Geometric Research Articles

Identification of Cause–Effect Relationships between Process Parameters and the Film Formation in the Semidry Electrode Production for Lithium‐Ion Batteries

Conventional electrode production for lithium‐ion batteries has high energy and plant space demand, due to the high solvent content of the slurry to be processed by slot die or doctor blade coating. By using the semidry electrode production, the solvent content is reduced by more than 50% compared to the conventional electrode production, decreasing energy demand and drying length. Regarding technology readiness level, the semidry electrode production is on the pilot scale, as the basic principles have been shown. However, many unknown cause–effect correlations exist between the process parameters and the product properties. This study aims to analyze process parameter variations and their influence on the geometric, electrochemical, and mechanical properties of the electrode. An experimental design is utilized to obtain statistically relevant conclusions. It is found that the first calender gap and the roller speed influence the mass loading and the porosity of the electrode. The roller speed significantly influences the ionic resistance within the electrode, which may be attributed to the used release foil.

Tailoring Superatomic Stability with Transition Metals in Silicon Cages: Shrinking to M@Si15 (M = Re, Os, Ir).

The design of materials with intriguing electronic properties is crucial for advancing nanoscale technologies, where precise control over atomic structure and electronic behavior is essential. Metal-encapsulating silicon cage superatoms (SAs) provide a new paradigm for molecular-scale material design, allowing fine-tuning of both structure and electronic characteristics. The formation of superatoms mimicking halogens, noble gases, and alkali metals has been well-studied, particularly with M@Si16, where early transition metals from groups 3 to 5 stabilize within a Si16 cage, achieving a 68-electron configuration. For late transition metals with excess electrons, a Si15 cage offers enhanced stability by fulfilling the 68-electron rule with one fewer Si atom. This research synthesizes Si15 cage-SAs with rhenium (Re) from group 7 and iridium (Ir) from group 9 on p-type and n-type organic substrates. The stability of Re@Si15 and Ir@Si15 is evaluated via oxidative reactivity with X-ray photoelectron spectroscopy and theoretical calculations, including osmium (Os) from group 8. Re@Si15-, Os@Si150, and Ir@Si15+ exhibit superatomic behaviors similar to halogens, noble gases, and alkali metals due to the 68-electron shell closure. Among them, Re@Si15- on p-type organic substrates shows superior electronic and geometric properties. These findings advance our understanding of M@Sin systems for transition metals, addressing longstanding questions about their properties at n = 15 and 16.

Geometric and Mechanical Properties of Ti6Al4V Skeletal Gyroid Structures Produced by Laser Powder Bed Fusion for Biomedical Implants

Skeletal gyroid structures possess promising applications in biomedical implants, owing to their smooth and continuously curved surfaces, open porosity, and customisable mechanical properties. This study simulated the geometric properties of Ti6Al4V skeletal gyroid structures, with relative densities ranging from 1.83% to 98.17%. The deformation behaviour of these structures was investigated through a combination of uniaxial compression tests and simulations, within a relative density range of 13.33% to 50% (simulation) and 15.19% to 41.69% (experimental tests). The results established explicit analytical correlations of pore size and strut diameter with the definition parameters of the structures, enabling precise control of these dimensions. Moreover, normalised Young’s modulus (ranging from 1.05% to 20.77% in simulations and 1.65% to 15.53% in tests) and normalised yield stress (ranging from 1.75% to 17.39% in simulations and 2.09% to 13.95% in tests) were found to be power correlated with relative density. These correlations facilitate the design of gyroid structures with low stiffness to mitigate the stress-shielding effect. The presence of macroscopic 45° fractures in the gyroid structures confirmed that the primary failure mechanism is induced by shear loads. The observed progressive failure and plateau region proved the bending-dominant behaviour and highlighted their excellent deformability. Additionally, the anisotropy of gyroid structures was confirmed through variations in stress and strain concentrations, deformation behaviour, and Young’s modulus under different loading directions.

