Particle Model Research Articles

NMC Charge Transfer Symmetry Breaks during Cycle Aging of Lithium-Ion Cells

Second harmonic nonlinear electrochemical impedance spectroscopy (2nd-NLIES) is a uniquely capable method for probing the symmetry of charge transfer in an electrochemical cell. [1,2] Kirk et al. are the first to try and quantify this symmetry-breaking using 2nd-NLEIS, but the single particle model (SPM) was not ideally matched to the thick porous electrodes under study. [3] Recently, we have introduced a systematic development of a porous electrodes model to describe the 2nd-NLEIS response along with the equivalent circuit presentation to bridge the gap between analytical solutions and well-accepted equivalent circuit models. [4] We have also demonstrated the performance of this model in analyzing 2nd-NLEIS data using the previously published experiments. [5] A data analysis pipeline and Python toolbox have been built to facilitate the simultaneous analysis of EIS and 2nd-NLEIS data. [5,6]In this work, we take advantage of the previously published data analysis pipeline and use it to analyze a much larger dataset of EIS and 2nd-NLEIS that is composed of 48 commercial 1.5 Ah LiNMC ∣ C LIBs (INR 18650–15 M). These batteries are cycled under four different aging conditions (Current: 3A or 4 A; Temperature: 5 oC or 25 oC) for up to 1500 charge-discharge cycles. These data were obtained at 10%, 30%, and 50% state of charge (SoC) of the designed stopping cycles. Simultaneous parameter estimation of linear EIS and 2nd-NLEIS is used to extract physical parameters that quantify battery aging under different operating conditions. In addition to the well-known increase of charge transfer resistance, [7] the breaking of charge transfer symmetry over aging for the cathode is elaborated with these extensive cycling data, confirming the growth in charge transfer asymmetry upon extended aging. Our results also reveal that low temperature operations can accelerate battery degradation, resulting in a substantial increase in charge transfer asymmetry than the room-temperature operation. Consequently, the degree of charge transfer asymmetry emerges as a crucial battery diagnostics characteristic that has never been measured before.

Tools for Parameterization of a Single Particle Model with Electrolyte Dynamics (SPMe) with Bayesian Experimental Design to Capture Degradation-Induced Capacity Fade in Lithium-Ion Batteries

The intelligent design of durable, next-generation lithium-ion batteries can be facilitated through the use of computationally efficient models that capture battery physics. In this work, we demonstrate a single particle model with electrolyte dynamics (SPMe), which accounts for battery capacity fade caused by mechanisms such as solid electrolyte interface (SEI) growth, lithium plating, and stress-induced particle cracking. The model is trained using both experimental data and data generated using a higher-fidelity Doyle-Fuller-Newman model so the ground truth parameters are known. To quantify and reduce the uncertainty in the unknown model parameters, we are developing a Bayesian experimental design approach that, with the aid of multiple models with varying fidelity, can rapidly identify optimal experimental input conditions leading to the greatest expected information gain.

Tailoring Solid-State Battery Performance through Computationally Tuning the Composition of LLZO-LCO Composite Cathodes

The composite cathode consisting of garnet-type solid-electrolyte Li7La3Zr2O12 (LLZO) and active material LiCoO2 (LCO) is one of the most promising solutions for the cathode design of all-solid-state lithium batteries. The transport properties of Li within the LLZO-LCO composite cathode are known to be sensitively dependent on the composition and microstructural features. This study focuses on computationally refining the performance of solid-state batteries by modifying the porosity and volume fractions of the LLZO-LCO composite cathode while considering the variations in the microstructural features. Various 2D and 3D microstructures were synthesized using a stochastic stacking particle model and the corresponding effective diffusivity of Li is calculated using a numerical homogenization method, which allows for a systematic assessment of the impact of composition on lithium transport within the microstructure. By identifying the optimal ratio between LLZO and LCO phases and porosity, this research yields crucial insights for improving the performance of solid-state batteries by tailoring the composite cathode.Figure 1: A) An example 3-dimensional microstructure with 20.3% percent vacuum (white space) and 39.25% percent LCO (yellow) and 40.45% LLZO (orange). B) The highest effective diffusivity (purple) is found when the LLZO percentage is highest. Once the vacuum percentage is 30% or higher, minimal effective diffusivity (red) is observed.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Figure 1

Investigating Temperature-Dependent Dynamics of SEI Growth and Battery Degradation

