The work set out to optimize the catalyst layer (CL) structure of proton exchange membrane fuel cells (PEMFCs) to maximize electrochemical performance, transport efficiency, and durability simultaneously. The coupled effects of platinum loading distribution, ionomer pathways, and porous microstructure on charge transport, oxygen diffusion, water management, and electrochemical kinetics are investigated through the development of a mechanistic multiphysics modeling framework. The model combines mass and charge conservation, Butler–Volmer reaction kinetics, and effective transport formulations to enable systematic comparison between a standard reference CL and three successively optimized architectures. The findings indicate that the optimized CL designs provide clear improvements in power density, voltage stability, oxygen transport, and electrochemically active surface utilization, while exhibiting lower ohmic losses and reduced transport resistance. Quantitative comparison with experimental data shows that the predictive accuracy improves significantly, with the root mean square error decreasing to 2.7 mAcm⁻² and the coefficient of determination increasing to 0.997 for the most developed design. Moreover, degradation-sensitive aspects, such as platinum loss and interfacial instability, are noticeably alleviated through controlled microstructural design. The main contribution of this work lies in integrating multi-parameter optimization of the catalyst layer architecture within a single mechanistic framework, offering a scalable and robust route toward high-performance.

When water contacts hydrophobic materials─such as air, hydrocarbons, or fluorocarbons-the interface acquires charge, yet how dynamic wetting-dewetting governs this electrification remains largely unexplored. Here, using controlled pipetting experiments with hydrophobic capillaries, we show that electrification at water-hydrophobe interfaces is governed by liquid-solid separation rather than contact formation. By systematically varying liquid uptake and release rates over 3 orders of magnitude, we find that the charge transferred during a pipetting cycle depends nonlinearly on the velocity and acceleration of the receding liquid meniscus, while the advancing (uptake) motion contributes negligibly. High-resolution charge measurements reveal that, although net charge is conserved, the charge generated during liquid release in a given cycle directly influences the charge acquired during liquid uptake in the subsequent cycle. These observations uncover a previously unrecognized intercycle coupling in water-hydrophobe electrification and demonstrate that charge conservation is more appropriately described across successive wetting-dewetting cycles rather than strictly within an individual cycle. This intercycle formulation accurately captures charge balance under dynamically varying flow conditions and resolves apparent inconsistencies observed when release rates are changed between cycles. These findings hold across hydrophobic capillaries with negative, near neutral, and positive surface charge densities. Thus, our report establishes liquid-solid separation kinetics as the dominant control parameter for electrification at water-hydrophobe interfaces and highlight the inherently history-dependent nature of interfacial charging. These insights advance the fundamental understanding of water-hydrophobe electrification and have implications for droplet-based technologies, micro- and nanofluidics, and liquid-handling processes.

A gradient-boosting based atomic-charge scheme, BoostCha, is introduced. The BoostCha model operates in three steps: it first predicts pseudo-charges for individual atoms based on their local environments, represented by three-dimensional descriptors of Kocer-Mason-Erturk type, then refines these values using global molecular information, and finally restores the charge conservation. The BoostCha charges are employed as input features in two independent machine-learning models for predicting solvation free energies in organic solvents: ESE-Boost, a gradient-boosting model, and ESE-ANN, a dense artificial neural network. Both approaches yield strong predictive performance, with average root-mean-square errors of 0.49 and 0.52 kcal/mol, respectively. The methods demonstrate consistent performance across diverse solvent classes and are particularly accurate for alkanes, alcohols, ethers, esters, ketones, and aromatic and haloaromatic solvents.

Radical-Net: A chemistry-enhanced transformer for elementary radical reactions in pollutant chemistry.

We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions.

