Discrete Modeling Techniques Research Articles

Enhanced LaRC05 failure criteria for investigating low-velocity impact on fiber-reinforced composites: An experimental and computational study

A finite element model was developed using both continuum and discrete damage modeling techniques to provide detailed predictions for ply-by-ply damage progression in composite laminates during low-velocity impact (LVI) events. A new fiber failure model was incorporated into the LaRC05 failure criteria to predict fiber pull-out and fiber crushing during the fiber damage evolution. In addition, the selective range golden section search (SRGSS) algorithm was implemented to efficiently predict fiber breakage, pull-out, splitting, kinking and crushing, and matrix cracking. The delamination was captured by cohesive element layers embedded between every adjacent composite ply. The interactions of intralaminar matrix cracking and delamination were modeled by deploying cohesive elements within each composite ply. The prediction results were validated by 30 J and 75 J drop-weight tests with different-sized impactors, as well as X-Ray CT inspections on 254 mm by 304.8 mm [0/45/90/-45]4s IM7/977–3 laminates. The model predicted the maximum deflection and contact duration with <2 % error, and the peak load, damaged areas, and absorbed energy with <8 % error. The matrix fracture plane and the fiber kink band angle were found with 1° precision 48 % faster via the SRGSS algorithm. The detailed sequences of damage occurrence were predicted by analyzing the energy dissipation histories through various damage modes. Although this modeling methodology was developed for LVI scenarios, it has broad applications for predicting failures in composites.

High-Profile Convoy Disruptions: Exploring Socioeconomic and Environmental Ramifications of Road Closures

Congestion persists despite various demand management techniques, particularly for handling recurrent congestion. However, non-recurrent congestion from events like VIP movements poses unique challenges, especially during peak hours. This study investigates the environmental and economic impacts of road blockages due to VIP movements in developing countries, focusing on Pakistan. Considering practiced standard operating procedures associated with VIP movements, this study finds significant delays and economic burdens in debt-ridden economies. It uses discrete choice modeling and microsimulation techniques to evaluate the value of travel time and quantifies road blockage effects on fuel consumption, travel time, and carbon emissions. Data from central blockage locations in Rawalpindi and Islamabad reveal a value of travel time estimated at 1.77 USD/h, with income and gender significantly influencing mode choices during VIP movements. Moreover, road blockages exceeding two minutes substantially negatively impact the environment and economy, particularly in developing nations. Urgent action is needed for effective mitigation strategies and sustainable transportation policies to address the detrimental effects and promote alternative transportation modes. Recommendations include limiting VIP blockages to a maximum of two minutes and implementing policies to discourage private car usage. Despite limitations, the study emphasizes the critical role of sustainable transportation policies in enhancing the well-being of road users in developing nations.

A Mathematical Model for Dynamic Electric Vehicles: Analysis and Optimization

In this article, we introduce a flexible and reliable technique to simulate and optimize the characteristics of a Dynamic Electrical Vehicle (DEV). The DEV model is a discrete event-based modeling technique used in electrical vehicle research to improve the effectiveness and performance of various electrical vehicles (EVs) components. Here, the DEVS model is applied to EV research in several ways, including battery management optimization, evaluation of power train design and control strategy, and driver behavior analysis. The essential power train elements, including the battery, motor, generator, internal combustion engine, and power electronics are included in the mathematical model for the dynamic electric vehicle. The model is derived using the conservation of energy principle. The model includes mathematical equations for the electrical power output, battery charge level, motor torque, motor power output, generator power output, internal combustion engine torque, mechanical power delivered to the generator, and the efficiencies of the power electronics, motor, generator, and engine. The model is examined by using a numerical method called the Runge–Kutta Method of order 4 for dynamic electric vehicle’s performance under various driving states for maximum effectiveness and performance. It is revealed that the DEV model provides a systematic method to simulate and optimize the behavior of complex EV systems.

