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The majority of materials used for membrane-based separation of gas mixtures are non-renewable and non-biodegradable, and the assessment of alternative bio-based polymers requires expensive and time-consuming experimental campaigns. This effort can be reduced by adopting suitable modelling approaches. In this series of works, we propose various modelling approaches to assess the CO2/CH4 separation performance of eight different copolymers of 3-hydroxybutyrate and 3-hydroxyvalerate (PHBV) using a limited amount of experimental data for model calibration. In part 1, we adopted a fully atomistic approach based on Molecular Dynamics (MD), while, in this work, we propose a multiscale methodology where a molecular description of the polymers is bridged to a macroscopic prediction of its gas sorption behaviour. PHBV structures were simulated using MD to obtain pressure–volume–temperature data, which were used to parametrise the Sanchez–Lacombe Equation of State. This, in turn, allows for the evaluation of the CO2 and CH4 solubility in the copolymers at various pressures and compositions with little computational effort, enabling the estimate of the sorption-based selectivity. The gas separation performance obtained with this multiscale technique was compared to results obtained with a fully atomistic model and experimental data. The solubility–selectivity for the CO2/CH4 mixture is in reasonable agreement between the two models and the experimental data. The multiscale method presented is a time-efficient alternative to fully atomistic methods and detailed experimental campaigns and can accelerate the introduction of renewable materials in different applications. [ABSTRACT FROM AUTHOR]

Prediction of composite materials failure is a valuable resource for ensuring structural integrity of aerospace structures. For the experimental part of the study, the sandwich specimens were fabricated using two aluminium cores, a Nomex core sandwiched between tool-facing and bag-facing sheets. A damaged slot was introduced and thereafter repaired with filler and repaired plies on the tool-facing sheet. The bonded-repaired sandwich composite facing sheet specimens were tested using a four-point bending setup under static loading conditions. A Multiscale Modelling (MSM) approach was developed to characterize the failure of a bonded-repaired sandwich composite tool-facing sheet. The MSM approach bridged three different length scales such as micro, meso and macro scales. The data processing and information transfer between the scales was facilitated by Visual Basic Applications scripts. Comparisons of micro, meso and micro-scale results were presented for both MSM and experimentation to validate the proposed MSM failure characterization approach. Numerical and fractographical results from MSM and experimentation matched very well for all three scales. In conclusion, the MSM failure characterization approach performed well against the experiment. It presents an opportunity to use an alternative composite materials failure characterization method for future research. [ABSTRACT FROM AUTHOR]

Lubrication modeling has long been dominated by the well-established Patir and Cheng flow factors method. The flow factors approach allows for accurate estimates of macroscale parameters (such as friction) in a reasonable amount of time. These methods are stochastic representations of microscale interactions and are not able to predict local scale (pressure, film thickness) phenomena with a suitable degree of accuracy. This contrasts with a deterministic approach, where a numerical grid must be applied that fully defines the microscale surface topography across the contact. The mesh resolution required leads to prohibitively long execution times and lacks scalability to engineering systems, but provides accurate predictions of local scale phenomena. In this paper, heterogeneous multiscale methods (HMM) are expanded to model varying and are, therefore, more representative of surface topography within lubricated contacts. This representative topography is derived from measured data, thereby allowing the accuracy of deterministic methods to be achieved with the speed of a flow factor method. This framework is then applied to compare key performance characteristics (pressure, film thickness, etc.) when idealized, Gaussian, and measured surface topography are modeled. The variations in microscale geometry are defined by measurements from across two tilted-pad bearings, demonstrating the ability of the expanded HMM framework to model representative surface topography. A comparison with a deterministic method is included as validation, and outputs of the HMM are discussed in the context of the lubrication across multiple length scales. [ABSTRACT FROM AUTHOR]

