Rigidity Values Research Articles

Evaluation of sonoelastography in differential diagnostics of endometrial hyperplastic processes

The article presents a description of complex ultrasound diagnostics of endometrial pathology using qualitative and quantitative echography. The parameters of changes in subendometrial and intraendometrial hemodynamics were identified and the average values of rigidity were calculated endometrium in benign and malignant endometrial pathology. The obtained results indicate the high efficiency of the method of qualitative and quantitative assessment of endometrial rigidity in identifying the characteristic features of malignant transformation, which plays an important role in clarifying diagnostics and choosing treatment tactics.

Effect of gluing garment materials with adhesive inserts on their multidirectional drape and bending rigidity

Abstract The article concerns the study on multidirectional drape and bending rigidity of six wool (clothing) fabrics with two types of adhesive inserts. The aim of research was to investigate the effect of joining woolen fabrics with “Freudenberg Vilene” adhesive inserts on the bending rigidity and multidirectional drape. The adhesive inserts were differentiated according to mass per square meter, while the fabrics were differentiated according to thickness, weave, and mass per square meter. Based on the scientific literature, the issues related to the methods of testing the bending rigidity and multidirectional drape coefficient were discussed. All the conducted tests were aimed at the proper selection of adhesive inserts for the designed clothing products. The use of adhesive inserts affects the bending stiffness and multidirectional drapeability of clothing material. The fabric weave significantly affects the values of bending rigidity and drapeability. As the thickness of adhesive inserts increases, the overall bending rigidity increases. The greater the fabric mass per square meter, the stiffer the fabric. As the mass per square meter and thickness increase, the multidirectional rigidity of fabrics increases. The value of bending rigidity for the plain fabric is higher compared to twill fabric.

Seismic Performance Analysis of Endo Indonesia Office Surabaya Building Structures Against Structural Irregularities

The structure of the building will be stable if the response of the structure is able to ignore the static and dynamic loads. The behavioral stability of the building structure is also influenced by geometry, configuration of horizontal and vertical elements, rigidity, lateral ability, and daktility of the structure. (Khanal Chaulagain, 2020). When the structure configuration of the building is irregular, there will be eccentricity which means that the center of the mass is incorrectly at the centre of rigidity (Faisal Darsono, 2019). If such conditions are not anticipated, the structure will be tortured until it eventually collapses. (Naveen dkk., 2019). In Surabaya there are office buildings that have irregular structures. This research will model the structure of the building into five variations. Each variation has a reduction in the value of structural irregularity. Next, we will examine the impact of structural irregularities on the reaction of structures of buildings. The results of the analysis showed that the irregularity of the inner angle had a significant impact on the shift of the roof, with the R-square of 0.9025 in the X axis and 0.9872 in the Y axis. Furthermore, based on the value of the soft level rigidity to the earthquake style at each level, R-quares of 0.8433 were found at the X-axis, and 0.825 at the Y-axe. Furthermore, changes in the inner angle of variations 2, 3, 4, and 5 resulted in successive increases in the mass of the structure by 0.18%, 4.09%, 7.86%, and 0.43%. These increases result in an increase in the basic sliding style in both directions. The variation 5 building designed without an inner angle showed an increase of 0.46% in the base sling style in either direction. Movement targets based on ASCE 41-13 NSP are 321.903 mm and 308.497 mm for the X and Y directions, respectively, which are in the Life Safety and Immediate Occupancy categories. While the total maximum drift values based on ATC-40 for the x and y directions are 0.0148 and 0.0150. The performance of the existing building structure is between B to C on the level of damage control (Immediate Occupancy to Life Safety), which means the building has suffered minor non-structural damage and may suffer structural damage but can still be repaired.

Ab initio modeling of human IRS1 protein to find novel target to dock with drug MH to mitigateT2DM diabetes by insulin signaling.

