Computer Simulation Research Articles

Evaluation of the Consolidation Parameters Obtained from Laboratory Tests for Numerical Modeling of Improved Soft Soil Using PVD at Semarang - Demak Toll Road, Indonesia

The consolidation analysis becomes complicated when conducted on varying layers of soil. To simplify and solve these problems, designers often employ Finite Element Method (FEM) modeling, a widely used technique for analyzing geotechnical issues. However, many limitations associated with this method can lead to model results that do not accurately reflect actual conditions. Consequently, the consolidation settlement analysis during design may differ from actual conditions in the field. This study examines the influence of consolidation parameters and explores how to analyze consolidation settlement using FEM for practical applications. Specifically, consolidation settlement was assessed on the Semarang-Demak toll road, which utilizes a Preloading-PVD improvement method across nine Stationing (STA) locations with varying soil layers. Numerical modeling was performed using Midas GTS NX 2021 (V.1.1) and was validated against instrumentation observation results, Settlement Plate. An evaluation using the back analysis method was conducted to investigate the impact of consolidation parameters on the accuracy of the final consolidation settlement results. The consolidation parameters reviewed are the compression index (Cc) and recompression index (Cr). The findings indicate that the Cc and Cr significantly influence the final consolidation settlement. By optimizing these consolidation parameter values, the deviation between observed results and numerical modeling for final consolidation settlement is reduced to less than 1%. Additionally, this research derived empirical equations for calculating consolidation parameters based on the Liquid Limit, a fundamental laboratory test. The results of this study can be proposed to analyze consolidation settlement using FEM modeling for soft clay to stiff clay, providing valuable insights for practical applications.

Impact of time-based variability on planning reliability in construction projects: analysis of production management systems

PurposeThis research article proposes a quantitative method for analyzing planning reliability and risk evaluation in construction projects through probabilistic numerical simulation models. The aim is to assess the combined time-based variability of activities across the project and its impact on planning reliability in various production management systems.Design/methodology/approachThe study examines different methods for comparing the impact of production management strategies, specifically standardization and lean construction practices, on project reliability. The article introduces Monte Carlo, importance sampling and first-order-second moment methods as quantitative tools for decision-making and continuous improvement in construction projects.FindingsThe utilization of multiple numerical simulation models demonstrates how the variability in activity durations directly affects planning reliability, leading to uncertainty and increased risk in construction projects. The study highlights the significance of lean construction principles and industrialized processes, such as standardization of processes and construction methods, in reducing variability and improving the average duration of activities. Furthermore, it quantifies the differential impact of various production management systems on project performance and planning reliability.Research limitations/implicationsThis study is based on a limited number of case studies, which may affect the generalizability of the findings. The results are specific to the construction projects analyzed in Colombia. Expanding the research to include a broader range of projects will improve the applicability of the findings. Developing more comprehensive numerical models can also enhance understanding of planning reliability across different construction management systems.Originality/valueCurrently, there are limited quantitative methods available for project managers to evaluate the impact of industrialized construction practices and production management strategies on planning reliability as well as quantifying the associated risk level in project delays. Consequently, the adoption of innovative construction methods is often limited to a few pilot projects, as managers lack numerical evidence to support the implementation of new methodologies that require changes in traditional operational practices.

Developed a solar still unit for saltwater desalination: numerical prediction and performance verification

Abstract In the globe, there is a rise in water demand for agricultural, industrial, and domestic purposes. Single-basin solar stills (SBSS) have been a subject of research in various countries, particularly in regions with water scarcity or limited access to clean drinking water. In this work, SBSS for desalinating high-salinity water were developed, tested, and evaluated based on a developed numerical model using MATLAB R2021a program to predict the best productivity through the best selection of raw materials used to develop the SBSS. A four-inclined SBSS was fabricated and examined experimentally according to numerical model findings for best design parameters at Marsa Matrouh, 31° 21′ 10.44″N, 27°14′14.10″ E, Agricultural Station—Agricultural Research Center (ARC), Egypt. The hourly experimental results are compared with the numerical results. A good correlation between the numerical and the experimental results with variations in water, and glass temperatures of 9, and 18% respectively, and a variation in cumulative productivity by 11%. The results clearly showed that instantaneous productivity increases by decreasing water depth to 10 mm and using the SBSS unit partially insulated from the bottom of the basin. Adding insulation in front of the sides and back of tempered glass increases the shading area and decreases water temperature hence the cumulative productivity by 15%. The cumulative productivity reached 3 L for the SBSS unit partially insulated from the bottom of the basin with an area of 0.6 m2 for only 12 h working system at a water depth of 10 mm.