Precipitation hardening, a cornerstone of alloy strengthening, finds widespread application in engineering materials. Comprehending the underlying mechanisms and formulating models bear crucial significance for engineering applications. While classical macroscopic theoretical models based on the line tension model have historically guided research efforts, their reliance on simplifications, assumptions, and parameter adjustments limits their predictability and expansibility. Moreover, the challenge of understanding the intricate coupling effects among various hardening mechanisms persists. One fundamental question to achieve the transition of material design paradigms from empirical trial-and-error methods to predictive-and-design approaches is to develop more physics-based multiscale modelling methods. This review aims to elucidate the physical mechanisms governing precipitation hardening and establish a tailored bottom-up multiscale modelling framework to steer the design of new alloys. The physical scenarios of precipitation hardening are firstly summarized, including particle shearing, Orowan bypass, and dislocation cross-slip and climb. Afterwards, an in-depth discussion is given regarding the application of macroscopic models and their correlation with the mechanisms and precipitation characteristics. As for the multiscale modelling methods, we categorize them into three main types: slip resistance based approaches, misfit stress field based approaches, and energy based approaches. By integrating multiscale modelling with the physical scenarios, we systematically addressed the key idea of the multiscale coupling framework, and their scale transfer procedure, applicability, advantages, and limitations. Some examples of coupling different types of multiscale methods and considering precipitates with complicated shapes are also presented. This study not only furnishes insightful comprehension of precipitation hardening, but also guides the development of multiscale modelling methodologies for other types of hardening effects in alloys. [ABSTRACT FROM AUTHOR]

Artificial ammonia synthesis via the Haber‐Bosch process is environmentally problematic due to the high energy consumption and corresponding CO2 ${_2 }$ emissions, produced during the reaction and before hand in hydrogen production upon methane steam reforming. Photocatalytic nitrogen fixation as a greener alternative to the conventional Haber‐Bosch process enables us to perform nitrogen reduction reaction (NRR) under mild conditions, harnessing light as the energy source. Herein, we systematically review first‐principles calculations used to determine the electronic/optical properties of photocatalysts, N2 adsorption and to expound possible NRR mechanisms. The most commonly studied photocatalysts for nitrogen fixation are usually modified with dopants, defects, co‐catalysts and Z‐scheme heterojunctions to prevent charge carrier recombination, improve charge separation efficiency and adjust a band gap to for utilizing a broader light spectrum. Most studies at the atomistic level of modeling are grounded upon density functional theory (DFT) calculations, wholly foregoing excitation effects paramount in photocatalysis. Hence, there is a dire need to consider methods beyond DFT to study the excited state properties more accurately. Furthermore, a few studies have been examined, which include higher level kinetics and macroscale simulations. Ultimately, we show there is still ample room for improvement with regard to first principles calculations and their integration in multiscale models. [ABSTRACT FROM AUTHOR]

Purifying biogas can enhance the performance of distributed smart grid systems while potentially yielding clean feedstock for downstream usage such as steam reforming. Recently, a novel anion-pillared metal–organic framework (MOF) was reported in the literature that shows good capacity to separate acetylene from carbon dioxide. The present study assesses the usefulness of this adsorbent for separating a typical biogas mixture (consisting of methane, nitrogen, oxygen, hydrogen, carbon dioxide, and hydrogen sulphide) using a multiscale approach. This approach couples atomistic Monte Carlo simulations in the grand canonical ensemble with the batch equilibrium modelling of a pressure swing adsorption system. The metal–organic framework displays selectivity at low pressures for carbon dioxide and especially hydrogen sulphide. An analysis of adsorption isotherm models coupled with statistical distributions of surface–gas interaction energies determined that both CH4 and CO2 exhibited Langmuir-type adsorption, while H2S displayed Langmuir-type behaviour at low pressures, with increasing adsorption site heterogeneity at high pressures. Batch equilibrium modelling of a vacuum swing adsorption system to purify a CH4/CO2 feedstock demonstrated that such a system can be incorporated into a solar biogas reforming process since the target purity of 93–94 mol-% methane for incorporation into the process was readily achievable. [ABSTRACT FROM AUTHOR]

Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a versatile multiscale approach to modelling a moving self-adhesive cell population that combines a careful microscopic description of a deterministic adhesion-driven motion component with an efficient mesoscopic representation of a stochastic velocity-jump process. This approach gives rise to mesoscopic models in the form of kinetic transport equations featuring multiple non-localities. Subsequent parabolic and hyperbolic scalings produce general classes of equations with non-local adhesion and myopic diffusion, a special case being the classical macroscopic model proposed in Armstrong et al. (J Theoret Biol 243(1): 98–113, 2006). Our simulations show how the combination of the two motion effects can unfold. Cell-cell adhesion relies on the subcellular cell adhesion molecule binding. Our approach lends itself conveniently to capturing this microscopic effect. On the macroscale, this results in an additional non-linear integral equation of a novel type that is coupled to the cell density equation. [ABSTRACT FROM AUTHOR]