IRS1 is a cytoplasmic adaptor protein that helps incellulargrowth, glucose metabolism, proliferation, anddifferentiation. Highly disordered (insulin receptor substrate 1) IRS1 protein sequence (mol.wt- 131,590.97da) has been used to develop model using ab initio modeling technique by I-Tassar tool and Discovery Studio/ DogSite Server to decipher a novel active site. The constructed protein model has been submitted with PMDB Id- PM0082210. GRAVY index of IRS1 model ( - 0.675) indicated surface protein-water interaction. Protparam tool instability index (75.22) demonstrated disorderedness combined with loops owing to prolines/glycines. After refinement,the Ramachandran plot showed that 88 percent of AAs were presentin the allowed region and only 0.5% in the disallowed region.Novel IRS1 model proteinhas 10 α-helices, 22 β-sheets, 20 β-hairpins, 5 β-bulges, 47 strands, 105 β-turns, and 8 γ-turns. Docking of IRS1 with drug MH demonstrated interaction of Ser-70, Thr-18, and Pro-69 with C-H bonds; Gln-71, and Glu-113 with hydrogen bonds; while both Glu-114 and Glu-113 with salt-bridge connection. Permissible 1.0-1.5Å range of RMSD fluctuation between 20 and 45ns was obtained in simulation of IRS1 and IRS1-met complex confirmed that both complexes were stable during whole simulation process. RMSF result showed that except positions 57AA and 114AA, the binding of drug had no severe effects on the flexibility of the IRS1 and IRS1-met complex. The RoG value of compactness and rigidity showed little change in IRS1 protein. SASA value of IRS1 indicated non-significant fluctuation between IRS1 and drug MH means ligand (drug) and IRS1 receptor form stable structure. Hydrogen bond strength of IRS1 and IRS1-met was 81.2 and 76.4, respectively, which suggested stable interaction.

Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments.

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

A Method for the Ambient Equivalent Dose Estimation in a Wide Range of Altitudes during SEP and GLE Events

The paper considers the modeling of proton transport through the Earth’s atmosphere during several SEP events (12 August 1989, 23 March 1991, and 8 November 2000), as well as during the GLE73 event. Solar sources and interplanetary medium conditions during these events are described in detail. Calculations are carried out using own model implemented with GEANT4. As the main results, quantitative estimates of the calculated ambient dose equivalent for altitudes in a wide range (also including civil aircraft flight altitudes of 10–11 km) for the geomagnetic cutoff rigidity values Rc = 0.13 GV are given.

Experimental study of flag fluid–structure interaction in a laminar jet and application of POD

A fluttering flag in a uniform laminar flow exhibits complex fluid–structure interaction (FSI) behavior. This investigation experimentally studied aerodynamic load behavior and its connection to the oscillation behavior, flag envelope and fluid flow parameters, and application of Proper Orthogonal Decomposition (POD) to fluid flow data to elucidate changes in flow behavior associated with the changes in oscillation modes and observed drag coefficient values. For this purpose, three flag models with varying lengths were used. The aerodynamic load forces were measured using a high-precision load cell, and two-dimensional Particle Image Velocimetry (PIV) was used to quantify the flow field around the flag. The Reynolds number (Re), mass ratio (R1), and dimensionless rigidity (R2) values were varied between 4.4×104−12.3×104, 1.48−2.77, and 1.3×10−3−15.1×10−3, respectively. The results showed the linear relationship between drag coefficients with normalized amplitude of oscillation and Strouhal number. The results also showed the connection between observed drag and change in flag oscillation modes. The POD analysis showed that the energy content of the POD modes changed with the change in flag oscillation from mode-2 to mode-3 oscillations. The phase portrait of the first four POD modes also showed a unique interplay of POD modes, resulting in a change in the velocity flow field associated with the change in oscillation modes. The low-order reconstruction using select POD modes and control volume analysis of the velocity flow field showed a connection between POD modes and observed drag.

A New Optimization Approach for the Tallest Column Design

Motivated by the classical brachistochrone we present a new pattern of finding the shape of a vertical column that attains the maximum height if its material and volume are prescribed. It comprises the optimal control problem with a free end point. Besides, the constitutive equation of the column is such that it can suffer flexure, compression and shear. The critical load of a heavy compressed column for the finite values of shear and extensional rigidity and the novel use of the Pontryagin maximum principle with the corresponding first integral yielding the non-vanishing optimal cross section as a solution of a quadratic equation are main novelties of this work. The classical solution for the tallest column under selfweight is covered as a special case for infinite values of shear and extensional rigidity.

