Macroscopic Model Research Articles

Magnetic particle capture in high‐gradient magnetic separation: A theoretical and experimental study

AbstractHigh‐gradient magnetic separation (HGMS) has traditionally been used in mineral processing, with many effective models developed for typically employed rod‐wire shaped matrices. However, its potential in bioprocessing, especially for high‐value products, introduces new demands on plant and matrix design. This study presents a multi‐scale model for HGMS that simulates new complex geometries, which enhance particle recovery. We have developed microscopic models to accurately simulate the trajectories of magnetic particles within the fluid flow and magnetic fields of HGMS systems. A pivotal aspect of our work is the effective translation of microscopic relationships into macroscopic transport models. The model is validated experimentally using a rotor‐stator HGMS system tailored for bioprocessing, with magnetic particle concentration measurements showing strong alignment with the model's predictions. The model's flexibility enables its application across various matrix shapes, overcoming the limitations of traditional rod‐wire models, and providing a robust framework for improved HGMS in‐silico process understanding and optimization.

Numerical Estimation of the Structural Integrity in an Existing Pipeline Network for the Transportation of Hydrogen Mixture in the Future

Hydrogen is gaining attention due to its potential to address key challenges in the sectors of energy, transportation and industry, since it is a much cleaner energy source when compared to fossil fuels. The transportation of hydrogen from the point of its production to the point of use can be performed by road, rail, sea, pipeline networks or a combination of the abovementioned. Being in the preliminary stage of hydrogen use, the utilization of the already existing natural gas pipeline networks for hydrogen mixtures transportation has been suggested as an efficient means of expanding hydrogen infrastructure. Yet, exploring this alternative, major challenges such as the pre-existence of cracks in the pipelines and the effect of hydrogen embrittlement on the material of the pipelines exist. In this paper, the macroscopic numerical modeling of pipeline segments with the use of the finite element method is performed. In more details, the structural integrity of intact and damaged pipeline segments, of different geometry and mechanical properties, was estimated. The effect of the pipeline geometry and material has been investigated in terms of stress contours with and without the influence of hydrogen. The results suggest that the structural integrity of the pipeline segments is more compromised by pre-existing longitudinal cracks, which might lead to an increase in the maximum value of equivalent Von Mises stress by up to four times, depending on their length-to-thickness ratio. This effect becomes more pronounced with the existence of hydrogen in the pipeline network.

A non-isothermal phase-field crystal model with lattice expansion: analysis and benchmarks

Abstract We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The fundamental thermodynamic relation between internal energy and entropy, as well as entropy production, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within an entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.

Electric-field manipulation of magnetization in an insulating dilute ferromagnet through piezoelectromagnetic coupling

The electric field control of magnetization is of significant interest in materials science due to potential applications in many devices such as sensors, actuators, and magnetic memories. Here, we report magnetization changes generated by an electric field in ferromagnetic Ga1−xMnxN grown by molecular beam epitaxy. Two classes of phenomena have been revealed. First, over a wide range of magnetic fields, the magnetoelectric signal is odd in the electric field and reversible. Employing a macroscopic spin model and atomistic Landau-Lifshitz-Gilbert theory with Langevin dynamics, we demonstrate that the magnetoelectric response results from the inverse piezoelectric effect that changes the trigonal single-ion magnetocrystalline anisotropy. Second, in the metastable regime of ferromagnetic hystereses, the magnetoelectric effect becomes non-linear and irreversible in response to a time-dependent electric field, which can reorient the magnetization direction. Interestingly, our observations are similar to those reported for another dilute ferromagnetic semiconductor Crx(Bi1−ySby)1−xTe3, in which magnetization was monitored as a function of the gate electric field. Those results constitute experimental support for theories describing the effects of time-dependent perturbation upon glasses far from thermal equilibrium in terms of an enhanced effective temperature.

A cross-scale transfer learning framework: prediction of SOD activity from leaf microstructure to macroscopic hyperspectral imaging.