In the realm of food industry, the choice of non-consumable materials used plays a crucial role in ensuring consumer safety and product quality. Aluminum is widely used in food packaging and food processing applications, including dairy products. However, the interaction between aluminum and milk content requires further investigation to understand its implications. In this work, we present the results of multiscale modelling of the interaction between various surfaces, that is (100), (110), and (111), of fcc aluminum with the most abundant milk proteins and lactose. Our approach combines atomistic molecular dynamics, a coarse-grained model of protein adsorption, and kinetic Monte Carlo simulations to predict the protein corona composition in the deposited milk layer on aluminum surfaces. We consider a simplified model of milk, which is composed of the six most abundant milk proteins found in natural cow milk and lactose, which is the most abundant sugar found in dairy. Through our study, we ranked selected proteins and lactose adsorption affinities based on their corresponding interaction strength with aluminum surfaces and predicted the content of the naturally forming biomolecular corona. Our comprehensive investigation sheds light on the implications of aluminum in food processing and packaging, particularly concerning its interaction with the most abundant milk proteins and lactose. By employing a multiscale modelling approach, we simulated the interaction between metallic aluminum surfaces and the proteins and lactose, considering different crystallographic orientations. The results of our study provide valuable insights into the mechanisms of lactose and protein deposition on aluminum surfaces, which can aid in the general understanding of protein corona formation.

The effective macroscopic behaviour of a material is a manifestation of the underlying microstructure and microscale processes. This renders the generation of highly accurate digital microstructure twins indispensable for multiscale simulations. Mosaic is a Python-based, open-source software tool designed to address the challenge of incorporating non-planar, periodic microstructures generated by the software Neper into simulations that require periodic boundary conditions. Mosaic transforms these complex microstructures into rectilinear periodic equivalents and, additionally, makes it possible to account for material interfaces such as grain and phase boundaries. This transformation enables continuous integration with various simulation tools and workflows, facilitating accurate and efficient simulations of the effective material response.

This study aims to review and highlight the important modelling methodologies used for studying carbon nanotubes (CNTs) and their composites. Understanding appropriate modelling methods for specific applications is crucial as CNTs become integral in achieving lighter, multifunctional composite structures. This paper explores a range of techniques, including finite element modelling (FEM), Molecular Dynamics (MD), Molecular Structural Mechanics (MSM), as well as nonlocal models, and the Cauchy-Born (CB) rule. Emphasis is placed on factors such as interphase effects between CNTs and the matrix, bonding interactions, non-bonded van der Waals (vdW) forces, and dynamic behaviour. Multiscale modelling is extensively discussed as a pivotal approach for efficiently addressing various length scales in nanocomposites. Modelling of failure, damage and its propagation, delamination, and instabilities such as buckling and fracture have been highlighted, and research gaps have been pointed out. [ABSTRACT FROM AUTHOR]

Understanding disease transmission in the workplace is essential for protecting workers. To model disease outbreaks, the small populations in many workplaces require that stochastic effects are considered, which results in higher uncertainty. The aim of this study was to quantify and interpret the uncertainty inherent in such circumstances. We assessed how uncertainty of an outbreak in workplaces depends on i) the infection dynamics in the community, ii) the workforce size, iii) spatial structure in the workplace, iv) heterogeneity in susceptibility of workers, and v) heterogeneity in infectiousness of workers. To address these questions, we developed a multiscale model: A deterministic model to predict community transmission, and a stochastic model to predict workplace transmission. We extended this basic workplace model to allow for spatial structure, and heterogeneity in susceptibility and infectiousness in workers. We found a non-monotonic relationship between the workplace transmission rate and the coefficient of variation (CV), which we use as a measure of uncertainty. Increasing community transmission, workforce size and heterogeneity in susceptibility decreased the CV. Conversely, increasing the level of spatial structure and heterogeneity in infectiousness increased the CV. However, when the model predicts bimodal distributions, for example when community transmission is low and workplace transmission is high, the CV fails to capture this uncertainty. Overall, our work informs modellers and policy makers on how model complexity impacts outbreak uncertainty. In particular: workforce size, community and workplace transmission, spatial structure and individual heterogeneity contribute in a specific and individual manner to the predicted workplace outbreak size distribution. [ABSTRACT FROM AUTHOR]