Interfaces of the two-dimensional voter model in the context of SLE

Abstract This paper investigates various geometrical properties of interfaces of the two-dimensional voter model. Despite its simplicity, the model exhibits dual characteristics, resembling both a critical system with long-range correlations, while also showing a tendency towards order similar to the Ising–Glauber model at zero temperature. This duality is reflected in the geometrical properties of its interfaces, which are examined here from the perspective of Schramm–Loewner evolution. Recent studies have delved into the geometrical properties of these interfaces within different lattice geometries and boundary conditions. We revisit these findings, focusing on a system within a box of linear size L with Dobrushin boundary conditions, where values of the spins are fixed to either +1 or −1 on two distinct halves of the boundary, in order to enforce the presence of a pinned interface with fixed endpoints (or chordal interface). We also expand the study to compare the geometrical properties of the interfaces of the voter model with those of the critical Ising model and other related models. Scaling arguments and numerical studies suggest that, while locally the chordal interface of the voter model has fractal dimension d f = 3 / 2 , corresponding to a parameter κ = 4, it becomes straight at large scales, confirming a conjecture made by Holmes et al (2015 J. Stat. Phys. 159 937–57), and ruling out the possibility of describing the chordal interface of the voter model by SLE κ , for any non-zero value of κ. This contrasts with the critical Ising model, which is described by SLE3, and whose interface fluctuations remain of order L, and more generally with related critical models, which are in the same universality class.

A study of novel telephone sequence spaces and some geometric properties

AbstractFor a nonnegative integer k, let $\mathcal {T}_{k}$ T k denote the kth telephone number. Consider the matrix $\mathfrak{T}=(\mathfrak {T}_{kr})$ T = ( T k r ) given by $$\begin{aligned} \mathfrak {T}_{kr}= \textstyle\begin{cases} \dfrac{r\mathcal {T}_{r-1}}{\mathcal {T}_{k+1}-1}, & 0\leq r\leq k, \\ 0 , & r>k, \end{cases}\displaystyle \end{aligned}$$ T k r = { r T r − 1 T k + 1 − 1 , 0 ≤ r ≤ k , 0 , r > k , where $k,r=0,1,2,\dots $ k , r = 0 , 1 , 2 , … Using the matrix $\mathfrak{T}$ T , we define matrix domains $\mathscr{T}_{p}:=(\ell _{p})_{\mathfrak{T}}$ T p : = ( ℓ p ) T for $0 < p < \infty $ 0 < p < ∞ and $\mathscr{T}_{\infty}:=(\ell _{\infty})_{\mathfrak{T}}$ T ∞ : = ( ℓ ∞ ) T . In this context, we construct a Schauder basis for $\mathscr{T}_{p}$ T p and identify their α-, β-, and γ-duals. We also derive various results pertaining to matrix transformations from the spaces $\mathscr{T}_{p}$ T p and $\mathscr{T}_{\infty}$ T ∞ to traditional spaces such as $\ell _{\infty}$ ℓ ∞ , c, $c_{0}$ c 0 , and $\ell _{1}$ ℓ 1 . Additionally, we explore several geometric attributes of the spaces $\mathscr{T}_{p}$ T p and $\mathscr{T}_{\infty}$ T ∞ , including the approximation property, D-P property, Hahn–Banach extension property, and rotundity.

Machine-Learning-Assisted Screening of Nanocluster Electrocatalysts: Mapping and Reshaping the Activity Volcano for the Oxygen Reduction Reaction.

In computational heterogeneous catalysis, Sabatier's principle-based activity volcano plots provide an intuitive guide to catalyst design but impose a fundamental constraint on the maximum achievable catalytic performance. Recently, subnano clusters have emerged as an exciting platform, offering high noble metal utilization and superior performance for various reactions compared to extended surfaces, reflecting a complex structure-activity relationship in the non-scalable regime. However, understanding their non-monotonic catalytic activity, attributed to the large configurational space and their fluxional identity, poses a formidable challenge. Here, we present a machine learning (ML) framework that captures the non-monotonic trends in oxygen reduction reaction (ORR) activity at the subnanometer scale, attributed to their dynamic fluxional characteristics. We demonstrate a size-dependent shifting and reshaping of the ORR activity volcano, with Au replacing Pt at the peak. Leveraging only upon the non-ab initio geometric and electronic properties, our trained ML model accurately captures the site-specific adsorption energies of intermediates at the subnanometer regime. To account for the inconsistent trend in activity, we analyzed the correlation between electronic and geometric properties. Our findings reveal that the d-filling and coupling matrix of the neighboring metal atom significantly influences the intermediate adsorption on the local chemical environment compared to the d-band center. Following this analysis, we utilized ML to map the catalyst distribution in the activity volcano and identified the five best sub-nano electrocatalysts, demonstrating overpotential values lower than or comparable to the Pt(111) surface for the ORR. This study provides intuitive guidelines for the rational designing of highly efficient electrocatalysts for fuel cell applications while modifying the activity volcano plots for electrocatalysts at the subnanometer regime.

