Search

Understanding the impact of the relativistic motion of a chiral molecule on its optical response is a prime challenge for fundamental science, but it also has a direct practical relevance in our search for extraterrestrial life. To contribute to these significant developments, we describe a multi–scale computational framework that combines quantum chemistry calculations and full–wave optical simulations to predict the chiral optical response from molecules moving at relativistic speeds. Specifically, the effect of a relativistic motion on the transmission circular dichroism (TCD) of three life–essential biomolecules, namely, B–DNA, chlorophyll a, and chlorophyll b, is investigated. Inspired by previous experiments to detect interstellar chiral molecules, we assume that the molecules move between a stationary observer and a light source, and we study the rotationally averaged TCD as a function of the speed of the molecule.We find that the TCD spectrum that contains the signatures of the molecules shifts with increasing speed to shorter wavelengths, with the effects already being visible for moderate velocities. [ABSTRACT FROM AUTHOR]

This study is aimed to predict the effect of layering of graphene sheets (GSs) embedment in conventional carbon matrix of 4-dimensional carbon/carbon (4D-C/C) composite on the elastic modulus of 4D-C/C composite. Molecular dynamics methodology is employed to execute the nano-scale modeling and analysis of the single GS/layered GSs. Predicted elastic modulus of GS/GSs is utilized to estimate the elastic modulus of GS/GSs reinforced carbon matrix by employing semi-empirical Halpin–Tsai approach. At macro-scale, finite element methodology is utilized and elastic modulus of GS/GSs reinforced 4D-C/C composite is predicted. The elastic moduli of 4D-C/C composite are established to be improved in compared to the without GS/GSs reinforced 4D-C/C composite, due to better load carrying capacity of GSs embedded carbon matrix. Therefore, GS-embedded 4D-C/C composites can successfully replace currently used C/C composites for high strength applications. [ABSTRACT FROM AUTHOR]

Abstract Understanding the impact of the relativistic motion of a chiral molecule on its optical response is a prime challenge for fundamental science, but it also has a direct practical relevance in our search for extraterrestrial life. To contribute to these significant developments, we describe a multi–scale computational framework that combines quantum chemistry calculations and full–wave optical simulations to predict the chiral optical response from molecules moving at relativistic speeds. Specifically, the effect of a relativistic motion on the transmission circular dichroism (TCD) of three life–essential biomolecules, namely, B–DNA, chlorophyll a, and chlorophyll b, is investigated. Inspired by previous experiments to detect interstellar chiral molecules, we assume that the molecules move between a stationary observer and a light source, and we study the rotationally averaged TCD as a function of the speed of the molecule.We find that the TCD spectrum that contains the signatures of the molecules shifts with increasing speed to shorter wavelengths, with the effects already being visible for moderate velocities.

We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at cross-links to form a network. Assuming that the inter-cross-link distance is much shorter than the length scale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterizing the cell rheology through the force–displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size. [ABSTRACT FROM AUTHOR]

Grain crushing underpins key mechanical behaviours of granular materials. A variety of factors, including grading, particle shapes and loading conditions, have been recognised to affect the crushability of grains and the overall behaviour of a granular material. Among them, the role of intermediate principal stress in a general stress condition on the shear behaviour of crushable granular sand remains less understood, owing to the scarcity of experimental data and analytical tools available. In this paper, a multi-scale computational approach is employed to investigate the shear behaviour of crushable granular sand under general stress conditions with varying intermediate principal stresses and confining pressures. The computational approach features multi-scale coupling between non-smooth contact dynamics and peridynamics, and offers a rigorous way to consider the intertwined evolution of particle size and shape during the process of grain crushing. The numerical study helps to quantify comprehensively and analyse the grain crushing-induced changes of macro- and micro-scale material behaviours including strength, deformability, particle size and shape evolution, particle-scale forces and contact conditions, and the development of anisotropy. The competition between a void-filling mechanism due to grain size change and enhanced friction and interlocking due to grain shape change in dictating the deformation of crushable sand is further discussed. The findings offer insights into the complex behaviours of crushable granular materials under general stress conditions and facilitate future development of physics-based constitutive theories on crushable sand. [ABSTRACT FROM AUTHOR]

The design of batch food processing plants is complex which requires the use of advanced simulation and optimisation methods. This paper presents how existing methods for multi-scale design and multi-objective optimisation can be combined together while carrying out the integrative design of these complex systems. To implement the Methodology for the Integrated, Multi-scale and Multi-Objective Design of Systems (MIMMODS), 8 tasks must be completed. The goal of the first 6 tasks is to build a design support tool that (i) simulates the behaviour of the processing plant and estimates its performance at different functional levels and whatever design variables it is made up of, (ii) takes into account the preferences of the decision-maker to convert the performances of a design solution into desirability indices and (iii) searches for the design solution(s) that best satisfies the design objectives and the preferences of the decision-maker. When the design support tool is functioning, the results have to be visualised and analysed in order to validate whether the resulting design solution is satisfactory, realistic, feasible and consistent or whether a new iteration of the methodology needs to be conducted to refine the design support tool. [ABSTRACT FROM AUTHOR]

Tidal turbine infrastructure is currently in the large-scale prototype and short-term demonstration phase. However, the immediate requirement is to develop materials, processes and long-term life predictive facilities for tidal turbine plant that has decades of operational lifetime requirements. Computational modelling is a key tool to interpret the experimental data, understand the relevant mechanisms and provide a predictive capability for the performance of aged components for industries. The goal of this paper is a prediction of the long-term life of marine-based glass/epoxy and carbon/epoxy composite laminates aged in artificial seawater with 3.5% salinity based on Arrhenius degradation theory and tensile strength retention over 180 days ageing at room temperature and 60°C. Three different analytical models (linear and exponential) were implemented to calculate time shift factors and corresponding life in a real marine environment. Additionally, multi-scale modelling has been implemented via a representative volume element approach for square and hexagonal cells, and two-step homogenization of textile composites in accordance with nanoindentation testing for matrix/resin cells and fibre constraint cells after 90 days of immersion in saltwater. In general, the multi-scale modelling in ABAQUS and TexGen4SC was able to approximate (with about 10% difference) the mechanical properties of dry and aged composite laminates. [ABSTRACT FROM AUTHOR]