Dynamics of the 1873 CE “Breccia De Fiore” phreatic eruption at Vulcano (Aeolian Islands, Italy) through historical chronicles, physical volcanology, and numerical modelling

Phreatic events may represent precursors of magmatic eruptions or occur independently as single or multiple episodes at volcanoes with hydrothermal systems. We examine the Breccia De Fiore deposit from the prolonged phreatic activity during September–October 1873 at the La Fossa cone of Vulcano (Aeolian Islands, Italy). By integrating data from historical chronicles, stratigraphy, sedimentology, physical analyses, and 3D numerical simulations, we investigate eruption dynamics. The sedimentological characteristics of the deposits, asymmetrically dispersed along the north-western flank of the cone, are interpreted as the simultaneous emplacement of pyroclastic density currents and ballistic projectiles. Numerical simulations model the eruptive mixture as an Eulerian gas-particle fluid coupled with Lagrangian ballistic particles. Results suggest the deposit originated from multiple, shallow, low-magnitude explosions (< 5 × 104 m3 cumulative volume). The deposit dispersal is well reproduced by simulating explosions from an inclined vent, driven by pressure build-up (up to 5 MPa) at shallow depths (< 150 m) within the hydrothermal system. This study helps constrain critical parameters of phreatic scenarios at La Fossa volcano, including erupted mass and specific energy, emphasising the hazards posed by such small events and the crucial need for improving hazard assessment, especially given the close presence of populated, touristic sites.

Probabilistic and FEM hydro-mechanical coupling analysis of rainfall-induced slope instability

The random field theory coupled with a FEM hydro-mechanical model was employed to analyse slope responses under rainfall, with a particular focus on post-rainfall behaviour. This study uniquely analysed the heterogeneity of soil strength and permeability through the application of random field theory, providing a novel perspective on its impact on slope stability. Numerical modelling under varying rainfall intensities revealed that the factor of safety (FoS) decreased with prolonged rainfall, particularly at higher intensities. Post-rainfall behaviour varied for different rainfall events, that gentle and moderate rainfalls led to a gradual decline in FoS due to water infiltration, while heavy rainfall allowed recovery through drainage, and extremely heavy rainfall triggered immediate failure. A novel finding is that post-rainfall water seepage can govern slope stability under extreme rainfall conditions. At failure, the surface layer of a fully saturated slope lost clay suction and exhibited concentrated plastic shear strain at its base. Weak zones with interconnected high-permeability channels significantly influenced slope stability by facilitating water infiltration. Probabilistic analysis further showed that the FoS at the end of simulations typically ranged from 1.1 to 1.4, with a recommended 5th percentile value of 1.1 for slope designs.

The effect of lateral position of heating surface and angular orientation of latent heat thermal energy storage system on the melting characteristics: a numerical investigation

Purpose This study aims to address the low thermal conductivity and suboptimal performance of phase change materials (PCMs) by examining the impact of geometric adjustments on their melting rate. Design/methodology/approach A two-dimensional numerical model was created to investigate the effect of different positions and angular inclinations of the inside heating surface (IHS) on the melting rate of PCM within a latent heat thermal energy storage system. The model analysed the IHS at the centre and below the centre at various positions (10, 20, 30 and 40 mm) and inclinations (0°, 15°, 30°, 45°, 60°, 75° and 90°). Findings The 90° inclination (vertical) significantly reduced the melting time by 75% compared to the 0° inclination (horizontal). The best melting performance was recorded with the IHS positioned 20 mm below the centre. At a 30° inclination, the maximum reduction in melting time was observed with the IHS at 30 and 40 mm placements. The system demonstrated the highest energy storage capacity of 307.72 kJ/kg at a 75° inclination with the IHS positioned 10 mm laterally, and the lowest capacity of 255.02 kJ/kg at a 0° inclination with the IHS at a 30 mm lateral position. Practical implications To address the deficient part of PCM like low thermal conductivity and below level performance characteristics, a structural (geometrical) adjustment was developed to study the effect on the melting rate of PCM without any cost addition. Using the computational model, an optimised thermal energy storage system is developed that can play a pivotal role in improving the applicability of thermal energy storage systems. Originality/value This research is novel in simultaneously investigating the numerical characteristics of PCM melting behaviour with different lateral positions and angular orientations of the IHS. A unique design modification was introduced, using a 2D numerical model and simulations to explore the effects under isothermal conditions.