Optical Characterization of Parasitic Motion in a Long-Stroke Shaker

Abstract We present an optical scheme to simultaneously characterize the cross-axis and rota- tional parasitic motions of a long-stroke shaker. By leveraging the geometric properties of a corner cube retroreflector mounted on the shaker load table, we independently sample pitch, yaw, and horizontal and vertical displacements with sampling rates above 10 kHz. We have applied our optical apparatus to a 400-mm-stroke shaker operated from 0.1 Hz to 100 Hz and present two forms of analysis: (A) Frequency-domain data for the four measured parasitic degrees of freedom, with the resulting implications for accelerometer calibration uncertainties, and (B) extracted trajectories of the shaker table, allowing visualization of the bowed linear guide below 0.5 Hz and higher harmonics and hysteresis above 10 Hz. Our findings demonstrate our optical measurement scheme to be an effective tool for the characterization of parasitic motion for long-stroke shakers. As an example, we determine the "gravity error" in accelerometer calibration with our shaker to be (1.3 ± 0.1) % times the acceleration amplitude at 0.1 Hz, providing a correction to reduce uncertainty from this effect by an order of magnitude.

Geometric Analysis of Black Hole with Primary Scalar Hair

Within the novel context of primary scalar hair black holes, this article explores the fascinating subject of black hole thermal stability. Thermodynamic stability is the main subject of our investigation, which involves measuring the bound points, divergence points, black hole mass, thermal temperature, and specific heat capacity. In addition, we determine the scalar curvatures of thermodynamic geometries like Ruppeiner, Weinhold, Hendi-Panahiyah-Eslam-Momennia, and geometrothermodynamics formulations inside the framework of primary scalar hair black holes and delve into their complexities. Improving our knowledge of fundamental scalar hair black holes, this study sheds light on the intricate thermal geometric properties of these objects.

The Mittag-Leffler-Prabhakar Functions of Le Roy Type and its Geometric Properties

The Mittag-Leffler-Prabhakar Functions of Le Roy Type and its Geometric Properties

Geometrical and Computational Properties of the Generalized Struve Functions

Geometrical and Computational Properties of the Generalized Struve Functions

Analytical Model for Contaminant Transport in the CGCW and Aquifer Dual-Domain System Considering GMB Holes

Composite geomembrane cut-off walls (CGCW) have been widely used for the remediation of polluted sites, especially where the environmental conditions are complex. Accurate predictions of the GMB hole leakage and CGCW performance are essential for engineering design and cost control. This paper establishes empirical equations to predict the leakages through the CGCWs based on the numerical models. Additionally, an analytical solution for contaminant migration through the CGCW is proposed considering the effects of GMB holes. The accuracy of the established equations and analytical solution is verified by the numerical models. The key effects of the GMB thickness (TG), head loss (HG), cut-off wall hydraulic conductivity (kG), hole radius (rG) and shape on the leakage and CGCW performance are investigated. The results show that compared with other hole shapes, the leakage through the circular hole is lowest. This is mainly because the shape factor for the circular hole is 1.15–1.3 times lower than that for other shapes of holes with the same area. Additionally, the effects of the hole geometric properties and head loss on the CGCW performance can be more significant when the cut-off wall hydraulic coefficient is small. For example, the breakthrough time differences between the cases with rG = 0.005 m and 0.05 m are 0.8 and 5.0 years when kG = 10−10 and 10−9 m/s, respectively. This is because the impermeability of the CGCW is good when kG is small. This will weaken the impacts of the hole geometric properties on the leakage. The proposed empirical equations and analytical solution can provide effective suggestions for the design of the CGCW in different GMB hole cases.

