Shape Parameters Research Articles

Reliability Assessment for Dual Constant‐Stress Accelerated Life Test Based on Weibull Distribution With Type‐II Censoring

ABSTRACTAccelerated life test (ALT) is a generally feasible and effective approach for evaluating the reliability of highly reliable products at normal operating conditions. This paper considers the reliability assessment for a dual constant‐stress ALT with Type‐II censoring for the Weibull distribution with constant shape parameter and a log‐linear link between the scale parameter and the stress factors. We derive the maximum likelihood estimates, weighted least squares estimates using a certain random variable transformation, and a combined maximum likelihood‐least squares estimates for the unknown parameters. In addition, we construct confidence intervals for the parameters of interest using both asymptotic theory and parametric bootstrap technique. Finally, simulation studies and an illustrative example are presented to demonstrate the effectiveness and feasibility of the proposed methods.

Double Stage Shrunken Technique For Estimate Shape Parameter of The Burr XII Distribution by Katti's Region

The current research is concerned with double stage shrunken technique in order to estimate the shape parameter (Burr XII) distribution, when previous knowledge regarding the value shape is available as the original estimate. The formulas for the relative efficiency, mean squared error, and bias ratio are derived, For the aforementioned expressions, numerical results and conclusions were shown.

Effects of value-driven social learning on cooperation in the prisoner's dilemma games.

Despite the growing attention and research on the impact of Q-learning-based strategy updating on the evolution of cooperation, the joint role of individual learners and social learners in evolutionary games has seldom been considered. Here, we propose a value-driven social learning model that incorporates a shape parameter, β, to characterize the degree of radicalism or conservatism in social learning. Using the prisoner's dilemma game on a square lattice as a paradigm, our simulation results show that the cooperation level has a non-trivial dependence of β, density ρ, and dilemma strength b. We find that both β and ρ have nonmonotonic effects on cooperation; specifically, moderate levels of radicalism in social learning can facilitate cooperation remarkably, and when slightly conservative, can form a favorable cooperation region with the appropriate ρ. Moreover, we have demonstrated that social learners play a key role in the formation of network reciprocity, whereas individual learners play a dual role of support and exploitation. Our results reveal a critical balance between individual learning and social learning that can maximize cooperation and provide insights into understanding the collective behavior in multi-agent systems.

Performance of the Shiryaev–Roberts‐Type Scheme in Monitoring Weibull Shape Parameter Based on Type II Censored Data

ABSTRACTThe Weibull distribution is very effective in modelling many different failure mechanisms given its intrinsic flexibility to represent different hazard functions via suitable selections of the shape and scale parameters. Given that the shape parameter of the distribution directly controls the hazard rate, we discuss a Shiryaev–Roberts (SR)–type scheme for monitoring the shape parameter with a fixed scale parameter when using Type II right‐censored Weibull lifetime data. A comparative analysis with existing schemes from the literature is provided by the average run length (ARL), along with the standard deviation of run length (SDRL) and some run‐length percentiles. The average extra quadratic loss (AEQL), the relative mean index (RMI) and the performance comparison index (PCI) are also considered to assess the overall performance. Our simulation results display certain advantages of the SR‐type scheme compared to those of traditional charts in detecting changes in censored lifetime data. An example based on the breaking strengths of the carbon fibre is also presented to demonstrate the proposed method's effectiveness in real situations.

Mitigating Temperature Effects in Curved Continuous Steel Box Girders: A Parametric Thermodynamic Analysis and Design Recommendations

Curved continuous steel box girders are extensively utilized in bridge construction due to their efficiency and environmental benefits. However, in regions with significant temperature fluctuations, temperature effects can result in cumulative deformation and stress concentration, which may severely impact structural safety and durability. This study examines the structural response of curved continuous steel box girders with five spans under diverse temperature conditions and also develops a comprehensive parameterized thermodynamic numerical model. The model assesses the influence of cross-sectional shape parameters, including the number of cross-sectional box chambers, diaphragm thickness, and height-to-width ratio, as well as longitudinal structural parameters such as planar configurations, width-to-span ratio, and support arrangements, along with the arrangement of stiffening ribs on the temperature-induced effects in the girders. The results indicate that optimizing the width and eccentricity of support stiffeners to 30% and 25%, respectively, in support plate size can significantly alleviate local temperature-induced stresses. Additionally, variations in longitudinal and transverse stiffeners manifest minimal impact on thermal performance. These findings provide a theoretical foundation for improved design and construction practices, offering practical design recommendations to mitigate temperature effects and enhance the longevity and safety of such structures.