Computational Fluid Dynamics-Based Simulation of Ventilation in a Zigzag Plastic Greenhouse

Zigzag plastic greenhouses are a type of greenhouse with a high natural ventilation capacity, and the number and quantities of their roof vents affect their ventilation and cooling effect. In this study, a CFD model of a greenhouse was constructed based on computational fluid dynamics (CFD) theory to simulate the temperature and airflow distribution of a zigzag plastic greenhouse and to investigate the effects that the number of zigzags and the construction orientation have on the cooling effect of this type of greenhouse. The results show that the average air temperature in a double zigzag plastic greenhouse (DZPG) was 0.58 °C lower than that in a single zigzag plastic greenhouse (SZPG) of the same size during the experiment. When the outdoor temperature is higher than 35 °C, the maximum temperature of the DZPG is significantly lower than that of the SZPG in a 1.5 m horizontal section; when the top vent is on the windward side, there is an obvious advantage of DZPG ventilation and the utilization efficiency of its top vent is higher, and when the top vent is on the leeward side, the distribution of the airflow in the DZPG is more intensive and more uniform. The maximum difference in the average temperature between the eight orientations of the DZPG was 0.17 °C. Therefore, the cooling effect in summer is not influenced by the construction orientation, but the airflow in the greenhouse is slightly worse when the direction of the roof vents is parallel to the prevailing wind direction.

Duffing Nonlinearity‐Enhanced Optomechanical Mass Sensor

AbstractMeasuring the mass of small molecules is crucial across various fields, and the cavity optomechanical system is a promising candidate for mass sensing due to the direct relationship between the oscillator's resonant frequency and the mass of the sample deposited on the cavity's surface. Previous research has shown that enhancing the effective frequency of the resonator can significantly improve the performance of mass sensors. In this study, the influence of the Duffing nonlinear term is investigated on the cavity optomechanical mass sensing. These computational and numerical simulation results demonstrate that increasing the strength of the Duffing nonlinear term effectively raises the resonator's effective frequency and directly boosts the performance of the mass sensor. These include enhancing detection resolution, reducing measurement errors, and expanding the effective measurement range of mass, which may have applications in fields such as biochemical sensing and environmental monitoring.

Harnessing Artificial Intelligence in Obesity Research and Management: A Comprehensive Review

Purpose: This review aims to explore the clinical and research applications of artificial intelligence (AI), particularly machine learning (ML) and deep learning (DL), in understanding, predicting, and managing obesity. It assesses the use of AI tools to identify obesity-related risk factors, predict outcomes, personalize treatments, and improve healthcare interventions for obesity. Methods: A comprehensive literature search was conducted using PubMed and Google Scholar, with keywords including “artificial intelligence”, “machine learning”, “deep learning”, “obesity”, “obesity management”, and related terms. Studies focusing on AI’s role in obesity research, management, and therapeutic interventions were reviewed, including observational studies, systematic reviews, and clinical applications. Results: This review identifies numerous AI-driven models, such as ML and DL, used in obesity prediction, patient stratification, and personalized management strategies. Applications of AI in obesity research include risk prediction, early detection, and individualization of treatment plans. AI has facilitated the development of predictive models utilizing various data sources, such as genetic, epigenetic, and clinical data. However, AI models vary in effectiveness, influenced by dataset type, research goals, and model interpretability. Performance metrics such as accuracy, precision, recall, and F1-score were evaluated to optimize model selection. Conclusions: AI offers promising advancements in obesity management, enabling more personalized and efficient care. While technology presents considerable potential, challenges such as data quality, ethical considerations, and technical requirements remain. Addressing these will be essential to fully harness AI’s potential in obesity research and treatment, supporting a shift toward precision healthcare.

