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For high accuracy and to improve simulated wave characteristics, this article extends the concept of staggered grids to novel multidimensional multiscale modelling enabling efficient computation on sparse patches. Computational schemes for wave-like systems with small dissipation are often inaccurate and unstable due to truncation errors and numerical roundoff errors. Hence simulations of wave-like systems lacking proper handling of these numerical issues often fail to represent the physical characteristics of wave phenomena. This challenge gets even more intricate for multiscale modelling, especially in multiple dimensions. But numerical schemes on staggered grids are significantly less dispersive, better model the group velocity, and preserve much of the wave characteristics. This article develops and exhaustively studies all 167 040 possible 2D multiscale staggered grids. Our catalog (Divahar, 2023) interactively plots all of them. Only 120 multiscale staggered patch grids give stable and accurate multiscale schemes. Specifically, this article develops these 120 multiscale staggered grids and demonstrates their stability, accuracy, and wave-preserving characteristic for equation-free multiscale modelling of weakly damped linear waves. These characteristics of the developed multiscale staggered grids must also hold in general for multiscale modelling of many complex spatio-temporal physical phenomena such as the general computational fluid dynamics. • We develop and comprehensively explore multidimensional multiscale staggered grids. • Among 167040 2D multiscale staggered grids, only 120 give stable and accurate schemes. • These 120 grids give highly accurate equation-free multiscale patch scheme for waves. • We show the accuracy for multiscale modelling of ideal and weakly damped linear waves. • This work provides an essential foundation to multiscale schemes for wave systems. [ABSTRACT FROM AUTHOR]

A new study on multiscale modeling examines the safety of mast climbing work platforms (MCWPs) used in construction projects. The study focuses on the role of anchorages in maintaining the stability of MCWPs and analyzes the reaction forces at the anchorages under different conditions. The results indicate that the anchorage reaction forces are sensitive to loading and operational conditions, and they can reflect the stability or risk potential of the MCWP structure. The findings can be used to develop a structural safety monitoring system and improve MCWP safety management and anchorage design. [Extracted from the article]

• Multiscale model of platelet-fibrin thrombus formation in the flow. • Model validation through simulation of an in vitro experiment. • Flow can detach the shell of the thrombus and stop clot growth. • Slower arterial flow provokes thrombosis while faster flow causes bleeding. • Clot growth is regulated by coagulation reactions in veins and platelet aggregation in arteries. Thrombosis is a life-threatening clinical condition characterized by the obstruction of blood flow in a vessel due to the formation of a large thrombus. The pathogenesis of thrombosis is complex because the type of formed clots depends on the location and function of the corresponding blood vessel. To explore this phenomenon, we develop a novel multiscale model of platelet-fibrin thrombus growth in the flow. In this model, the regulatory network of the coagulation cascade is described by partial differential equations. Blood flow is introduced using the Navier–Stokes equations and the clot is treated as a porous medium. Platelets are represented as discrete spheres that migrate with the flow. Each platelet can attach to the thrombus, aggregate, become activated, express proteins on its surface, detach, and/or become non-adhesive. The interaction of platelets with blood flow is captured using the Immersed Boundary Method (IBM). We use the model to investigate the role of flow conditions in shaping the dynamics of venous and arterial thrombi. We describe the formation of red and white thrombi under venous and arterial flow respectively and highlight the main characteristics of each type. We identify the different regimes of normal and pathological thrombus formation depending on flow conditions. [ABSTRACT FROM AUTHOR]