Efficient and Accurate Force Replay in Cosmological-baryonic Simulations

We construct time-evolving gravitational potential models for a Milky Way–mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical harmonics for the halo and azimuthal harmonics for the disk, and the radial or meridional plane variation with splines. We fit low-order expansions (four angular/harmonic terms) to the galaxy’s potential for each snapshot, spaced roughly 25 Myr apart, over the last 4 Gyr of its evolution, then extract the forces at discrete times and interpolate them between adjacent snapshots for forward orbit integration. Our method reconstructs the forces felt by simulation particles with high fidelity, with 95% of both stars and dark matter, outside of self-gravitating subhalos, exhibiting errors ≤4% in both the disk and the halo. Imposing symmetry on the model systematically increases these errors, particularly for disk particles, which show greater sensitivity to imposed symmetries. The majority of orbits recovered using the models exhibit positional errors ≤10% for 2–3 orbital periods, with higher errors for orbits that spend more time near the galactic center. Approximate integrals of motion are retrieved with high accuracy even with a larger potential sampling interval of 200 Myr. After 4 Gyr of integration, 43% and 70% of orbits have total energy and angular momentum errors within 10%, respectively. Consequently, there is higher reliability in orbital shape parameters such as pericenters and apocenters, with errors ∼10% even after multiple orbital periods. These techniques have diverse applications, including studying satellite disruption in cosmological contexts.

Disproportionality analysis of adverse events associated with asfotase alfa: a post-marketing study using the FDA Adverse Event Reporting System

ABSTRACT Background Asfotase alfa (AA) is an FDA-approved enzyme replacement therapy for hypophosphatasia (HPP). Limited real-world data on its adverse events (AEs) exist. This study evaluates AA-related AEs using the U.S. FDA’s Adverse Event Reporting System (FAERS) database. Methods Reports for AA were extracted from FAERS and analyzed per FDA guidelines. AEs were categorized using MedDRA version 26.1. Disproportionality analysis was conducted using the reporting odds ratio (ROR), proportional reporting ratio (PRR), Bayesian confidence propagation neural network (BCPNN), and empirical Bayes geometric mean (EBGM) algorithms. Time-to-onset (TTO) was calculated, with a Weibull shape parameter test to assess risk over time. Results Out of 13,702,373 reports, 5,040 AA-related AEs were identified, with 198 significant preferred terms (PTs). Common AEs included injection site reactions and pain, with additional PTs for ear/labyrinth disorders and infections. The median onset for 234 AEs with reported times was 170 days (IQR 18–390 days). No significant differences in AEs were found across gender or age groups. Conclusion Most AEs align with known data, but newly identified ear/labyrinth disorders and infections require further investigation to enhance AA’s safety profile.

Quantification analysis of high-speed train aerodynamics with geometric uncertainty of streamlined shape

Purpose This study aims to get a better understanding of the impact of streamlined high-speed trains (HSTs) with geometric uncertainty on aerodynamic performance, as well as the identification of the key parameters responsible for this impact. To reveal the critical parameters, this study creates a methodology for evaluating the uncertainty and sensitivity of drag coefficient induced by design parameters of HST streamlined shapes. Design/methodology/approach Bézier curves are used to parameterize the streamlined shape of HSTs, and there are eight design parameters required to fit the streamlined shape, followed by a series of steady Reynolds-averaged Navier–Stokes simulations. Combining the preparation work with the nonintrusive polynomial chaos method results in a workflow for uncertainty quantification and global sensitivity analysis. Based on this framework, this study quantifies the uncertainty of drag, pressure, surface friction coefficient and wake flow characteristics within the defined ranges of streamline shape parameters, as well as the contribution of each design parameter. Findings The results show that the change in drag reaches a maximum deviation of 15.37% from the baseline, and the impact on the tail car is more significant, with a deviation of up to 23.98%. The streamlined shape of the upper surface and the length of the pilot (The device is mounted on the front of a train’s locomotive and primarily serves to remove obstacles from the tracks, thereby preventing potential derailment.) are responsible for the dominant factors of the uncertainty in the drag for HSTs. Linear regression results show a significant quadratic polynomial relationship between the length of the pilot and the drag coefficient. The drag declines as the length of the pilot enlarges. By analyzing the case with the lowest drag, the positive pressure area in the front of pilot is greatly reduced, while the nose tip pressure of the tail is enhanced by altering the vortices in the wake. The counter-rotating vortex pair is significantly attenuated. Accordingly, exerts the impacts caused by geometric uncertainty can be found on the wake flow region, with pressure differences of up to 900 Pa. The parameters associated with the shape of the upper surface contribute significantly to the uncertainty in the core of the wake separation region. Originality/value The findings contribute to a better understanding of the impact of streamlined HSTs with geometric uncertainty on aerodynamic performance, as well as the identification of the key parameters responsible for this impact. Based on this study, future research could delve into the detailed design of critical areas in the streamlined shape of HSTs, as well as the direction of shape optimization to more precisely and efficiently reduce train aerodynamic drag under typical conditions.