The use of biocomposite materials in different fields requires enhanced knowledge of the nonlinear phenomena related to their complex mechanical behaviour. Namely, nonelastic mechanisms such as damage, plasticity, and rupture, potentially coupled with viscosity incidence, affect the structure's lifetime. In this context, the aim of this paper is to propose a simplified and accessible approach that leads to modelling the overall mechanical behaviour of the composite material. The studied laminate composites were made of thermoplastic Elium resin reinforced with flax plies. Experimental quasistatic and dynamic characterisations were conducted via tensile and cyclic tensile tests to investigate the structure's mechanical properties and corresponding failure mechanisms. The test results clearly demonstrated the presence of significant nonlinear specific coupling effects due to both flax fibre and Elium resin. The proposed multi-scale modelling analysis assumes two principal entities: the ply constituted by one or more layers of unidirectional fibres and the fibre-matrix interface considered as a surface layer of resin. Each entity was characterized by specific damage variables that were determined by mechanical tests. Model parameters were experimentally identified and expressed in the behaviour model to simulate the composite structure subjected to low-velocity impact using the Pam-Crash F.E. numerical code. [ABSTRACT FROM AUTHOR]

Asymptotic homogenisation offers a way to efficiently analyse the mechanical behaviour of multiscale configurations. But near a multiscale boundary, the homogenisation strategy should be modified, as the underlying periodicity assumption breaks down there. In this article, we introduce a machine‐learning‐based asymptotic homogenisation and localisation scheme to formulate such boundary layer effects. To this end, we define a set of boundary layer cells, where external loading conditions are imposed on one side of the cell, and matching conditions with the interior periodic cells are imposed on the opposite side. The formulation is also extended to cover situations where the multi‐scale structure is not fully periodic, but spatially varying. Implied from the asymptotic results, neural networks can be trained to memorise the interrelationship between key local quantities, such as the magnitude of the local maximum von Mises stress, and the local mechanical and geometric features. Equipped with the trained neural networks, the online calculation for key (boundary‐localised) quantities of interest under arbitrary loading conditions is expected to be accelerated substantially. Numerical examples are further presented to show the reliability of the proposed work for boundary stress prediction. [ABSTRACT FROM AUTHOR]

High‐temperature electrochemical cells have received increasing interest in the past years as important elements in an energy transition scenario. Their employment in power‐to‐gas or gas‐to‐power systems naturally requires an accurate design that takes into account the effect of operating conditions and geometries on both the performance of the cells themselves and their integration with other units. To this end, it is important to develop flexible yet comprehensive models for their description and to identify performance parameters that allow a concise assessment of their efficiency. The aim of the present work is to identify the limitations – in terms of applicability and consistency – of the mathematical models developed to date to describe high‐temperature electrochemical cells, as well as the key characteristics that they should possess. A brief review of literature in this field is then reported, to identify the research areas that still need to be explored. [ABSTRACT FROM AUTHOR]

The advancement of technology has led to a significant increase in thermal loads, thus presenting new challenges in heat dissipation. Traditional single-phase cooling systems are often inadequate to meet these demands. As a result, phase-change technologies utilizing boiling and condensation, which can achieve high heat transfer coefficients, have garnered considerable attention. To delve into the complex physics of boiling heat transfer, researchers are increasingly turning to numerical simulation methods such as the Volume of Fluid (VOF) and the Diffuse Interface (DI) approaches. The VOF method, widely employed for macro-scale simulations ranging from micrometers to millimeters, effectively tracks bubble growth and detachment. Conversely, the DI method represents the interface as a continuous phase field and is primarily used for mesoscale simulations spanning from nanometers to micrometers. While the DI method excels in resolving mesoscale interfacial phenomena, it is computationally expensive for larger domains. Considering the strengths and weaknesses of both the VOF and DI methods, there is a growing interest in developing a multi-scale modeling approach that amalgamates their benefits. To pursue this objective, initial efforts are being made to evaluate the scaling capability of VOF towards lower spatial and temporal limits. Hence, an enhanced and customized VOF methodology has been developed within the OpenFOAM toolbox. This methodology is employed to investigate various bubble growth scenarios, progressively exploring its applicability at lower temporal and spatial scales to identify the lower limits of its application. By taking this first step towards combining the strengths of both the VOF and DI methods through a multi-scale modeling approach, the presented paper paves the way for enhancing the accuracy and efficiency of modelling approaches for boiling heat transfer while tackling a challenge associated with varying spatial and temporal scales. This endeavor not only pushes the boundaries of computational fluid dynamics but also holds promise for addressing real-world thermal management issues in diverse technological applications.

This research article aims to estimate the consequence of graphene sheet (GSs) reinforcement in carbon fiber composite on the elastic modulus of the composite. Aluminum (Al) is taken as matrix material. Molecular dynamics (MD) approach is employed to perform the nanoscale modeling of the GS-embedded Al nanocomposite. The resulting elastic modulus of nanocomposite is further utilized to estimate the elastic modulus of nanocomposite at micro-and macro-scale. At higher scales, i.e. micro- and macro-scale, semi-empirical and analytical methods have been utilized to calculate the elastic modulus of the composite. The elastic moduli of carbon fiber–embedded GS–Al nanocomposites are found to be enhanced relative to the pristine carbon fiber–reinforced composites, irrespective of stacked or non-stacked GSs. It is established that stacking of GSs only affects marginally the elastic moduli of carbon fiber–reinforced Al composites. [ABSTRACT FROM AUTHOR]

The austenite-ferrite transformation is the key metallurgical tool to tailor properties of low alloyed steels and remains an active area of research. Models have yet to be developed with truly predictive capabilities for phase transformations in multi-component commercial steels. This review provides a critical analysis of the various austenite-to-ferrite diffusional transformation model approaches that have been significantly broadened over the past decade by modelling at different length scales, i.e. classical macro-scale models have been augmented with simulations at the meso-scale and atomistic scale. Both semi-empirical and fundamental models are reviewed with an emphasis on polygonal ferrite formation in low and medium carbon steels. Formation of ferrite with more complex morphologies (i.e. irregular/bainitic/Widmanstätten ferrite) is also discussed. In particular, approaches to describe the interaction of alloying elements with the austenite-ferrite interface are critically analysed. The paper concludes with an outlook on the proposed austenite-ferrite transformation modelling work for the next decade. [ABSTRACT FROM AUTHOR]