Abstract Oncolytic viruses (OV) are viruses that can replicate selectively within cancer cells and destroy them. While the past few decades have seen significant progress related to the use of these viruses in clinical contexts, the success of oncolytic therapies is dampened by the complex spatial tumour-OV interactions. In this work, we present a novel multiscale moving boundary modelling for the tumour-OV interactions, which is based on coupled systems of partial differential equations both at macro-scale (tissue-scale) and at micro-scale (cell-scale) that are connected through a double feedback link. At the macro-scale, we account for the coupled dynamics of uninfected cancer cells, OV-infected cancer cells, extracellular matrix (ECM) and oncolytic viruses. At the same time, at the micro scale, we focus on essential dynamics of urokinase plasminogen activator (uPA) system which is one of the important proteolytic systems responsible for the degradation of the ECM, with notable influence in cancer invasion. While sourced by the cancer cells that arrive during their macro-dynamics within the outer proliferating rim of the tumour, the uPA micro-dynamics is crucial in determining the movement of the macro-scale tumour boundary (both in terms of direction and displacement magnitude). In this investigation, we consider three scenarios for the macro-scale tumour-OV interactions. While assuming the usual context of reaction-diffusion-taxis coupled PDEs, the three macro-dynamics scenarios gradually explore the influence of the ECM taxis over the tumour - OV interaction, in the form of haptotaxis of both uninfected and infected cells populations as well as the indirect ECM taxis for the oncolytic virus. Finally, the complex tumour-OV interactions is investigated numerically through the development a new multiscale moving boundary computational framework. While further investigation is needed to validate the findings of our modelling, for the parameter regimes that we considered, our numerical simulations indicate that the viral therapy leads to control and decrease of the overall cancer expansion and in certain cases this can result even in the elimination of the tumour. [ABSTRACT FROM AUTHOR]

In this paper, the concept for modelling materials with fibre network microstructures introduced in Part I of this series is reconsidered. At first, an alternative representation of the theory is provided that entails advantages in terms of numerical implementation. Next, the new constitutive approach is applied to affine networks, whose fibre stretches are distributed according to the affine distribution. Despite the tremendously widespread use of this model, it seems that the general form of the corresponding distribution has remained largely unexplored to date. The thus obtained reformulation of the affine full network model provides deep insight into this concept, and may help overcoming well-known numerical problems with the associated spherical integration, e.g. when highly non-linear or piece-wise defined fibre laws are used. The latter case is typical for applications in biomechanics, where fibres are frequently assumed to have negligible compressive resistance. While the developments of our theory thus far had focused on isotropic networks, we here showcase for the affine case how the anisotropy caused by non-uniform directional distributions of the fibres can be incorporated in the novel approach. Finally, it is shown that several earlier approaches to model networks of affinely deforming fibres or polymer chains result as special cases of our theory. [ABSTRACT FROM AUTHOR]

A common feature of computational modelling and simulation research is the need to perform many tasks in complex sequences to achieve a usable result. This will typically involve tasks such as preparing input data, pre-processing, running simulations on a local or remote machine, post-processing, and performing coupling communications, validations and/or optimisations. Tasks like these can involve manual steps which are time and effort intensive, especially when it involves the management of large ensemble runs. Additionally, human errors become more likely and numerous as the research work becomes more complex, increasing the risk of damaging the credibility of simulation results. Automation tools can help ensure the credibility of simulation results by reducing the manual time and effort required to perform these research tasks, by making more rigorous procedures tractable, and by reducing the probability of human error due to a reduced number of manual actions. In addition, efficiency gained through automation can help researchers to perform more research within the budget and effort constraints imposed by their projects. This paper presents the main software release of FabSim3, and explains how our automation toolkit can improve and simplify a range of tasks for researchers and application developers. FabSim3 helps to prepare, submit, execute, retrieve, and analyze simulation workflows. By providing a suitable level of abstraction, FabSim3 reduces the complexity of setting up and managing a large-scale simulation scenario, while still providing transparent access to the underlying layers for effective debugging. The tool also facilitates job submission and management (including staging and curation of files and environments) for a range of different supercomputing environments. Although FabSim3 itself is application-agnostic, it supports a provably extensible plugin system where users automate simulation and analysis workflows for their own application domains. To highlight this, we briefly describe a selection of these plugins and we demonstrate the efficiency of the toolkit in handling large ensemble workflows. Program Title: FabSim3 CPC Library link to program files: https://doi.org/10.17632/6nfrwy7ptj.1 Licensing provisions: BSD 3-clause Programming language: Python 3 Nature of problem: Many aspects are crucial for obtaining reproducible and robust simulation results. For instance, we need to curate all the inputs and outputs for later scrutiny, scrutinize the model behaviour under slightly perturbed circumstances, quantify the propagation of key uncertainties from input data and known parameters and analyze the sensitivity for any parameters for which the exact specification eludes us. Solution method: FabSim3 uses a range of methods to provide automation. These primarily include: (i) SSH + Fabric2 to enable remote execution of SSH commands, (ii) an internal parameter state space using primarily Python dict objects that can be customized with machine- plugin- and user-specific modifications, (iii) Python templating to quickly enable the insertion of state space variables into supercomputing scripts, (iv) multiprocessing and/or QCG-PilotJob to enable efficient submission and execution of job arrays and (v) a system of flexibly installable and modifiable Python3 plugins which allows users to create and customize application-specific functionalities without modifying the core code base. In addition to the written code, FabSim3 also relies on a set of user conventions to maintain a separation of concerns (particularly between machine-, user- and application-specific settings). Additional comments including restrictions and unusual features: This paper serves as the definitive reference for FabSim3. [ABSTRACT FROM AUTHOR]