The local gauge coupling through the recipe [Formula: see text], which works so well with Dirac spinors in QED and in the gauge theories of the Standard Model, has a peculiarity when applied to scalar fields: it generates in the Lagrangian a coupling term [Formula: see text] in which [Formula: see text] does not coincide with the conserved Nöther current associated to the global gauge symmetry. This is not an inconsistency, just a feature that appears when working out the locally gauge invariant action and which ensures that the correct conserved current is the source of the gauge field. What would happen then if we were to assume for the scalar field the same coupling [Formula: see text] through a conserved current which holds for spinor QED and classical electrodynamics? The consequence is that one is forced in that case to renounce to the principle of local gauge symmetry and must thus consider the electromagnetic (e.m.) field to be described by electrodynamic theories compatible with that lack of invariance, like the extended electrodynamics by Aharonov–Bohm. No differences with the usual theory appear for fermion systems when strict local charge conservation applies. In particular, if we consider the nonrelativistic quantum theory as the low-energy limit of the relativistic theory, we would expect no modifications of Schrödinger equation when applied to fermion systems. However, when scalar boson systems are considered, like Cooper pairs quasi-particles in superconductors, in the new formulation the e.m. fields include a source, additional to the usual conserved four-current and, besides, the corresponding Schrödinger equation acquires a new term, proportional to [Formula: see text], which can lead to observable consequences, like a sizable change in the estimate of the magnetic penetration depth in certain superconductors, compatible with the experimental data. In conclusion, the alternative coupling considered yields a viable effective model for bosonic condensed matter systems, while for Dirac fermions it reduces to standard QED. Soft photon factorization and KLN cancellations in scalar QED fail in this framework, therefore particle physics scattering is outside the scope.

Lithium-ion batteries constitute a complex multiscale system, integrating physical phenomena across particle, electrode, and cell levels. The development of porous electrode models that bridge microstructural characteristics with macroscopic performance provides a computational foundation for intelligent battery design. Mechanochemical interactions arising during cycling affect the electrochemical processes and significantly influence rate capability and degradation behavior. This study introduces ETMbatteryFoam, a multi-scale simulation framework developed in OpenFOAM, resolving coupled electrochemical–thermal–mechanical phenomena across particle, electrode, and cell scales. By extending traditional concentrated solution theory with small-strain continuum mechanics, the solver formulates a system of partial differential equations describing mass transport, charge conservation, interfacial reaction kinetics, and stress evolution. A segregated iterative algorithm enables full multi-physics simulations of 1C charge/discharge within 1.5 min. Validation against in situ swelling experiments shows less than 8% deformation prediction error for lithium nickel cobalt manganese oxide/graphite systems. The modular and extensible framework provides high-fidelity resolution of electrochemical–mechanical coupling, thereby directly supporting the development of next-generation high-power batteries.

The D-measure of net-charge fluctuations quantifies the variance of net charge in strongly interacting matter. It was introduced over 20years ago as a potential signal of quark-gluon plasma (QGP) in heavy-ion collisions, where it is expected to be suppressed due to the fractional electric charges of quarks. Measurements have been performed at RHIC and LHC, but the conclusion has been elusive in the absence of quantitative calculations for both scenarios. We address this issue by employing a recently developed formalism of density correlations and incorporate resonance decays, local charge conservation, and experimental kinematic cuts. We find that the hadron gas scenario is in fair agreement with the ALICE data for sqrt[s_{NN}]=2.76 TeV Pb-Pb collisions only when a very short rapidity range of local charge conservation is enforced, while the QGP scenario is in excellent agreement with experimental data and largely insensitive to the range of local charge conservation. A Bayesian analysis of the data utilizing different priors yields moderate evidence for the freeze-out of charge fluctuations in the QGP phase relative to hadron gas. The upcoming high-fidelity measurements from LHC Run 2 will serve as a precision test of the two scenarios.

Higher rank gauge theories are generalizations of electromagnetism where, in addition to overall charge conservation, there is also conservation of higher rank multipoles such as the total dipole moment. In this work we study a four-dimensional lattice tensor gauge theory coupled to bosonic matter which has second rank tensor electric and magnetic fields and charge conservation on individual planes. Starting from the Hamiltonian, we derive the lattice action for the gauge fields coupled to q = 1 , 2 charged scalars. We use the action formulation to carry out Monte Carlo simulations to map the phase diagram as a function of the gauge ( β ) and matter ( κ ) couplings. We compute the nature of correlators at strong and weak coupling in the pure gauge theory and compare the results to numerical simulations. Simulations show that the naive weak coupling regime (small κ , large β ) does not survive in the thermodynamic limit. Instead, the strong coupling confined phase spans the whole phase diagram. It is a proliferation of instantons that destroys the weak coupling phase and we show, via a duality transformation, that the expected strong confinement is present in the analog of Wilson line correlators. For finite matter coupling at q = 1 we find a single thermodynamic phase albeit with a first-order phase transition terminating in a critical end point. For q = 2 it is known that the X-cube model with Z 2 fractonic topological order is recovered deep in the Higgs regime. The simulations indeed reveal a distinct Higgs phase in this case.