Abstract High‐temperature electrochemical cells have received increasing interest in the past years as important elements in an energy transition scenario. Their employment in power‐to‐gas or gas‐to‐power systems naturally requires an accurate design that takes into account the effect of operating conditions and geometries on both the performance of the cells themselves and their integration with other units. To this end, it is important to develop flexible yet comprehensive models for their description and to identify performance parameters that allow a concise assessment of their efficiency. The aim of the present work is to identify the limitations – in terms of applicability and consistency – of the mathematical models developed to date to describe high‐temperature electrochemical cells, as well as the key characteristics that they should possess. A brief review of literature in this field is then reported, to identify the research areas that still need to be explored.

Long-distance migrants are constrained by widely separated hospitable habitats in geographically isolated locations, making them vulnerable to environmental change, both through natural and anthropogenic causes. Knowledge about their resource selection decisions is imperative to understand the drivers of their declines. The distinct periods within an annual cycle, when individuals experience different environmental circumstances, are inextricably linked through carry-over effects which can have important consequences for the individual, and consequently the population. In this study, we employ precise archival GPS-tracking data of European Nightjars (Caprimulgus europaeus) and high-resolution global land cover data to examine habitat selection during the sedentary wintering and breeding periods, as well as during autumn and spring migration, using a correlational approach. We demonstrate how nightjars use general habitat characteristics, such as landscape diversity, for high-order habitat selection, while resource selection at a finer spatial scale is reliant on fine-scale variables related to a habitat’s suitability, such as surface area of grassland and shrubland. We show that nightjars favour spatially diverse landscapes, which allows them to minimize time spent searching for optimal habitats. The considerable variation in the drivers of habitat selection between and within seasons shows how anthropogenic land-use change can have an array of different impacts on migrants by influencing large- and fine-scale habitat selection. This study shows the advantages of an individual based GPS-tracking approach, combined with high spatial resolution remote sensing data, and highlights the need for full annual-cycle research on scale dependent habitat selection of long-distance avian migrants.

The rapid development of industrial technology and the increasing computational power have provided the possibility to improve the accuracy of multiphase flow field simulation studies. In addition, the chaotic nature of boiling phenomena increases the difficulty of experimental studies, and there is an urgent need to improve the computational methods to meet the needs of industrial applications. This paper presents a comprehensive review of the published literatures on the study of pool boiling using computational methods in the last two decades, including macroscopic-scale computational methods based on continuous medium theory, mesoscopic-scale methods based on lattice Boltzmann method (LBM), and nanoscale molecular dynamics. The advantages and disadvantages of different approaches to study bubble dynamics, including nucleation mechanisms, bubble growth, bubble detachment, and nucleation sites density, are evaluated based on different modeling features and phase change mechanisms. After considering micro-layer evaporation, wall convection, and transient conduction in the macroscopic scale model, the shape diffraction of isolated bubbles and departure diameters obtained by the macroscopic approach agree well with experimental data, and the Rensselaer Polytechnic Institute model achieves promising results for the simulation of low concentration nanofluids as well. The coupling of Shan–Chen model (S–C model) and Peng–Robinson (P–R) equation of state and considering the thermal lattice Boltzmann approach can effectively solve the phase separation problem, and the simulation results can match the theoretical analysis with the highest accuracy. In addition to the above results, a complete boiling heat transfer curve was successfully simulated for the first time using the LBM method. Molecular dynamics provides an in-depth mechanistic explanation of nucleation of nanobubbles in microstructures and on different wettability surfaces in terms of free energy and pressure fluctuations. Although different methods have achieved different degrees of success in pool boiling simulations, problems of boundary capture and heat and mass transfer near macroscopic methods, mesh accuracy in mesoscopic methods, treatment of density ratios and error terms, and accuracy of gas–liquid interfaces in molecular dynamics methods still limit the development of numerical computation. Therefore, this review also presents the challenges and future directions of simulation methods for modeling at different scales from the authors' perspective. Multi-scale coupling methods will be highlighted as an important goal to accommodate the development of advanced pool boiling simulations. [ABSTRACT FROM AUTHOR]

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods, PINNs have several advantages, for example their ability to provide mesh-free solutions of differential equations and their ability to carry out forward and inverse modelling within the same optimisation problem. Whilst promising, a key limitation to date is that PINNs have struggled to accurately and efficiently solve problems with large domains and/or multi-scale solutions, which is crucial for their real-world application. Multiple significant and related factors contribute to this issue, including the increasing complexity of the underlying PINN optimisation problem as the problem size grows and the spectral bias of neural networks. In this work, we propose a new, scalable approach for solving large problems relating to differential equations called finite basis physics-informed neural networks (FBPINNs). FBPINNs are inspired by classical finite element methods, where the solution of the differential equation is expressed as the sum of a finite set of basis functions with compact support. In FBPINNs, neural networks are used to learn these basis functions, which are defined over small, overlapping subdomains. FBINNs are designed to address the spectral bias of neural networks by using separate input normalisation over each subdomain and reduce the complexity of the underlying optimisation problem by using many smaller neural networks in a parallel divide-and-conquer approach. Our numerical experiments show that FBPINNs are effective in solving both small and larger, multi-scale problems, outperforming standard PINNs in both accuracy and computational resources required, potentially paving the way to the application of PINNs on large, real-world problems. [ABSTRACT FROM AUTHOR]

Recent progress in our understanding of cancer mostly relies on the systematic profiling of patient samples with high-throughput techniques like transcriptomics. With this approach, one can find gene signatures and networks underlying cancer aggressiveness and therapy resistance. However, omics data alone cannot generate insights into the spatiotemporal aspects of tumor progression. Here, multi-level computational modeling is a promising approach that would benefit from protocols to integrate the data generated by the high-throughput profiling of patient samples. We present a computational workflow to integrate transcriptomics data from tumor patients into hybrid, multi-scale cancer models. In the method, we conduct transcriptomics analysis to select key differentially regulated pathways in therapy responders and non-responders and link them to agent-based model parameters. We then determine global and local sensitivity through systematic model simulations that assess the relevance of parameter variations in triggering therapy resistance. We illustrate the methodology with a de novo generated agent-based model accounting for the interplay between tumor and immune cells in a melanoma micrometastasis. The application of the workflow identifies three distinct scenarios of therapy resistance.

