation↗

Similarity Metric for Data Optimization and Efficient Training of Reactive Machine Learning Force Fields for Hydrocarbon Radiolysis

Radiolysis is a common approach to sterilize polymers, chemically modify them for upcycling, and accelerate their decomposition for recycling purposes. Reactive molecular dynamics (MD) simulations provide a powerful tool to generate atomic-level trajectories of the reactive processes and quantify radiolytic chemical degradation pathways. For this, machine learning (ML) surrogate models for reactive force fields with quantum mechanical accuracy are now widely used, which require ML training data sets that can provide information on atomic environments for target chemical systems. However, radiolysis chemistry can be highly complex and diverse, which poses significant challenges for generating training data to parametrize ML models. In this regard, we developed a method for optimizing the training data set using a cosine similarity metric to help guide training set selection for radiolysis of polyethylene, a model hydrocarbon polymer, as well as to enhance the transferability of our reactive ML force field (MLFF) to a variety of molecular and polymeric systems. Our approach performs atom-by-atom comparisons between local atomic environments to pinpoint important data points associated with rare and localized events, such as radiolysis damage within structures. We apply this approach to train the Chebyshev Interaction Model for Efficient Simulation (ChIMES) MLFF model, which expresses the atomic interaction potentials in terms of linear combinations of many-body Chebyshev polynomials. We first show that our method can reduce our training set size by ∼70% while improving overall accuracy compared to more standard MD model fitting approaches. We then validate our optimum model against diverse hydrocarbon simulation data, including simple alkanes and systems with unsaturated carbon bonds, over a wide range of thermodynamic conditions. Finally, we use our ChIMES model to perform MD simulations of radiolytic damage with large-scale systems that help avoid system size effects. Overall, our approach yields an MD force field that retains most of the accuracy of the underlying quantum method while yielding many orders of improvement in computational efficiency. In conclusion, our efforts will have impact on future hydrocarbon polymer radiolysis studies, where the chemical details of the polymer–radiation interactions can have a strong effect on the resulting products observed in experiments.

Hydrocarbons↗

Surface Interactions and Nanoconfinement of Methane and Methane plus CO2 Revealed by High-Pressure Magic Angle Spinning NMR Spectroscopy and Molecular Dynamics

This study explores the fundamental, molecular- to microscopic-level behavior of methane gas confined into nanoporous silica proxies with different pore diameters and surface-to-volume (S/V) ratios. Surfaces and pore walls of nanoporous silica matrices are decorated with hydroxyl (-OH) groups, resembling natural heterogeneity. High-pressure MAS NMR was utilized to characterize the interactions between methane and the engineered nanoporous silica proxies under various temperature and pressure regimes. There was a change in the chemical shift position of confined methane slightly in the mixtures with nanoporous silica up to 393 K, as shown by high-pressure 13C-NMR. The 13C-NMR chemical shift of methane was changed by pressure, explained by the densification of methane inside the nanoporous silica materials. The influence of pore diameter and S/V of the nanoporous silica materials on the behaviors and dynamics of methane were studied. The presence of CO2 in mixtures of silica and methane needs analysis with caution because CO2 in a supercritical state and gaseous CO2 change the original structure of nanoporous silica and change surface area and pore volume. According to simulation, the picosecond scale dynamics of methane confined in larger pores of amorphous silica is faster. In the 4 nm pore, the diffusivity obtained from MD simulations in the pore with a higher S/V ratio is slower due to the trapping of methane molecules in adsorbed layers close to the corrugated pore surface. In contrast, relaxation measured with NMR for smaller pores (higher S/V) exhibits larger T1, indicating slower relaxation.

03 NATURAL GAS↗

Predicting CaO-(MgO)-Al2O3-SiO2 glass reactivity in alkaline environments from force field molecular dynamics simulations

In this investigation, force field-based molecular dynamics (MD) simulations have been employed to generate detailed structural representations for a range of amorphous quaternary CaO-MgO-Al{sub 2}O{sub 3}-SiO{sub 2} (CMAS) and ternary CaO-Al{sub 2}O{sub 3}-SiO{sub 2} (CAS) glasses. Comparison of the simulation results with select experimental X-ray and neutron total scattering and literature data reveals that the MD-generated structures have captured the key structural features of these CMAS and CAS glasses. Based on the MD-generated structural representations, we have developed two structural descriptors, specifically (i) average metal oxide dissociation energy (AMODE) and (ii) average self-diffusion coefficient (ASDC) of all the atoms at melting. Both structural descriptors are seen to more accurately predict the relative glass reactivity than the commonly used degree of depolymerization parameter, especially for the eight synthetic CAS glasses that span a wide compositional range. Hence these descriptors hold great promise for predicting CMAS and CAS glass reactivity in alkaline environments from compositional information.