An efficient method for image denoising based on a new nonlinear wavelet thresholding function

Image noise is random variation of brightness or color information in images, and is usually an aspect of electronic noise. It can be produced by the image sensor and circuitry of a scanner or digital camera. In fact, there are different kinds of noise functions such as Gaussian noise, salt and pepper noise and speckle noise. Hence, image denoising is the process of removing noise from an image using one of the denoising methods such as spatial or transform techniques. The main aim of an image denoising technique is to achieve both noise reduction and feature preservation. In this context, the wavelet denoising method works in the transform domain, where the noise is uniformly spread throughout coefficients while most of the image information is concentrated in a few large ones.Therefore, the first wavelet-based denoising methods were based on thresholding of detail subband coefficients. However, most of the wavelet thresholding methods suffer from the drawback that the chosen threshold may not match the specific distribution of the image and noise components. Another thing: Studies have proven that the thresholding function has an effective role in obtaining better quality of the denoised image. To address these disadvantages, in this paper, we propose an efficient method for image denoising in wavelets domain. This method is based on a new nonlinear wavelet thresholding function, that is characterized by main mathematical properties and a shape parameter. The theoretical study of this new method proves that we can overcome the drawbacks of classical thresholding methods and by freely adjusting the shape parameter, we achieve a compromise between Hard and Soft thresholding. The experimental results show that our proposed method provides better performance compared to classical thresholding methods in terms of the visual quality of the denoised image.

A novel meshless method for solving long-term evolution problem on irregular domain

In the context of method of approximate particular solutions (MAPS), we propose a novel meshless computational scheme based on hybrid radial basis function (RBF)-polynomial bases to solve both parabolic and hyperbolic partial differential equations over a large terminal time interval on irregular spatial domain. By using space–time approach, the original time-dependent problem is firstly reformulated into an elliptic boundary value problem. Integrated polyharmonic splines (PS)-type RBF kernels in conjunction with multivariate polynomials are then employed to construct the approximate solution space. This superior combination enables us to stably achieve highly accurate solution. Due to the adoption of the polyharmonic splines, the difficulty of determining a suitable shape parameter of RBF is alleviated. Moreover, employing the recently developed ghost point method, the precision and stability of the approximation can be further enhanced. For numerical verification, four examples are investigated to demonstrate the robustness of the proposed methodology in terms of the aforementioned advantages.

Engineering and Clinical Study of Surface Geometry of Clear Aligners at the Nanoscale

This paper investigates the evolution of the outer surface geometry of Invisalign®—clear orthodontic aligners—caused by degradation triggered by wearing. The obtained results served to confirm whether or not the aligners could continue to be used once their wear time in the therapeutic procedure had ended, taking both their geometric and mechanical features into account. The measurements were performed using atomic force microscopy which allowed the mapping of nanomechanical properties. The obtained images were then processed to determine statistical and functional surface geometry parameters in accordance with relevant ISO standards. The results revealed that the unrepeatability of the manufacturing process causes the surface shape parameters of new aligners to be irregular; however, these features become gradually consistent for worn samples. On the other hand, properly used aligners may change in two ways: the outer layer flattens and its thickness decreases, and at the same time the Young’s modulus of the material decreases. It follows that the degradation processes may be caused by tribological phenomena (abrasion of contact surfaces) and/or biochemical phenomena (biofilm growth, decomposition of the material under the influence of enzymes in the oral cavity).