Rate equation modelling is performed to simulate ${\mathrm{D_2}}$ and ${\mathrm{D_2}}+{\mathrm{D}_2^+}$ exposure of the ${\mathrm{W}(110)}$ surface with varying coverage of oxygen atoms (O) from the clean surface up to 0.75 monolayer of O. Density Functional Theory (DFT) calculated energetics are used as inputs for the surface processes and desorption energies are optimized to best reproduce the Thermal Desorption Spectrometry (TDS) experiments obtained for ${\mathrm{D_2}}$ exposure. For the clean surface, the optimized desorption energies (1.10 eV–1.40 eV) are below the DFT ones (1.30 eV–1.50 eV). For the O covered surface, the main desorption peak is reproduced with desorption energies of 1.10 eV and 1.00 eV for 0.50 and 0.75 monolayer of O respectively. This is slightly higher than the DFT predicted desorption energies. In order to simulate satisfactorily the total retention obtained experimentally for ${\mathrm{D_2}}+{\mathrm{D}_2^+}$ exposure, a sputtering process needs to be added to the model, describing the sputtering of adsorbed species (D atoms) by the incident D ions. The impact of the sputtering process on the shape of the TDS spectra, on the total retention and on the recycling of D from the wall is discussed. In order to better characterize the sputtering process, especially its products and yields, atomistic calculations such as molecular dynamics are suggested as a next step for this study.

Automating the creation and calibration of microkinetic models enables researchers to perform detailed analysis of reaction mechanisms as well as multi‐scale modelling of reactors based on ab initio calculations. The example of electrochemical CO2 reduction shows that this requires a structured and standardised representation of concepts across multiple scales. Massive progress has been made in this area through dynamic knowledge graphs, whereby the first partial successes can be reported in the area of mechanism generation, quantum mechanical calculations as well as calibration with experimental data. [ABSTRACT FROM AUTHOR]

A new model for the multi-scale simulation of solute transport in concrete is presented. The model employs plurigaussian simulations to generate stochastic representations of concrete micro- and meso-structures. These are idealised as two-phase medium comprising mortar matrix and pores for the micro-structure, and mortar and large aggregate particles for the meso-structure. The generated micro- and meso-structures are employed in a finite element analysis for the simulation of steady-state diffusion of solutes. The results of the simulations are used to calculate effective diffusion coefficients of the two-phase micro- and meso-structures, and in turn, the effective diffusion coefficient at the macro-scale at which the concrete material is considered homogenous. Multiple micro- and meso-structures are generated to account for uncertainty at the macro-scale. In addition, the level of uncertainty in the calculated effective diffusion coefficients is quantified through a statistical analysis. The numerical predictions are validated against experimental observations concerning the diffusion of chloride through a concrete specimen, suggesting that the generated structures are representative of the pore-space and coarse aggregate seen at the micro- and meso-scales, respectively. The method also has a clear advantage over many other structural generation methods, such as packing algorithms, due to its low computational expense. The stochastic generation method has the ability to represent many complex phenomena in particulate materials, the characteristics of which may be controlled through the careful choice of intrinsic field parameters and lithotype rules. [ABSTRACT FROM AUTHOR]

While the modification of surface contacts offers significant potential for friction reduction, obtaining an underlying consistent friction behaviour of real-life experiments and virtual simulations is still an ongoing challenge. In particular, most works in the literature only consider idealised geometries that can be parametrised with simple analytical functions. In contrast to this approach, the current work describes the establishment of a digital twin of a pin-on-disk tribometer whose virtual geometry is completely replicated from real-life post-test topography measurements and fed into a two-scale mixed lubrication solver. Subsequently, several calibration steps are performed to identify the sensitivities of the friction behaviour towards certain geometry features and enable the digital twin to robustly represent the Stribeck curve of the physical experiments. Furthermore, a derivation of the Hersey number is used to generalise the obtained friction behaviour for different dynamic viscosities and allow the validation of the presented method. [ABSTRACT FROM AUTHOR]

The discrete element method (DEM) is the most dominant method for the numerical prediction of dynamic behaviour at grain or particle scale. Nevertheless, due to its discontinuous nature, the DEM is inherently unable to describe microscopic features of individual bodies which can be considered as continuous bodies. To incorporate microscopic features, efficient numerical coupling of the DEM with a continuous method is generally necessary. Thus, a generalised multi-scale PD–DEM framework is developed in this work. In the developed framework, meshfree discretised Peridynamics (PD) is used to describe intra-particle forces within bodies to capture microscopic features. The inter-particle forces of rigid bodies are defined by the DEM whereas a hybrid approach is applied at the PD–DEM interface. In addition, a staggered multi-scale time integration scheme is formulated to allow for an efficient numerical treatment of both methods. Validation examples are presented and the applicability of the developed framework to capture the characteristics mixtures with rigid and deformable bodies is shown. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic promoted a lot of research activities in relation to mucosalivary fluid airborne transport. Indeed, infection mechanisms are the result of mucosalivary fluid droplets exchange and the knowledge in this area is still largely inadequate. One of the main challenges concerns the modelling of mucosalivary fluid complex nature. Specifically, this is a key element to predict small diameters dry nuclei formation which are highly relevant from the transmission risk point of view. For this reason, in this paper we present and discuss the development of a new multi-scale modelling technique which incorporates the Population Balance Equation into a standard particle-source-in-cell method. Thus, the effectiveness of the aforementioned technique in droplet nuclei generation modelling is showed and discussed. Also the impact of velocity boundary conditions at the mouth print is assessed as well as the effect of the correlations for mass transfer showing that their neglect causes an underestimation in distance reached by the droplets. [ABSTRACT FROM AUTHOR]