Superoxide dismutase (SOD) plays an important role to respond in the defence against damage when tomato leaves are under different types of adversity stresses. This work employed microhyperspectral imaging (MHSI) and visible near-infrared (Vis-NIR) hyperspectral imaging (HSI) technologies to predict tomato leaf SOD activity. The macroscopic model of SOD activity in tomato leaves was constructed using the convolutional neural network in conjunction with the long and short-term temporal memory (CNN-LSTM) technique. Using heterogeneous two-dimensional correlation spectra (H2D-COS), the sensitive macroscopic and microscopic absorption peaks connected to tomato leaves' SOD activity were made clear. The combination of CNN-LSTM algorithm and H2D-COS analysis was used to research transfer learning between microscopic and macroscopic models based on sensitive wavelengths. The results demonstrated that the CNN-LSTM model, which was based on the FD preprocessed spectra, had the best performance for the microscopic model, with RC and RP reaching 0.9311 and 0.9075, and RMSEC and RMSEP reaching 0.0109 U/mg and 0.0127 U/mg respectively. There were 10 macroscopic and 10 microscopic significant sensitivity peaks found. The transfer learning was carried out using sensitive wavelengths, and the model performed well with an RP value of 0.7549 and an RMSEP of 0.0725 U/mg. The combined CNN algorithm and H2D-COS analysis demonstrated the viability of transfer learning across microscopic and macroscopic models for quantitative tomato leaf SOD prediction.

Near-infrared luminescence AgPd alloy superatomic clusters

Superatomic alloy Ag14Pd clusters exhibit strong near-infrared luminescence in both solid and solution states, and for the first time, superatomic clusters have been used as inks for 3D printing various macroscopic models.

Mitigating stop-and-go traffic congestion with operator learning

This paper presents a novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways. The freeway traffic dynamics are described by second-order coupled hyperbolic partial differential equations (PDEs), i.e. the Aw–Rascle–Zhang (ARZ) macroscopic traffic flow model. The proposed framework learns feedback boundary control strategies from the closed-loop PDE solution using backstepping controllers, which are widely employed for boundary stabilization of PDE systems. The PDE backstepping control design is time-consuming and requires intensive depth of expertise, since it involves constructing and solving backstepping control kernels. Existing machine learning methods for solving PDE control problems, such as physics-informed neural networks (PINNs) and reinforcement learning (RL), face the challenge of retraining when PDE system parameters and initial conditions change. To address these challenges, we present neural operator (NO) learning schemes for the ARZ traffic system that not only ensure closed-loop stability robust to parameter and initial condition variations but also accelerate boundary controller computation. The first scheme embeds NO-approximated control gain kernels within a analytical state feedback backstepping controller, while the second one directly learns a boundary control law from functional mapping between model parameters to closed-loop PDE solution. The stability guarantee of the NO-approximated control laws is obtained using Lyapunov analysis. We further propose the physics-informed neural operator (PINO) to reduce the reliance on extensive training data. The performance of the NO schemes is evaluated by simulated and real traffic data, compared with the benchmark backstepping controller, a Proportional Integral (PI) controller, and a PINN-based controller. The NO-approximated methods achieve a computational speedup of approximately 300 times with only a 1% error trade-off compared to the backstepping controller, while outperforming the other two controllers in both accuracy and computational efficiency. The robustness of the NO schemes is validated using real traffic data, and tested across various initial traffic conditions and demand scenarios. The results show that neural operators can significantly expedite and simplify the process of obtaining controllers for traffic PDE systems with great potential application for traffic management.