Chiral charge conservation and ballistic magnetotransport in a disordered Weyl semimetal

Solid oxide fuel cells offer a clean and efficient alternative to conventional power generation based on fossil fuel combustion. However, their commercialization remains challenging due to various forms of polarization, primarily associated with the slow oxygen reduction reaction (ORR) rate. This study presents the development of a one-dimensional (1D) isothermal model for an electrolyte-supported solid oxide cell.The model incorporates mass balance equations for gaseous chemical species, adsorbed species and ions on electrode surfaces, and lattice species within the electrodes. It also accounts for charge and momentum conservation. At the electrodes, a microkinetic model describes species adsorption, electron transfer, and ion transfer processes for oxidation and reduction reactions. Percolation theory is employed to determine the microstructural and textural properties of the active layers, enabling the calculation of effective electrode properties. The model was developed using COMSOL Multiphysics® and validated against experimental data, including polarization curves for a Ni-YSZ|YSZ|CGO|LSCF cell tested at different temperatures (700°C to 900°C).This model bridges multiple scales, from the atomic scale, where elementary reaction steps are described, to the mesoscale, where the electrode is treated as a continuum percolating cluster, to the macroscale, which accounts for the cell’s current output at a given overvoltage.The cell’s performance was evaluated using hydrogen diluted in an inert gas, followed by an assessment of CO₂ addition to the fuel mixture. Model calibration and validation were performed using multiple datasets, and sensitivity analyses were conducted to evaluate parameter influence, identify limiting processes under different operating conditions, and assess the current output. Most kinetic parameters of the elementary reaction steps were fitted during calibration, while others were retrieved from the literature.This work aims to develop and calibrate the model based on experimental data obtained at the Department of Chemical Sciences of the University of Padua. The model can then be used to investigate the phenomena limiting the cell’s current output under various operating conditions, such as temperature, feed flow rate, composition, and applied voltage. Another application is the rational design of the Ni-YSZ|YSZ|CGO|LSCF cell, optimizing both electrode size and textural properties. Finally, the model can be adapted for other electrode materials and employed in the design of new mixed ionic-electronic conductor (MIEC) materials. Since a change in MIEC composition affects only the model parameters, while the governing equations remain unchanged, the model can be applied to new materials once their kinetic parameters are determined from symmetric cell experiments.The model effectively captures all forms of polarization, distinguishing between different regimes depending on temperature. The cell is kinetically limited near the open-circuit voltage (OCV) and diffusion-limited at high current densities. In the kinetic regime, the limiting elementary reaction was found to be temperature-dependent; however, it was consistently related to oxygen consumption, confirming ORR as the primary limiting process in overall cell performance and highlighting the need for more active cathode materials.The structural properties of electrodes significantly influence cell performance. Specifically, reducing the thickness and increasing the porosity of the LSCF cathode shifted concentration polarization to lower voltages, thereby improving performance. However, excessive porosity reduced particle contact, diminishing current output in the kinetic regime. Increasing pore formation by adding pore formers during electrode manufacturing mitigated diffusion limitations at high cell utilization but required careful balancing to maintain optimal performance and prevent mechanical failure of the electrodes.Additionally, the model assessed the impact of lattice species composition on cell performance. Increased LSCF doping enhanced ionic conductivity and reduced cell resistance, highlighting opportunities for electrode composition optimization.To reduce computational costs and evaluate the significance of various physical and electrochemical phenomena in the overall device performance, simplified models were developed. Three main sub-models were considered: (i) a model with simplified kinetics, where the semi-reaction mechanism was neglected and the ORR and HOR reactions were treated as single-step processes, omitting adsorption-related phenomena; (ii) a model neglecting gaseous species diffusion through the porous electrodes and the mobility of the oxygen vacancy/lattice oxygen pair in the MIEC material or ionic conductor; and (iii) a model replacing the complex Dusty Gas Model (DGM) with the simpler Stefan-Maxwell diffusion model in the kinetic regime. The results showed that a detailed anode microkinetic model was unnecessary in the diffusive regime, and replacing the DGM with the Stefan-Maxwell model provided a computationally efficient alternative without significant loss of accuracy