The relationship between intraocular pressure and age-related variations in ocular rigidity

This study aimed to identify the correlation between age-related fluctuations in the average values of rigidity of the fibrous tunic of the eye (FTE) and corresponding ranges of true intraocular pressure (IOP) in healthy eyes and eyes with open-angle glaucoma (OAG); using the identified ranges of FTE rigidity, to establish the appropriate IOP zones for healthy and glaucomatous eyes, taking into account the aging periods as classified by the World Health Organization (WHO). Ocular-Response Analyzer tonometry was used according to the Koshits-Svetlova dynamic diagnostic method to examine 674 patients with healthy eyes and 518 patients with glaucomatous eyes, aged 18 to 90 years, classified according to the WHO aging periods, and a theoretical analysis was conducted to estimate clinical values of FTE rigidity, the current level of true IOP, and the calculated individual IOP level in a patient's eye during youth. The following IOP level zones were identified for patients with healthy and glaucomatous eyes: low IOP zone (≤13 mm Hg); medium IOP zone (14-20 mm Hg); elevated IOP zone (21-26 mm Hg); high IOP zone (27-32 mm Hg); subcompensated IOP zone (33-39 mm Hg); and decompensated IOP zone (≥40 mm Hg). The fundamental physiological criterion "rigidity" does not depend on central corneal thickness and consistently reflects the current level of true IOP. In all examined patients, both with healthy and glaucomatous eyes, healthy and glaucoma eyes with the same level of current rigidity had the same level of IOP. The ability to assign a given healthy or glaucomatous eye to a specific individual IOP zone is particularly important for the polyclinic system.

COMPLEX RESISTANCE OF A COMPRESSED-BENT ROD TAKINGINTO ACCOUNT ELASTIC COMPLIANCE OF ITS SUPPORT

This work deals with the urgent problem in the mechanics of a deformable solid: studying factors of the stress-strain state of a single-span statically indeterminate beam with complex boundary conditions that is under conditions of complex resistance (axial compression with plane transverse bending). To solve the problem, both analytical methods (the method of forces in the form of “five” support moments, the method of initial parameters) and the numerical finite difference method with a “linear” grid with density n=8 were used. The necessary resolving equations and matrices are given to take into account changes in the rigidity parameter of the right hinged support and variations in concentrated and uniformly distributed loads, both along the axis of the beam and across it. In the final form, diagrams of deflections, bending moments and shear forces were constructed for specific values of bending rigidity and the degree of elastic compliance of the right hinge-yielding support. Reliability of the theoretical principles and applied results obtained by the authors is confirmed on the basis of the given alternative calculation methods.

Effect of Sloping Bottom on Wave Interaction With Multiple Flexible Moored Breakwaters

Abstract An analytical framework is developed to analyze the interaction of oblique waves with multiple flexible porous breakwaters under the consideration of bottom undulation. The mathematical problem is tackled using the small amplitude water-wave theory, with Darcy’s law being applied to account for wave interaction with porous media. The bottom topography is considered to have a finite length, flanked by two semi-infinite sections of uniform bottom. The solution to the boundary value problem is approached by employing the eigenfunction expansion method within the uniform bottom regions. For the varying bottom topography, a modified mild-slope equation (MMSE) is utilized. To address the solution at the slope discontinuity at the bottom, a mass-conserving jump condition is applied. By matching solutions at the interfaces, a set of equations is derived. This system of equations encapsulates the behavior of reflection and transmission coefficients, as well as the force exerted on the breakwaters. These parameters are then investigated across various factors such as the length of the varying bottom, depth ratio, angle of the mooring line, angle of incidence, and flexural rigidity. Graphical representations of the reflection and transmission coefficients, along with the breakwater force, provide insights into the system’s behavior under different conditions. The water wave energy can be dissipated for the optimum values of flexural rigidity. The transmission coefficient is observed to be least for higher mooring angle.