A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city

A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city

Simplifications of macroscopic models for heat and mass transfer in porous media

Simplifications of macroscopic models for heat and mass transfer in porous media

Nonlocal macroscopic models of multi-population pedestrian flows for walking facilities optimization

Nonlocal macroscopic models of multi-population pedestrian flows for walking facilities optimization

Kinetic and macroscopic modelling for dense gas flow simulations

Kinetic and macroscopic modelling for dense gas flow simulations

I-METANET: Macroscopic Freeway Model for Real-Time Incident Impact Estimation and Traffic Management

Macroscopic traffic flow models, notably METANET, have been instrumental in the real-time estimation and optimization of control strategies for recurrent traffic congestions owing to their computational efficiency and robust performance. Their embedded formulations, however, are not best tailored to capture the traffic dynamics during roadway lane blockage owing to incidents where rapid and surging queue waves often propagate to upstream segments at time-varying but much faster speeds than under recurrent traffic congestion. Therefore, this study introduces I-METANET for use in incident traffic modeling and management, grounded mainly in METANET’s core mechanism but with the following enhancements: (1) reflecting incident-induced merging behaviors and their significant but attenuate impacts on the speed propagation over upstream segments; (2) incorporating the concurrent impacts of the approaching upstream traffic flows and the downstream incident-incurred queue waves on a subject segment’s evolving speed; and (3) integrating the compound effects of ramp-flows’ weaving maneuvers and the presence of incident queues on an interchange segment’s traffic conditions. The proposed I-METANET, calibrated and evaluated by the field data from Interstate 4 (I-4) in Florida, has demonstrated its expected improvements over METANET under incident scenarios, based on the produced time-varying speeds and flow rates over each roadway segment during incident clearance periods. An extensive sensitivity analysis with respect to key parameters in I-METANET has also been conducted, and evaluation results have confirmed the robustness of I-METANET for simulating freeway traffic dynamics during incident-incurred traffic scenarios.

Enabling Electric Field Model of Microscopically Realistic Brain.

Modeling brain stimulation at the microscopic scale may reveal new paradigms for various stimulation modalities. We present the largest map to date of extracellular electric field distributions within a layer L2/L3 mouse primary visual cortex brain sample. This was enabled by the automated analysis of serial section electron microscopy images with improved handling of image defects, covering a volume of 250 × 140 × 90 μm³. The map was obtained by applying a uniform brain stimulation electric field at three different polarizations and accurately computing microscopic field perturbations using the boundary element fast multipole method. We used the map to identify the effect of microscopic field perturbations on the activation thresholds of individual neurons. Previous relevant studies modeled a macroscopically homogeneous cortical volume. Our result shows that the microscopic field perturbations - an 'electric field spatial noise' with a mean value of zero - only modestly influence the macroscopically predicted stimulation field strengths necessary for neuronal activation. The thresholds do not change by more than 10% on average. Under the stated limitations and assumptions of our method, this result essentially justifies the conventional theory of "invisible" neurons embedded in a macroscopic brain model for transcranial magnetic and transcranial electrical stimulation. However, our result is solely sample-specific and is only relevant to this relatively small sample with 396 neurons. It largely neglects the effect of the microcapillary network. Furthermore, we only considered the uniform impressed field and a single-pulse stimulation time course.

Taylor’s Law from Gaussian diffusions

Abstract Taylor’s Law, also known as fluctuation scaling, manifests a power relation between the means and the variances of statistical distributions. The class of Gaussian-selfsimilar stochastic motions offers a plethora of macroscopic diffusion models, regular and anomalous alike. This class includes Brownian motion, scaled Brownian motion, fractional Brownian motion, and more. Within this class, power Brownian motion (PBM) is the sub-class of motions that are also Markovian. Considering conditional distributions of motion positions, this paper establishes that: the Gaussian-selfsimilar class universally generates Taylor’s Law, doing so with both positive and negative Taylor exponents. The paper also unveils a profound interplay between PBM and the universal generation of Taylor’s Law from the Gaussian-selfsimilar class.

A PDE-ODE Coupled Model for Biofilm Growth in Porous Media That Accounts for Longitudinal Diffusion and Its Effect on Substrate Degradation

We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of departure for our work, to the new model—we noticed significant changes in system dynamics. Our results suggest that neglecting it can lead to underestimation of quenching length and biofilm accumulation downstream, even in the advection-dominated regime. The effects of attachment and detachment of suspended bacteria on biofilm formation and substrate degradation were also examined. In the one-dimensional model, it was found that attachment has a stronger influence on substrate depletion, which becomes more pronounced as diffusion in the pore space increases.