Several studies have contributed to the current understanding of the temperature-dependent behavior of solid-electrolyte interphase (SEI) formation in lithium-ion batteries and its impact on battery capacity and lifespan. Liu et al. developed a thermal-electrochemical model that revealed the complex interplay between diffusivity, reaction kinetics, and temperature on SEI growth1. Leng et al. presented an electrochemistry-based electrical model to examine the temperature's effect on battery aging2. Alipour et al. reviewed temperature-dependent electrochemical properties3, while Lubhani Mishra et al. provided a detailed physics-based analysis of battery degradation and temperature inhomogeneities4. These studies collectively indicate higher temperatures accelerating and promoting growth of compact and less permeable SEI structures leading to an increase in capacity loss and cell resistance, and lower temperatures resulting in slow ionic transport through the SEI also causing higher ohmic loss. In the present work, we study SEI growth and resulting effect on battery capacity fade using continuum scale modeling under the assumption of constant battery cell temperature as well as considering actual dynamically changing temperature data from experiments. SEI growth under these two considerations is compared and the comparison is used in determining scenarios where considering dynamically varying temperature is crucial for accuracy. The detailed analysis of the internal states from the simulation results contributes to the understanding of the effect of the thermal dynamics on battery cell degradation due to SEI growth. To achieve these objectives, a physics-based model, specifically the Single Particle Model (SPM), is utilized. The model uses temporal temperature data obtained from past experimental studies as well as temperature dependent properties of SEI provided in the literature as inputs for this investigation. The ultimate aim of this study is to better understand how temperature influences SEI characteristics, thereby contributing to improved battery performance and longevity across diverse thermal environments. References Liu, L., Park, J., Lin, X., Sastry, A. M., & Lu, W. (2014). A thermal-electrochemical model that gives spatial-dependent growth of solid electrolyte interphase in a Li-ion battery. Journal of power sources, 268, 482-490.Leng, F., Tan, C. M., & Pecht, M. (2015). Effect of temperature on the aging rate of Li-ion battery operating above room temperature. Scientific reports, 5(1), 12967.Alipour, M., Ziebert, C., Conte, F. V., & Kizilel, R. (2020). A review on temperature-dependent electrochemical properties, aging, and performance of lithium-ion cells. Batteries, 6(3), 35.Mishra, L., Subramaniam, A., Jang, T., Garrick, T. R., & Subramanian, V. R. (2022, October). Model Development for Temperature-Dependent Degradation in Large Format Lithium-Ion Batteries. In Electrochemical Society Meeting s 242 (No. 28, pp. 1075-1075). The Electrochemical Society, Inc.

A Novel Multi-Stage Stochastic Estimation Algorithm for Estimating the Parameters of the Extended Single Particle Model of a Lithium-Ion Battery