Study on Metro Operation Safety Based on a Specific Contact Model for Resilient Wheel

Abstract Resilient wheel (RW) is gradually promoted for use in China’s subway vehicles recent years, which has been widely used in tram in Europe and China. As measured, the RWs in service on the metro trains have experienced eccentric wear and even polygonization of high order after 30,000 km running. Given that most subway lines have small curve radii, this study assesses the operation safety of vehicle passing through curves with RWs having polygonal wear, as well as their effect on vibration reduction compared to conventional wheels. A numeric simulation model is developed to model the metro vehicle-track dynamic system installed with resilient wheel, where a conventional wheel-rail contact model is modified considering the composite structure of a RW. A RW-rail contact model considering relatively independent motion of the wheel hub and rim is developed, which is integrated into a metro vehicle-track dynamic system model equipped with the RWs. Upon comparing the curving performance of vehicles equipped with conventional wheels, the findings reveal that, in scenarios of surplus-superelevation, the wheel load reduction ratio (WLRR) of conventional wheels demonstrates superior performance. While curving in the case of deficient-superelevation, the WLRR of RWs is lower. Furthermore, the safety performance of the RWs surpasses that of conventional wheels, particularly as the severity of polygonal wear on the wheel increases. These conclusions can be used as a reference for maintenance strategy of the RW applied on metro trains, which is urgently to be built considering the potentially wide promotion of the RW to the subway system.

Laboratory-Scale Natural Gas Hydrate Extraction Numerical Simulation Under Phase Transition Effect

Phase transition in gas hydrate reservoirs has a significant effect on the fluid flow dynamic when performing test production, which should be carefully studied. This study systematically investigates the phase transition characteristics of natural gas hydrates during the depressurization extraction process through laboratory-scale numerical simulations. First, a laboratory-scale numerical simulation model is established with dimensions of 1 m × 1 m × 1 m. In the simulation, the nanoscale and microscale effect on phase transition is considered. Then, the analysis of how different sediment types and their properties affecting gas production dynamics is presented. The results show that hydrate dissociation and formation are significantly influenced by factors such as the pore scale, salinity, and water content. In particular, montmorillonite had the most significant effect, leading to a 525.25% increase in gas production, while the impact of silty soil was relatively smaller. The increase in salinity inhibited hydrate formation but promoted dissociation, resulting in a significant increase in gas production, especially when the salinity reached to 3.5%, where gas production increased by 590.21%. An increase in water content led to a significant decrease in production. Through monitoring temperature and pressure changes during the extraction process, the different physical fields are analyzed, providing important theoretical support and practical guidance for the efficient extraction of natural gas hydrates.

Machine learning optimized design of THz piezoelectric perovskite-based biosensor for the detection of formalin in aqueous environments

Abstract This investigation presents the development and characterization of an advanced piezoelectric perovskite-based biosensing platform optimized for formalin detection in aqueous media through the implementation of Locally Weighted Linear Regression (LWLR) machine learning algorithms. The sensor architecture operates within the terahertz spectral region and incorporates an advanced nanomaterial composite system comprising black phosphorus, gold nanostructures, graphene, and barium titanate to maximize detection sensitivity and operational performance metrics. The engineered platform integrates a circular graphene metasurfaces configuration with a gold-based H-resonator assembly and concentrically arranged circular ring resonators. Computational simulations demonstrate vigorous sensing capabilities across three discrete frequency bands, achieving remarkable sensitivity parameters of 444 GHzRIU⁻¹, accompanied by a quality factor of 5.970 and detection accuracy of 7.576. The integration of LWLR-based optimization protocols substantially enhances prediction accuracy while reducing computational time by ≥ 85% as well as cutting down the required resources. The proposed sensor architecture presents significant potential for environmental monitoring and clinical applications, offering a highly sensitive and efficient methodology for quantitative formalin detection in aqueous environments.

The Splendor of Plainness: A Transformation of the Process of Qi as Expressed in the Generative Artwork UKON

Abstract The authors thoroughly examine the creative process behind UKON, which uses computer simulation to reinterpret the Song Dynasty’s aesthetic of “plainness.” By treating random numbers as representations of Qi, the artwork undergoes a transformation that both complicates and simplifies its visual elements. This approach not only transcends simple visual depiction but also reflects a profound exploration of “the extreme splendor of plainness,” capturing its essence in a contemporary form. The work showcases the artist’s deep understanding of traditional aesthetics and illustrates how modern technology can reinvent these concepts as a new visual language.

