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• A multiscale model is established to study the spatial ALD on porous electrodes. • The macro-scale CFD and pore-scale diffusion–reaction kinetics are coupled. • A lower pressure increases the coating depth but also causes precursor intermixing. • Various process conditions are optimized to improve the coating efficiency. • With a gradient porosity design, the maximum precursor utilization reaches 78%. The self-limiting surface reaction characteristic of atomic layer deposition (ALD) makes it ideal for the surface modification of electrode materials for lithium-ion batteries (LIBs). Spatial ALD shows promise as a scalable method for the coating on pre-fabricated electrode sheets. As a strong-coupled multiscale process, various process conditions and microstructure parameters have great influences on the macroscale fluid dynamics and the pore-scale diffusion–reaction process, thus affecting the coating efficiency. This study presents a multiscale numerical model that combines computational fluid dynamics (CFD) with multilevel pore-scale diffusion–reaction kinetics to explore the spatial ALD process on porous LIB electrodes. The dynamic mesh method is utilized to simulate electrode movement. The considerable active surface-to-volume ratio of the porous structure limits the precursor infiltration depth due to the low diffusion rate and inadequate precursor supply. As the electrode velocity increases, an asymmetric distribution of precursor concentration under the injector is observed with a rapid decrease. Elevating both the precursor concentration and inlet gas velocity augments the coating depth by enhancing the supply of the precursor. The experimental data aligns well with our numerical results, verifying the accuracy of the multiscale CFD model. Our observations reveal that a relatively lower operating pressure, around 0.1 atm, compared to 0.01 atm and 1 atm, optimizes the deposition rate along the electrode depth during the half-ALD cycle, especially when the pore size is larger. Electrode porosity of about 0.4 notably improves coating uniformity by elevating the precursor diffusion rate. Predictions show that with a substrate velocity of 0.2 m/s, the coating depth on an electrode having higher porosity at the top compared to the bottom via atmospheric spatial ALD could reach a depth of 38 μm with a precursor utilization of 78 %. [ABSTRACT FROM AUTHOR]

Determination of the changes in cellular-level structural, mechanical, rheological and transport properties during the processing of plant-based food materials (PBFM) is extremely complicated and therefore, mostly unknown. Moreover, for mathematical modelling of the processes, such as drying, accurate properties are necessary. Due to the lack of these properties, such predictions made remain less accurate, less generalised and ignoring multiscale aspects. Recent advances in cellular-level microscopy and related micro imaging techniques, such as X-ray Micro Computed Tomography (X-ray μCT), Atomic Force Microscopy (AFM), Nuclear Magnetic Resonance (NMR), have spurred interest in such investigations particularly within plant and animal cells while only a few have been applied in PBFM drying research. This review aims to provide comprehensive understanding on recent advancements in exploring evolving cellular-level properties during the thermal processing of PBFM, with a primary emphasis on the drying process. Potential advancements in such investigations, limitations and possible remediation have also been reported. The nature of PBFM, their multiscale nature, cellular-level microstructure, and the dynamic nature of process conditions applied during PBFM drying result in various interconnected and interdependent cellular-level property alterations. The evolving structure due to water migration during drying primarily governs other cellular property alterations. Cellular-level mechanical and rheological property alterations during PBFM drying have not been studied so far. The adoption of advanced methods/protocols applied in similar research fields, is expected to contribute to investigating qualitative and quantitative properties of PBFM while facilitating paradigm shift towards multiscale drying modelling. • Cellular-level property changes in PBFM during drying are complicated and mostly unexplored. • Evolving cell structure governs other properties including mechanical, rheological, and transport properties. • Cell-level changes can be unveiled by employing advanced micro-imaging techniques and protocols. • Understanding of cell-level property changes will aid in optimising process using modelling/simulation approaches. [ABSTRACT FROM AUTHOR]

• Gaining deeper insight in kraft pulping delignification. • Modelling the phenolic and non-phenolic β O 4 bonds splitting during delignification. • Decoupling kinetics and solubility phenomena. • Discussion of further research direction related to mass transfer limitation. This article presents a novel concept for modelling the kinetics and related phenomena of the kraft pulping process on a macromolecule level with the initial objective to explicitly model and relate the breakage of phenolic and non-phenolic β O 4 bonds to the observed three-stage delignification profile. The modelling frameworks consist of the building and the fragmentation of the lignin macromolecules. The macromolecules are modelled as stochastic graphs where monolignol object nodes are reassembled in a Monte Carlo approach into internal structures, which aggregate to a lignin macromolecule interconnected through chemical bonds represented by the edges of the graphs. The fractionation follows the splitting of β O 4 ether bonds with different configurations resulting from functional groups attached to the monolignols, namely the phenolic and non-phenolic β O 4 bonds with their respective stereochemistry. It is tested against a previously published model based on an extension of the established Purdue kinetic model and experimental data. The results align with the observed delignification trajectory during kraft pulping, and the hypothesis that β O 4 bonds splitting is mainly responsible for the delignification. However, some discrepancies between the current model, the previous model and experimental data are presented. These differences are discussed in the context of recent experimental findings indicating that β O 4 bonds splitting might not entirely be responsible for the delignification due to mass transfer/solubility effects limitations. [ABSTRACT FROM AUTHOR]