Lithium-ion batteries (LiBs) are commonly used as energy storage for many applications due to LiBs’ high energy density, long cycle life, and reliable manufacturing processes. Hence, effective performance management of LiBs is important and is implemented via Battery Management Systems (BMS)[1]. A BMS also maximises the safety and lifetime of battery packs; and therefore, needs to estimate the internal battery states including State of Charge (SoC) and State of Safety (SoS). Accurate estimation of battery SoX can be realized with the use of an accurate battery model [2].From the different types of battery models, electrochemical models (EMs) are considered the most accurate type of cell-level model [2]. EMs are sets of coupled-partial differential equation systems, where each equation is derived from the physics occurring in the cell. Of the different EMs, the partial two-dimensional model (P2D) is considered the most accurate cell-level model. However, the P2D model is complex and has no analytical solution, thus requiring computationally expensive iterative solvers for implementation. This makes practical implementation of the P2D model on BMS platforms challenging. Hence, most approaches seen in the literature prefer the use of reduced order versions (ROM) of the P2D model, that require far less computational power for implementation [1].One such ROM is the extended Single Particle Model (eSPM) which differs from the P2D model in considering each electrode to be modelled by a single spherical particle and charge conservation in the electrolyte to follow a simplified linear relationship. These assumptions help the model be accurate up to a 2C operational current, and enable an analytical solution to be derived using direct solving of the eSPM equations [2]. Due to fast-forward computation and reasonable accuracy, we’ve chosen the eSPM model for parameter estimation (PE). For accurate measurements of the model parameters, expensive and invasive experimental techniques are typically required. Non-destructive PE methods have a growing interest in the literature as they are not only non-invasive but also enable real-time dynamic PE to be done on a BMS [3].PE of EMs can be categorized under two approaches: deterministic methods and stochastic methods. Deterministic methods require a form of gradient descent to be used, wherein partial derivatives of the parameters of the model need to be calculated. This approach tends to be computationally expensive and tends to converge to local minima instead of searching the parameter space thoroughly. Hence, stochastic approaches incorporate randomness, thus searching the entire parameter space for the global optima [3]. Multiple different stochastic approaches have been employed for PE of EMs [4]. In this work, we compare and contrast some of the commonly used approaches and propose a novel multi-stage approach based on a combination of different stochastic PE algorithms.The proposed algorithm (see Figure (1)) requires three sets of data as inputs: the cell chemistry, constant current discharge data and the parameter boundaries of the eSPM model. Using these definitions, the first stage of the algorithm estimates a parameter set that has a reasonable level of accuracy i.e. less than 4% root mean square error (RMSE). The second stage of the algorithm does region-by-region optimisation, where parameters sensitive to different regions of the discharge curve are varied until the overall error is reduced to less than 1% RMSE. The proposed approach significantly reduces the estimation processing time compared to the ‘brute-force’ approach and is flexible in selecting different algorithms for each stage.Thus, contributions of this paper are briefly explained as follows: A performance comparison of the proposed algorithm with different stochastic estimation algorithms including the genetic algorithm, the particle swarm optimisation algorithm and the simulated annealing algorithm.A fast and adaptable multi-stage PE algorithm for the LiB eSPM model, with average estimation speeds of less than fifteen minutes for a typical BMS processor, with accuracy of less than 1% RMSE error.Validation of the algorithm with dynamic drive-cycle test data. [1] L. Lu et al, “A review on the key issues for lithium-ion battery management in electric vehicles,” Journal of Power Sources, vol. 226. pp. 272–288, Mar. 15, 2013. doi: 10.1016/j.jpowsour.2012.10.060.[2] S. Abada et al, “Safety focused modeling of lithium-ion batteries: A review,” J Power Sources, vol. 306, pp. 178–192, Feb. 2016, doi: 10.1016/J.JPOWSOUR.2015.11.100.[3] E. Miguel et al, “Review of computational parameter estimation methods for electrochemical models,” Journal of Energy Storage, vol. 44. Elsevier Ltd, Dec. 15, 2021. doi: 10.1016/j.est.2021.103388.[4] A. Jokar et al, “An Inverse Method for Estimating the Electrochemical Parameters of Lithium-Ion Batteries,” J Electrochem Soc, vol. 163, no. 14, p. A2876, Oct. 2016, doi: 10.1149/2.0191614JES. Figure 1

Thermal Modeling of Li-Ion Cylindrical Cells at Scale

The electric vehicle industry has created a demand for batteries with higher power densities. The current design choice for low-weight lithium-ion battery packs for electric vehicles is to create stacks arranged in parallel or series configurations to match the power demands. The individual cells are separated and placed in a cooling duct to pull heat away from the longitudinal surface convective. The amount of cooling is dependent on the internal temperature of batteries core. The current design of the cylindrical cell is to roll the cathode, anode, and separators into a jelly roll together and attach a tab to the cathode and anode at opposite corners of the sheet. The tabs connect to the positive and negative terminals of the cell to draw current away from the cell. The tabs may act as an agent for drawing heat away from the center of the battery. Currently, commonly used cylindrical cells have a form factor of 18650, 21700, or 26650. The thermal, geometrical, and electrical properties of 18650 and 21700 cylindrical cells are studied and it is found that the 21700 cells showed additional degradation and stronger heating. Recently, companies like Tesla have produced cylindrical cells with a 4680-form factor, which is a decent way to increase the ratio of active material vs. inactive material in a cylindrical cell. However, large diameter thick cylindrical cells suffer from thermal issues. Even large format pouch cells suffer through heat trapped within the stack.Since the thermal conductivity of the anode and cathode electrodes is often near 1 W/m-K, it becomes difficult for the heat to be extracted from the center of a large-diameter cylindrical cell without forming a considerable thermal gradient. PyBaMM, an open-source mathematical modeling software written in Python programming language, has the capability to simulate different electrochemical models such as the Doyle-Fuller-Newman (DFN), Single particle model (SPM), and SPMe, and varying chemistry. The software provides easy access to the cell parameters modification and graphical user interface capabilities. The PyBaMM framework also allows to simulation lumped, isothermal, and base thermal models which are electrochemically coupled. PyBaMM uses CasADi (computer algebra systems algorithmic differentiation). The thermal gradient and heat dynamics within a porous electrode are modeled using PoreSpy and openpnm, two open-source Python libraries used to design porous networks and model physical equations such as governing heat flow, concentration gradient, and movement of water/oil through porous shale media.We have explored and combined heat dynamic models for Li-Ion cylindrical cells at both cell and electrode levels with reduced-order Doyle-Fuller-Newman electro-chemical model frameworks implemented in the PyBaMM python library. Radial temperature gradient at cell and electrode levels were both generated from simulations with a distributed parameter model as a function of electrolyte and separator thickness and thermodynamic properties. Figure 1