Protonic ceramic fuel cells (PCFC) is an electrochemical conversion device with excellent kinetic performance at intermediate temperatures(673-923K) [1][2]. The tubular PCFC is a configuration known for its high structural strength and resistance to thermal shock, making it suitable for portable and mobile applications [3]. Currently, some simulation studies have been conducted on planar PCFC single cells and stacks [4][5]. However, research on tubular PCFC stacks is still lacking and has not been widely reported. A three-dimensional physical model plays an important role in the design and optimization of PCFC stacks [3]. Therefore, this study develops a 4-cell in parallel three-dimensional PCFC stack model. Unlike traditional oxygen ion conductor solid oxide fuel cells, PCFC electrolytes are typically perovskite materials [6], such as BZY and BCZYYb, where three types of charged defects are formed inside the electrolyte (OHO •,OO • , VO ••) [7]. In this case, the charge conservation of a single ion is no longer sufficient to describe the charge transport inside the electrolyte. Thus, this study solves the multi-ion transport process within the electrolyte based on the chemical equilibrium of gases and defects, as well as the Nernst-Planck equation. Using this model, the distribution of physical quantities within the stack was studied, as well as the effects of inlet temperature and humidity on the electrochemical performance and current efficiency of the stack.To validate the accuracy of the model, we fabricated a 4-cell in parallel PCFC stack, as shown in Fig. 1(a). The composition, geometric structure, and fabrication process of the PCFC single cells used can be referenced from our previous work [8][9]. The discharge performance of the stack was experimentally tested at three different temperatures, as shown in Fig. 1(b). The geometric structure of the three-dimensional multi-physics coupling PCFC stack model is shown in Fig. 1(c), which includes the gas distribution chamber, the cell body, and the cathode chamber.Fig. 2(a) shows the surface flux density distribution of O-site polarons for two cells at different positions. The cell near the air inlet exhibits a gradually increasing flux density of O-site polarons along the air flow direction, while the cell near the air outlet shows the opposite trend. Fig. 2(b) presents the total flux of O-site polarons in the PCFC stack at different temperatures. It can be observed that as the temperature increases, the total flux of O-site polarons increases, with the total flux at 650°C being an order of magnitude higher than that at 550°C. Fig. 2(d) shows the total flux of O-site polarons at different inlet water vapor concentrations on the air side. As the water vapor concentration increases, the total flux of O-site polarons decreases.This study built a PCFC stack model that considers the coupling of multiple physical and chemical processes. The multi-ion transport process inside the electrolyte is calculated by Nernst-Planck equation. Using this model, the temperature distribution, component distribution, and multi-ion transport inside the electrolyte of the PCFC stack can be obtained. Studies show that regions with high oxygen concentration and high temperature enhance the transport of O-site polarons, increasing the local leakage current density; lower inlet temperatures can suppress the transport of O-site polarons, thereby reducing leakage current; Increasing the inlet water vapor concentration on the air side can promote the hydration reaction, thereby inhibiting the generation of O-site polarons and improving current efficiency. This study will provide a reference for future experimental and simulation research on PCFC stacks.

Abstract The thermodynamic properties of an ideal bosonic system composed of particles and antiparticles at finite temperatures are examined within the framework of a scalar field model. It is assumed that particle–antiparticle pair creation occurs; however, the system is simultaneously subject to exact charge (isospin) conservation. To implement this constraint, we first consider the system within the Grand Canonical Ensemble and then transform to the Canonical Ensemble using a Legendre transformation. This procedure provides a formally consistent scheme for incorporating the chemical potential at the microscopic level into the Canonical Ensemble framework. To enforce exact conservation of charge (isospin, N I ), we further analyze the thermodynamic properties of the system within the extended Canonical Ensemble , in which the chemical potential becomes a thermodynamic function of the temperature and conserved charge. It is shown that as the temperature decreases, the system undergoes a second-order phase transition to a Bose–Einstein condensate at the critical temperature T c , but only when the conserved charge is finite, N I = const ≠ 0. In a particle–antiparticle system, the condensate forms exclusively in the component with the dominant particle number density, which determines the excess charge. We demonstrate that the symmetry breaking of the ground state at T = 0 results from a first-order phase transition associated with the formation of a Bose–Einstein condensate . Although the transition involves symmetry breaking, it is not spontaneous in the strict field-theoretic sense, but is instead induced by the external injection of particles. Potential experimental signals of Bose–Einstein condensation of pions produced in high-energy nuclear collisions are briefly discussed.