36 MATERIALS SCIENCE↗

Clustering Effects on the Structure of Ionomer Solutions: A Combined SANS and Simulations Study

Ionic assemblies, or clusters, determine the structure and dynamics of ionizable polymers and enable their many applications. Fundamental to attaining well-defined materials is controlling the balance between van der Waals interactions that govern the backbone behavior and the forces that drive the formation of ionic clusters. Here, using small angle neutron scattering and fully atomistic molecular dynamics simulations, the structure of a model ionomer, sulfonated polystyrene in toluene solutions, was investigated as the cluster cohesion was tweaked by the addition of ethanol. The static structure factor was measured by both techniques and correlated with the size of the ionic clusters as the polymer concentration was varied. The conjunction of SANS results and molecular insight from MD simulations enabled the determination of the structure in these inhomogeneous networks on multiple length scales. Additionally, we find that across the entire concentration range studied, a network driven by the formation of ionic clusters was formed, where the size of the clusters drives the inhomogeneity of these systems. Tweaking the ionic clusters through the addition of ethanol impacts the packing of the sulfonated groups, their shape, and their size distribution, which in turn, affects the structure of these networks.

36 MATERIALS SCIENCE↗

Large-Scale Molecular Dynamics Simulation of the Dehydration of a Suspension of Smectite Clay Nanoparticles

Fine-grained sediments and sedimentary rocks play important roles in a variety of modern energy technologies from petroleum geology to geological carbon sequestration and radioactive waste management. However, despite their utility and ubiquity, many of their properties remain poorly understood. In particular, the ability to predict the permeability and mechanics of these media remains a persistent fundamental challenge in the geosciences. In the present work, we show how large-scale classical molecular dynamics (MD) simulations can help interpret the properties of fine-grained sedimentary material. All-atom simulations containing 30 discrete clay particles are utilized to understand the evolution of a clay nanoparticle suspension during its progressive dehydration. Microstructural (pore size distribution, tortuosity, anisotropy), thermodynamic (enthalpy and free energy of hydration, anion exclusion), mechanical (total suction), and transport properties (diffusion coefficient tensors of water and sodium) are calculated and compared to the experiment. Overall, our results provide new insight into the coupled chemistry, mechanics, and transport properties of disordered nanoparticle assemblages and shed light upon the important role of water films in controlling these properties.

02 PETROLEUM↗

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. Additionally, we analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

42 ENGINEERING↗

Quantifying selective solvent transport under an electric field in mixed-solvent electrolytes

Electrolytes in lithium-ion batteries comprise solvent mixtures, but analysis of ion transport is always based on treating the solvents as a single-entity. We combine electrophoretic NMR (eNMR) measurements and molecular dynamics (MD) simulations to quantify electric-field-induced transport in a concentrated solution containing LiPF 6 salt dissolved in an ethylene carbonate/ethyl methyl carbonate (EC/EMC) mixture. The selective transport of EC relative to EMC is reflected in the difference between two transference numbers, defined as the fraction of current carried by cations relative to the velocity of each solvent species. This difference arises from the preferential solvation of cations by EC and its dynamic consequences. The simulations reveal the presence of a large variety of transient solvent-containing clusters which migrate at different velocities. Rigorous averaging over different solvation environments is essential for comparing simulated and measured transference numbers. Our study emphasizes the necessity of acknowledging the presence of four species in mixed-solvent electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Full scale structural, mechanical and dynamical properties of HIV-1 liposomes

Enveloped viruses are enclosed by a lipid membrane inside of which are all of the components necessary for the virus life cycle; viral proteins, the viral genome and metabolites. Viral envelopes are lipid bilayers that adopt morphologies ranging from spheres to tubes. The envelope is derived from the host cell during viral replication. Thus, the composition of the bilayer depends on the complex constitution of lipids from the host-cell’s organelle(s) where assembly and/or budding of the viral particle occurs. Here, molecular dynamics (MD) simulations of authentic, asymmetric HIV-1 liposomes are used to derive a unique level of resolution of its full-scale structure, mechanics and dynamics. Analysis of the structural properties reveal the distribution of thicknesses of the bilayers over the entire liposome as well as its global fluctuations. Moreover, full-scale mechanical analyses are employed to derive the global bending rigidity of HIV-1 liposomes. Finally, dynamical properties of the lipid molecules reveal important relationships between their 3D diffusion, the location of lipid-rafts and the asymmetrical composition of the envelope. Overall, our simulations reveal complex relationships between the rich lipid composition of the HIV-1 liposome and its structural, mechanical and dynamical properties with critical consequences to different stages of HIV-1’s life cycle.