A new modeling approach for microplastic drag and settling velocity

Understanding microplastics' (MPs') transport and settling behaviors in aquatic environments is crucial for devising effective management strategies. This study contributes a novel modeling framework to develop accurate and interpretable drag and velocity models for MPs using machine learning techniques. It achieves faster model creation and improved accuracy than traditional methods like theoretical analysis and data fitting. The framework demonstrates high predictive accuracy across different MP types (1D, 2D, 3D, and mixed), with a coefficient of determination CD = 0.86–0.95 for the drag models and CD = 0.92–0.95 for the velocity models. Compared with best-performing empirical approaches, the new drag models exhibit an average reduction in root mean square error (RMSE) by 59% and mean absolute error (MAE) by 62%. Similarly, the velocity models show a mean decrease in RMSE and MAE by 27% and 25%, respectively. Moreover, the framework outperforms commonly used symbolic regression methods, reducing errors by 18%–27%. The sensitivity analysis reveals that the relative density difference and the dimensionless diameter are essential for predicting the settling of all MP types, while the effective shape parameters vary across different MP categories. By providing accurate predictions of MPs' settling dynamics, this study offers insights for developing targeted mitigation strategies to reduce MPs' environmental impacts.

Optimization flutter response of laminated smart nanocomposite truncated conical shell under supersonic aerodynamic pressure using hybrid IGWO-DQHFEM

Given the wide application of conical shells in the aerospace and aircraft industry, there comes a need for dynamic analysis and optimum design of these structures against supersonic aerodynamic forces, which induce a phenomenon called flutter. As the key contribution of this paper, a new method has been developed and applied to optimize the dynamic and flutter control of truncated conical shells under supersonic aerodynamic loads. Here, a truncated conical shell with a layered configuration is considered for the optimization of supersonic aerodynamic conditions with smart control, shape, and size optimum design, wherein every layer is reinforced with carbon nanotubes (CNTs). Moreover, a conical shell is considered with piezoelectric properties to smartly control the aerodynamic behavior of the structure, so by applying voltage, it will be possible to control flutter or critical aerodynamic pressure and frequency. The objective of the optimization model is defined based on aerodynamic pressure and frequency of conical shells. Mathematical modeling of the structure with high accuracy is carried out to optimize the model. The supersonic aerodynamic force is considered employing piston theory, where seven variables are used through a high-order shear deformation theory. In the new numerical method, the differential quadrature hierarchical finite element method (DQHFM) is used for the solution of the coupled electro- dynamic equations of the structure and computing the frequency of the structure along with the flutter or critical aerodynamic pressure. The optimization model obtained by the DQHFM method is applied to search the optimum conditions using an Improved Grey Wolf Optimization (IGWO) method. In IGWO, the local search condition is proposed based on the optimum positions and statistical properties of agents in previous positions. Finally, the optimum size, shape, and smart control parameters of the structure such as the length and radius of the cone, cone apex angle, external voltage, CNTs volume fraction, number of layers, and airflow angle are drawn out and discussed by IGWO and DQHFM. The results show that by increasing the cone angle from 30 o to 60 o, the optimum voltage that has to be applied decreases. On the other hand, an optimal radius stabilizes at around 1 m and the optimum volume fraction of the CNTs is 10 %.

Glucagon-like peptide-1 receptor agonists and impaired gastric emptying: a pharmacovigilance analysis of the US Food and Drug Administration adverse event reporting system