To relate the thermomechanical behaviour and microstructural evolution of the heat-assisted incremental sheet forming (SPIF) for Ti–6Al–4 V sheet, multi-scale models based on crystal plasticity finite element model (CPFEM), representative elementary volume (RVE), and cellular automaton (CA) were established in this article. An experimental-scale CPFEM was built in advance to provide macrograin level strain, strain rate, and temperature output data, which were then used in RVE and CA as inputs to simulate the microstructural evolution throughout the SPIF process. The output results include the pole figures, dynamic recrystallisation (DRX) maps, and statistics results of the alpha (α) phase of the Ti–6Al–4 V (α-Ti) alloy from stage to stage throughout the 700 ∘ C SPIF. The obtained statistics results of dislocation density, grain orientation angles, and grain size were verified with electron backscatter diffraction (EBSD). The CA analysis of the DRX progress at the upper, centre, and lower regions of the deformed workpiece has discovered that the incremental increase of the strain rate has significant effects on the dislocation density that produced a proportional relationship to the DRX percentage. The results revealed that the strain rate has strong domination in affecting the slip of grains orientation, which overcomes the effect of temperature increase in this SPIF process. Furthermore, it was found that a large amount of DRXed grains were generated at the grain boundaries, which reduced the mean grain size and increased the DRX percentage, which produced an inversely proportional relationship to the dislocation density. The thermomechanical behaviour on the SPIF workpiece was increased incrementally, which is insufficient for DRX initiation in the upper region, and the behaviour was enhanced at the centre and lower region, which can be corresponded to the microstructural evolution throughout the process. [ABSTRACT FROM AUTHOR]

We study crystalline surface evolution in extreme environments, where high-energy atoms impinge on a crystalline surface to cause sputtering, growth and surface roughening. For our model system, we study the evolution of the Ni(111) surface under Ni atom bombardment, using Molecular Dynamics (MD) simulation and a Sutton-Chen force field, where the uppermost surface layers are free to move, supported by thermostatically controlled layers above a rigid template. The MD statistics of sputtering and sticking are used to aid the development of a computationally efficient kinetic Monte Carlo (KMC) code. Comparisons between the simulation surface morphologies are used to tune the KMC growth rules so that the key statistical features of the MD structures are captured by the KMC model. This model is then employed to explore the predicted behaviour over length and times scales much larger than those accessible to MD. While the MD-KMC approach is well known, this application to the complex surface growth encountered in energetic atomic bombardment illuminates the complexities of relating atomistic events to morphological evolution. The work shows how simulation methodology can be extended to provide predictive capabilities, paving the way for design tools for engineering processes such as plasma deposition film growth. [ABSTRACT FROM AUTHOR]

Laser-Based Powder Bed Fusion is one of the most widely used additive manufacturing processes, mainly due to its high-quality output. End users would greatly benefit from a virtual simulation of the process; however, the modelling of the process is very complicated and slow and therefore restricted mainly to academic users. In this work, a computationally efficient approach to the thermal modelling of PBF-LB/M is presented. This approach is based on the enthalpy method and the division of the simulation into three characteristic scales of the process. Despite the small runtime of the simulations, the model captures the critical phenomena of the process achieving sufficient accuracy. [ABSTRACT FROM AUTHOR]

Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they do not allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'. [ABSTRACT FROM AUTHOR]

In this review paper, a critical assessment of the main degradation processes in three key components of solid oxide fuel cells and electrolysers (negative and positive electrodes and the interconnect) is undertaken, attempting prioritization of respective degradation effects and recommendation of the best approaches in their experimental ascertainment and numerical modeling. Besides different approaches to quantifying the degradation rate of an operating solid oxide cell (SOC), the latest advancements in microstructural representation (3D imaging and reconstruction) of SOC electrodes are reviewed, applied to the quantification of triple‐phase boundary (TPB) lengths and morphology evolution over time. The intrinsic degradation processes in the negative (fuel) electrode and the positive (oxygen) electrode are discussed, covering first the composition and governing mechanisms of the respective electrodes, followed by a comprehensive evaluation of the most important factors of degradation during operation. By this systematic identification of dominant degradation processes, measurement techniques, and modeling approaches, the foundations are laid for the definition of meaningful accelerated stress testing of SOC cells and stacks, which will help the technology achieve the constantly more demanding durability targets in market applications. [ABSTRACT FROM AUTHOR]

As a solid waste from steel making, steel slag can be recycled to replace natural aggregates (NA) for developing steel slag aggregate (SSA) concrete, an environmentally friendly construction material. In order to evaluate the effect of steel slag on the permeability of SSA concrete, which may have a potential impact on the structure durability, this study presented a multi-scale finite element (FE) method for investigating the seepage process and mechanism inside the SSA concrete. The above FE method consisted of a microscale mortar model and a mesoscale concrete model, developed by integrating image processing technique and random aggregate method. The permeability coefficient of SSA concrete was evaluated with the above multi-scale FE method and was validated with experiment. The relative differences between the numerical simulation and experimental mean values of the permeability coefficients are 3.38∼5.94 %. Based on the validated method, the effects of steel slag on the seepage characteristics of concrete were analyzed. Results show that the incorporation of steel slag could decrease the permeability of concrete by reducing the mortar porosity in the microscale and reducing the thickness of the interfacial transition zone (ITZ) between aggregate and mortar in the mesoscale. Using over-simplified aggregate shapes in numerical simulation may underestimate the permeability coefficient of concrete, which emphasizes the importance of refined modelling. The permeability coefficient of concrete may exhibit anisotropy. When considering lateral water permeation, aggregates with aspect ratios close to one may offer superior resistance to seepage. The analysis findings provide insights for better material design of concrete with recycled materials. • Developed and validated multi-scale model of concrete containing steel slag aggregate for prediction of permeability. • Measured permeability of concrete and aggregate and observed interfacial transition zone of concrete using microscopy imaging. • Analyzed effects of steel slag on seepage characteristics and permeability of concrete. [ABSTRACT FROM AUTHOR]

Abstract In this review paper, a critical assessment of the main degradation processes in three key components of solid oxide fuel cells and electrolysers (negative and positive electrodes and the interconnect) is undertaken, attempting prioritization of respective degradation effects and recommendation of the best approaches in their experimental ascertainment and numerical modeling. Besides different approaches to quantifying the degradation rate of an operating solid oxide cell (SOC), the latest advancements in microstructural representation (3D imaging and reconstruction) of SOC electrodes are reviewed, applied to the quantification of triple‐phase boundary (TPB) lengths and morphology evolution over time. The intrinsic degradation processes in the negative (fuel) electrode and the positive (oxygen) electrode are discussed, covering first the composition and governing mechanisms of the respective electrodes, followed by a comprehensive evaluation of the most important factors of degradation during operation. By this systematic identification of dominant degradation processes, measurement techniques, and modeling approaches, the foundations are laid for the definition of meaningful accelerated stress testing of SOC cells and stacks, which will help the technology achieve the constantly more demanding durability targets in market applications.