Modeling the Vibratory Compaction Process for Roads

This paper presents results obtained for the vibratory compaction process of road structures, in which the natural soil is used for the foundation infrastructure. The experiments and the optimization of the compaction process were carried out on five road lanes in Transilvania, Romania. A self-propelled single-drum roller compactor, BOMAG BW 213 S-5, was used for the compaction, layer by layer, with six successive passes over each layer. For each layer, the initial degree of compaction was measured, and after the fifth pass, it achieved the value prescribed in the road construction project. After each pass over the same layer, its settlement increased due to the plastic deformation and the soil’s rigidity receiving discrete higher values. This is how five different discrete values for rigidity were obtained. Modeling the compaction process is carried out using the Kelvin–Voigt model, with discrete variable experimental values for soil rigidity and assumed constant viscous damping values. Based on the two-degree-of-freedom linear elastic model, graphs were plotted for vibration amplitude variation and for the force transmitted to the soil when the excitation pulsation varies continuously and the soil rigidity varies discretely. There is a relationship between the initial and final degree of compaction values in the ratio that was proven to be dependent on the ratio of amplitude values corresponding to the final and initial roller passes cycle. The result is a useful relationship for the “in-situ” estimation of the compaction process effect. The novelty of this research is that it demonstrates the change in soil rigidity values after each pass of the vibratory roller and, thus, the increase of its settlement (plastic deformation) and the “slipping” for the amplitude resonance peak by discrete increasing values. Calibration of the resonance vibrations regime in accordance with the degree of compaction determined by geotechnical methods for “in-situ” sample prelevation stands as a fast and efficient method for the evaluation of the final degree of compaction value. This is, implicitly, the method for estimating the number of vibratory roller passes in the road construction project. In conclusion, the novelty of the research consists in the fact that, through using the resonance response of the vibratory roller, a correlation was made with the degree of compaction achieved after each pass.

Torsion Improvement of Reinforced Self-Compacting Concrete Beams Using Epoxy Injection and CFRP

Few researchers have investigated the internal torsional reinforcement of box timbers, so little research has been conducted on this particular fortification method. The primary objective is to find out the possibility of adding a certain percentage of RCA to the NC mixtures, as well as verifying the success achieved in repairing the cracks that occurred as a result of torsion with CFRP or injecting with epoxy, which has not been addressed in previous research and literature reviews. This study reinforces reinforced SCC box columns subjected to complete torsion with CFRP sheets and epoxy resin injections. Four reinforced SCC specimens (the first beam with 0%, the second beam with 33.3%, the third beam with 67.7%, and the fourth beam with 100% RCA by weight) were subjected to pure torsion until failure. The dimensions and reinforcement of every specimen are identical. In addition, the applied torque-twist angle relationship at the midspan and end span was investigated. Bending experiments were performed to establish load-deflection curves and assess failure modes. After structural rehabilitation, all beams exhibited increased rigidity values, according to the results. Epoxy resin and CFRP sheet contributed to the specimens' increased ultimate load. The ultimate strength of RCA beams strengthened with CFRP and injected with epoxy increased. The specimens' flexural strength was considerably enhanced by the combination of surface roughness and fracture injection, and the effectiveness of using RCA was very good; it could be replaced with NCA in concrete mixtures, according to the ratio and need. Doi: 10.28991/CEJ-2023-09-11-05 Full Text: PDF

On the Torsional Rigidity of Orthotropic Beams with Rectangular Cross Section

The paper deals with the torsional rigidity of homogenous and orthotropic beam with rectangular crosssection. The torsional rigidity of the considered beam is defined in the framework of the Saint-Venant theory ofuniform torsion. Exact and approximate solutions are given to the determination of the torsional rigidity. The shapeof cross section is determined which gives maximum value of the torsional rigidity for a given cross-sectional area.The dependence of torsional rigidity as a function of the ratio shear moduli of beam is also studied.