Electromobility Prospects in Greece by 2030: A Regional Perspective on Strategic Policy Analysis

Electromobility represents a strong option for reducing carbon emissions in the road transport sector. This study presents a methodology and a simulation tool that project the evolution of the market share of electric vehicles (EVs) in the new car market. The analysis adopts a stylized regional resolution, which accounts for attributes on the NUTS-2 level, such as the population density, GDP/capita, education levels, and current EV charger distribution, to simulate the uptake of BEVs in different regions. The methodology applies discrete choice modelling techniques, considering tangible and intangible factors, including purchasing and operation costs, an estimated cost for range anxiety and public charging, and a market maturity index. The analysis is based on four different scenarios, referring to the updated Greek National Energy Climate Plan. The results reveal that regions with a higher average income, GDP/capita, and population density show a higher uptake of EVs. Overall, the tool implements a method of simulating the market evolution of EVs up to 2030 in reference to regional parameters and, hence, highlights the regions that require the most attention in order to achieve national targets. The results can inform policymakers in developing tailored strategies and financial support to accelerate the adoption of BEVs, particularly in regions where their uptake prospects are lower.

Maximizing Utility or Avoiding Losses? Uncovering Decision Rule-Heterogeneity in Sociological Research with an Application to Neighbourhood Choice

Empirical studies on individual behaviour often, implicitly or explicitly, assume a single type of decision rule. Other studies do not specify behavioural assumptions at all. We advance sociological research by introducing (random) regret minimization, which is related to loss aversion, into the sociological literature and by testing it against (random) utility maximization, which is the most prominent decision rule in sociological research on individual behaviour. With an application to neighbourhood choice, in a sample of four European cities, we combine stated choice experiment data and discrete choice modelling techniques and find a considerable degree of decision rule-heterogeneity, with a strong prevalence of regret minimization and hence loss aversion. We also provide indicative evidence that decision rules can affect expected neighbourhood demand at the macro level. Our approach allows identifying heterogeneity in decision rules, that is, the degree of regret/loss aversion, at the level of choice attributes such as the share of foreigners when comparing neighbourhoods, and can improve sociological practice related to linking theories and social research on decision-making.

Simulations of ammonia spray evaporation, cooling, mixture formation and combustion in a direct injection compression ignition engine

This study investigates the novel approach of direct liquid ammonia injection into the combustion chamber of a compression ignition engine. Unlike traditional gaseous ammonia port injection, this method shows promise in reducing ammonia slip and emissions. To simulate and analyze the behavior of the liquid ammonia spray, we employed numerical models based on existing literature on flashing and non-flashing spray simulations, as well as recent experimental studies on ammonia spray characteristics using a gasoline direct injection (GDI) injector. Our approach utilized a Lagrangian discrete phase modelling technique to perform a series of three-dimensional computational fluid dynamics (CFD) simulations. The primary objectives of this research were to evaluate the evaporation process of ammonia and its cooling effect, as well as to gain insights into mixture formation within the engine cylinder under different operating conditions. The simulations encompassed the entire engine cycle, considering a multi-hole GDI ammonia spray in conjunction with pilot n-heptane, a diesel surrogate, in equal proportions on an energy basis. Three distinct injection timings for ammonia were examined, leading to varying thermodynamic conditions within the combustion chamber during each spray formation. Consequently, different modelling parameters and initial conditions were necessary to accurately replicate the spray behavior. To address this, we proposed a systematic procedure for assigning pre-defined spray angles. The non-reacting, evaporating spray simulations yielded valuable insights into the mixture formation process, which guided our analysis. Finally, reacting conditions were considered to evaluate engine performance and resulting exhaust gas emissions. This study provides a comprehensive overview of critical aspects related to direct ammonia injection in internal combustion engine (ICE) systems. Moreover, it uncovers performance trends that can serve as a foundation for future investigations in this field.

Assessing Seismic Crack Performance of Diyarbakır Çüngüş Masonry Stone Bridge Considering 2023 Kahramanmaraş, Hatay, Malatya, Gaziantep Earthquakes

