Multiscale modelling:approaches and challenges

Multiscale systems that are characterized by a great range of spatial–temporal scales arise widely in many scientific domains. These range from the study of protein conformational dynamics to multiphase processes in, for example, granular media or haemodynamics, and from nuclear reactor physics to astrophysics. Despite the diversity in subject areas and terminology, there are many common challenges in multiscale modelling, including validation and design of tools for programming and executing multiscale simulations. This Theme Issue seeks to establish common frameworks for theoretical modelling, computing and validation, and to help practical applications to benefit from the modelling results. This Theme Issue has been inspired by discussions held during two recent workshops in 2013: ‘Multiscale modelling and simulation’ at the Lorentz Center, Leiden (http://www.lorentzcenter.nl/lc/web/2013/569/info.php3?wsid=569&venue=Snellius), and ‘Multiscale systems: linking quantum chemistry, molecular dynamics and microfluidic hydrodynamics’ at the Royal Society Kavli Centre. The objective of both meetings was to identify common approaches for dealing with multiscale problems across different applications in fluid and soft matter systems. This was achieved by bringing together experts from several diverse communities.

Multiscale molecular dynamics/hydrodynamics implementation of two dimensional “Mercedes Benz” water model

A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the two-way coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed.

Simultaneous material and structural optimization by multiscale topology optimization

Acknowledgments The authors acknowledge the support from Engineering and Physical Sciences Research Council, grant number EP/M002322/1. The authors would also like to thank Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/).

Multiscale photoacoustic tomography using reversibly switchable bacterial phytochrome as a near-infrared photochromic probe.

Photoacoustic tomography (PAT) of genetically encoded probes allows for imaging of targeted biological processes deep in tissues with high spatial resolution; however, high background signals from blood can limit the achievable detection sensitivity. Here we describe a reversibly switchable nonfluorescent bacterial phytochrome for use in multiscale photoacoustic imaging, BphP1, with the most red-shifted absorption among genetically encoded probes. BphP1 binds a heme-derived biliverdin chromophore and is reversibly photoconvertible between red and near-infrared light-absorption states. We combined single-wavelength PAT with efficient BphP1 photoswitching, which enabled differential imaging with substantially decreased background signals, enhanced detection sensitivity, increased penetration depth and improved spatial resolution. We monitored tumor growth and metastasis with ∼ 100-μm resolution at depths approaching 10 mm using photoacoustic computed tomography, and we imaged individual cancer cells with a suboptical-diffraction resolution of ∼ 140 nm using photoacoustic microscopy. This technology is promising for biomedical studies at several scales.

Multiscale Analysis for Field-Effect Penetration through Two-Dimensional Materials

Gate-tunable two-dimensional (2D) materials-based quantum capacitors (QCs) and van der Waals heterostructures involve tuning transport or optoelectronic characteristics by the field effect. Recent studies have attributed the observed gate-tunable characteristics to the change of the Fermi level in the first 2D layer adjacent to the dielectrics, whereas the penetration of the field effect through the one-molecule-thick material is often ignored or oversimplified. Here, we present a multiscale theoretical approach that combines first-principles electronic structure calculations and the Poisson–Boltzmann equation methods to model penetration of the field effect through graphene in a metal–oxide–graphene–semiconductor (MOGS) QC, including quantifying the degree of “transparency” for graphene two-dimensional electron gas (2DEG) to an electric displacement field. We find that the space charge density in the semiconductor layer can be modulated by gating in a nonlinear manner, forming an accumulation or inversion layer at the semiconductor/graphene interface. The degree of transparency is determined by the combined effect of graphene quantum capacitance and the semiconductor capacitance, which allows us to predict the ranking for a variety of monolayer 2D materials according to their transparency to an electric displacement field as follows: graphene > silicene > germanene > WS2 > WTe2 > WSe2 > MoS2 > phosphorene > MoSe2 > MoTe2, when the majority carrier is electron. Our findings reveal a general picture of operation modes and design rules for the 2D-materials-based QCs.

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Multiscale morphology design of hybrid halide perovskites through a polymeric template

Hybrid halide perovskites have emerged as promising active constituents of next generation solution processable optoelectronic devices. During their assembling process, perovskite components undergo very complex dynamic equilibria starting in solution and progressing throughout film formation. Finding a methodology to control and affect these equilibria, responsible for the unique morphological diversity observed in perovskite films, constitutes a fundamental step towards a reproducible material processability. Here we propose the exploitation of polymer matrices as cooperative assembling components of novel perovskite CH3NH3PbI3 : polymer composites, in which the control of the chemical interactions in solution allows a predictable tuning of the final film morphology. We reveal that the nature of the interactions between perovskite precursors and polymer functional groups, probed by Nuclear Magnetic Resonance (NMR) spectroscopy and Dynamic Light Scattering (DLS) techniques, allows the control of aggregates in solution whose characteristics are strictly maintained in the solid film, and permits the formation of nanostructures that are inaccessible to conventional perovskite depositions. These results demonstrate how the fundamental chemistry of perovskite precursors in solution has a paramount influence on controlling and monitoring the final morphology of CH3NH3PbI3 (MAPbI3) thin films, foreseeing the possibility of designing perovskite : polymer composites targeting diverse optoelectronic applications.

Impact of Thresholds and Load Patterns when Executing HPC Applications with Cloud Elasticity

Elasticity is one of the most known capabilities related to cloud computing, being largely deployed reactively using thresholds. In this way, maximum and minimum limits are used to drive resource allocation and deallocation actions, leading to the following problem statements: How can cloud users set the threshold values to enable elasticity in their cloud applications? And what is the impact of the application’s load pattern in the elasticity? This article tries to answer these questions for iterative high performance computing applications, showing the impact of both thresholds and load patterns on application performance and resource consumption. To accomplish this, we developed a reactive and PaaS-based elasticity model called AutoElastic and employed it over a private cloud to execute a numerical integration application. Here, we are presenting an analysis of best practices and possible optimizations regarding the elasticity and HPC pair. Considering the results, we observed that the maximum threshold influences the application time more than the minimum one. We concluded that threshold values close to 100% of CPU load are directly related to a weaker reactivity, postponing resource reconfiguration when its activation in advance could be pertinent for reducing the application runtime.

Structure dependencies for multiscale polymer composites using extrusion processes

Multiscale reinforcement, using carbon microfibers and multi-walled carbon nanotubes, of polymer matrix composites manufactured by twin-screw extrusion is investigated for enhanced mechanical and thermal properties with an emphasis on the use of a diverging flow in the die for fluid mechanical fiber manipulation. Using fillers at different length scales (microscale and nanoscale), synergistic combinations have been identified to produce distinct mechanical and thermal behavior. Fiber manipulation has been demonstrated experimentally and computationally, and has been shown to enhance thermal conductivity significantly. Finally, a new physics driven predictive model for thermal conductivity has been developed based on fiber orientation during flow, which is shown to successfully capture composite thermal conductivity.

Multiscale Schemes for the BGK--Vlasov--Poisson System in the Quasi-Neutral and Fluid Limits. Stability Analysis and First Order Schemes

This paper deals with the development and the analysis of asymptotically stable and consistent schemes in the joint quasi-neutral and fluid limits for the collisional Vlasov-Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Refined composite multiscale permutation entropy to overcome multiscale permutation entropy length dependence

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