The human brain is the most complicated biological structure on the planet. A major challenge of brain network modelling lies in its multi-scale spatio-temporal nature, covering scales from synapses to the whole brain. The coupled multiphysics and biochemical activities which spread through such a complex system shape brain capacity inside a structure-function relationship that requires a particular mathematical framework. Next-generation coupled-based mathematical modelling approaches to brain networks and the analysis of data-driven dynamical systems are needed to advance state-of-the-art therapeutic strategies for treating neurodegenerative diseases (NDDs) that affect millions of people worldwide, such as Alzheimer's disease (AD) and Parkinson's disease (PD). Importantly, AD is marked by the presence of amyloid-beta (A β) plaques and tau (τ) proteins. Some disease-specific misfolded proteins can interact with healthy proteins to form long chains and aggregates of different sizes that have different transport properties and toxicity. An improved large-scale brain network model is proposed here to understand the pathogenesis of AD, especially the role of astrocytes in the presence of misfolded proteins (A β and τ). The idea involves astrocytic clearance, which assists in eliminating toxic A β via fragmentation. We use the general Smoluchowski theory of nucleation, aggregation, and fragmentation to predict the development and propagation of aggregates of misfolded proteins in the brain. It has been shown that the developed model leads to different size distributions and propagation along the network. We predicted that astrocytic clearance varies with the aggregate size, which is key to slowing down AD progression. The clearance and fragmentation of toxic proteins span several spatial and temporal scales, and this research will potentially yield new insight into the associated processes and brain networks in health and disease. Detailed multi-scale brain modelling provides a promising approach for consolidating, organizing, and bridging the data sets of data-driven brain network models. • Large-scale brain network model is proposed to understand Alzheimer's pathogenesis. • Spatio-temporal monomer patterns obtained over large-scale brain networks. • Brain data is collected from Human Connectome Project. • Astrocytic clearance aids elimination of toxic amyloid beta via fragmentation. • Simulation validates size distributions and network propagation in model. [ABSTRACT FROM AUTHOR]

The main objective of the study was to implement the wave model in two independent systems fed respectively by wind fields with a 4 km resolution in the Baltic-wide area and a 2 km resolution in the shallow coastal regions of the southern Baltic for operational work. The study included the selection the best parameterization, which was carried out using measured data and model data from the verified SWAN-COSMO system. The chosen best parameterization of the model, including the time step, iteration, wind scaling, dispersion coefficients and swell formula, among others, allowed the identification of the optimal system that guarantees the most reliable predictions. The most reliable forecasts reproducing real conditions, both for the model powered by wind fields with a resolution of 4 km and 2 km, were obtained for the configuration characterized by the parameters: 30-min time step, 3 iterations, a wind scaling factor of 32 using DEBIAS equal to 0.89, coefficients related to local dissipation and cumulative of 2.8 × 10–6 and 3.5 × 10–5, respectively, and Ardhiun's swell formula of 1.20. The values of the correlation coefficient with both the measured data and the results of the comparative model for significant wave height and wave period, respectively, were no lower than: 0.95 and 0.73 (Petrobaltic) and 0.96 and 0.90 (Pomeranian Bay). Root mean square error (RMSE) values were <0.23 m and <0.20 s (Petrobaltic) and <0.20 m and <0.74 s (Pomeranian Bay) for significant wave height and mean wave period, respectively. Analysis of the forecast results showed some limitations in using the mesoscale model in coastal areas, and the solution was to use the high-resolution model in this zone. It was shown that the stand-alone high-resolution model (domain: southern Baltic Sea) obtained similar results to the same model system but nested in the mesoscale model (domain: Baltic Sea). In addition, this model showed shorter simulation computation time and represents an independent, less vulnerable to discontinuity in forecast generation (lack of assimilation of boundary and initial conditions from a lower resolution model). A noticeable improvement in the quality of forecasts was shown by the AROME wind-field-powered model, which, due to its high resolution of the computational grid and wind data, maps well the wave dynamics in areas with limited wave exposure (the Vistula Lagoon, the Puck Lagoon) or complex coastline (the Hel Split) and seabed (the shallows of the Pomeranian Gulf and the Słupsk Shoal. The coupled data from the ALARO and AROME models, processed internally at IMWM-NRI, provide continuity and independence from global models and indicate applicability in generating wave forecasts by other Baltic countries. • SWAN wave model coupled with ALARO and AROME has been implemented for the Baltic. • The best parameterization was selected for both models based on ST6 physics. • SWAN ST6 physics have been calibrated for the Southern Baltic. • Coupled wave model with ALARO and AROME showed more reliable results in the coastal zone than COSMO. • Nested high-resolution model showed no significant differences compared to the standalone model. [ABSTRACT FROM AUTHOR]

In recent years, the multi-particle finite element method (MPFEM) has demonstrated its suitability for the micromechanical modelling of granular systems made up of highly deformable particles. This method combines the advantages of the finite element method to compute particles' deformations and of the discrete element method to simulate particles' interactions. Being computationally expensive, its main drawback is the limitation of the number of particles which can be included in a simulation. However, using a multi-scale approach, it is possible to deduce mesoscopic material properties from the simulation of a relatively small number of particles within an elementary volume, through appropriate averaging techniques. Such simulations are significantly influenced by the boundary conditions (BCs) applied. Periodic BCs are commonly admitted to be the most accurate. However, they are technically rather difficult to implement in the MPFEM because of the multiple contacts which need to be handled in the model. As a result, simplified BCs involving for example, rigid walls, remain used. This study analyses the effect of different types of BCs on the simulated mechanical response of a numerical granular sample, under quasi-static loading. Two different techniques for implementing full or simplified periodic BCs, introduced by Schmidt et al. [1] and Loidolt et al. [2] , respectively, were compared with simpler, non-periodic BCs. In the comparison, the same initial microstructure was used; it consisted of an assembly of 50 spherical particles with a periodic topology. The results suggest that considering the additional computational cost induced by the implementation of multi-point constraints, the advantage brought by periodic BCs is relatively limited. The study also highlights the differences between BC types and provides interpretations relative to the particularities of the numerical method used. [ABSTRACT FROM AUTHOR]

As global power generation is currently relying on fossil fuel-based power plants, more anthropogenic CO2 is being released into the atmosphere. During the transition period to alternative energy sources, carbon capture and storage seems to be a promising solution. Chemical-looping combustion (CLC) is an energy conversion technology designed for combustion of fossil fuel with advantageous carbon capture capabilities. In this work, a 1D computational fluid dynamics (CFD) multiscale model was developed to study the reduction step in a syngas-based CLC system and was validated using literature data (R=0.99). In order to investigate mass transfer effects, flow rate and particle dimension studies were carried out. Sharper mass transfer rates were seen at lower flow rates and smaller granule sizes due to suppression of diffusion limitations. In addition, a 3D CFD particle model was developed to investigate in depth the reduction within an ilmenite particle, with focus on heat transfer effects. Minor differences of 1 K were seen when comparing temperature changes predicted by the two models during the slightly exothermic reduction reaction with syngas.