Electrophoresis facilitated cancer treatment has demonstrated experimental efficacy in enhancing drug delivery within vascularised tumours. However, the lack of realistic mathematical models with direct measurements in the context of electrochemotherapy poses a challenge. We investigate the impact of an applied electric potential on the flow of Darcian-type fluid occurring in two distinct phases: the tumour and healthy regions. We employ the asymptotic homogenisation technique, assuming that the macroscale of the tumour domain is larger than the microscale characterised by vessel heterogeneities. We retain information about the microstructure by encoding information in the homogenised coefficients. We take into account both vascularisation and the microscale variations of the leading order and fine scale electric potential. The resulting effective differential problem reads as a Darcy-type system of PDEs, where the flow is driven by an effective source. The novel model can be used to predict the effect of an applied electric field on cancerous biological tissues, paving a new way of improving current electrochemotherapy protocols. [ABSTRACT FROM AUTHOR]

The capacity of small cerebral arteries (SCAs) to adapt to pressure fluctuations has a fundamental physiological role and appears to be relevant in different pathological conditions. Here, we present a new computational model for quantifying the link, and its contributors, between luminal pressure and vascular tone generation in SCAs. This is assembled by combining a chemical sub-model, representing pressure-induced smooth muscle cell (SMC) signalling, with a mechanical sub-model for the tone generation and its transduction at tissue level. The devised model can accurately reproduce the impact of luminal pressure on different cytoplasmic components involved in myogenic signalling, both in the control case and when combined with some specific pharmacological interventions. Furthermore, the model is also able to capture and predict experimentally recorded pressure-outer diameter relationships obtained for vessels under control conditions, both in a Ca 2 + -free bath and under drug inhibition. The modularity of the proposed framework allows the integration of new components for the study of a broad range of processes involved in the vascular function. [ABSTRACT FROM AUTHOR]

We introduce a discrete mathematical model for the mechanical behaviour of a planar slice of human corneal tissue, in equilibrium under the action of physiological intraocular pressure (IOP). The model considers a regular (two-dimensional) network of structural elements mimicking a discrete number of parallel collagen lamellae connected by proteoglycan-based chemical bonds (crosslinks). Since the thickness of each collagen lamella is small compared to the overall corneal thickness, we upscale the discrete force balance into a continuum system of partial differential equations and deduce the corresponding macroscopic stress tensor and strain energy function for the micro-structured corneal tissue. We demonstrate that, for physiological values of the IOP, the predictions of the discrete model converge to those of the continuum model. We use the continuum model to simulate the progression of the degenerative disease known as keratoconus, characterized by a localized bulging of the corneal shell. We assign a spatial distribution of damage (i.e. reduction of the stiffness) to the mechanical properties of the structural elements and predict the resulting macroscopic shape of the cornea, showing that a large reduction in the element stiffness results in substantial corneal thinning and a significant increase in the curvature of both the anterior and posterior surfaces.

The majority of materials used for membrane-based separation of gas mixtures are non-renewable and non-biodegradable, and the assessment of alternative bio-based polymers requires expensive and time-consuming experimental campaigns. This effort can be reduced by adopting suitable modelling approaches. In this series of works, we propose various modelling approaches to assess the CO2/CH4 separation performance of eight different copolymers of 3-hydroxybutyrate and 3-hydroxyvalerate (PHBV) using a limited amount of experimental data for model calibration. In part 1, we adopted a fully atomistic approach based on Molecular Dynamics (MD), while, in this work, we propose a multiscale methodology where a molecular description of the polymers is bridged to a macroscopic prediction of its gas sorption behaviour. PHBV structures were simulated using MD to obtain pressure–volume–temperature data, which were used to parametrise the Sanchez–Lacombe Equation of State. This, in turn, allows for the evaluation of the CO2 and CH4 solubility in the copolymers at various pressures and compositions with little computational effort, enabling the estimate of the sorption-based selectivity. The gas separation performance obtained with this multiscale technique was compared to results obtained with a fully atomistic model and experimental data. The solubility–selectivity for the CO2/CH4 mixture is in reasonable agreement between the two models and the experimental data. The multiscale method presented is a time-efficient alternative to fully atomistic methods and detailed experimental campaigns and can accelerate the introduction of renewable materials in different applications.