Precise control of light-induced electrical signals at the biotic-abiotic interface remains a central challenge in advancing next-generation bioelectronic systems. In particular, achieving bidirectional signal modulation is essential for effective neural interface applications. Here, a spatially resolved, bidirectional photoelectric response at the silicon (Si) membrane-solution interface, induced by laser illumination is presented. Notably, a clear reversal in signal polarity between the illuminated regions (bright zones) and adjacent non-illuminated areas (dark zones) is observed. This signal orientation can be dynamically tuned by adjusting the light spot position and tailoring interfacial properties. To understand the underlying mechanism, the author systematically examined how various experimental parameters influence photoelectric behavior. These include the choice of adhesive, substrate conductivity (conductive vs insulating), boundary conditions (fixed vs free edges), and membrane geometry (e.g., grids and rectangles). These results reveal a cooperative effect between intrinsic charge conservation in the Si membrane and capacitive coupling at the interface. Moreover, in vivo studies show that integrating a conductive substrate beneath the Si membrane significantly enhances the modulation of sciatic nerve activity. Together, these findings define a new framework for light-responsive bioelectronic interfaces and point toward their broad utility in bioelectronic and neuromodulation applications.

Abstract The gauge invariant minimal couplings for a class of relativistic free matter fields with global symmetry (related to usual charge conservation) have been obtained by incorporating an iterative Noether mechanism. Non-relativistic reduction of both matter and gauge sectors of the obtained interacting theory is then performed simultaneously which in turn yield a set of new effective actions which are invariant under the Galilean relativistic framework. To be precise, we show that one can obtain the Schrödinger field theory coupled to Galilean electromagnetism from the scalar quantum electrodynamics theory. Higher derivative corrections have also been included for which the non-relativistic reductions have been consistently carried out once again. On the other hand, the action for quantum electrodynamics leads to the Galilean Pauli–Schrödinger theory where the gauge field is non-relativistic or Galilean. Further, some novel relations are found (in both the electric and magnetic limits) between various components appearing in the Galilean avatar of electrodynamics.

The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, nonintegrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation.

We demonstrate the existence of a universal phase diagram of quantum chains with range-k interactions subject to the conservation of a total charge and its dipole moment. These systems exhibit “freezing” transitions between strongly and weakly Hilbert-space-fragmented phases as the charge filling ν is varied. We show that these continuous phase transitions occur at a critical charge filling of νc=(k−2)−1 of the on-site Hilbert-space dimension d. To this end, we analytically prove that, for any d, any state with ν<νc hosts a finite density of sites belonging to “blockages,” which we define as subregions of the chain across which transport of charge and dipole moment cannot occur. Some blockages arise from sequences of frozen sites, i.e., sites with an unchanging on-site charge, while others do not involve frozen sites at all. We prove that the presence of blockages implies strong fragmentation of typical symmetry sectors into Krylov subspaces, each of which forms an exponentially vanishing fraction of the total sector. By studying the distribution of blockages we analytically characterize how typical states are subdivided into dynamically disconnected local “active bubbles” and prove that typical eigenstates at these charge fillings exhibit area-law entanglement entropy, while there exist rare eigenstates featuring non-area-law scaling. We also numerically show that for ν>νc and arbitrary d, typical symmetry sectors are weakly fragmented, with their dominant Krylov sectors constituted of states that are free of blockages. We analytically derive some critical exponents characterizing the transition and numerically determine the density of blockages at ν=νc, with clear implications for transport at the critical point. Finally, we investigate the properties of special-case models for which no phase transitions occur.

Field theory of monitored interacting fermion dynamics with charge conservation

Abstract We study the quantum transport generated by the bipartite entanglement in two-dimensional conformal field theory at finite density with the U(1) × U(1) symmetry associated to the conservation of the electric charge and of the helicity. The bipartition given by an interval is considered, either on the line or on the circle. The continuity equations and the corresponding conserved quantities for the modular flows of the currents and of the energy-momentum tensor are derived. We investigate the mean values of the associated currents and their quantum fluctuations in the finite density representation, which describe the properties of the modular quantum transport. The modular analogues of the Johnson- Nyquist law and of the fluctuation-dissipation relation are found, which encode the thermal nature of the modular evolution.