As landscape‐scale conservation models grow in prominence, assessments of how wildlife utilise multiple‐use landscapes are required to inform effective conservation and management planning. Such efforts should incorporate multi‐species perspectives to maximise value for conservation, and should account for scale to accurately capture species‐environment relationships.We show that the random forest machine learning algorithm can be used to model large‐scale sign‐based data in a multi‐scale framework. We used this method to investigate scale‐dependent habitat associations for 16 mammal species of high conservation importance across the southern Kavango Zambezi (KAZA) Transfrontier Conservation Area in Botswana and Zimbabwe.Our findings revealed substantial variation in factors shaping habitat use across species, and illustrate that different species often have divergent responses to the same environmental and anthropogenic factors, and differ in the scales at which they respond to them. For all variables across all species, scale optimisation most often selected our largest scale.Precipitation, soil nutrients, and vegetation appeared to be the most important factors determining mammal distributions, likely through their associations with food resources for herbivores and, in turn, prey availability for carnivores.Anthropogenic pressures also had an important influence, with many species selecting against areas with high cattle density. The variety of relationships with human density indicated that species vary in their tolerance of humans. We found a consistent positive relationship with areas under high protection, and negative relationship with unprotected and less‐strictly protected areas.Policy implications. Through a novel application of random forest modelling to spoor data from 16 mammal species, this study highlights the importance of adopting a multi‐scale, multi‐species approach for decision‐making processes that depend on understanding wildlife distributions and habitat associations, such as protected area and corridor prioritisation. The findings identify changing rainfall patterns and increasing livestock numbers as emerging trends that may impact wildlife distributions, both within sub‐Saharan Africa and on a global scale. Wildlife management authorities should use modelling exercises and adaptive management to ensure that protected area networks remain fit for purpose under anticipated changes in rainfall under climate change, and explore initiatives that promote coexistence of wildlife and livestock. [ABSTRACT FROM AUTHOR]

Increasing efforts points to the understanding of how to maximize the capabilities of the adaptive immune system to fight against the development of immune and inflammatory disorders. Here we focus on the role of T cells as immune cells which subtype imbalance may lead to disease onset. Specifically, we propose that autoimmune disorders may develop as a consequence of a metabolic imbalance that modulates switching between T cell phenotypes. We highlight a Systems Biology strategy that integrates computational metabolic modelling with experimental data to investigate the metabolic requirements of T cell phenotypes, and to predict metabolic genes that may be targeted in autoimmune inflammatory diseases. Thus, we propose a new perspective of targeting T cell metabolism to modulate the immune response and prevent T cell phenotype imbalance, which may help to repurpose already existing drugs targeting metabolism for therapeutic treatment. [ABSTRACT FROM AUTHOR]

Background: Repetitive transcranial magnetic stimulation (rTMS) induces long-term changes of synapses, but the mechanisms behind these modifications are not fully understood. Although there has been progress in the development of multi-scale modeling tools, no comprehensive module for simulating rTMS-induced synaptic plasticity in biophysically realistic neurons exists.., Objective: We developed a modelling framework that allows the replication and detailed prediction of long-term changes of excitatory synapses in neurons stimulated by rTMS., Methods: We implemented a voltage-dependent plasticity model that has been previously established for simulating frequency-, time-, and compartment-dependent spatio-temporal changes of excitatory synapses in neuronal dendrites. The plasticity model can be incorporated into biophysical neuronal models and coupled to electrical field simulations., Results: We show that the plasticity modelling framework replicates long-term potentiation (LTP)-like plasticity in hippocampal CA1 pyramidal cells evoked by 10-Hz repetitive magnetic stimulation (rMS). This plasticity was strongly distance dependent and concentrated at the proximal synapses of the neuron. We predicted a decrease in the plasticity amplitude for 5 Hz and 1 Hz protocols with decreasing frequency. Finally, we successfully modelled plasticity in distal synapses upon local electrical theta-burst stimulation (TBS) and predicted proximal and distal plasticity for rMS TBS. Notably, the rMS TBS-evoked synaptic plasticity exhibited robust facilitation by dendritic spikes and low sensitivity to inhibitory suppression., Conclusion: The plasticity modelling framework enables precise simulations of LTP-like cellular effects with high spatio-temporal resolution, enhancing the efficiency of parameter screening and the development of plasticity-inducing rTMS protocols., Competing Interests: Conflict of interest statement The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Abstract Increasing efforts points to the understanding of how to maximize the capabilities of the adaptive immune system to fight against the development of immune and inflammatory disorders. Here we focus on the role of T cells as immune cells which subtype imbalance may lead to disease onset. Specifically, we propose that autoimmune disorders may develop as a consequence of a metabolic imbalance that modulates switching between T cell phenotypes. We highlight a Systems Biology strategy that integrates computational metabolic modelling with experimental data to investigate the metabolic requirements of T cell phenotypes, and to predict metabolic genes that may be targeted in autoimmune inflammatory diseases. Thus, we propose a new perspective of targeting T cell metabolism to modulate the immune response and prevent T cell phenotype imbalance, which may help to repurpose already existing drugs targeting metabolism for therapeutic treatment.