Fibre-reinforced composite materials are used in structural applications in marine, offshore, and oil and gas industries due to their light weight and excellent mechanical properties. However, the exposure of such materials to water leads to environmental ageing, weakening the composite over time. A typical design lifetime of offshore composite structures, being in direct contact with water and humid air, spans 25 years or more. Thus, the prediction and modelling of environmental ageing phenomena has become highly important, especially for predicting long-term environmental durability. In this study, a systematic and modular approach for quantitatively modelling such phenomena is provided. The modular methodology presented in this work can, and should, be further expanded—it is multiscale and scalable. A state-of-the-art degradation framework is not yet complete; however, it is a systematic step towards the multiscale modelling paradigm for composite materials. The topic of the environmental durability of composite materials is being actively developed and is expected to continue growing in the future. There are three constituents in a composite: matrix, fibres, and an interphase. Each constituent degrades differently and may also affect the degradation behaviour of each other. Therefore, a modular multiscale approach is preferred. The modules are based on the physics and chemistry of individual constituents’ interaction with the environment, including the diffusion, molecular mechanisms, and kinetics of environmental ageing [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. The methodology is seen as a useful approach for both industry and academia, including such use cases as accelerated testing, prediction of the lifetime of composite materials and structures, as well as improving the understanding of environmental ageing effects and the time-dependent properties of composites due to environmental ageing.

Modelling of infectious disease systems has entered a new era in which disease modellers are increasingly turning to multiscale modelling to extend traditional modelling frameworks into new application areas and to achieve higher levels of detail and accuracy in characterizing infectious disease systems. In this paper we present a categorization framework for categorizing multiscale models of infectious disease systems. The categorization framework consists of five integration frameworks and five criteria. We use the categorization framework to give a complete categorization of host-level immuno-epidemiological models (HL-IEMs). This categorization framework is also shown to be applicable in categorizing other types of multiscale models of infectious diseases beyond HL-IEMs through modifying the initial categorization framework presented in this study. Categorization of multiscale models of infectious disease systems in this way is useful in bringing some order to the discussion on the structure of these multiscale models.

Volume change and large deformation occur in different solid and semi-solid foods during processing, e.g., shrinkage of fruits and vegetables during drying and of meat during cooking, swelling of grains during hydration, and expansion of dough during baking and of snacks during extrusion and puffing. In addition, food is broken down during oral processing. Such phenomena are the result of complex and dynamic relationships between composition and structure of foods, and driving forces established by processes and operating conditions. In particular, water plays a key role as plasticizer, strongly influencing the state of amorphous materials via the glass transition and, thus, their mechanical properties. Therefore, it is important to improve the understanding about these complex phenomena and to develop useful prediction tools. For this aim, different modelling approaches have been applied in the food engineering field. The objective of this article is to provide a general (non-systematic) review of recent (2005–2021) and relevant works regarding the modelling and simulation of volume change and large deformation in various food products/processes. Empirical- and physics-based models are considered, as well as different driving forces for deformation, in order to identify common bottlenecks and challenges in food engineering applications.

Aerostatic bearing slideways have been increasingly applied in the precision engineering industry and other high-tech sectors over the last two decades or so, due to their considerable advantages over mechanical slideways in terms of high motion accuracy, high speeds, low friction, and environment-friendly operations. However, new challenges in air bearings design and analysis have been occurring and often imposed along the journeys. An industrial-feasible approach for the design and development of aerostatic bearing slideways as standard engineering products is essential and much needed particularly for addressing their rapid demands in diverse precision engineering sectors, and better applications and services in a continuous sustainable manner. This paper presents the multiscale modelling and analysis-based approach for design and development of the aerostatic bearing slideways and its digital twin. The multiscale modelling and analysis and the associated simulation development can be the kernel of the digital twin, which cover the mechanical design, direct drive and control, dynamics tuning of the slideway, and their entire mechatronic system integration. Using this approach and implementation, the performance of an aerostatic bearing slideway can be predicted and assessed in the process. The implementation perspectives for the sideway digital twin are presented and discussed in steps. The digital simulations and digital twin system can be fundamentally important for continuously improving the design and development of aerostatic bearing slideways, and their applications and services in the context of industry 4.0 and beyond.

The modern era of research in immunology is characterized by an unprecedented level of detail about structural characteristics of the immune system and the regulation of activities of its numerous components, which function together as a whole distributed-parameter system. Mathematical modeling provides an analytical tool to describe, analyze, and predict the dynamics of immune responses by applying a reductionist approach. In modern systems immunology and mathematical immunology as a new interdisciplinary field, a great challenge is to formulate the mathematical models of the human immune system that reflect the level achieved in understanding its structure and describe the processes that sustain its function. To this end, a systematic development of multiscale mathematical models has to be advanced. An appropriate methodology should consider (1) the intracellular processes of immune cell fate regulation, (2) the population dynamics of immune cells in various organs, and (3) systemic immunophysiological processes in the whole host organism. Main studies aimed at modeling the intracellular regulatory networks are reviewed in the context of multiscale mathematical modelling. The processes considered determine the regulation of the immune cell fate, including activation, division, differentiation, apoptosis, and migration. Because of the complexity and high dimensionality of the regulatory networks, identifying the parsimonious descriptions of signaling pathways and regulatory loops is a pressing problem of modern mathematical immunology. [ABSTRACT FROM AUTHOR]