Lubrication modeling has long been dominated by the well-established Patir and Cheng flow factors method. The flow factors approach allows for accurate estimates of macroscale parameters (such as friction) in a reasonable amount of time. These methods are stochastic representations of microscale interactions and are not able to predict local scale (pressure, film thickness) phenomena with a suitable degree of accuracy. This contrasts with a deterministic approach, where a numerical grid must be applied that fully defines the microscale surface topography across the contact. The mesh resolution required leads to prohibitively long execution times and lacks scalability to engineering systems, but provides accurate predictions of local scale phenomena. In this paper, heterogeneous multiscale methods (HMM) are expanded to model varying and are, therefore, more representative of surface topography within lubricated contacts. This representative topography is derived from measured data, thereby allowing the accuracy of deterministic methods to be achieved with the speed of a flow factor method. This framework is then applied to compare key performance characteristics (pressure, film thickness, etc.) when idealized, Gaussian, and measured surface topography are modeled. The variations in microscale geometry are defined by measurements from across two tilted-pad bearings, demonstrating the ability of the expanded HMM framework to model representative surface topography. A comparison with a deterministic method is included as validation, and outputs of the HMM are discussed in the context of the lubrication across multiple length scales.

In this work we address the role of the microstructural properties of a vascularised poroelastic material, characterised by the coupling between a poroelastic matrix and a viscous fluid vessels network, on its overall response in terms of pressures, velocities and stress maps. We embrace the recently developed model (Penta and Merodio in Meccanica 52(14):3321–3343, 2017) as a theoretical starting point and present the results obtained by solving the full interplay between the microscale, represented by the intervessels' distance, and the macroscale, representing the size of the overall tissue. We encode the influence of the vessels' density and the poroelastic matrix compressibility in the poroelastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double-poroelastic model (Penta and Merodio 2017) is then solved at the macroscale in the context of vascular tumours, for different values of vessels' walls permeability. The results clearly indicate that improving the compressibility of the matrix and decreasing the vessels' density enhances the transvascular pressure difference and hence transport of fluid and drug within a tumour mass after a transient time. Our results suggest to combine vessel and interstitial normalization in tumours to allow for better drug delivery into the lesions. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of averaging for a class of piecewise deterministic Markov processes (PDMPs) whose dynamic is constrained by the presence of a boundary. On reaching the boundary, the process is forced to jump away from it. We assume that this boundary is attractive for the process in question in the sense that its averaged flow is not tangent to it. Our averaging result relies strongly on the existence of densities for the process, allowing us to study the average number of crossings of a smooth hypersurface by an unconstrained PDMP and to deduce from this study averaging results for constrained PDMPs. [ABSTRACT FROM AUTHOR]

Human prostatic tissue exhibits complex mechanical behaviour due to its multiphasic, heterogeneous nature, with hierarchical microstructures involving epithelial compartments, acinar lumens and stromal tissue all interconnected in complex networks. This study aims to establish a computational homogenization framework for quantifying the mechanical behaviour of prostate tissue, considering its multiphasic heterogeneous microstructures and the mechanical characteristics of tissue constituents. Representative tissue microstructure models were reconstructed from high‐resolution histology images. Parametric studies on the mechanical properties of the tissue constituents, particularly the fibre‐reinforced hyper‐elasticity of the stromal tissue, were carried out to investigate their effects on the apparent tissue properties. These were then benchmarked against the experimental data reported in literature. Results showed significant anisotropy, both structural and mechanical, and tension‐compression asymmetry of the apparent behaviours of the prostatic tissue. Strong correlation with the key microstructural indices such as area fractions of tissue constituents and the tissue fabric tensor was also observed. The correlation between the stromal tissue orientation and the principal directions of the apparent properties suggested an essential role of stromal tissue in determining the directions of anisotropy and the compression‐tension asymmetry characteristics in normal human prostatic tissue. This work presented a homogenization and histology‐based computational approach to characterize the apparent mechanical behaviours of human prostatic or other similar glandular tissues, with the ultimate aim of assessing how pathological conditions (e.g., prostate cancer and benign prostatic hyperplasia) could affect the tissue mechanical properties in a future study. [ABSTRACT FROM AUTHOR]