Slip-pulses drive frictional motion of dissimilar materials: Universality, dynamics, and evolution

Frictional slip between bodies having different elastic or geometrical properties (bimaterial interfaces) creates a unique type of rupture, bimaterial "slip pulses." These slip pulses propagate along the interfaces separating elastically different contacting bodies. They exhibit highly localized slip with accompanying local normal stress reduction. These pulses do not result from properties of "friction laws" but, instead, are formed via the elastic mismatch of the contacting bodies. Here, we experimentally study slip pulse dynamics, evolution, and structure in seven different bimaterial interfaces. We find that slip pulses are a major vehicle for frictional motion in bimaterial interfaces, they exist in well-defined velocity windows and undergo unstable growth consistent with theoretical predictions coined the "Adams instability." When scaled properly, slip pulses exhibit both universal spatial structure and growth dynamics. While slip pulse amplitudes vary considerably within different interfaces, this variation is, surprisingly, not highly dependent on the contrast of the elastic properties of the contacting materials. Instead, slip pulse amplitudes are closely related to the interfaces' aging properties and, hence, to material plasticity at the interface. As bimaterial interfaces are generic, these results are fundamentally important to both frictional dynamics and the dynamics of earthquakes within a wide class of natural faults.

Wear and Damage Study of Straw Chopper Knives in Combine Harvesters

Most of the biomass of cereal straw is chopped and left on the field as organic fertilizer, but its conversion into fertilizer depends on the quality of chopping, which is influenced by the wear of the chopping blades. The aim of the study was to determine the influence of the contamination of the cereal straw on the wear of the combine chopper blades. The study was conducted during the harvest in 2022, when 30 ± 1% of the grain was lodged and contaminated with abrasive soil particles (poor conditions), and in 2023, when the straw was unlodged and clean (excellent conditions). Six sets of blades with different mechanical and geometric properties were selected. The results showed that the wear ranges were very different: 1.47–2.99 g/100 ha in 2022 and 0.72–2.14 g/100 ha in 2023. For micro-abrasive wear, the hardness of the blades (349–568 HV) and the cutting edge angle (20°–29°) were important factors of their wear resistance. When the clean straw was chopped, the influence of the blade hardness and cutting edge angle on wear was not significant, and the wear was less. The wear of the blades had a sinusoidal character, which was related to the position of the blades on the chopping drum. This character depends on the design of the chopper and not on the straw quality.

Numerical analysis of axially loaded concrete-filled steel tubular columns strengthened with CFRP grid-reinforced ECC

Carbon fiber-reinforced polymer (CFRP) and engineered cementitious composites (ECC) are commonly used to reinforce structural elements, with proven effectiveness in enhancing the performance of concrete-filled steel tube (CFST) columns as shown in prior experimental studies. However, the complex interaction among the components of the reinforced columns, including CFRP, ECC, the steel tube, and the concrete core, as well as the underlying mechanical mechanisms, remain insufficiently understood. This research aims to fill these gaps by developing a 3D finite element (FE) model of circular CFST short columns reinforced with CFRP grid-reinforced ECC for comprehensive numerical analysis. Sensitivity analyses are conducted to determine the governing parameters in the numerical simulation, including mesh size and critical plasticity parameters for the concrete damage model, such as the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian (Kc), and the dilation angle (ψ) for both the concrete core and ECC. The model also accounts for the effects of concrete confinement provided by the CFRP grid-reinforced ECC layer and the circular steel tube. The accuracy of the FE model is validated against existing experimental data, and the model is subsequently used to investigate the behavior of reinforced CFST columns under varying geometric and material properties. The study examines failure modes, axial load-displacement responses, stress distributions, and the contribution of each material component to the load-bearing capacity of the strengthened columns. The results indicate an increase in ultimate axial strength ranging from 13% to 20% for the reinforced CFST columns. While the compressive strength of the ECC has a moderate effect on axial resistance, increasing ECC thickness, concrete strength, and steel tube yield strength significantly enhances the columns’ load-bearing capacity. Finally, a novel design model is proposed and validated, which accounts for the confinement effects provided by the CFRP grid and ECC on the concrete core.