In this work, we investigated the effect of carbon nanotubes addition and agglomeration formation on the mechanical and electrical properties of CNT–polymer-based nanocomposites. Six specimens with carbon nanotubes (CNTs) fractions of 0%, 0.5%, 1%, 2%, 4% and 5% were manufactured and characterized by dynamic mechanical analysis (DMA) and four-probe method. The stress–strain curves and electrical conductivity properties were obtained. Scanning electron microscopy (SEM) was used to characterize both agglomeration and porosity formation. By employing micromechanics, through representative volume element (RVE), finite element analysis (FEA) and resistor network model (RNM), the Young's modulus and electrical conductivity values were calculated. The samples' elastic moduli showed an increment, reaching the maximum value at a CNTs fraction of 2%, thereafter an adverse effect was caused in the high CNT percentage samples. The final electrical conductivity seemed greatly altered with the addition of CNTs, reaching the percolation threshold at 2%. The unavoidable formation of CNT agglomerates appeared to influence the final physical properties. The CNT agglomerates adversely affect the mechanical performance of high-CNT-percentage samples. Conversely, an exponential increment in the electrical conductivity was presented as the agglomerates formed networks allowing the transport of electrons through the tunnelling effect. These phenomena were experimentally and numerically confirmed, showing a good correlation. [ABSTRACT FROM AUTHOR]

Architected materials and mechanical metamaterials are known for their unique macroscopic properties and complex behaviour that often defy conventional continuum mechanics. Therefore, in this contribution, a recent multi-scale second-order computational homogenisation method (Dos Santos et al., 2023) is employed to explore these materials under finite strains. The approach combines a second gradient continuum theory at the macro-scale and a representative volume element (RVE) with classical first-order continuum mechanics at the micro-scale. The Method of Multi-scale Virtual Power ensures a consistent scale transition. The predictive capability and applicability of the second-order computational strategy are evaluated through coupled multi-scale numerical simulations. These simulations involve two- and three-dimensional problems, with a strong focus on the development of novel metamaterials, while also accounting for diverse loading conditions, such as tension/compression-induced undulation, bending, and compression-induced torsion. Comparisons with first-order homogenisation and Direct Numerical Simulations validate the approach. Analysis of homogenised consistent tangents reveals valuable insights into macroscopic properties. Overall, the results highlight the capability of the second-order strategy to capture significant phenomena, including second-order deformation modes, coupling deformation mechanisms, and size effects. • A multi-scale second-order homogenisation method is used to explore metamaterials. • A second gradient continuum theory is combined with first-order continuum mechanics. • An assessment is conducted through coupled multi-scale numerical simulations. • Novel metamaterials are investigated for diverse loading conditions. • Higher-order deformation modes, coupling mechanisms and size effects are captured. [ABSTRACT FROM AUTHOR]

While the modification of surface contacts offers significant potential for friction reduction, obtaining an underlying consistent friction behaviour of real-life experiments and virtual simulations is still an ongoing challenge. In particular, most works in the literature only consider idealised geometries that can be parametrised with simple analytical functions. In contrast to this approach, the current work describes the establishment of a digital twin of a pin-on-disk tribometer whose virtual geometry is completely replicated from real-life post-test topography measurements and fed into a two-scale mixed lubrication solver. Subsequently, several calibration steps are performed to identify the sensitivities of the friction behaviour towards certain geometry features and enable the digital twin to robustly represent the Stribeck curve of the physical experiments. Furthermore, a derivation of the Hersey number is used to generalise the obtained friction behaviour for different dynamic viscosities and allow the validation of the presented method.

The ultra-high molecular weight polyethylene (UHMWPE) is a popular biomaterial. Pre-clinical evaluation of UHMWPE in terms of wear resistance is extremely important to avoid the effect of implant loosening after implantation. This work proposed an efficient and accurate computational modelling approach to predict elasto-plastic properties at meso-scale, and further integrated at macro-scale to predict adhesive wear in dry tribo-pairs condition. The representative volume element (RVE) based finite element technique was used to predict elastoplastic behaviour of nano-hydroxyapatite (nHA) reinforced UHMWPE composite. The predicted values were validated experimentally and applied as a material property of pin during a numerical investigation of adhesive wear by a macro-scale modelling approach. The CoCr alloy was taken as the counter disc material. The integration of Archard's wear model and user-subroutine was done for numerical prediction of wear. The numerically obtained wear rate and friction coefficient results were validated experimentally by a pin on the disc wear setup under dry conditions. The fabrication of the specimen for validation was done by microwave-assisted compression moulding (MACM). The microstructural investigation of worn surfaces was done by scanning electron microscopy (SEM) to understand the mechanism of adhesive wear. The surface mapping of worn surfaces was done using an optical profilometer to observe the surface roughness after adhesive wear. Biocompatibility of the composite material was confirmed by In-vitro direct contact cytotoxicity test [ABSTRACT FROM AUTHOR]

Using the notion of eigenstrain produced by the defects formed in a material exposed to high energy neutron irradiation, we develop a method for computing macroscopic elastic stress and strain arising in components of a fusion power plant during operation. In a microstructurally isotropic material, the primary cause of macroscopic elastic stress and strain fields is the spatial variation of neutron exposure. We show that under traction-free boundary conditions, the volume-average elastic stress always vanishes, signifying the formation of a spatially heterogeneous stress state, combining compressive and tensile elastic deformations at different locations in the same component, and resulting solely from the spatial variation of radiation exposure. Several case studies pertinent to the design of a fusion power plant are analysed analytically and numerically, showing that a spatially varying distribution of defects produces significant elastic stresses in ion-irradiated thin films, pressurised cylindrical tubes and breeding blanket modules. [ABSTRACT FROM AUTHOR]