Effect of Different Weft Yarns, Twill Direction, and Washing Methods on Objective Hand Values of Denim Fabrics

ABSTRACT Denim fabrics are products that provide durability and ease of use, and are used by young people or people of all ages who prefer comfortable wear in daily life. In this study, the objective hand values of denim fabrics with three weft yarn types (100% cotton elastane, 85% cotton 15% Modal elastane, and 85% cotton 15% Tencel elastane), two twill directions (3/1 Z and S), and four washing processes (bleach, enzyme, rinse, and stone) were investigated. For this purpose, the compressibility, overall flexural rigidity, drape, surface roughness, and shear rigidity values of industrial washed denim fabrics were measured. It was found that there was no statistically significant effect of weft yarn type on objective hand values, and washing differences were statistically significant on the objective hand values of the denim fabrics. The results showed that enzyme-washed fabrics show better hand and lower hardness properties; stone-washed fabrics have a higher fluffy feel, bleach-washed fabrics have worse hand, and rinse-washed fabrics have stiffer and rougher surfaces. It was also observed that the twill direction affects only the shear rigidity values of the denim fabrics.

Modern approaches to interpretation of Maklakov tonometry results

Based on the presumption that the average values of ocular rigidity determined ex vivo are sufficient for clinical evaluation of intraocular pressure (IOP), calibration of the Maklakov tonometer is done without taking into due account the biomechanical properties of the tunics of the eye, which can affect the results of IOP measurements. Corneal-compensated IOP (IOPcc) allows evaluating patients' individual structural features of the fibrous tunic of the eye, and according to literature sources, for glaucoma it is a parameter with higher diagnostic value. Comparison of Maklakov tonometer readings and IOPcc from the same patients can improve our understanding of the diagnostic value of tonometry. This article aims to determine based on sufficient clinical data the ranges of corneal-compensated IOP corresponding to applanation tonometry readings performed with a 10-g Maklakov tonometer, and to reveal the dependency between the tip diameter and the IOP with consideration of the variability of biomechanical properties of the fibrous tunic in the population. The comparison study analyzed the readings of 10-g Maklakov tonometer and corneal-compensated intraocular pressure in 14 440 eyes of 7 220 patients (mean age 60.1±10.8 years old) with primary open-angle glaucoma and suspected glaucoma. For analysis, IOPcc values of 6 to 35 were included, with a prerequisite of corneal thickness/ hysteresis data being of high quality. The tip diameter was measured with a Vernier caliper within the accuracy of 0.1 mm according to the instructions from the tonometer manual. It was established that with equal tip diameter the readings of applanation tonometry can still vary significantly, which is associated with population variability in the structure of the fibrous tunic of the eye. A measuring scale was derived consisting of a computation chart with markings denoting the borders of confidence intervals for IOPcc values for 10-g Maklakov tonometer. Mean IOPcc is connected to the applanation tip diameter and the cornea by the following equation: IOP=4.14×D2 -62.4×D+248, which can be used for calibrating Maklakov tonometer in the lower and upper ranges of IOP values. The results of 10-g Maklakov tonometry can be presented as a range of IOP values, which with a certain probability includes the individual IOP level of the patient.

Experimental study on flexural strength of stitched foam composites

Sandwich composites and laminate composites are considered as major classes of lightweight structures in a wide range of engineering applications. Lightweight potential of fabric has demonstrated the specific mechanical properties of sandwich composites with or without core material. Many studies have shown that tension, compression, flexure, stress is improved or degraded up to 20% by a stitched process. The present paper focuses on the study of structural improvements of stitched foam composite and also to compare it with unstitched composite of the same glass fiber material. The use of vacuum bagging process to make the stitched foam composite structure and a simple hand lay-up technique for unstitched composite. These composites are made by using E Glass fiber 180GSM, aradur hy 951 hardener, Araldite ly 556 epoxy resin and glass fiber yarn. For stitched foam composite, laminates are stitched in transverse direction i.e., through thickness direction with high strength yarn. 3-point bending test is done to find flexural strength of both composites and compare their results stitched sample showed higher value of flexural strength and flexural rigidity after three-point bending test the strength of stitched composite is 40% more than unstitched composite material.