Aerodynamic optimisation of flat-upper-surface wing

Purpose The paper aims to optimise several concepts of the flat-upper-surface wing that could install the largest possible number of photovoltaic cells and test them in flight. A wing ideal flat upper surface was necessary to provide the same lighting conditions for each tested cell. Design/methodology/approach The optimised wings were built based on a developed family of airfoils having 75% of their upper surface flat. Within the developed parametric model of the wings, the design parameters described the spanwise distribution of base airfoils. Maximisation of the endurance factor was assumed as the main objective. The aerodynamic properties of optimised wings were evaluated using a panel method coupled with boundary layer analysis. Findings The paper proves that it is possible to design wings with 75% of their upper surface perfectly flat, which are also characterised by good aerodynamic properties. Practical implications The research conducted will allow designing an experimental unmanned aerial vehicle dedicated to investigating the properties of electrical propulsion systems at various altitudes. Data obtained in these investigations will help in the development of future generations of electric-propulsion aircraft. Originality/value The innovative wings, developed within the research are unique due to their unusual geometric and aerodynamic properties. They have 75% of their upper surface perfectly flat. That makes them ideal for testing various photovoltaic cells in flight. The biggest challenge was to design the wings so that their specific geometric features did not impair their aerodynamic properties. The paper proves that this challenge has been fully overcome.

Optical system characterization in Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recent technique to overcome the diffraction limit of a low numerical aperture (NA) objective lens by algorithmic post-processing of several low-resolution images. It can increase the space-bandwidth product of an optical system by computationally combining images captured under different illumination conditions. Vignetting determines the spatial extent of the bright and dark regions in the captured images. State-of-the-art analyses treat vignetting as a nuisance that needs to be reduced or excluded from algorithmic consideration using ad hoc decision rules. In contrast, this work investigates vignetting effects as a tool to infer a range of properties of the optical system. Generally, the goal of the FPM reconstruction algorithm is to achieve results that closely resemble the actual specimen at the highest resolution possible. However, as the optimization process does not necessarily guarantee a unique solution, we identify system properties that support alignment between computational predictions and empirical observations, potentially leading to a more accurate and reliable analysis. To achieve this, we characterize the individual system components of the experimental setup and compare experimental data to both, geometrical and wave optical simulations. We demonstrate that using vignetting as an analytical tool enables the modeling of the geometric and coherence properties of the optical system as evidenced by the good agreement between our simulation and experiment.

Riemannian Manifold-Aided Data-driven Diagnosis of Photovoltaic Hot Spots

Abstract This paper proposes a novel data-driven approach for hot-spot fault detection in photovoltaic (PV) modules, utilizing a curved Riemannian manifold (RM) to characterize the sample space. The proposed method detects hot spots in PV systems by mining geometric features in high-dimensional data. The RM-based method combines the geometric properties of Riemannian manifolds for fault detection. In addition, it also provides information about the severity of the hot spots. The proposed method has three main advantages:
1) it is capable of actively learning fault characteristics and can be applied to diagnose various degrees of hot spots;
2) unlike other data-driven methods, the proposed method considers non-Euclidean spatial data features, which further improves the accuracy of the method and reduces the false alarm rate (FAR);
3) it does not rely on mathematical models or expert knowledge, making it able to meet the real-time monitoring needs of actual PV systems.
The effectiveness and superiority of the proposed approach are verified through 12 sets of hot spots tests conducted on a PV experimental platform.

Geometric neural operators (gnps) for data-driven deep learning in non-euclidean settings

Abstract We introduce Geometric Neural Operators (GNPs) for data-driven deep learning of geometric features for tasks in non-euclidean settings. We present a formulation for accounting for geometric contributions along with practical neural network architectures and factorizations for training. We then demonstrate how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures of surfaces, (ii) to approximate solutions of geometric partial differential equations on manifolds, and (iii) to solve Bayesian inverse problems for identifying manifold shapes. These results show a few ways GNPs can be used for incorporating the roles of geometry in the data-driven learning of operators.