• Present a novel multiscale model to capture the dynamic blood flow and autoregulation in the brain vasculature. • Dynamic behaviour due to the fluid-wall interactions affects blood flow. • Important to achieve accurate, scale-invariant and computationally feasible coupling at the vessel-capillary interface. • The myogenic response might be insufficient by itself to restore blood flow following a drop in blood pressure. • Parameter space analysis gives insight into the range and influence of the model parameters prior to data extraction. Models of the micro-circulatory blood flow in the brain can play a key role in understanding the variety of cerebrovascular diseases that occur in the microvasculature. These conditions are often linked to structural modifications in the vessel network, alterations in the blood flow patterns, as well as impairment in the autoregulatory response, all of which are pathological changes that the model should be able to address if it were to have any clinical value. Furthermore, if the model results were to be validated against clinical MRI data, the model simulations need to be computationally feasible when used on networks on the scale of an MRI voxel. This requires some form of an upscaling approach that bypasses the need for an explicit architectural representation of the whole network while maintaining the relevant anatomical connections. To this end, we developed a hybrid multiscale model of blood flow and autoregulation that traces the dynamic changes in blood flow, volume, and pressure in the cortical microvasculature, where the discrete topology of the penetrating vessels is preserved, and these are then appropriately coupled to the homogenised capillary bed by a spatially distributing support function in the terminal endings. In contrast to the other multiscale models, the model developed here accounts for the dynamic physiological phenomena of the blood flow and the autoregulation processes in the microvessels. We show how the adaptive meshing scheme for the capillary bed developed in this study can be employed to ensure a scale-invariant coupling formulation and numerically accurate simulations, all without compromising the computational feasibility of the model. A statistically accurate cortical network on the scale of an MRI voxel is generated, and the model parameter values are calibrated using a Monte Carlo Filtering analysis to ensure that the model results are physiologically informed. The model is found to be able to capture the steep pressure gradients that have been reported to occur at coupling interfaces. Furthermore, in response to an upstream pressure drop, the network is found to be able to recover cerebral blood flow while exhibiting the characteristic autoregulatory behaviour in terms of changes in vessel calibre and the biphasic flow response. Overall, the model developed here offers a high-quality characterisation of dynamic flow and autoregulation in the microvasculature at improved computational efficiency and lays the ground for whole-brain dynamic simulations. [ABSTRACT FROM AUTHOR]

We propose the governing equations for a pre-stressed poroelastic composite material. The structure that we investigate possesses a porous elastic matrix with embedded elastic subphases with an incompressible Newtonian fluid flowing in the pores. Both the matrix and individual subphases are assumed to be linear elastic and pre-stressed. We are able to apply the asymptotic homogenisation technique by exploiting the length-scale separation that exists between the porescale and the overall size of the material (the macroscale). We derive the novel macroscale model which describes a poroelastic composite material where the elastic phases possess a pre-stress. We extend the current literature for poroelastic composites by addressing the role of the pre-stresses in the functional form of the new system of derived partial differential equations and its coefficients. The latter are computed by solving appropriate periodic cell differential problems which encode the specific contribution related to the pre-stresses. The model in the first instance is derived in the most general scenario and then specified for a variety of particular cases which are associated with different macroscale behaviour of materials. [ABSTRACT FROM AUTHOR]

Mineralized collagen scaffold is one of the best choices for bone defects treatment, but weak mechanical strength is the main factor restricting its development. Recent studies demonstrated that despite being a fundamental form of mechanical stimulation in human activities, the impact of cyclic compressive stress on collagen mineralization remains unclear, with even less known about the dynamic mechanical mechanism. This study employed cyclic compressive stress to investigate its effect on collagen mineralization. The findings revealed that cyclic compressive strain promotes collagen mineralization by facilitating increased mineral penetration into the collagen and altering mineral morphology on the collagen surface. As the mineral volume fraction of mineralized collagen rises, its elastic modulus also increases. Additionally, the finite element simulation results proved that cyclic compressive stress can impact mineral distribution by affecting their transport and deposition, consequently influencing the stress distribution and regulating mechanical properties of mineralized collagen. Alterations in mechanical properties provide feedback on internal stress distribution, subsequently impacting mineral mineralization. This study achieves a closed-loop study on the mechanical regulated collagen mineralization, offers insight into the mechanism of collagen mineralization, paving the way for further exploration of biomineralization mechanisms and potentially inspiring novel approaches for the fabrication of mineralized collagen scaffolds.