Variational inference of ice shelf rheology with physics-informed machine learning

AbstractFloating ice shelves that fringe the coast of Antarctica resist the flow of grounded ice into the ocean. One of the key factors governing the amount of flow resistance an ice shelf provides is the rigidity (related to viscosity) of the ice that constitutes it. Ice rigidity is highly heterogeneous and must be calibrated from spatially continuous surface observations assimilated into an ice-flow model. Realistic uncertainties in calibrated rigidity values are needed to quantify uncertainties in ice sheet and sea-level forecasts. Here, we present a physics-informed machine learning framework for inferring the full probability distribution of rigidity values for a given ice shelf, conditioned on ice surface velocity and thickness fields derived from remote-sensing data. We employ variational inference to jointly train neural networks and a variational Gaussian Process to reconstruct surface observations, rigidity values and uncertainties. Applying the framework to synthetic and large ice shelves in Antarctica demonstrates that rigidity is well-constrained where ice deformation is measurable within the noise level of the observations. Further reduction in uncertainties can be achieved by complementing variational inference with conventional inversion methods. Our results demonstrate a path forward for continuously updated calibrations of ice flow parameters from remote-sensing observations.

On adequate zones of true intraocular pressure in healthy and glaucoma eyes

PURPOSE. The study was conducted to reveal using the Ocular Response Analyzer (ORA) the possible ranges of mean values of the “rigidity” and “fluctuation” criteria for fibrous membrane of healthy and glaucoma eyes with consideration of the age periods according to the classification by WHO, and to identify adequate true intraocular pressure (IOP) zones corresponding to these ranges.METHODS. The study consisted of a theoretical analysis of clinical measurements of rigidity and fluctuation of the fibrous membrane, the current level of true IOP and the individual level of IOP calculated in youth using ORA by the method of dynamic diagnosis of Koshitsa-Svetlova, and involved in total 674 healthy and 518 glaucoma eyes from individuals aged 18 to 90 years, who were distributed by age periods according to WHO.RESULTS. A "step pattern" of the distribution of Average values of rigidity and fluctuation in healthy and glaucoma eyes were distributed in a “step pattern”, which made it possible to rank the IOP zones adequately to these steps, taking into account the age periods according to WHO. The following adequate ranges of IOP levels for healthy and glaucoma eyes were identified: low IOP zone (up to 13 mm Hg); medium IOP zone (14–20 mm Hg); elevated IOP zone (21–26 mm Hg); high IOP zone (27–32 mm Hg); IOP subcompensation zone (33–39 mm Hg) and uncompensated IOP zone (≥40 mm Hg). The "steps" of the average values of rigidity, fluctuations, and the IOP ranges adequate to them do not intersect. The current value of the rigidity of the fibrous membrane and the IOP value calculated in youth make it possible to reliably attribute each healthy or glaucoma eye to its individual IOP zone.CONCLUSION. Rigidity of the fibrous membrane consistently determines the level of IOP (p>0.001), while the rigidity and fluctuation of the sclera directly influence its current level. The fundamental criteria — rigidity and fluctuation of the fibrous membrane of the eye — do not depend on the central corneal thickness and objectively determine the current functional state of the fibrous membrane. The ability to objectively and reliably determine whether a healthy or glaucoma eye belongs to its individual IOP zone is particularly important for the polyclinic network. The time such express diagnostics takes is 0.02 seconds.

Transferring Tsyganenko 1989 magnetospheric modulation for cosmic radiation cutoff rigidity values to different epochs of the International geomagnetic reference field

A technique has been developed that will transfer the Tsyganenko 1989 modulation for cutoff rigidity values to different epochs of the International Geomagnetic Reference Field (IGRF). The technique separates the effect of the Tsyganenko external currents on cutoff rigidity values previously calculated at 450 km using the 1995 IGRF such that these effects can be applied to other models of the IGRF. The Tsyganenko modulation effects were then applied to the 2020 internal field model. Two improvements to the original set of calculations include a three-point longitudinal smoothing to reduce the unevenness of the penumbral effects and a replacement of the original −100 Dst values for Kp values > 5 to −50 Dst increments. These changes have extended the original library of 88 world grids to a total of 128 world grids of cutoff rigidity values that are applicable for all Kp values (0–9 + ) and Dst values to −500 nT.