We consider basic and easily extendible transport formulations for lithium batteries consisting of an anode (Li-foil), a separator (polymer electrolyte), and a composite cathode (composed of electrolyte and intercalation particles). Our mathematical investigations show the following novel features: (i) complete and very basic description of mixed transport processes relying on a neutral, binary symmetric electrolyte resulting in a non-standard Poisson equation for the electric potential together with interstitial diffusion approximated by classical diffusion; (ii) upscaled and basic composite cathode equations allowing to take geometric and material features of electrodes into account ; (iii) the derived effective macroscopic model can be numerically solved with well-known numerical strategies for homogeneous domains and hence does not require to solve a high-dimensional numerical problem or to depend on computationally involved multiscale discretization strategies where highly heterogeneous and realistic, nonlinear, and reactive boundary conditions are still unexplored. We believe that the here proposed basic and easily extendible formulations will serve as a basic and simple setup towards a systematic theoretical and experimental understanding of complex electrochemical systems and their optimization, e.g. Li-batteries. [ABSTRACT FROM AUTHOR]

Non-prescriptive design within fire engineering is becoming more prevalent as buildings get taller and more complex. This necessitates the increased use of reliable deterministic predictions, typically computational fluid dynamics-based models. Driven by time constraints, modellers are required to limit the domain to reduce wall time. This ignores the two-way coupling of a fire and a total building system which could embody risk to life. One way to address this risk is the use of coupled hybrid modelling to expand the domain, explicitly quantifying risk-related quantities in the far field whilst maintaining practicable wall times. Fire Dynamics Simulator (FDS) version 5.5 opened the door to coupled hybrid modelling within FDS and introduced the HVAC network submodel. Until FDS version 6.5.3, the submodel did not account for transient transport or mass storage. In this work, a new transient transport and mass storage subroutine has been introduced into HVAC which is available in FDS version 6.5.3 onwards. The relevant conservation equations and numerical solution are described. Successful verification cases are presented for various arrangements to test the implementation of the solution scheme. To demonstrate the benefits of the new method, a fire engineering test case is presented. The test case illustrates the potential risks contained within the pre-existing coupled hybrid modelling method. These risks include unrealistic predictions of hot layer height and head height temperatures and visibility. The test case demonstrates that the new coupled hybrid modelling method address these shortcomings and could form part of a most robust fire safety engineering solution. Based on experimental benchmarking exercises, recommended model correction coefficients are put forward. The new model implementation can be used by designers to quantitatively examine the fire hazard embodied within the two-way coupling of a fire and a total building system. [ABSTRACT FROM AUTHOR]

Experimental method and multiscale modelling based on molecular dynamics simulation have been used to determine mechanical properties of carbon nanotube and graphene nanoplatelet hybrid nanocomposites. Samples containing two different mix ratios of hybrid nanofillers were subjected to tensile loading. Also, micrographs were obtained from samples fracture surfaces using field emission scanning electron microscope and SEM. These images showed that nanofillers were well dispersed in the matrix. In multiscale modelling, a new method has been developed to estimate the Young's moduli of hybrid nanocomposite samples. To this end, atomistic modelling has been employed to investigate the mechanical properties of molecular samples at nanoscale level. In this step, epoxy cross-linked atomic models have been constructed utilizing molecular dynamics. Next, micromechanical modelling was used to bridge elastic constants of molecular samples from nanoscale to microscale. Also, the calculated Young's moduli of the hybrid nanocomposite samples obtained from multiscale modelling were compared with experimental measurements and differences less than 7% were observed. Finally, the effects of effective fibre aspect ratio on elastic modulus of hybrid nanocomposite were investigated using the multiscale method. The results indicated an increase in hybrid nanocomposite Young's modulus with effective fibre aspect ratio. In summary, this paper presents a new method for calculating the hybrid polymer-based nanocomposite properties using a multiscale method. [ABSTRACT FROM AUTHOR]

Two multiscale algorithms for stochastic simulations of reaction–diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction–diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches. [ABSTRACT FROM AUTHOR]

Recognised as one of the hallmarks of cancer, local cancer cell invasion is a complex multiscale process that combines the secretion of matrix-degrading enzymes with a series of altered key cell processes (such as abnormal cell proliferation and changes in cell–cell and cell–matrix adhesion leading to enhanced migration) to degrade important components of the surrounding extracellular matrix (ECM) and this way spread further in the human tissue. In order to gain a deeper understanding of the invasion process, we pay special attention to the interacting dynamics between the cancer cell population and various constituents of the surrounding tumour microenvironment. To that end, we consider the key role that ECM plays within the human body tissue, and in particular we focus on the special contribution of its fibrous proteins components, such as collagen and fibronectin, which play an important part in cell proliferation and migration. In this work, we consider the two-scale dynamic cross-talk between cancer cells and a two-component ECM (consisting of both a fibre and a non-fibre phase). To that end, we incorporate the interlinked two-scale dynamics of cell–ECM interactions within the tumour support that contributes simultaneously both to cell adhesion and to the dynamic rearrangement and restructuring of the ECM fibres. Furthermore, this is embedded within a multiscale moving boundary approach for the invading cancer cell population, in the presence of cell adhesion at the tissue scale and cell-scale fibre redistribution activity and leading edge matrix-degrading enzyme molecular proteolytic processes. The overall modelling framework will be accompanied by computational results that will explore the impact on cancer invasion patterns of different levels of cell adhesion in conjunction with the continuous ECM fibres rearrangement. [ABSTRACT FROM AUTHOR]

• Refined multiscale model is employed to investigate nonlinear response of the graphene sheets. • The effect of the dihedral energy terms on the nonlinear response of the graphene sheets is reported. • The atomistic and continuum deformations are coupled through the Cauchy–Born rule. • Proposed multiscale model is more accurate as compare to existing models because of its greater accuracy on the bending modulus. Computationally efficient multiscale model based on the refined constitutive law, including second generation reactive empirical bond order potential with dihedral energy term, is employed to investigate the static response of the graphene sheets under transverse and in-plane compressive loads including material nonlinearity through atomic interactions and Green-Lagrange geometric nonlinearity through the strain displacement relations. The bending modulus of the graphene sheet predicted without considering the dihedral energy term in the constitutive law is almost half than those of predicted through first principle calculations. The inclusion of the dihedral energy term predicts bending modulus close to those of through first principle calculations. The atomistic and continuum deformations are coupled through the Cauchy–Born rule. In the present study, the effect of the dihedral energy term on the linear and nonlinear bending and postbuckling response of the graphene sheets under transverse and in-plane compressive loads is investigated in detail. The governing finite element equations for the graphene sheet are derived through the principle of minimum potential energy. The spatial approximation of the graphene sheet at the continuum scale is attained through the finite element method. [ABSTRACT FROM AUTHOR]