Examination of the creep behavior of historical buildings and interpretation of seismic failures in historical buildings are of great importance for the safety and future of these important structures. In this study, time-dependent settlement and three-dimensional (3D) seismic analyzes of a historical stone bridge are investigated using the 3D discrete element modeling technique. For the settlement and seismic analyses, the historical single-span Çüngüş bridge which was built in the 18th century in Diyarbakır-Turkey by Ottoman Empire is used. Since Diyarbakır is in a dangerous zone according to the Turkey seismic map, the examination of this structure is very critical for the history of Turkey. The 3D model of the bridge is created using the FLAC3D program based on the finite difference method and all the stone elements in the historical bridge are modeled separately as blocks. Special interaction elements are defined between the discretely modeled stones. For settlement creep analyses, the Burger-creep material model, which was not used for the creep behavior of historical buildings in the past, is utilized. Firstly, the 500-year long-term creep behavior of the bridge is examined by considering the fix boundary condition and full reservoir condition. According to the creep analyses, it is seen that the most deformation and failure section of the bridge is the arch section. Then, for the seismic analyses of the bridge, free-field and quiet non-reflecting boundary conditions are defined in the model. Furthermore, hysteresis damping coefficients are taken into account in seismic analyzes with the help of special fish functions. 10 various earthquakes are considered for seismic analyses. According to the earthquake analyses, the earthquake behavior of the Çüngüş historical bridge is assessed by considering the full reservoir condition and it is understood that 2023 Kahramanmaraş, Hatay, Malatya, Gaziantep earthquakes significantly changed the seismic safety behavior of Çüngüş single-span historical bridge.

Piecewise Linear Strain Cosserat Model for Soft Slender Manipulator

Recently soft robotics has rapidly become a novel and promising area of research with many designs and applications due to their flexible and compliant structure. However, it is more difficult to derive the nonlinear dynamic model of such soft robots. The differential kinematics and dynamics of the soft manipulator can be formulated as a set of highly nonlinear partial differential equations (PDEs) via the classic Cosserat rod theory. In this work, we propose a discrete modeling technique named piecewise linear strain (PLS) to solve the PDEs of Cosserat-based models, based on which the associated analytic models are deduced. To validate the accuracy of the proposed Cosserat model, the static model of the conical cantilever rod under gravity as a simple example is simulated by using different discretization methods. Results indicate that PLS Cosserat model is comparable to the mechanical deformation behavior of a real-world soft manipulator. Finally, a parameters identification scheme for this model is established, and the simulation as well as experimental validation demonstrate that using this method can identify the model physical parameters with high accuracy.

Shared micromobility and public transport integration - A mode choice study using stated preference data

This paper uses stated preference data collected in the city of Rotterdam and discrete choice modelling techniques to study the relationship between public transport and shared micromobility. It assumes a hypothetical condition of integrated systems and studies the relationships of complement and competition between these modes. The findings suggest that shared micromobility modes are viable alternatives as egress modes for metro trips. Shared micromobility can be seen as a complement to metro, yet shared e-mopeds proved to also be a viable option as individual modes for long-distance trips. Different characteristics proved to be important in choices in this context: frequency of public transport use, previous use of shared micromobility, and age. Considering the results obtained, collaboration between shared micromobility and transit operators might benefit them as well as travellers. Collaborations should be designed so that they help travellers to decrease total travel time, even if it implies longer egress legs. However, the costs of these shared modes should not be as high as to prevent travellers to use them as egress alternatives. Finally, young travellers and frequent transit users could be specifically targeted, as they showed to have a better perception of shared micromobility.

High-fidelity simulation of low-velocity impact damage in fiber-reinforced composite laminates using integrated discrete and continuum damage models

A high-fidelity finite element (FE) model based on integrated discrete and continuum damage modeling techniques was developed to predict damage modes, locations, sizes, and damage occurrence sequence in a composite laminate during a low-velocity impact event. Fiber breakage and transverse matrix cracking were captured using the three-dimensional Hashin’s criteria, and delamination was captured by inserting a layer of cohesive elements between every adjacent composite ply. Delamination progression from one layer to another was captured by embedding cohesive elements inside each composite ply aligned with the fiber orientation and with a 45° angle to the thickness direction. The refined mesh and intralaminar cohesive elements were only used in the predicted damage region based on an analytical solution. The FE model predicted impact response was validated by drop-weight tests, and the layer-by-layer damage areas were validated and characterized by X-Ray CT inspections on 254 mm by 304.8 mm IM7/977-3 laminates with a stacking sequence of [0/45/90/-45]4s. The absorbed energy, damage areas, maximum deflection, contact time, and peak load were predicted with less than 10% error. The detailed damage occurrence sequence during the impact event was predicted through histories of energies dissipated by different damage modes. The modeling methodology developed in this work highlights the effects of modeling parameters on convergence, solution accuracy and computational efficiency, and provides an effective approach for progressive damage modeling of composite laminates.