The effect of data-driving and relaxation models on magnetic flux rope evolution and stability

Understanding the flux rope eruptivity and effects of data driving in modelling solar eruptions is crucial for correctly applying different models and interpreting their results. We aim to investigate these by analysing the fully data-driven modelled eruption of the active regions (ARs) 12473 and AR11176, as well as preforming relaxation runs for AR12473 (found to be eruptive) where the driving is switched off systematically at different time steps. We intend to analyse the behaviour and evolution of fundamental quantities that are essential for understanding the eruptivity of magnetic flux ropes (MFRs). The data-driven simulations were carried out with the time-dependent magnetofrictional model (TMFM) for AR12473 and AR11176. For the relaxation runs, we employed the magnetofrictional method (MFM) and a zero-beta magnetohydrodynamic (MHD) model to investigate how significant the differences between the two relaxation procedures are when started from the same initial conditions. In total, 22 simulations were studied. To determine the eruptivity of the MFRs, we calculated and analysed characteristic geometric properties such as the cross-section, MFR height, and physical stability parameters such as MFR twist and the decay index. Furthermore, for the eruptive cases, we investigated the effect of sustained driving beyond the point of eruptivity on the MFR properties and evolution. We find that the fully driven AR12473 MFR is eruptive, while the AR11176 MFR is not. For the relaxation runs, we find that the MFM MFRs are eruptive when the driving is stopped around the flare time or later, while the MHD MFRs show eruptive behaviour even if the driving is switched off one and a half days before the flare occurs. We also find that characteristic MFR properties can vary greatly even for the eruptive cases of different relaxation simulations. The results suggest that data driving can significantly influence the evolution of the eruption, with differences appearing even when the relaxation time is set to later stages of the simulation when the MFRs have already entered an eruptive phase. Moreover, the relaxation model affects the results significantly, as highlighted by the differences between the MFM and MHD MFRs, showing that eruptivity in MHD does not directly translate to eruptivity in the MFM, despite the same initial conditions. Finally, if the exact critical values of instability parameters are unknown, tracking the evolution of typical MFR properties can be a powerful tool for determining MFR eruptivity.

Multiscale Modeling and Simulation of Falling Collision Damage Sensitivity of Kiwifruit.

Falling damage is the most common form of damage sustained by kiwifruit during the process of picking and post-processing, and it is difficult to conduct a quantitative analysis of this phenomenon through traditional experimental methods. In order to deeply understand the sensitivity of kiwifruit to falling collision damage, the finite element numerical simulation method was used to evaluate and predict the sensitivity of kiwifruit to falling collision damage during harvesting. First, we obtained the appearance characteristics of kiwifruit through reverse engineering technology and determined the geometric and mechanical property parameters of kiwifruit through physical mechanics experiments. Then, according to the characteristics of fruit tissue structure, a multiscale finite element model, including the skin, pulp, and core, was constructed to simulate the effects of different falling heights, collision angles, and contact surface materials on fruit damage, and the accuracy of the model was verified through falling experiments. Finally, based on the simulation results, the Box-Behnken design was employed within the response surface methodology to establish a sensitivity prediction model for the drop damage sensitivity of kiwifruit across different contact materials. The results showed that the maximum relative error between the speed change obtained using finite element simulation and the speed obtained by the high-speed camera was 5.19%. The model showed high rationality in energy distribution, with the maximum value of hourglass energy not exceeding 0.08% of the internal energy. On the contact surface material with a large elastic modulus, a higher falling height and larger collision angle will significantly increase the risk of fruit bruise. When the contact surface material was a steel plate, the falling height was 1 m, and the collision angle was 90°; the maximum bruise sensitivity of kiwifruit reached 6716.07 mm3 J-1. However, when the contact surface material was neoprene, the falling height was 0.25 m, and the collision angle was 0°, the damage sensitivity was the lowest, at 1570.59 mm3 J-1. The multiscale finite element model of kiwifruit falling collision constructed in this study can accurately predict the damage of kiwifruit during falling collision and provide an effective tool for the quantitative analysis of kiwifruit falling collision damage. At the same time, this study can also provide guidance for the design and optimization of the loss reduction method of the harvesting mechanism, which has important theoretical significance and practical value.