Shannon Entropy in Uncertainty Quantification for the Physical Effective Parameter Computations of Some Nanofluids

The main aim of this study is probabilistic computer simulation of the effective physical parameters of fluids containing nanoparticles. A deterministic model following the rule of mixtures and some semi-empirical formulas are employed to calculate effective density, heat conductivity, heat capacity, as well as viscosity for the given nanofluid. This models is randomized here using the Monte-Carlo simulation apparatus for estimation of the Shannon entropy of all these physical parameters, which is the crucial novelty of this study. The volume fraction of the nanoparticles is assumed for this purpose as the Gaussian uncertainty source with the given first two moments. The basic probabilistic characteristics of the nanofluids’ homogenized parameters have also been determined here for some validation of Shannon entropy variations in addition to the statistical disorder of the nanoparticle fraction. These research findings contribute to advancing nanofluidic and microfluidic research, offering robust tools for uncertainty analysis and enhancing the reliability of physical parameter predictions in applications requiring high numerical and/or experimental precision.

Effect of Warpage Pattern of Printed Circuit Board on Solder Paste Volume in Stencil Printing Process

Abstract This study examines the influence of printed circuit board (PCB) warpage patterns on solder paste distribution during the stencil printing process (SPP). A multi-stage numerical model was developed and validated with experimental data, showing a deviation of less than 4%, to simulate the SPP with various warped PCB configurations. Various warpage patterns, including horizontal, vertical, spherical, and diagonal warpage, were analyzed along with key process parameters such as stopper load, squeegee load, and the positioning of clamping plates to identify the conditions that most significantly affect solder paste distribution. Results indicate that increasing the stopper load to 170 N can reduce PCB warpage by approximately 60%, leading to a more even solder paste volume distribution. The squeegee load had minimal impact on gap reduction due to the constraints imposed by the side-clamping plates. Among the warpage patterns, diagonal warpage yielded the most uniform solder paste distribution, with up to 43% better consistency compared to horizontal warpage, which exhibited the greatest variation.

Mainshock-Aftershock Ground Motion Sequences Selection and its Implication on Bridge Seismic Fragility

ABSTRACT In seismic-prone regions, the evaluation of structural performance of bridges under mainshock-aftershock ground motion sequences is imperative for ensuring their safety and facilitating effective response measures. However, the limited availability of real-recorded mainshock-aftershock ground motion sequences for region-specific condition results in the adoption of artificially generated sequences for seismic fragility assessment of bridges. This study presents a new approach for the artificial generation of ground motion sequences by quantifying the relationship between parameters of real-recorded mainshock-aftershock sequences, while also considering regional seismicity. The proposed framework is employed to obtain a suite of region-specific mainshock-aftershock sequences for the Himalayan region, and is subsequently applied to a case-study bridge for vulnerability assessment. An experimentally validated bridge numerical model is developed to simulate the degradation caused by multiple cyclic loadings of mainshock-aftershock sequences. An optimal engineering demand parameter is identified to capture the cumulative damage under mainshock-aftershock sequences and seismic fragility curves are developed using incremental dynamic analysis-based approach. Results reveal a higher seismic fragility under ground motion sequences compared to mainshocks alone, with similar trends observed across different bridge geometries. Notably, the finding indicates a close match between the seismic fragility curves developed using mainshock-aftershock sequences selected through the proposed framework and those derived using real-recorded sequences.

Numerical and analytical modelling of wellbore storage effects in low-enthalpy geothermal well tests

In geothermal wells, build-up phases of well tests are typically executed with a surface shut-in, rather than with a downhole shut-in. Therefore, wellbore physics may play a dominant, but undesirable, role in the system's pressure response as recorded by the downhole pressure gauge. Numerical simulations were carried out to investigate to what extent these effects complicate the analysis of the well test and the deduction of the reservoir characteristics. Numerical models, supported by analytical modelling of well tests of field cases, show that significant portions of the Bourdet derivatives of geothermal well tests are expressions of physical effects in the wellbore, rather than the reservoir's pressure response. These wellbore storage effects in low-enthalpy geothermal wells are more intense than commonly reported in the literature. In addition, they may last for a very long time and vary continuously during the build-up. They cannot be represented accurately with the known analytical solutions commonly available in analytical well-test software. In many cases the early, middle and late time regions of the reservoir response on the derivative plot have only developed partially, or might be completely missing. Due to their intensity and duration, the wellbore storage effects can obliterate the true reservoir response, thereby making a reliable analysis of the reservoir characteristics impossible. This will undoubtedly lead to incorrect interpretations of the skin or reservoir properties. It is therefore strongly recommended that well tests in geothermal wells are executed using a downhole shut-in device, such that the unwanted wellbore physics are fully eliminated and the downhole pressure gauges only measure the true reservoir response.