We present FabSim, a toolkit developed to simplify a range of computational tasks for researchers in diverse disciplines. FabSim is flexible, adaptable, and allows users to perform a wide range of tasks with ease. It also provides a systematic way to automate the use of resources, including HPC and distributed machines, and to make tasks easier to repeat by recording contextual information. To demonstrate this, we present three use cases where FabSim has enhanced our research productivity. These include simulating cerebrovascular bloodflow, modelling clay-polymer nanocomposites across multiple scales, and calculating ligand–protein binding affinities. Program summary Program title: FabSim Catalogue identifier: AFAO_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAO_v1_0.html Program obtainable from: CPC Programme Library, Queen’s University, Belfast, N. Ireland Licensing provisions: BSD 3-Clause No. of lines in distributed program, including test data, etc.: 268282 No. of bytes in distributed program, including test data, etc.: 2791792 Distribution format: tar.gz Programming language: Python. Computer: PC or Mac. Operating system: Unix, OSX. RAM: 1 Gbytes Classification: 3, 4, 6.5. External routines: NumPy, SciPy, Fabric (1.5 or newer), PyYaml Nature of problem: Running advanced computations using remote resources is an activity that requires considerable time and human attention. These activities, such as organizing data, configuring software and setting up individual runs often vary slightly each time they are performed. To lighten this burden, we required an approach that introduced little burden of its own to set up and adapt, beyond which very substantial productivity ensues. Solution method: We present a toolkit which helps to simplify and automate the activities which surround computational science research. FabSim is aimed squarely at the experienced computational scientist, who can use the command line interface and a system of modifiable content to quickly automate sets of research tasks. Restrictions: FabSim relies on a command-line interface, and assumes some level of scripting knowledge from the user. Unusual features: FabSim has a proven track record of being easy to adapt. It has already been extensively adapted to facilitate leading research in the modelling of bloodflow, nanomaterials, and ligand–protein binding. Running time: FabSim can be used interactively, typically requiring a few seconds to perform a basic task. [ABSTRACT FROM AUTHOR]

In this paper, a multiscale rationale is applied to develop a bottom-up modelling strategy for analysing the elasto-damage response of osteons, resulting in a first step towards a refined mechanical description of cortical bone tissue at the macroscale. Main structural features over multiple length scales are encompassed. A single osteon is described by considering a multi-layered arrangement of cylindrical lamellae and accounting for both lacunar micro-voids and thin interlamellar regions, these latter modelled as soft interfaces. A multi-step homogenization procedure has been conceived and numerically applied to describe the equivalent mechanical response of osteon constituents, upscaling dominant subscale mechanisms. A progressive stress-based damage approach has been implemented via a finite-element technique, allowing to describe interlaminar and/or intralaminar brittle failure modes. Proposed approach has been successfully validated by numerically reproducing available experimental tests of isolated osteons under different loading conditions. Present histologically-oriented multiscale model revealed to be sound and consistent, opening towards further insights about the influence on bone biomechanics of through-the-scales biophysical/biochemical alterations, possibly related to ageing or diseases. [ABSTRACT FROM AUTHOR]