BackgroundGlucagon-like peptide-1 receptor agonists (GLP-1RAs) potentially increase the risk of pulmonary aspiration resulting from impaired gastric emptying (IGE). We evaluated the association between GLP-1RAs and IGE using the US Food and Drug Administration Adverse Event Reporting System (FAERS). MethodsWe analysed FAERS data from 2004 Q1 to 2024 Q1, identifying the top 10 drugs linked to IGE and determining the proportion of GLP-1RA use. Disproportionality analysis using the reporting odds ratio was conducted to assess the relative IGE risk for each drug. Logistic regression analysed the impact of age, weight, and sex on IGE risk. Cumulative incidence and time to onset of IGE events were examined using Kaplan–Meier and Weibull shape parameter tests. ResultsAmong the top 10 drugs associated with IGE reports, five were GLP-1RAs, accounting for 49.5% (982/1982) of cases. Dulaglutide (odds ratio [OR] 0.97, 95% confidence interval [CI] 0.94–1.00, P=0.033) and semaglutide (OR 0.96, 95% CI 0.94–0.97, P=0.001) showed lower IGE risk with older age. For exenatide, higher weight (OR 0.99, 95% CI 0.98–1.00, P=0.033) and male sex (OR 0.39, 95% CI 0.20–0.68, P=0.033) were associated with lower IGE risk. Median onset times ranged from 40.5 days (semaglutide) to 107.5 days (tirzepatide) from intitiation of therapy. The Weibull shape parameter β was <1 for all GLP-1RAs, indicating a higher IGE risk early in treatment. ConclusionsGLP-1RAs were notably associated with reports of impaired gastric emptying in the FAERS. Age, weight, and sex were significantly associated with impaired gastric emptying risk for certain GLP-1RAs. IGE events tended to occur early in treatment, with risk diminishing over time. These findings provide valuable references for future research on perioperative safety with GLP-1RAs.

Optimization on the design of nano-patterned ZnS:Cu LED surface using FDTD simulation

Communication technology is one of the most important parts of human history and is fast developing. Visible Light Communication (VLC) can be categorized as a Light Fidelity (Li-Fi) communication that uses visible light through a Light Emitting Diode (LED) to transfer data and information. Even though LEDs are considered as very good light sources, they also have problems with effectiveness, which is influenced by their surface structures. The LEDs must also be able to focus the transmitted data and greatly reduce the signal-to-noise ratio. One of the problems encountered with LEDs is the presence of Total Internal Reflection (TIR) due to the large difference in refractive index between the LED and air, which causes photons to be trapped in the LED. Some trapped photons' energy may change into heat, thus reducing the LED's Light Extraction Efficiency (LEE). Using nanopatterns on the surface of LEDs is one way to reduce TIR on LEDs and enhance photon extraction from LEDs. Many parameters can influence the performance of nanopatterns on LEDs, so modelling efforts are needed before fabrication to save time and cost. Ansys Lumerical FDTD can be used to simulate and model the effects of nanopatterns on LED surfaces on LEE and beam focusing effect. In this study, simulations were carried out using Ansys Lumerical FDTD with variations in nanopattern shape parameters in the form of grating, blaze grating, triangular grating, and hemisphere. Apart from that, variations were also made to the height and width parameters of the grating to see the effect of these parameters on the efficiency of the LED. The FDTD simulation codes were validated using the Ansys database. The optimization results show that the most optimum shape is the grating nanopattern with a width of 216 nm and a height of 300 nm, which produces a peak wavelength of 480 nm in the far field pattern and has the highest increase in the LEE of 300 times in ±15° and 5500 times in ±5°. The huge spike in LEE enhancement at ±5° indicates that the nanopattern caused a focusing effect. The simulation results were compared using previous experimental data of Fabricated ZnS:Cu LED. It is shown that the simulation results are in line with the experimental data. The result shows that the simulation is very useful in designing the nano-patterned ZnS:Cu LED surface to achieve the best performance in the LEE and LED focusing effect for a specific application such as the VLC.

Statistical Inference for Counting Processes Under Shape Heterogeneity.

Proportional rate models are among the most popular methods for analyzing recurrent event data. Although providing a straightforward rate-ratio interpretation of covariate effects, the proportional rate assumption implies that covariates do not modify the shape of the rate function. When the proportionality assumption fails to hold, we propose to characterize covariate effects on the rate function through two types of parameters: the shape parameters and the size parameters. The former allows the covariates to flexibly affect the shape of the rate function, and the latter retains the interpretability of covariate effects on the magnitude of the rate function. To overcome the challenges in simultaneously estimating the two sets of parameters, we propose a conditional pseudolikelihood approach to eliminate the size parameters in shape estimation, followed by an event count projection approach for size estimation. The proposed estimators are asymptotically normal with a root- convergence rate. Simulation studies and an analysis of recurrent hospitalizations using SEER-Medicare data are conducted to illustrate the proposed methods.