Numerical modeling and validation of auxetic cell geometries for FDM infill pattern improvement

Abstract The vehicle construction sector is constantly engaged in the pursuit of lightweight structures to reduce the overall weight of vehicles. This objective aligns well with sustainability requirements, as reducing structural weight and excessive raw material usage simultaneously lowers fuel consumption. However, these lightweight panels sometimes experience a decline in mechanical properties or exhibit unpredictable failure mechanisms due to their large internal voids. To optimize material usage, 3D printing was explored, enabling the creation of highly customized infill patterns. The innovative aspect of this research lies in developing a cellular design by selecting an optimal infill configuration capable of withstanding the expected loads. Numerical modeling was employed to analyze how different cell specifications interact with the geometry of the structure and the applied loading conditions. As a result, an auxetic design was chosen for the cellular structures. This design was fabricated using fused deposition modeling (FDM) and tested under flexural and impact loading. A comparative analysis was then conducted with samples of equivalent infill density but featuring conventional infill patterns to assess performance differences. Even if the flexural tests show a decrease in resistance and stiffness of the auxetic structures than the traditional ones, the last under-impact load shows an increase in impact rigidity which is also influenced by the angle value. Furthermore, the specimens can preserve their impact absorption capacity failure mode even if load absorption and damage are completely different. A numerical model development was useful for understanding the different behaviors and it was able to reproduce the impact behavior with high precision.

Truncated cylindrical array plate for mid-air imaging

Abstract Mid-air imaging, a visual display technology for augmented reality (AR) that enables multiple people to view images simultaneously without the need for special eyewear, involves the formation of real images in mid-air through various optical elements. This paper presents a novel mid-air imaging optical plate, termed the truncated cylindrical array plate (TCAP). TCAP is composed of transparent cylinders with obliquely truncated ends and mirrors, specifically designed to address issues such as stray light and limited viewing angles in existing mid-air imaging optical elements. We evaluated TCAP through computer simulations and by fabricating a prototype optical element. Ray tracing simulations and stereo matching algorithms demonstrated that mid-air images are symmetrically formed on the side opposite of the light source relative to the TCAP. Furthermore, the simulations indicated that a bright, stray-light-free mid-air image could be achieved within a horizontal viewing angle of approximately $$\pm \, 40 ^\circ $$ ± 40 ∘ . Experimental evaluation using a handcrafted prototype further confirmed the plane symmetry of mid-air image formation, validating its functionality as a mid-air imaging element. The proposed method is advantageous in systems where stray light is problematic, such as mid-air image interaction systems or optical systems utilizing mid-air imaging elements.

Engineering Lithium-Magnesium Selectivity in Hydrated Polymer Membranes through Polymer Backbone Rigidity.

Using computer simulations and experiments, we demonstrate that polymer backbone rigidity can be used to tune selectivities and permeabilities of lithium over magnesium in hydrated polymer membranes. Coarse-grained molecular dynamics (CGMD) simulations suggest a strong dependence of cation diffusion coefficients on polymer segmental dynamics and cation-solvent coordination strength, with water content and backbone dynamics having distinct effects on transport properties. Experimentally, we synthesized 2-hydroxyethyl acrylate-co-ethyl acrylate (HEA-co-EA) and 2-hydroxyethyl methacrylate-co-methyl methacrylate (HEMA-co-MMA) membranes. These polymers have different levels of backbone flexibility while maintaining similar chemistry. LiCl and MgCl2 salt permeabilities and sorption coefficients were measured for membranes with varying water content. Magnesium chloride permeability and diffusion coefficients show a stronger dependence on backbone dynamics than lithium chloride, whereas backbone dynamics has a minor impact on salt sorption. Overall, these factors allow permeability and selectivity of LiCl relative to MgCl2 to be increased simultaneously by increasing both water content and backbone rigidity.