Purifying biogas can enhance the performance of distributed smart grid systems while potentially yielding clean feedstock for downstream usage such as steam reforming. Recently, a novel anion-pillared metal–organic framework (MOF) was reported in the literature that shows good capacity to separate acetylene from carbon dioxide. The present study assesses the usefulness of this adsorbent for separating a typical biogas mixture (consisting of methane, nitrogen, oxygen, hydrogen, carbon dioxide, and hydrogen sulphide) using a multiscale approach. This approach couples atomistic Monte Carlo simulations in the grand canonical ensemble with the batch equilibrium modelling of a pressure swing adsorption system. The metal–organic framework displays selectivity at low pressures for carbon dioxide and especially hydrogen sulphide. An analysis of adsorption isotherm models coupled with statistical distributions of surface–gas interaction energies determined that both CH4 and CO2 exhibited Langmuir-type adsorption, while H2S displayed Langmuir-type behaviour at low pressures, with increasing adsorption site heterogeneity at high pressures. Batch equilibrium modelling of a vacuum swing adsorption system to purify a CH4/CO2 feedstock demonstrated that such a system can be incorporated into a solar biogas reforming process since the target purity of 93–94 mol-% methane for incorporation into the process was readily achievable.

Biological organisms have an immense diversity of forms. Some of them exhibit conspicuous and fascinating fractal structures that present self-similar patterns at all scales. How such structures are produced by biological processes is intriguing. In a recent publication, we used a multi-scale modelling approach to understand how gene activity can produce macroscopic cauliflower curds. Our work provides a plausible explanation for the appearance of fractal-like structures in plants, linking gene activity with development.

Abstract The healthcare industry is different from other industries–patient data are sensitive, their storage needs to be handled with care and in compliance with regulative, while prediction accuracy needs to be high. This fast expansion in medical image modalities and data collection leads to generation of so called “Big Data” which is time-consuming to be analyzed by medical experts. This paper provides an insight into the Big Data from the aspect of its role in multiscale modelling. Special attention is paid to the workflow, starting from medical image processing all the way to creation of personalized models and their analysis. A review of literature regarding Big Data in healthcare is provided and two proposed solutions are described–carotid artery ultrasound image processing and 3D reconstruction, and drug testing on personalized heart models. Related to the carotid artery ultrasound image processing, the starting point is ultrasound images, which are segmented using convolutional neural network U-net, while segmented masks were further used in 3D reconstruction of geometry. Related to the drug testing on personalized heart model, similar approach was proposed, images were used in creation of personalized 3D geometrical model that is used in computational modelling to determine pressure in the left ventricle before and after drug testing. All the aforementioned methodologies are complex, include Big Data analysis and should be performed using servers or high-performance computing. Future development of Big Data applications in healthcare domains offers a lot of potential due to new data standards, rapid development of research and technology, as well as strong government incentives.

Lithium-ion batteries (LIBs) are leading the energy storage market. Significant efforts are being made to widely adopt LIBs due to their inherent performance benefits and reduced environmental impact for transportation electrification. However, achieving this widespread adoption still requires overcoming critical technological constraints impacting battery aging and safety. Battery aging, an inevitable consequence of battery function, might lead to premature performance losses and exacerbated safety concerns if effective thermo-electrical battery management strategies are not implemented. Battery aging effects must be better understood and mitigated, leveraging the predictive power of aging modelling methods. This review paper presents a comprehensive overview of the most recent aging modelling methods. Furthermore, a multiscale approach is adopted, reviewing these methods at the particle, cell, and battery pack scales, along with corresponding opportunities for future research in LIB aging modelling across these scales. Battery testing strategies are also reviewed to illustrate how current numerical aging models are validated, thereby providing a holistic aging modelling strategy. Finally, this paper proposes a combined multiphysics- and data-based modelling framework to achieve accurate and computationally efficient LIB aging simulations. [ABSTRACT FROM AUTHOR]

Neural closure models have recently been proposed as a method for efficiently approximating small scales in multiscale systems with neural networks. The choice of loss function and associated training procedure has a large effect on the accuracy and stability of the resulting neural closure model. In this work, we systematically compare three distinct procedures: "derivative fitting", "trajectory fitting" with discretise-then-optimise, and "trajectory fitting" with optimise-then-discretise. Derivative fitting is conceptually the simplest and computationally the most efficient approach and is found to perform reasonably well on one of the test problems (Kuramoto-Sivashinsky) but poorly on the other (Burgers). Trajectory fitting is computationally more expensive but is more robust and is therefore the preferred approach. Of the two trajectory fitting procedures, the discretise-then-optimise approach produces more accurate models than the optimise-then-discretise approach. While the optimise-then-discretise approach can still produce accurate models, care must be taken in choosing the length of the trajectories used for training, in order to train the models on long-term behaviour while still producing reasonably accurate gradients during training. Two existing theorems are interpreted in a novel way that gives insight into the long-term accuracy of a neural closure model based on how accurate it is in the short term. • Analysis of neural closure models with "derivative fitting" and "trajectory fitting". • Trajectory fitting with discretise-then-optimise gives the best results. • Theoretical support is given by two theorems that bound the long-term error. • Two test problems are investigated: Burgers' and Kuramoto-Sivashinsky equations. [ABSTRACT FROM AUTHOR]