The thrust of this paper is that micromechanics goes beyond homogenization when it is regarded as a multiscale modeling approach. Using metal plasticity as an example, the paper illustrates how macroscopic irreversibility is a natural consequence of emergent behaviour in space and in time. Special attention is given to the currently weak link between discrete dislocation plasticity and continuum crystal plasticity, and how dislocation interactions give rise to power law viscoplasticity. As an outlook it is suggested that, by enlarging its mission to coarse graining in space ànd time, micromechanics can play an important role in the understanding and description of new supramolecular materials. [ABSTRACT FROM AUTHOR]

Background: Inference of gene regulatory networks from gene expression data has been a long-standing and notoriously difficult task in systems biology. Recently, single-cell transcriptomic data have been massively used for gene regulatory network inference, with both successes and limitations. Results: In the present work we propose an iterative algorithm called WASABI, dedicated to inferring a causal dynamical network from time-stamped single-cell data, which tackles some of the limitations associated with current approaches. We first introduce the concept of waves, which posits that the information provided by an external stimulus will affect genes one-by-one through a cascade, like waves spreading through a network. This concept allows us to infer the network one gene at a time, after genes have been ordered regarding their time of regulation. We then demonstrate the ability of WASABI to correctly infer small networks, which have been simulated in silico using a mechanistic model consisting of coupled piecewise-deterministic Markov processes for the proper description of gene expression at the single-cell level. We finally apply WASABI on in vitro generated data on an avian model of erythroid differentiation. The structure of the resulting gene regulatory network sheds a new light on the molecular mechanisms controlling this process. In particular, we find no evidence for hub genes and a much more distributed network structure than expected. Interestingly, we find that a majority of genes are under the direct control of the differentiation-inducing stimulus. Conclusions: Together, these results demonstrate WASABI versatility and ability to tackle some general gene regulatory networks inference issues. It is our hope that WASABI will prove useful in helping biologists to fully exploit the power of time-stamped single-cell data. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Simulation of convection-reaction-diffusion for heterogenous catalytic reactors. • Numerical computation of bulk mutual diffusivity using SRD. • Incorporation of complex reaction systems while maintaining the interfacial physics. • Dimensionless analysis to convey physical information between reactive systems. • Different modeling examples show from linear systems to nonlinear reaction systems. Abstract Particle based approaches are one of the recent modeling techniques to overcome the computational limitation in multiscale modeling of complex processes, for example a heterogeneous catalytic reactor. We propose an efficient model for a chemical reactor where hydrodynamics of the solvent is determined by Stochastic Rotation Dynamics and a reaction occurs over a catalytic surface where the reaction kinetics follows the mean-field assumption. We highlight the modeling techniques required to simulate such a system and then validate the model for its separate and combined components of convection, diffusion and reaction(s). A dimensionless analysis helps compare processes occurring at different scales. We determine the Reynolds number, Re , and the Damkohler numbers, Da and Da L in terms of key quantities. The approach is then used to analyse a reaction (a) following the Langmuir-Hinshelwood kinetics, (b) generating product particles with different self-diffusivity values as compared to the reactant particles. The model developed can further incorporate reactions occurring inside complex geometries (pore diffusion) and also be used to study complex reaction systems for which the mean-field assumption is no longer valid. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a multi-scale structure finite element modelling scheme to analyse the damage behaviors of Kenaf fiber reinforced composite materials subjected to high strain rate compressions. The proposed modelling framework includes a micro-scale structure model with periodic boundary conditions for homogenizing the heterogeneous fiber/resin system into a unit cell, and a meso-scale model with established constitutive relationship for the constituents integrated with failure criterion to account for the stiffness degradation and subsequent element removal. The finite element results from the model provide the localities of stress propagation, the stress distribution, and the progressive failure behaviour within the Kenaf fiber reinforced composite materials. The results which are stress-strain behaviour and developed damages are found to be in fair agreement with the available test data. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

We explore the efficiency of a semi-intrusive uncertainty quantification (UQ) method for multiscale models as proposed by us in an earlier publication. We applied the multiscale metamodelling UQ method to a two-dimensional multiscale model for the wound healing response in a coronary artery after stenting (in-stent restenosis). The results obtained by the semi-intrusive method show a good match to those obtained by a black-box quasi-Monte Carlo method. Moreover, we significantly reduce the computational cost of the UQ. We conclude that the semi-intrusive metamodelling method is reliable and efficient, and can be applied to such complex models as the in-stent restenosis ISR2D model. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'. [ABSTRACT FROM AUTHOR]

The extreme scaling pattern of the ComPat project is applied to a multi-scale workflow relevant to the magnetically confined fusion problem. This workflow combines transport, turbulence and equilibrium codes (together with additional auxiliaries such as initial conditions and numerical module), which aims at calculating the behaviour of a fusion plasma on long (transport) time scales based on information from much faster (turbulence) time scales. Initial findings of profile measurements are reported in this paper and indicate that, depending on the chosen performance metric for defining 'cost', such as time to completion, efficiency and total energy consumption of the mutliscale workflow, different choices on the number of cores would be made when determining the optimal execution configuration. A variant of the workflow which increases the inherent parallelism is presented, and shown to produce equivalent results at (typically) lower cost compared with the original workflow. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'. [ABSTRACT FROM AUTHOR]