Modeling of intra-city transport choice behaviour in Budapest, Hungary

The discrete choice modeling and decisions-tree technique are used to understand the travel behavior of people in Budapest. The discrete choice modeling is applied to develop transport mode choice that mimics the travel behavior of people using their personal and travel characteristics. A revealed preference (RP) survey was conducted by the Hungarian Census Bureau which contains information about the households in Budapest in 2014, is used. Understanding the daily main trips of people is firstly analyzed using decisions-tree technique, where the impact of each variable is presented based on its importance in affecting the travel choice mode. In random utility theory, travelers choose one option out of certain available options to them to maximize their utility. The Multinomial Logit (MNL) model is used to examine the relationship between various variables connected to travelers in order to understand the travel behavior pattern. The result of the analysis shows a clear pattern between car ownership and each of family size, and age, and trip cost variables. The result of decision tree analysis demonstrates that travelers’ trip duration is the most important factor that has impact on their transport mode choice, which is mainly distributed within private cars, public transportation, and walking. The developed multinomial transport mode choice model includes sociodemographic, economic, and travel characteristics. The trip time, trip cost, age, car ownership index, trip purpose, gender, employment, and income are the main determinants the impact the transport choice mode. The developed models (i.e., decision tree and the multinomial transport logit choice) are beneficial for the decision-makers who can used it in predicting the travel demand.

A novel discrete modeling technique and Stabilization Analysis of the two-order Inverter System

LC-filter-based H6-bridge inverter (LC-H6) is a two-order inverter system, which is an appropriate circuit for the medium or high power inverter field. A novel discrete modeling technique with coefficient linearization based on stroboscopic map method is presented to reduce iterative computation and memory expense of the LC-filter-based H6-bridge inverter with PI controller (LCH6-PI) system. Meanwhile, the collision border lines of i are deduced. Then, based on the coefficient linear discrete model, stability regions of control parameter k p, DC voltage E and load inductance L are analyzed. Finally, the simplified discrete model is verified by circuit simulation and experimental results. Stabilization analysis indicates that the stability boundary and chaos boundary can be obtained by period-doubling bifurcation and border collision, respectively.

Discrete Phase Analysis of Self Heating Particles Over an Immersion Liquid Cooled High Power Blue Light-Emitting Diode With Suspended Phosphor Particles

Abstract In recent years, the interaction of unrestricted particles with dispersed multiphase flows has been linked to a number of important engineering applications. Among these applications, the novel idea of immersion-cooled phosphor particles, which has the potential of significantly increasing the thermal limits of phosphor converted white light-emitting diode (LEDs) (Pc-WLEDs), has yet to be thoroughly investigated. With this objective, this research utilizes the discrete phase modeling (DPM) technique for the characterization of phosphor location and movements within a buoyancy-driven flow, which is the determining factor in the optical behavior of the newly proposed Pc-WLED configuration. Two-phase flow analysis is conducted to characterize particle movement. Heat transfer, flow, and energy paths of self-heating phosphor particles are extracted, and the influence of particle sizes is analyzed in detail. The results show that with immersion liquid cooling, the highest phosphor particle temperature is recorded to be under 420 K, while larger size particles introduce higher heat transfer rates to the Pc-WLED package for the same number of particles. Moreover, depending on the particle size and position, individual phosphor particles can follow a different trajectory that can affect the probability of obtaining white light emission.

Applications of Passive GPS Data to Characterize the Movement of Freight Trucks—A Case Study in the Calgary Region of Canada

The movement of trucks represents a significant portion of travel. Surveys have traditionally been used to measure truck movement, but this costly and limited data collection method typically involves in-person interviews and requiring high workload. This study explores different ways in which passive truck GPS data can be used to complement traditional data collection methods, for obtaining detailed information about the travel behaviors of freight trucks. First, we develop a heuristic-based model to identify truck stops. A new methodology is proposed to classify truck stops into a primary or secondary sto, which make identifying trip purposes possible. Primary stops are defined as the locations where the loading or unloading of the goods takes place. Secondary stops are those associated with all other purposes, including refueling, and driver breaks. Finally, we develop a destination choice model for modeling truck movements. This model applies a discrete choice modeling technique to distribute truck trips within the Calgary region, Canada. We test the utility function in the destination choice model to include of business establishment data, travel impedances, and other dummy variables that are likely to influence truck demand. The results show that a combination of trucks’ dwelling times and their entropy can be used to classify truck stops by purpose. This study also shows the potential of using passive GPS data to gain additional insights into truck movements characterization and truck trip distribution modeling.