(Invited) Lifetime Predictive Model of Capacity Loss, Resistance Increase, and Irreversible Thickness Growth

We present a battery lifetime model that predicts Irreversible battery thickness change under constant pressure operation as the battery ages, along with capacity loss and resistance growth. These metrics are very important for predicting lithium-ion battery state of health (SOH) and remaining useful life due to their interdependence with battery packaging and safety. To design and operate battery storage systems safely, we must be able to predict and detect changes in all three SOH metrics over life accurately and simultaneously. Traditionally, these three SOH metrics have been modeled separately. However, we developed a single model that simultaneously predicts battery capacity, resistance, and expansion over its lifetime.In this work, battery degradation is modeled using the single particle model (SPM) framework, including mechanical damage in the electrodes, which results in loss of active material (LAM), and the side reactions for SEI growth and Li plating, which result in loss of lithium inventory (LLI). We introduce an equivalent stress and concentration dependence of stress to the mechanical damage model. Commonly used fatigue models assume symmetric cycles (zero-mean stress) [1]. To account for cycling conditions with different currents on charge and discharge, an equivalent stress that adjusts for non-zero mean stress is needed. The concentration dependency of strain and the resulting stress allows us to capture different degradation rates for cells cycled at different depths of discharge (DOD). Lithium plating at the separator interface is often described as a spatially non-uniform process using the pseudo-2D (P2D) model. This phenomenon can be captured in the SPM framework using a current-dependent dynamic term to account for spatial-nonuniformity of electrolyte dynamics at higher currents.Experimental data from cells cycling with periodic reference performance tests were used to tune the degradation model. In addition to the standard I, V, and T measurements, continuous measurements of the thickness change of the battery pouch cells were recorded. From this data, we extracted the capacity, electrode state of health (eSOH), resistance, and reversible and irreversible expansion. The test conditions were designed to excite different dominant degradation mechanisms (e.g. mechanical damage) by cycling the cells at different conditions (C-rate, temperature, preload pressure, and DOD). The tuning, which uses accelerated aging simulations [2] (to speed up the tuning process), results in a single set of parameters that predicts capacity loss, resistance growth, and irreversible thickness change as the battery ages, even for conditions that were not used for parameter tuning.The tuning is performed in two sequential steps. First, the parameters related to the electrochemical and mechanical degradation rates, which result in LLI and LAM, are tuned to match the extracted eSOH variables at each Reference Performance Test (RPT). The first tuning gives us the amount of plated Li, SEI growth, and mechanical damage in the particles. We then relate these quantities to irreversible expansion using a linear relationship in the case of SEI and mechanical damage and quadratic in the case of Li plating [3]. The same relationship is used for all cells, and this represents the 2nd tuning step. Our data set and calibration are unique in that the dominant degradation mode is the loss of lithium inventory due to the loss of active anode material. Most prior work on lifetime predictive models relied on SEI growth as the dominant degradation mode. Figure 2 shows the tuned model prediction of the three performance metrics over the cycle life of cells for various cycling conditions. The markers represent the measurement at each reference performance test, and the lines correspond to the model.

An Analytical Model for Predicting the Rate Performance of Battery Cells Under Mixed Kinetic Control