In the last few decades, multiscale modelling has emerged as one of the dominant modelling paradigms in many areas of science and engineering. Its rise to dominance is primarily driven by advancements in computing power and the need to model systems of increasing complexity. The multiscale modelling paradigm is now accompanied by a vibrant ecosystem of multiscale computing software (MCS) which promises to address many challenges in the development of multiscale applications. In this paper, we define the common steps in the multiscale application development process and investigate to what degree a set of 21 representative MCS tools enhance each development step. We observe several gaps in the features provided by MCS tools, especially for application deployment and the preparation and management of production runs. In addition, we find that many MCS tools are tailored to a particular multiscale computing pattern, even though they are otherwise application agnostic. We conclude that the gaps we identify are characteristic of a field that is still maturing and features that enhance the deployment and production steps of multiscale application development are desirable for the long-term success of MCS in its application fields. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'. [ABSTRACT FROM AUTHOR]

For it is not the abundance of knowledge, but the interior feeling and taste of things, which is accustomed to satisfy the desire of the soul. (Saint Ignatius of Loyola). We argue that the boldest claims of big data (BD) are in need of revision and toning-down, in view of a few basic lessons learned from the science of complex systems. We point out that, once the most extravagant claims of BD are properly discarded, a synergistic merging of BD with big theory offers considerable potential to spawn a new scientific paradigm capable of overcoming some of the major barriers confronted by the modern scientific method originating with Galileo. These obstacles are due to the presence of nonlinearity, non-locality and hyperdimensions which one encounters frequently in multi-scale modelling of complex systems. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a new polymorphic element modelling approach for multi-scale simulation, with an application to fracture in composite structures. We propose the concept of polymorphic elements; these are elements that exist as an evolving superposition of various states, each representing the relevant physics with the required level of fidelity. During a numerical simulation, polymorphic elements can change their formulation to more effectively represent the structural state or to improve computational efficiency. This change is achieved by transitioning progressively between states and by repartitioning each state on-the-fly as required at any given instant during the analysis. In this way, polymorphic elements offer the possibility to carry out a multiscale simulation without having to define a priori where the local model should be located. Polymorphic elements can be implemented as simple user-defined elements which can be readily integrated in a Finite Element code. Each individual user-defined polymorphic element contains all the relevant superposed states (and their coupling), as well as the ability to self-refine. We implemented a polymorphic element with continuum (plain strain) and structural (beam) states for the multiscale simulation of crack propagation. To verify the formulation, we applied it to the multiscale simulation of known mode I, mode II andmixed-mode I and II crack propagation scenarios, obtaining good accuracy and up to 70% reduction in computational time —the reduction in computational time can potentially be even more significant for large engineering structures where the local model is a small portion of the total. We further applied our polymorphic element formulation to the multiscale simulation of a more complex problem involving interaction between cracks (delamination migration), thereby demonstrating the potential impact of the proposed multiscale modelling approach for realistic engineering problems. Highlights • New polymorphic Floating Node Method for multiscale analysis. • Element-level management of coupling between scales. • Location and extent of high-fidelity scale able to evolve during analysis. • Implementation of VCCT and CZM within polymorphic elements for multi-scale failure analysis of composite structures. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Charged impurities influence functional properties of two-dimensional materials and a detailed theoretical understanding of charged defects is required to enable a rational design of defect-engineered nanomaterials for applications in ultrathin devices. To achieve this goal, we have developed multiscale approaches that combine atomistic first-principles theories, such as density-functional theory, with coarse-grained continuum models, such as effective mass models. This allows us to model large supercells which are required to accurately describe the slow decay of the screened defect potential and the defect-induced changes in the electronic properties of the two-dimensional host material. I will describe the results of our multiscale calculations for charged defects in doped graphene and in transition-metal dichalcogenide monolayers which have revealed novel mechanisms for controlling and tuning the electronic structure of two-dimensional materials. [ABSTRACT FROM AUTHOR]

Abstract Precipitation during high temperature aging of Al−Cu alloys is analysed by means of the integration of classical nucleation theory and phase-field simulations into a multiscale modelling approach based on well-established thermodynamics principles. In particular, thermal stability of θ'', θ′ and θ precipitates was assessed from first principles calculations of the Helmholtz free energy while homogeneous and heterogeneous nucleation of θ'' and θ′ was analysed using classical nucleation theory. Precipitate growth was finally computed by means of a mesoscopic phase-field model. The model parameters that determine quantitatively the driving forces for each transformation were obtained by means of first principles calculations and computational thermodynamics. The predictions of the models were in good agreement with experimental results and provided a comprehensive understanding of the precipitation pathway in Al−Cu alloys. It is envisaged that the strategy presented in this investigation can be used in the future to design optimum microstructures based on the information of the different energy contributions obtained from first principles calculations. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

The material microstructure decisively controls the mechanical properties of the work materials and hence its machinability. Therefore, the consideration of the microstructure in machinability modelling is a very important issue. This paper deals with experimental and simulation investigations on the machinability of the ferritic-pearlitic steel C60 with different microstructures. Based on the Representative Volume Element (RVE) technique, an effective Johnson-Cook material law is derived for the investigated steel C60 via homogenization and is used in orthogonal cutting simulations based on the Coupled Eulerian-Lagrange formulation. The machinability prediction is validated with the experimental results proving the adopted microstructure-based approach. [ABSTRACT FROM AUTHOR]

Pattern formation is typically controlled through the interaction between molecular signals within a given tissue. During early embryonic development, roots of the model plant Arabidopsis thaliana have a radially symmetric pattern, but a heterogeneous input of the hormone auxin from the two cotyledons forces the vascular cylinder to develop a diarch pattern with two xylem poles. Molecular analyses and mathematical approaches have uncovered the regulatory circuit that propagates this initial auxin signal into a stable cellular pattern. The diarch pattern seen in Arabidopsis is relatively uncommon among flowering plants, with most species having between three and eight xylem poles. Here, we have used multiscale mathematical modelling to demonstrate that this regulatory module does not require a heterogeneous auxin input to specify the vascular pattern. Instead, the pattern can emerge dynamically, with its final form dependent upon spatial constraints and growth. The predictions of our simulations compare to experimental observations of xylem pole number across a range of species, as well as in transgenic systems in Arabidopsis in which we manipulate the size of the vascular cylinder. By considering the spatial constraints, our model is able to explain much of the diversity seen in different flowering plant species. [ABSTRACT FROM AUTHOR]