59 BASIC BIOLOGICAL SCIENCES↗

Allosterically coupled conformational dynamics in solution prepare the sterol transfer protein StarD4 to release its cargo upon interaction with target membranes

Complex mechanisms regulate the cellular distribution of cholesterol, a critical component of eukaryote membranes involved in regulation of membrane protein functions directly and through the physiochemical properties of membranes. StarD4, a member of the steroidogenic acute regulator-related lipid-transfer (StART) domain (StARD)-containing protein family, is a highly efficient sterol-specific transfer protein involved in cholesterol homeostasis. Its mechanism of cargo loading and release remains unknown despite recent insights into the key role of phosphatidylinositol phosphates in modulating its interactions with target membranes. We have used large-scale atomistic Molecular dynamics (MD) simulations to study how the dynamics of cholesterol bound to the StarD4 protein can affect interaction with target membranes, and cargo delivery. We identify the two major cholesterol (CHL) binding modes in the hydrophobic pocket of StarD4, one near S136&S147 (the Ser-mode), and another closer to the putative release gate located near W171, R92&Y117 (the Trp-mode). We show that conformational changes of StarD4 associated directly with the transition between these binding modes facilitate the opening of the gate. To understand the dynamics of this connection we apply a machine-learning algorithm for the detection of rare events in MD trajectories (RED), which reveals the structural motifs involved in the opening of a front gate and a back corridor in the StarD4 structure occurring together with the spontaneous transition of CHL from the Ser-mode of binding to the Trp-mode. Further analysis of MD trajectory data with the information-theory based NbIT method reveals the allosteric network connecting the CHL binding site to the functionally important structural components of the gate and corridor. Mutations of residues in the allosteric network are shown to affect the performance of the allosteric connection. These findings outline an allosteric mechanism which prepares the CHL-bound StarD4 to release and deliver the cargo when it is bound to the target membrane.

59 BASIC BIOLOGICAL SCIENCES↗

Effect of Sulfonation Level on the Percolated Morphology and Proton Conductivity of Hydrated Fluorine-Free Copolymers: Experiments and Simulations

Using all-atom molecular dynamics simulations and a variety of experimental methods, we previously reported on a linear polyethylene with pendant phenyl sulfonated groups precisely on every fifth carbon along the backbone. With increasing relative humidity this fluorine-free polymer self-assembled to form nanoscale water channels and exhibited exceptional proton conductivity. Expanding upon those findings, here we explore partially sulfonated random copolymers, referred to as p 5PhSH-Y. Using either acetyl sulfate or sulfuric acid, a wide range of sulfonation levels were prepared ( Y = 34−98%) corresponding to ion-exchange capacities (IEC) of 2.0−4.4 mmol/g. Combining experimental techniques and all-atom molecular dynamics simulations, we study the effect of Y on water uptake, nanoscale morphology, and the proton/water transport properties of p5PhSH- Y . The proton conductivity of p 5PhSH- Y increases with relative humidity and with Y and achieves values in excess of 0.1 S/cm. These high conductivities are attributed to high IEC and welldeveloped nanoscale percolated hydrophilic domains made possible by the flexible backbone. We quantitatively describe the nature of the water channels using the characteristic distance, channel width distribution, the area per sulfonate group at the hydrophilic/ hydrophobic interface, and the fractal dimension. Notably, the channel widths and the areas per sulfonate group are nominally independent of the level of sulfonation, while depending significantly on the level of hydration. The fractal dimension of the water channels correlates strongly with the water diffusion coefficients calculated from the molecular dynamics (MD) simulations. These findings demonstrate that the p 5PhSH- Y hydrocarbon copolymers can be modified to tune properties, particularly proton conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Implementing a neural network interatomic model with performance portability for emerging exascale architectures

The two main thrusts of computational science are increasingly accurate predictions and faster calculations; to this end, the zeitgeist in molecular dynamics (MD) simulations is pursuing machine learned and data driven interatomic models, e.g. neural network potentials, and novel hardware architectures, e.g. GPUs. Current implementations of neural network potentials are orders of magnitude slower than traditional interatomic models and while looming exascale computing offers the ability to run large, accurate simulations with these models, achieving portable performance for MD with new and varied exascale hardware requires rethinking traditional algorithms, using novel data structures, and library solutions. We re-implement a neural network interatomic model in CabanaMD, an MD proxy application, built on libraries developed for performance portability. Our implementation shows significantly improved thread scaling in this complex kernel as compared to a current LAMMPS implementation, across both strong and weak scaling. Our single-source solution enables simulations up to 20 million atoms on a single CPU node and 4 million atoms with improved performance on a single GPU. Furthermore, we also explore parallelism and data layout choices (using flexible data structures called AoSoAs) and their effect on performance, seeing up to ~50% and ~5% improvements in performance on a GPU by choosing the right level of parallelism and data layout respectively.

97 MATHEMATICS AND COMPUTING↗