In this contribution, we propose a novel continuum mechanical concept to determine the homogenised mechanical response of random fibre networks. Their free energy is calculated as an average of the fibre free energy over the distribution of stretch, which forms the core of the new theory. The fibre-scale kinematic information contained in this distribution is intrinsic to the model and available for any state of macroscopic deformation in addition to the homogenised macroscopic response. In contrast to the various approaches that use directional averaging over the unit sphere, the presented model does not rely on a relation between fibre deformation and orientation, and therefore applies to highly non-affine networks as well as affine ones. In the present Part I of the work, the new concept is formally introduced, put into perspective with current approaches, and elaborated for the case of networks of elastic fibres with uniform orientation distribution, which generate a macroscopically isotropic hyperelastic response. The essential constitutive assumption of the theory establishes a relation between the macroscopic deformation of the network and the microscopic stretch distribution within. A phenomenological approach is used to illustrate the new concept, expressing statistical moments of the stretch distribution in terms of the macroscopic principal strain invariants. Application of the concept to 2D and 3D Voronoi networks with fibres of different properties finally exemplifies the accurate agreement of the model with discrete network simulations in terms of both the macroscopic and microscopic response. While the here presented phenomenological variant of the approach therefore represents an advance in the analytical multiscale modelling of network materials itself, the work also provides the basis for further developments, where the relation between the stretch distribution and macroscopic strain is derived from alternative principles. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation. Design/methodology/approach – The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis. Findings – This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation. Originality/value – The presentation of winding functions allows to generically describe the coupling, embed the circuit equations into the de Rham complex and visualize them by Tonti diagrams. This is of value for scientists interested in differential geometry and engineers that work in the field of numerical simulation of field-circuit coupled problems. [ABSTRACT FROM AUTHOR]

Abstract: We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement. [Copyright &y& Elsevier]

We present a model of hydrogen embrittlement based upon: (i) a cohesive law dependent on impurity coverage that is calculated from first principles; (ii) a stress-assisted diffusion equation with appropriate boundary conditions accounting for the environment; (iii) a static continuum analysis of crack growth including plasticity; and (iv) the Langmuir relation determining the impurity coverage from its bulk concentration. We consider the effect of the following parameters: yield strength, stress intensity factor, hydrogen concentration in the environment, and temperature. The calculations reproduce the following experimental trends: (i) time to initiation and its dependence on yield strength and stress intensity factor; (ii) finite crack jump at initiation; (iii) intermittent crack growth; (iv) stages I and II of crack growth and their dependence on yield strength; (v) the effect of the environmental impurity concentration on the threshold stress intensity factor; and (vi) the effect of temperature on stage II crack velocity in the low-temperature range. In addition, the theoretically and experimentally observed intermittent cracking may be understood as being due to a time lag in the diffusion of hydrogen towards the cohesive zone, since a buildup of hydrogen is necessary in order for the crack to advance. The predictions of the model are in good quantitative agreement with available measurements, suggesting that hydrogen-induced degradation of cohesion is a likely mechanism for hydrogen-assisted cracking. [Copyright &y& Elsevier]

A computational method (CADD) is presented whereby a continuum region containing dislocation defects is coupled to a fully atomistic region. The model is related to previous hybrid models in which continuum finite elements are coupled to a fully atomistic region, with two key advantages: the ability to accomodate discrete dislocations in the continuum region and an algorithm for automatically detecting dislocations as they move from the atomistic region to the continuum region and then correctly “converting” the atomistic dislocations into discrete dislocations, or vice-versa. The resulting CADD model allows for the study of 2d problems involving large numbers of defects where the system size is too big for fully atomistic simulation, and improves upon existing discrete dislocation techniques by preserving accurate atomistic details of dislocation nucleation and other atomic scale phenomena. Applications to nanoindentation, atomic scale void growth under tensile stress, and fracture are used to validate and demonstrate the capabilities of the model. [Copyright &y& Elsevier]

Materials often possess complex microstructure showing structural hierarchy covering a wide range of scales. An example of material with multiscale structure is the Earth's crust. The simplest model of such material structure is self-similarity making the scale dependent quantities to be expressed by the power law. Somewhat more realistic model is the discrete self-similarity that is the material structure is self-similar only over a discrete (and self-similar) set of scales. We show that in discrete self-similarity the power law dependence is preserved but only over the discrete sets of scales. The main result of this work is that as long as discrete-scaling quantities are in a linear relationship, they must either scale with the same exponent or vanish; we call this property the Universality of scaling exponents. In particular, non-zero components of the same tensor must scale with the same exponent. This leads to the same scaling of the elastic moduli and, consequently, to the same scaling of the wave velocities. Average stress and strain and their higher statistical moments also scale by power law; simple relationships are identified between the scaling exponents of average strain, stress, their higher moments and the elastic moduli. As the scaling of average strain could be determined from observations and scaling moduli can be inferred from the measured wave velocities, the derived relationships can be used to infer the scaling of the statistical parameters of stress distributions. The presented concept will be useful in characterising properties of both the meta- and hybrid materials and geomaterials. [ABSTRACT FROM AUTHOR]