Abstract The so-called Locally Resonant Acoustic Metamaterials (LRAM) are considered for the design of specifically engineered devices capable of stopping waves from propagating in certain frequency regions (bandgaps), this making them applicable for acoustic insulation purposes. This fact has inspired the design of a new kind of lightweight acoustic insulation panels with the ability to attenuate noise sources in the low frequency range (below 5000 Hz) without requiring thick pieces of very dense materials. A design procedure based on different computational mechanics tools, namely, (1) a multiscale homogenization framework, (2) model order reduction strategies and (3) topological optimization procedures, is proposed. It aims at attenuating sound waves through the panel for a target set of resonance frequencies as well as maximizing the associated bandgaps. The resulting design's performance is later studied by introducing viscoelastic properties in the coating phase, in order to both analyse their effects on the overall design and account for more realistic behaviour. The study displays the emerging field of Computational Material Design (CMD) as a computational mechanics area with enormous potential for the design of metamaterial-based industrial acoustic parts. [ABSTRACT FROM AUTHOR]

Abstract High performance fibre-reinforced polymers (FRP) have successfully been established in the aerospace industry. The performance of epoxy resins used for carbon fibre reinforced plastics can be significantly improved by the incorporation of nanoparticles. A Transformation field analysis (TFA) proposed by Dvorak and co-workers is utilized to predict the properties of a representative volume of inelastic heterogeneous materials consisting of polymers and nanoparticles. Thus, the TFA method at the nanoscale can be implemented as a user routine integrated into RVE micro scale model, where the modified matrix is reinforced by a certain volume fraction of aligned fibres. This yields to save computational resources and time in combination with good efficiency compared to todays established multiscale approaches. To the author's knowledge, this is the first implementation of the TFA method for three-dimensional nanocomposites problems. Finally, a single nano level application based TFA approach and numerical multi-scale (micro/FEA-nano/TFA) application are implemented to verify the behaviour of elastic-plastic epoxy nanocomposite consisting of agglomerating fillers in nano-scale and reinforced by aligned fibres in micro-scale under different external loads. To validate this multiscale approach, a multiscale approach based TFA micro scale and TFA nano scale is processed. [ABSTRACT FROM AUTHOR]

Abstract In this contribution, a full 3D finite element model of electrospun networks is presented. The model explicitly accounts for the specific microstructure of these networks by generating representative volume elements through a particular fibre deposition method inspired by the process of network formation during electrospinning. The modelled fibre material and structural properties, such as different fibre shapes and distributions in diameter, can vary over a wide range, and mutual fibre contact is considered in addition to permanent cross-links. In addition to the homogenized mechanical response to macroscopic in-plane loads, the model provides access to structural information which can hardly be determined in experiments, such as fibre disposition and interconnectivity. In the present work, this asset is used to inform a recent 2.5D modelling approach (Zündel et al., 2017) and to validate inherent assumptions on network structure. The comparison between the responses of the two approaches reveals that for networks of high porosity, the reduced 2.5D model captures well the mechanical behaviour in plane stress load cases. At lower porosities though, the increasing out-of-plane orientation of fibre segments leads to effects that cannot be captured by planar approaches and necessitate a 3D approach. [ABSTRACT FROM AUTHOR]

Abstract A heterogeneous method of coupled multiscale strength model is presented in this paper for calculating the strength of medical polyesters such as polylactide (PLA), polyglycolide (PGA) and their copolymers during degradation by bulk erosion. The macroscopic device is discretized into an array of mesoscopic cells. A polymer chain is assumed to stay in one cell. With the polymer chain scission, it is found that the molecular weight, chain recrystallization induced by polymer chain scissions, and the cavities formation due to polymer cell collapse play different roles in the composition of mechanical strength of the polymer. Therefore, three types of strength phases were proposed to display the heterogeneous strength structures and to represent different strength contribution to polymers, which are amorphous phase, crystallinity phase and strength vacancy phase, respectively. The strength of the amorphous phase is related to the molecular weight; strength of the crystallinity phase is related to molecular weight and degree of crystallization; and the strength vacancy phase has negligible strength. The vacancy strength phase includes not only the cells with cavity status but also those with an amorphous status, but a molecular weight value below a threshold molecular weight. This heterogeneous strength model is coupled with micro chain scission, chain recrystallization and a macro oligomer diffusion equation to form a multiscale strength model which can simulate the strength phase evolution, cells status evolution, molecular weight, degree of crystallinity, weight loss and device strength during degradation. Different example cases are used to verify this model. The results demonstrate a good fit to experimental data. [ABSTRACT FROM AUTHOR]

Abstract Z-pinning was originally designed to improve the delamination toughness and the impact resistance of composite laminates. However, there is extensive experimental evidence that this improvement is accompanied by a reduction of the in-plane properties. The main mechanisms responsible for this deterioration are the local change in fiber content, fiber distortion, and the inclusion of resin-rich regions near the Z-pin. The shape of these geometrical features strongly depends on the laminate stacking sequence and on pin parameters such as pin diameter, pin content, and initial pin inclination angle. Their shape complexity challenges analytical modelling approaches which are currently used to generate RVE geometries for simulations. A computational approach is presented to generate such geometrical models. Resin-rich regions are modelled by initially straight discretized lines which are gradually shaped by a set of geometrical operations mimicking pin insertion, pin rotation and fiber deflection. Fiber distortion is modelled in a post-processing stage in cross-sections accounting for the preservation of the amount of fibers. These models are then transformed into finite element mechanical models in order to investigate how local fiber volume fraction changes, fiber misalignment, or distortions in reinforcement due to pin rotation, affect the global stiffness and local stress concentrations. [ABSTRACT FROM AUTHOR]