Self-adaptive discrete grey model based on a novel fractional order reverse accumulation sequence and its application in forecasting clean energy power generation in China

With the increasing power consumption in China and the urgent demand for environmental protection, promoting the development of clean energy power generation industry is the only way to optimize the energy power generation structure. It is very important to effectively predict the development trend of China's clean energy power generation system with complex, changeable and limited data. To address this issue, this paper defines a novel fractional self-adaptive reverse accumulation sequence, and combines discrete modeling techniques and time power terms to propose a novel fractional self-adaptive reverse accumulation with time power terms. The parameter estimation and time response formula of the new model are derived. The matrix perturbation theory is used to prove that the new model satisfies the new information priority principle. The Grey Wolf Optimizer is used to optimize the self-adaptive parameter r and non-negative constant α. Finally, the prediction model is constructed for the power generation capacity of five representative types of clean energy in China: biomass, wind, nuclear, natural gas and hydro power, the prediction result shows that the new model has higher prediction accuracy and data applicability than the other five grey models. According to these prediction results, relevant suggestions on the development of China's clean energy are provided to decision makers.

A unified framework of cell population dynamics and mechanical stimulus using a discrete approach in bone remodelling

Multiphysics models have become a key tool in understanding the way different phenomenon are related in bone remodeling and various approaches have been proposed, yet, to the best of the author’s knowledge there is no model able to link a cell population model with a mechanical stimulus model using a discrete approach, which allows for an easy implementation. This article couples two classical models, the cell population model from Komarova and the Nackenhorst model in a 2D domain, where correlations between the mechanical loading and the cell population dynamics can be established, furthermore the effect of different paracrine and autocrine regulators is seen on the overall density of a portion of trabecular bone. A discretization is performed using frame 1D finite elements, representing the trabecular structure. The Nackenhorst model is implemented by using the finite element method to calculate the strain energy as the main mechanical stimulus that determines the bone mass density evolution in time. This density is normalized to be added to the bone mass percentage proposed by the Komarova model, where coupling terms have been added as well that guarantee a stable response. In the simulations, the equations were solved employing the finite element method with a user subroutine implemented in ABAQUS (2017) and by applying a direct formulation. The methodology presented can model the cell dynamics occurring in bone remodelling in accordance with the asynchronous nature of this process, yet allowing to differentiate zones with higher density, the main trabecular groups are obtained for the proximal femur. Finally, the model is tested in pathological cases, such as osteoporosis and osteopetrosis, yielding results similar to the pathology behavior. Furthermore, the discrete modelling technique is shown to be of use in this particular application.

Stochastic lattice discrete particle modeling of fracture in pervious concrete

AbstractThis article presents a stochastic modeling approach for simulating the mechanical behavior of pervious concrete, based on novel extensions of the lattice discrete particle model. Selected digital images of the internal mesostructure, obtained from physical specimens, are used to survey material features and produce statistically representative descriptions of the pore networks. A procedure for estimating the statistical features of the mesostructure is proposed, and samples of a spatially correlated random field are utilized to numerically reproduce the distribution of the large, connected pores in the material. The numerical samples are linked to the topology of the lattice network by means of two novel techniques proposed herein: (1) a random placement procedure for the poly‐sized spheres representing coarse aggregate and (2) a ray tracing technique, which is used to evaluate the effective distributions of mass, stiffness, and strength of each lattice element according to the local distribution of porosity. Numerical results demonstrate how the proposed model is capable of simulating both the large scatter in strength and the variety of failure modes that are observed when testing physical specimens of pervious concrete. The proposed procedure is generally applicable to different types of materials with varying porosity, opening up new possibilities for the simulation of porous media by means of lattice discrete particle modeling techniques.