The prediction of battery performance conventionally relies on resource-intensive numerical simulations based on the porous electrode theory. For computational speedup, simplified physics-based models have proven attractive as they still capture the underlying reaction mechanisms to a certain degree. In this class of models, physical complexity is usually reduced by assuming a single rate-limiting reaction. For example, the single particle model describes battery cells limited only by the solid diffusion pathway [1]. On the flipside, our previous analytical model exploited inefficiency of electrolyte transport, particularly in thick electrodes [2]. With advancement in both electrode and electrolyte technologies, however, it becomes challenging for these models to handle more realistic batteries.In this work, we propose an improved physics-based analytical model that enables mixed control of both kinetic processes, reflecting both salt depletion and particle size effect. An extension to our uniform reaction (UR) model, the new model uses salt distribution in electrolyte to probe the accessible lithium in the electrode level. The added solid diffusion module calculates the equilibrium potential at particle surface, lithium concentration at particle surface (Cs), and in turn the particle-level depth of discharge. We refer to the model as the URCs model, recognizing its two components. The model features higher tunability as it now accepts function-valued electrode and electrolyte properties. It also allows for prediction of discharge voltage curves and energy output of the cell.The model is compared with numerical simulation over a wide range of cell parameters. It shows good agreement with simulated results in rate performance test, specific energy output test, and discharge voltage curves. Better alignment is observed for the NMC/Li half cell than the NMC/Gr full cell, likely due to mixed reaction type in the graphite anode. Figure 1 shows the comparison of voltage curves across various C rates for a half cell with 70um NMC electrode and particles of 4um radius. Additionally, the cells are optimized for their specific capacity against electrode thickness and porosity. The optimal parameters predicted by the model lie closely to the global optimum from numerical simulation. Figure 2 shows the optimization results for a full cell with particles of 4um radius, overlaid on contour lines generated from the URCs model.The model offers a speed up of over 500 times compared with state-of-art P2D solvers [3]. Furthermore, its compatibility with gradient-based optimization algorithms opens possibilities for more efficient global optimization schemes, in which the number of function calls can be reduced. The high efficiency and the analytical nature of the URCs model render it a powerful tool for both on-board applications and battery cell design.[1] Doyle, M. and Newman, J., 1997. Analysis of capacity–rate data for lithium batteries using simplified models of the discharge process. Journal of Applied Electrochemistry, 27, pp.846-856.[2] Wang, F. and Tang, M., 2020. A quantitative analytical model for predicting and optimizing the rate performance of battery cells. Cell Reports Physical Science, 1(9).[3] Sulzer, V., Marquis, S.G., Timms, R., Robinson, M. and Chapman, S.J., 2021. Python battery mathematical modelling (PyBaMM). Journal of Open Research Software, 9(1). Figure 1

Estimating Parameters of Physics-Based Battery Models – What Machine Learning Can and Cannot Do

With the widespread use of Lithium-ion (Li-ion) batteries in multiple industries, the design space for the electrochemical cells has increased drastically. Li-ion batteries’ design parameters and material properties, such as porosity, electrode thickness, active material loading, and solid phase diffusivities, typically vary substantially due to different design goals and variation in the manufacturing process. Due to the difficulty in obtaining these and other battery cell parameters, many battery management systems used to control and monitor Li-ion batteries opt for the simplified resistor-capacitor circuit-based battery cell representation over using physics-based battery models. However, if these parameters become obtainable, scientists could implement advanced battery management systems using physics-based battery models to capture precisely how the battery performs and degrades in a wide variety of applications. Multiple methods, such as genetic algorithms, statistics, and machine learning, have been attempted for the parametrization and characterization of battery cells to enable accurate battery simulations using physics-based models [1, 2]. However, there are inherent limitations to the type and number of parameters that can be estimated using these methods if only the standard battery cell cycling data is utilized for this purpose. The present work elucidates and quantifies these limitations specifically in the case of machine learning based approach and provides deeper insights into these limitations that may help develop more robust cell characterization protocols. In the present work, model parameters are varied in a continuum-level physics-based model and simulations are performed for: (1) constant current-constant voltage (CC-CV) charging and constant current discharge at different C-rates, and (2) electrochemical impedance spectroscopy (EIS) in the relevant frequency range at multiple states of charge (SOCs). The Single Particle Model (SPM) is used for performing these simulations due to its relative simplicity and small number of parameters. At first, the charge and discharge data are input as training data in a long short-term memory neural network (LSTM NN), and EIS data is input as training data in a convolutional neural network (CNN). Once trained, the machine learning (ML) model uses charge, discharge, and EIS data withheld from the original training data set to predict SPM parameters. The estimated parameters are compared with the true parameters used for SPM charge, discharge, and EIS simulations, and the error in parameter estimation is quantified. A rigorous grid convergence analysis is performed to highlight the importance of ensuring that the spatial discretization error of the model does not influence the parameter estimation accuracy. For the first error quantification, all parameters are varied concurrently to obtain the parameter estimation error that arises from a large, undetermined parameter set. Parameters are then analyzed individually and in clusters related to diffusion, kinetics, and stoichiometric limitations. Further analysis is performed on parameters that could not be estimated with sufficient accuracy, including theoretical explanations for the incurred error and the effect of this error on the internal state predictions.