[Display omitted] • Lewis number deviates from one in the entrance length. • The catalyst activity do not modify the initial Nu and Sh inside of the channels. • Re modifies the thermal entrance length because of the reduction of the flow area. This paper is devoted to the multi-scale model of the heat and mass transfer inside of a honeycomb monolith substrate. Due to computational limitations, monoliths are modelled as a continuum in full-scale catalytic reactors models. That makes it necessary to use correlations or sub-models derived from channel scale results to account for a physically consistent heat and mass transfer inside of the substrate. In this paper detailed computational models at a channel and reactor scales are analyzed. Catalytic oxidation of CO is used as a reaction and the fluid properties are considered to be temperature-dependent. First, a channel scale model is used to analyze Nusselt, Sherwood, Lewis, and Damköhler numbers inside of the monolith channels. Secondly, sub-models obtained at a channel level are implemented in a full-scale reactor model using the continuum approach, to evaluate the impact of using detailed vs. highly simplified correlations for heat and mass transfer. The reactor scale model accounts for the transitions of the flow regime, entrance length effects, an-isotropic substrate thermal conductivity and temperature-dependent fluid properties. According to the results, the Lewis number can deviate significantly from one in the entrance length, however, it approaches asymptotically to unity as the flow develops. Regarding Nusselt and Sherwood, current interpolating methodologies are not able to predict the correct value in the entrance region when Damköhler is low, nonetheless, are reasonably accurate for the asymptotic one. [ABSTRACT FROM AUTHOR]

Cancer invasion of the surrounding tissue is a multiscale process of collective cell movement that involves not only tumour cells but also other immune cells in the environment, such as the tumour-associated macrophages (TAMs). The heterogeneity of these immune cells, with the two extremes being the pro-inflammatory and anti-tumour M1 cells, and the anti-inflammatory and pro-tumour M2 cells, has a significant impact on cancer invasion as these cells interact in different ways with the tumour cells and with the ExtraCellular Matrix (ECM). Experimental studies have shown that cancer cells co-migrate with TAMs, but the impact of these different TAM sub-populations (which can change their phenotype and re-polarise depending on the microenvironment) on this co-migration is not fully understood. In this study, we extend a previous multi-scale moving boundary mathematical model, by introducing the M1-like macrophages alongside with their exerted multi-scale effects on the tumour invasion process. With the help of this model we investigate numerically the impact of re-polarising the M2 TAMs into the anti-tumoral M1 phenotype and how such a strategy affects the overall tumour progression. In particular, we investigate numerically whether the M2→M1 re-polarisation could depend on time and/or space, and what would be the macroscopic effects of this spatial- and temporal-dependent re-polarisation on tumour invasion.

The sensory hairs of the Venus flytrap (Dionaea muscipula Ellis) detect mechanical stimuli imparted by their prey and fire bursts of electrical signals called action potentials (APs). APs are elicited when the hairs are sufficiently stimulated and two consecutive APs can trigger closure of the trap. Earlier experiments have identified thresholds for the relevant stimulus parameters, namely the angular displacement θ and angular velocity ω . However, these experiments could not trace the deformation of the trigger hair's sensory cells, which are known to transduce the mechanical stimulus. To understand the kinematics at the cellular level, we investigate the role of two relevant mechanical phenomena: viscoelasticity and intercellular fluid transport using a multi-scale numerical model of the sensory hair. We hypothesize that the combined influence of these two phenomena and ω contribute to the flytrap's rate-dependent response to stimuli. In this study, we firstly perform sustained deflection tests on the hair to estimate the viscoelastic material properties of the tissue. Thereafter, through simulations of hair deflection tests at different loading rates, we were able to establish a multi-scale kinematic link between ω and the cell wall stretch δ . Furthermore, we find that the rate at which δ evolves during a stimulus is also proportional to ω . This suggests that mechanosensitive ion channels, expected to be stretch-activated and localized in the plasma membrane of the sensory cells, could be additionally sensitive to the rate at which stretch is applied. [ABSTRACT FROM AUTHOR]

Tissue engineered bone scaffolds are potential alternatives to bone allografts and autografts. Porous scaffolds based on triply periodic minimal surfaces (TPMS) are good candidates for tissue growth because they offer high surface-to-volume ratio, have tailorable stiffness, and can be easily fabricated by additive manufacturing. However, the range of TPMS scaffold types is extensive, and it is not yet clear which type provides the fastest cell or tissue growth while being sufficiently stiff to act as a bone graft. Nor is there currently an established methodology for TPMS bone scaffold design which can be quickly adopted by medical designers or biologists designing implants. In this study, we examine six TPMS scaffold types for use as tissue growth scaffolds and propose a general methodology to optimise their geometry. At the macro-scale, the optimisation routine ensures a scaffold stiffness within suitable limits for bone, while at the micro-scale it maximises the cell growth rate. The optimisation procedure also ensures the scaffold pores are of sufficient diameter to allow oxygen and nutrient delivery via capillaries. Of the examined TPMS structures, the Lidinoid and Split P cell types provide the greatest cell growth rates and are therefore the best candidates for bone scaffolds. [ABSTRACT FROM AUTHOR]

In this paper, a multi-scale modelling approach has been developed to predict the progressive damage and failure behaviour of 2D woven SiC/SiC composites. At the tow scale, non-linear tow properties have been determined by a micromechanics-based damage model, in which two scalar damage variables were introduced to characterize the fibre-dominated and matrix-dominated damage, respectively. Based on periodic boundary conditions, a meso-scale unit cell model has been established to simulate the macroscopic stress-strain responses and progressive damage processes of the composite under uniaxial tensile, compressive and in-plane shear loadings, respectively. In the numerical method, the non-linear properties of constituent materials have been implemented by the user defined subroutine, USDFLD of the finite element package, Abaqus. The numerical results and their comparisons with experimental stress-strain curves have been presented. The failure mechanisms of the composite under each loading have been also discussed. The high efficiency and prediction accuracy of the model make it possible to analyse large scale woven composites. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic promoted a lot of research activities in relation to mucosalivary fluid airborne transport. Indeed, infection mechanisms are the result of mucosalivary fluid droplets exchange and the knowledge in this area is still largely inadequate. One of the main challenges concerns the modelling of mucosalivary fluid complex nature. Specifically, this is a key element to predict small diameters dry nuclei formation which are highly relevant from the transmission risk point of view. For this reason, in this paper we present and discuss the development of a new multi-scale modelling technique which incorporates the Population Balance Equation into a standard particle-source-in-cell method. Thus, the effectiveness of the aforementioned technique in droplet nuclei generation modelling is showed and discussed. Also the impact of velocity boundary conditions at the mouth print is assessed as well as the effect of the correlations for mass transfer showing that their neglect causes an underestimation in distance reached by the droplets.