Bifurcation analysis and control of the full velocity difference model with delayed velocity difference.

With the increase in the number of urban vehicles, various traffic problems have gradually emerged. Studying the causes of traffic congestion and proposing effective mitigation strategies have important practical significance. This paper proposes a macroscopic traffic flow model that considers the delayed speed difference. This paper applies nonlinear bifurcation to describe and predict nonlinear traffic phenomena on highways from the perspective of global stability of the traffic system. By using the traveling wave transformation, the proposed car-following model is converted into a macroscopic traffic flow model. Next, this paper employs the linear stability analysis to find the bifurcation points of the stability transition in the traffic system, exploring the qualitative characteristics of the inhomogeneous continuous traffic flow model. Theoretical derivations demonstrate the existence of bifurcation points within the model. Additionally, this paper plots the density-time space diagrams and phase plane diagrams of the system to visually present the sudden changes in traffic flow as variable parameters pass through these bifurcation points. Finally, this paper designs a feedback controller to regulate the Hopf bifurcation, aiming to delay or eliminate the occurrence of Hopf bifurcations in the stochastic system.

Advances in Multi‐Scale Biomechanics of Fruits and Vegetables: A Review

ABSTRACTFruits and vegetable (F&V) account for a large proportion of the market output, and reducing mechanical damage can improve economic benefits. During harvesting and storage of F&V, visible mechanical damage and unseen bruises can result from external loads. However, there are relatively few studies on the micro‐damage of F&V, and the micro‐damage changes are reflected in the macro. Therefore, it is necessary to establish macroscopic, mesoscopic, and microscopic mechanical structure models. In this paper, the factors influencing the mechanics of F&V are analyzed, macroscopic, mesoscopic, and microscopic mechanical analysis methods of F&V are reviewed, multi‐scale mechanical relationships are explored, and future research directions of multi‐scale biomechanics of F&V are prospected. The results show that future research direction should mainly focus on the force analysis of microscopic single cell, as it is the basis of mechanical analysis of F&V.

Kinetic simulations of nuclear burning plasmas in inertial confinement fusions taking into account the large-angle collisions

Although ignition had been achieved at the National Ignition Facility (NIF), recent observations of the experiments indicate novel physics that beyond theoretical predictions emerge, e.g., the neutron analysis of experiments has revealed deviations from the Maxwellian distributions in ion relative kinetic energies of burning plasmas, with the surprising emergence of supra-thermal deuterium and tritium (DT) ions that fall outside the predictions of macroscopic statistical hydrodynamic models. Via our newly developed hybrid-particle-in-cell code, incorporating the newly-proposed model of large-angle collisions, we infer that this could be attributed to the increased significance of large-angle collisions among DT ions and α-particles in the burning plasma. Extensive and unprecedented kinetic investigations into the implications of large-angle collisions in the burning plasma have yield several key findings, including an ignition moment promotion by ∼10ps, the presence of supra-thermal ions below an energy threshold, and approximately twice the expected deposition of α-particles densities. The rationality of our findings is confirmed through the congruency between the neutron spectral moment analyses conducted by the NIF and our kinetic simulations, both highlighting progressively widening disparities between neutron spectral moment analyses and hydrodynamics predictions, which becomes more pronounced as the yield increases. Our kinetic simulations with large-angle collisions not only provide novel insights for experiment interpretation but also open new research opportunities for the largely unexplored regime of the nuclear burning plasmas, which are distinguished by their exceptionally high energy densities and hold immense potential for illuminating the intricate physics that underpins the evolution of the early universe.

The Integration of Macroscopic Traffic Optimization Control and Microscopic Traffic Flow Model for Mixed Traffic: A Cyber-Physical System Perspective

The Integration of Macroscopic Traffic Optimization Control and Microscopic Traffic Flow Model for Mixed Traffic: A Cyber-Physical System Perspective

Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow

Inverting the fundamental diagram and forecasting boundary conditions: how machine learning can improve macroscopic models for traffic flow