A Comparative Study of Numerical Methods for Lithium-Ion Battery Electrochemical Modeling

Lithium-ion battery (LIB) with high specific energy density and long cycle life is one widely used energy storage technology. In order to ensure longevity and safety of the battery system, a battery management system (BMS) that relies on battery model is required. With the development of BMS technique, more attention has been given to electrochemical models that provide insights into the battery internal states. In general, battery electrochemical models consist of partial differential equations (PDEs) describing the thermodynamic and electrochemical process inside the cell, and those PDEs can only be solved numerically due to their complexity.Existing battery simulation software utilize numerical methods such as finite difference method (FDM), finite volume method (FVM), and finite element method (FEM) to solve PDEs in battery models. However, there are little discussions for the selection of a specific numerical methods. In our recent study [1], we compare two spatial discretization methods commonly used to numerically solve the governing PDEs of LIB electrochemical models, namely FDM and FVM, in terms of model accuracy and mass conservation guarantee. First, we provide the mathematical details of the spatial discretization process for both FDM and FVM to solve the battery single particle model (SPM), this result has not been shown in any publication before. Second, we propose a new Hermite extrapolation based FVM scheme leading to higher accuracy when compared to the normally used linear extrapolation based FVM scheme. Then, SPM parameters are identified using experimental data, and a comprehensive parameter sensitivity analysis is conducted under different current input profiles to study parameter identifiability. Finally, model accuracy and mass conservation analysis of the FDM and FVM schemes are presented. Our study shows that the FVM scheme with Hermite extrapolation leads to accurate and robust control-oriented battery model while guaranteeing mass conservation and high accuracy. Also, the proposed new FVM scheme can be extended to solve other battery models, such as SPM model with electrolyte and Doyle-Fuller-Newman model. Moreover, we provide findings of mass conservation analysis for FDM and FVM schemes, which we hope can facilitate BMS model selection.

Interacting particle models on the impact of spatially heterogeneous human behavioral factors on dynamics of infectious diseases.

Human behaviors have non-negligible impacts on spread of contagious disease. For instance, large-scale gathering and high mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may effectively reduce contacts and suppress the peak of the outbreak. In order to understand how spatial characteristics like population mobility and clustering interplay with epidemic outbreaks, we formulate a stochastic-statistical environment-epidemic dynamic system (SEEDS) via an agent-based biased random walk model on a two-dimensional lattice. The "popularity" and "awareness" variables are taken into consideration to capture human natural and preventive behavioral factors, which are assumed to guide and bias agent movement in a combined way. It is found that the presence of the spatial heterogeneity, like social influence locality and spatial clustering induced by self-aggregation, potentially suppresses the contacts between agents and consequently flats the epidemic curve. Surprisedly, disease responses might not necessarily reduce the susceptibility of informed individuals and even aggravate disease outbreak if each individual responds independently upon their awareness. The disease control is achieved effectively only if there are coordinated public-health interventions and public compliance to these measures. Therefore, our model may be useful for quantitative evaluations of a variety of public-health policies.

Fluctuation-induced first order transition to collective motion

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

A sustainable mineral process for silicon and quartz recovery from quartz crucible waste ash via electrical separation

Driven by the explosive development of the photovoltaic (PV) industry, the treatment of the quartz crucible waste ash (QCWA) from monocrystalline silicon rod production must be considered to combat the shortage of silicon materials and promote sustainable development. In particular, the loss of grade 4 N high-purity silicon in QCWA is a frustrating fact for the silicon supply chain. In this work, an electrical separation process is proposed for the recovery of silicon and quartz from QCWA to realize waste resource reutilization. The charging processes and forces in the feed QCWA are first analyzed. Then, the electric field distribution during electrical separation is simulated to clarify the movement models of silicon and quartz particles and formulate reasonable electrical separation parameters. After systematic theoretical analysis, calculation, and simulation, electrical separation experiments were conducted. The results prove that the content of silicon in the concentrate and the corresponding content of quartz in the tailing respectively exceeded 93 % and 61 % under a particle size of 80 ∼ 120 mesh, a voltage of 40 kV, and a roll speed of 75 r/min. This work demonstrates that electrical separation is a sustainable process that could be recommended for silicon and quartz recovery from QCWA.

Analytical Solution for Predicting the Elastic Modulus of a Cement Slurry System with the Effect of Calcium Dissolution.