Direct Manipulation of Procedural Implicit Surfaces

Procedural implicit surfaces are a popular representation for shape modeling. They provide a simple framework for complex geometric operations such as Booleans, blending and deformations. However, their editability remains a challenging task: as the definition of the shape is purely implicit, direct manipulation of the shape cannot be performed. Thus, parameters of the model are often exposed through abstract sliders, which have to be nontrivially created by the user and understood by others for each individual model to modify. Further, each of these sliders needs to be set one by one to achieve the desired appearance. To circumvent this laborious process while preserving editability, we propose to directly manipulate the implicit surface in the viewport. We let the user naturally interact with the output shape, leveraging points on a co-parameterization we design specifically for implicit surfaces, to guide the parameter updates and reach the desired appearance faster. We leverage our automatic differentiation of the procedural implicit surface to propagate interactions made by the user in the viewport to the shape parameters themselves. We further design a solver that uses such information to guide an intuitive and smooth user workflow. We demonstrate different editing processes across multiple implicit shapes and parameters that would be tedious by tuning sliders.

The Identification, Separation, and Clamp Function of an Intelligent Flexible Blueberry Picking Robot

Identifying fruit maturity accurately and achieving damage-free harvesting are challenges in designing blueberry-picking robots. This paper presents an intelligent flexible picking system. First, we trained a deep learning-based YOLOv8n network to locate the position of the fruit and determine fruit ripeness. We used a neural network to establish the relationship between fruit hardness and shape parameters, achieving an adaptive gripping force for different fruits. To address the issue of dense clusters in some blueberry varieties, we designed a fruit separation subsystem using a combination of flow field analysis and pressure-sensitive experiments. The results show that the mean average precision can reach 84.62%, the precision is 94.49%, the recall is 83.85%, the F1 score is 88.85%, and the test time is 0.12 s, which can meet the requirements for blueberry fruit recognition accuracy and speed. The spacing between closely packed fruits can increase by 4 mm, and the damage-free picking rate exceeds 92%, achieving stable, damage-free harvesting.

Comprehensive Geometric Parameterization and Computationally Efficient 3D Shape Matching Optimization of Realistic Stents

Abstract Flexible and compact shape representation schemes are essential for design optimization problems. Current shape representation schemes for coronary stent designs concern predominantly idealized or independent ring (IR) designs, which are outdated and only consider a small number of core design variables (such as strut width, height, and thickness) and ignore clinically critical design characteristics such as the number of connectors. No reports exist on the geometry parameterization of the latest helical stents (HS) that have more complex geometric designs than IR stents. Here, we present two new shape parameterization schemes to fully capture the 3D designs of contemporary IR and double-helix HS stents. We developed a 3D stent geometry builder based on 17 (IR) and 18 (HS) design variables, including strut width, thickness, height, number of connectors and rings, stent length, and strut centerline shape. The shape of the strut centerline was derived via a combination of NURBS, PARSEC, quarter circle, and straight line segments. Shape matching for complex 3D geometries, such as the contemporary stents within limited function evaluations, is not trivial and requires efficient parameterization and optimization algorithms. We used shape matching optimization with a limited function evaluation budget to test the proposed parameterization and two surrogate-assisted optimization algorithms relying on predictor believer and an expected improvement maximization formulation. The performance of these algorithms is objectively compared with a gradient-based optimization method to highlight their strengths. Our work paves the way for more realistic, full-fledged stent design optimization with structural and hemodynamic objectives in the future.

Local-scale variability in packed beds of polyhedral particles: Structural and thermal distribution

Heat transfer in packed beds largely depends on the bed structure, which is strongly linked to particle shape, yet most prior work focuses on spherical particles. This work contributes towards a better understanding of particle shape effect on the local-scale and its variability. Particle beds are generated numerically and steady-state thermal simulations are conducted for 12 different particle shapes and three particle-to-gas conductivity ratios. Voronoi cells are extracted to obtain local cell porosities; distributions are studied statistically. Another crucial parameter, particle-particle contact areas, are evaluated and compared with shapes. Variability in local structure results in varied temperature profiles. Thermal fluctuations are substantially affected by irregular shapes, an effect that increases for highly conductive particles. Notably, the spatial distribution of phases with different conductance has a strong influence on the distribution of local heat flux. Predominantly, these outcomes also indicate the relevancy of including shape parameters in developing reactors or modeling other granular applications.