Highlights • An established meso-scale model for plane-woven fabric membrane materials is enhanced. • Material parameters are identified by the solution of an inverse problem. • Using a meso-macro transition membrane structures are computed within finite element analyses. Abstract Due to their structure of crossed yarns embedded in coating, woven fabric membranes are characterised by a highly nonlinear stress-strain behaviour. In order to determine an accurate structural response of membrane structures, a suitable description of the material behaviour is required. Typical phenomenological material models like linear-elastic orthotropic models only allow a limited determination of the real material behaviour. A more accurate approach becomes evident by focusing on the meso-scale, which reveals an inhomogeneous however periodic structure of woven fabrics. The present work focuses on an established meso-scale model. The novelty of this work is an enhancement of this model with regard to the coating stiffness. By performing an inverse process of parameter identification using a state-of-the-art Levenberg-Marquardt algorithm, a close fit w.r.t. measured data from a common biaxial test is shown and compared to results applying established models. Subsequently, the enhanced meso-scale model is processed into a multi-scale model and is implemented as a material law into a finite element program. Within finite element analyses of an exemplary full scale membrane structure by using the implemented material model as well as by using established material models, the results are compared and discussed. [ABSTRACT FROM AUTHOR]

Although metallic materials with gradient microstructure exhibit notable performance in harsh environmental conditions, they can also exhibit unusual mechanical behaviour. This is attributed to both grain size and the gradient of grain size distribution in the structure. Metallic materials with a homogenous distribution of grain size follow the traditional Hall-Petch relationship, in which strength increases with decreasing grain size at the expense of ductility. However, studies show that materials with a gradient of grain size microstructure do not follow the Hall-Petch relationship, and thus have improved strength and ductility. This suggests that with creative design and engineering of microstructure, the strength-ductility trade-off can be reduced or prevented. In this study, we developed and implemented a dislocation density based model to investigate the mechanical behaviour of nano-microstructure. We designed a multi-scale modelling framework, coupling VPSC (Viscoplastic Self Consistent model) with CDD (Continuum Dislocation Dynamics), applying crystal plasticity equations to simulate dislocation interaction in polycrystalline metallic materials. We also developed design parameters and a model to predict the strength and ductility of materials with gradient microstructure. [ABSTRACT FROM AUTHOR]

Abstract The microstructural deformation of ex-service 9Cr-1Mo steel, with a tempered martensitic microstructure, has been examined in this study, through the combined use of electron backscatter diffraction (EBSD) and multiscale modelling techniques. Both the experimental and predicted deformation of the material at a notch root on a range of scales from the specimen level down to the microstructural block level are compared. A tension loaded notch specimen of the material which was extracted from an ex-service power plant pipe was used for this analysis. The deformation at the specimen level was quantified by analysis of the load displacement curves and notch opening displacement, which showed excellent agreement with the predicted results from the experimentally calibrated elastic-plastic finite-element model of the specimen geometry. The microstructural deformation was experimentally measured through the use of EBSD carried out at the notch root before and after high temperature mechanical testing. The initial orientation of the microstructure as well as the displacement around the boundary of the area of interest in the macroscale model were applied to a representative volume element (RVE) and a slip based crystal plasticity modelling framework was implemented to model the in-elastic deformation of the material under high temperature loading. [ABSTRACT FROM AUTHOR]

Abstract In this work the possibility to reverse engineer the transverse isotropic carbon fibre properties from the 3D homogenized elastic tensor of the UD ply for the prediction of woven ply properties is explored. Ultrasonic insonification is used to measure the propagation velocity of both the longitudinally and transversally polarized bulk waves at various symmetry planes of a unidirectional (UD) Carbon/Epoxy laminate. These velocities and the samples' dimensions and density are combined to obtain the full 3D orthotropic stiffness tensor of the ply. The properties are subsequently used to reverse engineer the stiffness tensor, assumed to be transversely isotropic, of the carbon fibres. To this end, four micro-scale homogenization methods are explored: 2 analytical models (Mori-Tanaka and Mori-Tanaka-Lielens), 1 semi-empirical (Chamis) and 1 finite-element (FE) homogenization (randomly distributed fibres in a Representative Volume Element). Next, the identified fibre properties are used to predict the elastic parameters of UD plies with multiple fibre volume fractions. These are then used to model the fibre bundles (yarns) in a meso-scale FE model of a plain woven carbon/epoxy material. Finally, the predicted elastic response of the woven carbon/epoxy is compared to the experimentally obtained elastic stiffness tensor. The predicted and measured properties are in good agreement. Some discrepancy exists between the ultrasonically measured value of the Poisson's ratio and the predicted value. Nonetheless, it is shown that virtual identification and prediction of mechanical properties for woven plies is feasible. [ABSTRACT FROM AUTHOR]

Highlights • A novel hybrid multiscale model is developed to simulate thin film deposition. • Continuum models and stochastic PDE used to capture deposition multiscale behaviour. • Artificial neural networks used to predict SPDE's model parameters. • Hybrid multiscale model validated using kinetic Monte Carlo based thin film model. • Hybrid multiscale model used to perform optimization & control on thin film growth. Abstract This work details the construction and evaluation of a low computational cost hybrid multiscale thin film deposition model that couples artificial neural networks (ANNs) with a mechanistic (first-principles) multiscale model. The multiscale model combines continuum differential equations, which describe the transport of the precursor gas phase, with a stochastic partial differential equation (SPDE) that predicts the evolution of the thin film surface. In order to allow the SPDE to accurately predict the thin film growth over a range of system parameters, an ANN is developed and trained to predict the values of the SPDE coefficients. The fully-assembled hybrid multiscale model is validated through comparison against a kinetic Monte Carlo-based thin film multiscale model. The model is subsequently applied to a series of optimization and control studies to test its performance under different scenarios. These studies illustrate the computational efficiency of the proposed hybrid multiscale model for optimization and control applications. [ABSTRACT FROM AUTHOR]