The dissolution of calcium ions in concrete in a low-alkalinity environment is an important factor causing a significant increase in the porosity of internal concrete, leading to a deterioration in its mechanical properties and affecting the durability of the concrete structure. In order to improve the reliability of concrete durability design and significantly increase the service life of concrete structures located in soft water environments, it is crucial to establish an analytical method to predict the elastic modulus (Edc) of cement slurry systems suffering from calcium dissolution. Firstly, the hydrated cement particles are regarded as a three-phase composite sphere composed of unhydrated cement particles (UC), a high-density hydrated layer (H-HL), and a low-density hydrated layer (L-HL). By introducing the equivalent inclusion phase (EQ) composed of UC and H-HL, the three-phase composite sphere model can be simplified into an equivalent hydrated cement particle model composed of EQ and L-HL. Finally, the Edc of the two-phase composite sphere composed of the equivalent hydrated cement particles and the porosity of the dissolved cement slurry system are solved by using elasticity theory. The effectiveness of the developed analytical method is verified by comparing it with third-party numerical results. Based on this method, the effects of hydration degree, volume ratio of calcium hydroxide (CH) to hydrated calcium silicate (C-S-H), and volume ratio of inner C-S-H to outer C-S-H on the Edc of the dissolved cement slurry system are analyzed. The parameter analysis indicates that among the three influencing parameters, the hydration degree has the greatest effect on the Edc of the dissolved cement slurry system. This study provides an analytical method for predicting Edc, which can provide some references for the durability design of concrete after calcium dissolution.

Movement characteristics of coal powders at bottom of coalbed methane well under jet flow

AbstractThe removal and discharge of coal powders from coalbed methane wellbore is the key to maintaining continuous production. For this reason, based on the submerged jet theory, the force and migration starting conditions of coal powder particles deposited at the bottom of the coalbed methane well are analyzed by analyzing the cohesiveness of coal powders, and a model for the starting and migration of coal powders at the bottom of the well under submerged jet conditions is established; Considering the adhesion between coal dust, the adhesion coefficient is used to characterize the adhesion between particles, a mechanical model of coal dust particles deposited at the bottom of the well is established, and the corresponding calculation formula for the outlet flow rate of the coal dust cleaning nozzle is derived. The fluid mechanics parameters of the bottom of the well coal dust cleaning under different conditions are obtained, and the numerical simulation method is used to simulate the whole process of jet flushing of the bottom of the well coal dust deposited, and the effect of the bottom of the well jet flushing of coal dust deposits is analyzed, providing a theoretical basis for the bottom of the well coal dust flushing process.

Multiple temperatures and melting of a colloidal active crystal

Thermal fluctuations constantly excite all relaxation modes in an equilibrium crystal. As the temperature rises, these fluctuations promote the formation of defects and eventually melting. In active solids, the self-propulsion of “atomic” units provides an additional source of non-equilibrium fluctuations whose effect on the melting scenario is still largely unexplored. Here we show that when a colloidal crystal is activated by a bath of swimming bacteria, solvent temperature and active temperature cooperate to define dynamic and thermodynamic properties. Our system consists of repulsive paramagnetic particles confined in two dimensions and immersed in a bath of light-driven E. coli. The relative balance between fluctuations and interactions can be adjusted in two ways: by changing the strength of the magnetic field and by tuning activity with light. When the persistence time of active fluctuations is short, a single effective temperature controls both the amplitudes of relaxation modes and the melting transition. For more persistent active noise, energy equipartition is broken and multiple temperatures emerge, whereas melting occurs before the Lindemann parameter reaches its equilibrium critical value. We show that this phenomenology is fully confirmed by numerical simulations and framed within a minimal model of a single active particle in a periodic potential.

Validity of gyrokinetic theory in magnetized plasmas

Gyrokinetics, as a reduced kinetic theory derived from adiabaticity, provides a general framework for the long-term dynamics of magnetized plasmas. While its validity limits are stated in terms of formal expansion parameters, more quantitative test of such is not widely mentioned even if it existed. Here we show, by detailed analyses of the Hamiltonian map with a test particle model, that gyrokinetic theory rests on the inherent nature of particle dynamics as a boundary layer problem. For low-frequency fluctuations, we demonstrate the existence of a frequency-independent threshold in the normalized amplitude, below which gyrokinetics is generally applicable. However, this threshold becomes sensitive to wave parameters in the high-frequency regime, which raises concerns about the generality of high-frequency gyrokinetic theory. Further analyses indicate that constructing a reduced kinetic equation based on superadiabaticity is not feasible. These findings contribute to a deeper understanding of the basic physics behind gyrokinetic theory.