Adaptive multi-fidelity (AMF) modelling of progressive damage in notched composite laminates

In recent years, high-fidelity simulations with discrete crack modelling techniques have been shown to accurately model the mechanics of progressive failure in composite laminates. However, these require high computational effort and are currently not practical beyond small coupon-sized specimens with a few tens of plies. In this paper, an adaptive multi-fidelity (AMF) modelling approach is proposed, wherein actively damaging areas are modelled with high-fidelity three-dimensional (3D) brick elements and discrete cracks, while dormant and inactive sites are modelled with lower-fidelity shell elements and smeared cracks. The transition criteria between the two levels of modelling are studied in order to preserve as much fidelity to the physics as necessary while improving computational efficiency. The results are benchmarked with that of high-fidelity simulations and experimental data of open-hole tension (OHT) of cross-ply and quasi-isotropic laminates in the literature.

Spatter Formation and Splashing Induced Defects in Laser-Based Powder Bed Fusion of AlSi10Mg Alloy: A Novel Hydrodynamics Modelling with Empirical Testing

Powder spattering and splashing in the melt pool are common phenomena during Laser-based Powder Bed Fusion (LPBF) of metallic materials having high fluidity. For this purpose, analytical and computational fluid dynamics (CFD) models have been deduced for the LPBF of AlSi10Mg alloy. The single printed layer’s dimensions were estimated using primary operating conditions for the analytical model. In CFD modelling, the volume of fluid and discrete element modelling techniques were applied to illustrate the splashing and spatter phenomena, providing a novel hydrodynamics CFD model for LPBF of AlSi10Mg alloy. The computational results were compared with the experimental analyses. A trial-and-error method was used to propose an optimized set of parameters for the LPBF of AlSi10Mg alloy. Laser scanning speed, laser spot diameter and laser power were changed. On the other hand, the powder layer thickness and hatch distance were kept constant. Following on, 20 samples were fabricated using the LPBF process. The printed samples’ microstructures were used to select optimized parameters for achieving defect-free parts. It was found that the recoil pressure, vaporization, high-speed vapor cloud, Marangoni flow, hydraulic pressure and buoyancy are all controlled by the laser-material interaction time. As the laser-AlSi10Mg material interaction period progresses, the forces presented above become dominant. Splashing occurs due to a combination of increased recoil pressure, laser-material interaction time, higher material’s fluidity, vaporization, dominancy of Marangoni flow, high-speed vapor cloud, hydraulic pressure, buoyancy, and transformation of keyhole from J-shape to reverse triangle-shape that is a tongue-like protrusion in the keyhole. In the LPBF of AlSi10Mg alloy, only the conduction mode melt flow has been determined. For multi-layers printing of AlSi10Mg alloy, the optimum operating conditions are laser power = 140 W, laser spot diameter = 180 µm, laser scanning speed = 0.6 m/s, powder layer thickness = 50 µm and hatch distance = 112 µm. These conditions have been identified using sample microstructures.

Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation.

In the laser powder bed fusion (LPBF) process, the operating conditions are essential in determining laser-induced keyhole regimes based on the thermal distribution. These regimes, classified into shallow and deep keyholes, control the probability and defects formation intensity in the LPBF process. To study and control the keyhole in the LPBF process, mathematical and computational fluid dynamics (CFD) models are presented. For CFD, the volume of fluid method with the discrete element modeling technique was used, while a mathematical model was developed by including the laser beam absorption by the powder bed voids and surface. The dynamic melt pool behavior is explored in detail. Quantitative comparisons are made among experimental, CFD simulation and analytical computing results leading to a good correspondence. In LPBF, the temperature around the laser irradiation zone rises rapidly compared to the surroundings in the powder layer due to the high thermal resistance and the air between the powder particles, resulting in a slow travel of laser transverse heat waves. In LPBF, the keyhole can be classified into shallow and deep keyhole mode, controlled by the energy density. Increasing the energy density, the shallow keyhole mode transforms into the deep keyhole mode. The energy density in a deep keyhole is higher due to the multiple reflections and concentrations of secondary reflected beams within the keyhole, causing the material to vaporize quickly. Due to an elevated temperature distribution in deep keyhole mode, the probability of pores forming is much higher than in a shallow keyhole as the liquid material is close to the vaporization temperature. When the temperature increases rapidly, the material density drops quickly, thus, raising the fluid volume due to the specific heat and fusion latent heat. In return, this lowers the surface tension and affects the melt pool uniformity.