Batteries are one of the key technologies for energy transition. Building batteries that have a high energy density and are amenable to extreme fast charging while remaining safe, requires a detailed understanding of the underlying electrochemical processes.Modeling and simulation provide complementary tools to experiments for studying these processes, which often take place in complex three-dimensional porous electrodes. Advanced simulation capabilities can contribute to a better scientific understanding by resolving some of the coupled, multi-physics processes inside these systems. They can also lead to better engineering designs of battery systems by enabling parameter studies necessary for optimized battery architectures. Developing these simulations as digital twins of battery systems is a difficult task for multiple reasons.Processes in an electrochemical battery system involve many orders of magnitude in both length and timescales. The length scales range from O(Å) on the atomic scale to O(m) for the size of a battery pack. The timescales range from O(ps) to O(years) for the entire lifetime of a battery. There is a lot of focus on upscaled models, such as the single-particle (SPM) or pseudo-two-dimensional (P2D) models, that can model the battery dynamics over many cycles. In terms of computational complexity, these models are relatively cheap compared to more detailed approaches. However, they are lacking a detailed description of the three-dimensional pore space of battery electrodes. At the molecular scale, simulations resolve individual atoms and molecules to focus on the understanding of detailed individual processes. These simulations are computationally very demanding and are therefore limited in the number of molecules and timescales they can resolve.Pore-scale modeling tries to bridge the gap between these different scales by resolving the three-dimensional pore space of the battery electrodes while using a continuum-based description. By resolving the pore space, it can provide insights into phenomena like current hotspots, concentration gradients, Li+ transport, and intercalation dynamics on an electrode-resolved level. By still adopting a continuum-based description, although the simulations are expensive, efficient techniques for their solution have been developed [4]. Motivated by these challenges and the potential of pore-scale models, we developed our own pore-scale simulator to solve the coupled mass and charge conservation equations inside the complex, three-dimensional microstructure.We focus on a traditional Li-ion system and solve the coupled mass and charge conservation in the solid electrodes as well as the liquid electrolyte as described in Latz and Zausch [5] and Schneider [6]. We use a finite volume scheme in space and a fully implicit time integration to discretize the governing equations. To resolve solid-liquid interfaces inside the pore space, we use an octree-refined grid [3]. The code is developed in C++, building on the open-source deal.II library [1]. The set of non-linear equations is solved using a Newton-Raphson algorithm. The arising linear systems are solved using a preconditioning method described by Fang et al. [4].We compare the code in 1D against available solutions in the literature [7]. We report on the convergence and parallel performance of the solver. Finally, we use the developed code to perform a pore-scale simulation of a Li-ion battery with a graphite anode and an NMC cathode using openly available computed tomography data [2]. The presented solver is a starting point for the development of more sophisticated solvers. Possible extensions include an additional energy equation, the resolution of double layers, or simulation of other battery chemistries.[1] Pasquale C. Africa et al. The deal.II library, Version 9.6. 2024. doi: 10.1515/jnma-2024-0137.[2] Battery Microstructures Library — nrel.gov. https : / / www.nrel.gov/transportation/microstructure.html. [Accessed 16-12-2024].[3] Carsten Burstedde, Lucas C. Wilcox, and Omar Ghattas. “p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees”. In: SIAM Journal on Scientific Computing 33.3 (2011), pp. 1103–1133. doi:10.1137/100791634.[4] Rui Fang et al. “Parallel, physics-oriented, monolithic solvers for three-dimensional, coupled finite element models of lithium-ion cells”. In: Computer Methods in Applied Mechanics and Engineering 350 (2019), pp. 803–835.[5] Arnulf Latz and Jochen Zausch. “Thermodynamic consistent transport theory of Li-ion batteries”. In: Journal of Power Sources 196.6 (2011), pp. 3296–3302.[6] Falco Schneider. Development and Analysis of Numerical Simulation Methods for Lithium-Ion Battery Degradation. Fraunhofer Verlag, 2023.[7] Shiquan Zhang et al. “Comparison of two approaches for treatment of the interface conditions in FV discretization of pore scale models for Li-ion batteries”. In: Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems: FVCA 7, Berlin, June 2014. Springer. 2014, pp. 731–738.