Energetic Electrons Accelerated and Trapped in a Magnetic Bottle above a Solar Flare Arcade

Where and how flares efficiently accelerate charged particles remains an unresolved question. Recent studies revealed that a “magnetic bottle” structure, which forms near the bottom of a large-scale reconnection current sheet above the flare arcade, is an excellent candidate for confining and accelerating charged particles. However, further understanding its role requires linking the various observational signatures to the underlying coupled plasma and particle processes. Here we present the first study combining multiwavelength observations with data-informed macroscopic magnetohydrodynamics and particle modeling in a realistic eruptive flare geometry. The presence of an above-the-loop-top magnetic bottle structure is strongly supported by the observations, which feature not only a local minimum of magnetic field strength but also abruptly slowing plasma downflows. It also coincides with a compact above-the-loop-top hard X-ray source and an extended microwave source that bestrides the flare arcade. Spatially resolved spectral analysis suggests that nonthermal electrons are highly concentrated in this region. Our model returns synthetic emission signatures that are well matched to the observations. The results suggest that the energetic electrons are strongly trapped in the magnetic bottle region due to turbulence, with only a small fraction managing to escape. The electrons are primarily accelerated by plasma compression and facilitated by a fast-mode termination shock via the Fermi mechanism. Our results provide concrete support for the magnetic bottle as the primary electron acceleration site in eruptive solar flares. They also offer new insights into understanding the previously reported small population of flare-accelerated electrons entering interplanetary space.

Modeling Soft X‐Ray Emissions at the Dayside Magnetopause

AbstractIn this study, we simulate the Solar Wind Charge Exchange (SWCX) soft X‐ray emissions at dayside magnetosheath and cusps by using magnetohydrodynamic (MHD) and LAtmos TEst Particle (LaTeP) models. MHD models are unable to resolve the particle kinetic effects, such as the different behaviors of ions with different q/m, or distinguish the magnetospheric plasma from the solar wind plasma. We investigate these effects with the LaTeP model. As the LaTeP model does not self‐compute magnetic and electric field, the magnetic and electric field data obtained from Open Geospace General Circulation Model (OpenGGCM) and Lagrangian version of the piecewise parabolic method (PPMLR) MHD model are used as the input to LaTeP model. The soft X‐ray emissivity maps simulated from pure OpenGGCM and PPMLR MHD approaches and from LaTeP‐OpenGGCM and LaTeP‐PPMLR approaches are presented and compared. The results indicate that the LaTeP model can well resolve the kinetic effects and can be used to investigate the individual spectral characteristics. Therefore, the LaTeP model is a complementary approach for simulating the X‐ray emissions near the dayside magnetopause. We also calculate the ratio of integrated OVII/OVIII line intensities, produced by charge exchange of O7+ ions and O8+ ions, respectively. We find a relatively higher ratio at the bow shock compared to the surrounding areas, suggesting that this ratio can be an effective parameter to identify the bow shock location.

Study on the spray characteristics of transverse jets with elliptical nozzles in supersonic crossflows using the volume of fluid–discrete phase model

The atomization characteristics of liquid jets injected transversely into a supersonic crossflow significantly affect the performance of scramjet engines. Existing research on this topic has mainly focused on circular nozzles, while the influence of nozzle geometry, particularly elliptical nozzles, has received relatively limited attention. Therefore, this study employs a numerical simulation method coupling the volume of fluid and discrete particle model to investigate the breakup and atomization characteristics of transverse liquid jets from elliptical nozzles with different aspect ratios under supersonic crossflow conditions, as well as the total pressure loss. The simulation model is validated against experimental data obtained from a pulse wind tunnel, including measurements of the liquid jet penetration depth and the Sauter mean diameter (SMD). The results indicate that for elliptical nozzles with an aspect ratio (AR) greater than 1, columnar breakup occurs earlier, and the columnar breakup length is shorter compared to circular nozzles. As the AR increases, the jet penetration depth decreases, while the spray expansion angle increases. Furthermore, the SMD of the atomized spray field from the circular nozzle is larger than that from the elliptical nozzles, and the SMD of the spray field is smallest for an elliptical nozzle with AR of 4. Finally, the elliptical nozzles exhibit a higher total pressure recovery coefficient, indicating reduced total pressure loss in the combustion chamber. This reduction in pressure loss is expected to improve the thrust performance of the scramjet engine.