The electric properties of conductive fibre networks, which can be representative of carbon nanotube networks, are investigated by means of numerical simulations and a dimensionless unified macroscale model is developed. Fibres are represented as rigid chains of discrete element method particles and we compress systems of fibres in a representative volume element periodic in three dimensions. In the used electric resistor network method, the particles are used as discretisation points to construct a system of linear equations linking the particle conductivities to their local electric potentials and in turn allowing for predictions on the electric macroscale properties of the fibre system. A carried out dimensional analysis suggests suitable scaling laws to unify different macroscale fibre systems in two different regimes - a percolating and a conductive regime. The dimensionless macroscale conductance is found to depend on the percolation threshold and percolation probability. It is moreover found that the critical solid volume fraction for rigid fibres is not only dependent on the fibre aspect ratio, but can also depend on the compression height of the system. Additionally, correlations between transmittance and solid volume fractions are found allowing for possibly simple solid volume fraction estimations in experiments.

Invasion of the surrounding tissue is a key aspect of cancer growth and spread involving a coordinated effort between cell migration and matrix degradation, and has been the subject of mathematical modelling for almost 30 years. In this current paper we address a long-standing question in the field of cancer cell migration modelling. Namely, identify the migratory pattern and spread of individual cancer cells, or small clusters of cancer cells, when the macroscopic evolution of the cancer cell colony is dictated by a specific partial differential equation (PDE). We show that the usual heuristic understanding of the diffusion and advection terms of the PDE being one-to-one responsible for the random and biased motion of the solitary cancer cells, respectively, is not precise. On the contrary, we show that the drift term of the correct stochastic differential equation scheme that dictates the individual cancer cell migration, should account also for the divergence of the diffusion of the PDE. We support our claims with a number of numerical experiments and computational simulations. [ABSTRACT FROM AUTHOR]

The increasingly harsh environment of the nuclear reactors and the insurmountable flaws of in-service materials have created an urgent need for the development of the brand-new alloys. For last decade, the high-entropy alloys (HEAs), a novel composition-design strategy, have received much attention due to their promise for the nuclear fields. The application of the multiscale modelling is to explore the irradiation performance and underlying mechanisms of HEAs. Abundant results and data deepen the understanding of the irradiation response, and accelerate the development of advanced irradiation-resistant HEAs. This review introduces the state-of-art multiscale modelling used for studying the irradiated properties of HEAs. Representative irradiation-induced microstructures and properties, as well as damage, are summarized. By strengthening the application of multiscale modelling, a rational design of high irradiation-resistant HEAs is expected. [ABSTRACT FROM AUTHOR]

A computationally efficient mixed atomistic-continuum coupled modelling is employed to investigate the vibrational characteristics and large deformation static response of some nitride and phosphide-based nanotubes. The atomic entities bond lengths/angles and continuum entities strains/curvature tensors are coupled through the kinematics of quadratic-type Cauchy–Born rule considering curvature effects on the atomic entities. The finite element model is formulated in a cylindrical coordinate system considering geometric nonlinearity through nonlinear strain–displacement relations and material nonlinearity through interatomic potential. The present study is carried out using a four nodded membrane consistent element wherein smoothened interpolation functions derived through least square minimization are used to interpolate the circumferential strain to avoid membrane locking. The atomic interactions are modelled using Tersoff–Brenner type interatomic potential with recently reported new empirical parameters. The effects of length and diameter, boundary conditions and length-to-diameter ratio on the natural frequency of the different nanotubes are also reported. The results obtained through multiscale modelling are also compared with those obtained through molecular dynamics (MD) simulation. The effect of material nonlinearity on the fundamental frequency of the nanotubes under applied pressure is also reported. [ABSTRACT FROM AUTHOR]