Integration Step Research Articles

CONVERGENCE TEST FOR THE EXTENDED 3 - POINT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR INTEGRATING STIFF IVP

In this work, a new scheme is generated from the extended 3–point super class of block backward differentiation formula for integrating stiff IVP and the proposed method is subjected to convergence test. The proposed scheme is found to be zero stable, consistent and of order 5. Thus, possess all the required criteria for convergence. The scheme can approximate the values of three points at a time per integration step. The scheme maintained the same technique of co-opting a stability control parameter () in the formula and by adjusting its value within the interval , more A-stabled schemes can be generated. However, this research considers and arrived at zero and A– Stabled method, capable of solving any stiff IVPs. Hence, the proposed convergent scheme can be used for integrating stiff IVPs and archives accuracy of scale error and less executional time.

Dynamical homotopy transient-based technique to improve the convergence of ill-posed power flow problem

This paper proposes a hybrid technique to solve the ill-posed Power Flow Problem (PFP), considering a homotopy approach. The primary proposal is to solve large-scale problems where the traditional Newton–Raphson (NR) fails to converge, as in the case of ill-posed systems. The method explores a dynamical homotopy transient-based technique to improve the convergence of the ill-conditioned problem instead of using the classical static method. Depending on the integration selected scheme and the integration step, the result furnished by the dynamical homotopy method has low accuracy. Then, the NR method is employed to refine the low-accuracy result and accurately determine the ill-posed PFP solution. The proposed approach can be implemented efficiently using only one Jacobian matrix computation and LU factorization per point of the homotopy path. In the static homotopy problem, a PFP using previous results must be solved per path point. In this case, some LU factorizations are necessary for each path point. The technique’s performance was evaluated through experiments, including a 70,000-bus large-scale system. The approximate dynamical homotopy result used as an initial estimate provided appropriate convergence quality for the NR method to determine a high-precision solution to the PFP.

Synthesis and Characterization of Mg-Hydroxyapatite and Its β-Cyclodextrin Composite as Enhanced Bio-Carrier of 5-Fluorouracil Drug; Equilibrium and Release Kinetics.

An advanced form of magnesium-doped hydroxyapatite (Mg·HAP) was integrated in composite with β-cyclodextrin producing a safe biocomposite (β-CD/HAP) as an enhanced delivery structure of traditional 5-fluorouracil (5-FU) chemotherapy during the treatment stages of colorectal cancer cells. The qualifications of β-CD/HAP as a carrier for 5-FU were followed based on the loading, release, and cytotoxicity as compared to Mg·HAP. β-CD/HAP composite exhibits notably higher 5-FU encapsulation capacity (272.3 mg/g) than Mg·HAP phase (164.9 mg/g). The 5-FU encapsulation processes into β-CD/HAP display the isotherm behavior of the Freundlich model (R2 = 0.99) and kinetic assumptions of pseudo-first order kinetic (R2 > 0.95). The steric studies reflect a strong increment in the quantities of the free sites after the β-CD integration steps (Nm = 61.2 mg/g) as compared to pure Mg·HAP (Nm = 42.4 mg/g). Also, the capacity of each site was enhanced to be loaded by 5 of 5-FU molecules (n = 4.45) in a vertical orientation. The 5-FU encapsulation energy into β-CD/HAP (<40 kJ/mol) reflects physical encapsulation reactions involving van der Waals forces and hydrogen bonding. The 5-FU release profiles of β-CD/HAP exhibit slow and controlled properties for about 80 h either in gastric fluid (pH 1.2) or in intestinal fluid (pH 7.4). The release kinetics and diffusion exponent (>0.45) signify non-Fickian transport and complex erosion/diffusion release mechanism. The free β-CD/HAP particles display a considerable cytotoxic effect on the HCT-116 cancer cells (33.62% cell viability) and its 5-FU-loaded product shows a strong cytotoxic effect (2.91% cell viability).

Effectiveness of KS Elements for Satellite Orbit Predictions With Earth’s Gravity and Drag Force

This study is meant for understanding the efficiency of KS regular equations for satellite orbit prediction. The analysis is mainly concentrated on Low-Earth satellite orbit, where the forces due to non spherical nature of the Earth and atmospheric drag, plays important role. The classical Newtonian equations of motions for which solutions are unstable, cannot be used for long term prediction of orbit. Hence, in literature many transformations have emerged to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing to use a large integration step sizes, or both in the transformed space. KS transformation introduced by Kustaanheimo and Stiefel, regularize the nonlinear equation of motion to linear differential equations of a harmonic oscillator of constant frequency. In this paper a detailed analysis on KS differential equations is carried out by including perturbations of Earth’s gravity and atmospheric drag for orbit predictions. The recurrence relations of associated Legendre polynomial and its derivatives are used for including higher order Earth’s gravity terms. To know the effectiveness of the theory, results are compared with the orbit of the actual space object, CZ-2D R/B, for 7 days duration. The comparison shows that the KS theory is one of the best theories for orbit predictions available at present.

Orbit Predictions Using KS Elements With Earth’s Flattening

Predicting the orbit of a satellite is a fundamental requirement in many areas of aerospace, such as mission planning, satellite geodesy, re-entry prediction, maneuver planning, collision avoidance, formation flying, etc. For near-Earth orbits, the forces due to the non spherical nature of the Earth and atmospheric drag plays an important role and are mainly responsible to bring the satellite back to the Earth. Thus inclusion of the effect of these perturbing forces becomes important for precise orbit computation of near-Earth orbits. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel [1], who regularized the nonlinear Kepler equation of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. In this paper a detailed analysis is carried out for orbit prediction using KS differential equations by including the non spherical gravitational potential of the Earth as the perturbing force. Earths zonal and tesseral harmonics, which produce bands of constant deviation from the spherical field along lines of latitude and longitude, are included to precisely model the Earth’s gravitational potential. Higher order Earth’s flattening terms are included by utilizing the recurrence relations of associated Legendre polynomial and its derivatives. To know the effectiveness of the theory, the results are compared with the real IRS-1A satellite data and the results of other existing solutions for a long duration of nearly a month time. The comparison shows that the KS method provides one of the most and accurate techniques for orbit prediction available at present.

Wave packet theory for non-resonant x-ray emission and non-resonant Auger electron emission in molecules.

We present a time-dependent theory for non-resonant x-ray emission spectrum (XES) and normal Auger spectrum (NAS) calculation, based on a fully quantum description of nuclear dynamics using the vibrational wave packet concept. We compare two formulations of the time-dependent theory, either employing a two-time propagation scheme or using spectral integration over the electron energy continuum. We find that the latter formulation is more efficient for numerical simulations, providing a reasonable accuracy when the integration step is shorter than the lifetime broadening of the core-ionized state. We demonstrate our approach using the example of non-resonant x-ray emission from a water molecule, considering the lowest core-ionized K-1 and first core-ionized shake-up K-1V-1V1 intermediate states. These channels exemplify the developed theory on bound-bound, bound-continuum, continuum-bound, and continuum-continuum transitions. Our results suggest that the time-dependent approach is efficient for simulating XES involving dissociative states, whereas the time-independent approach, based on Franck-Condon factors, is more efficient for bound-bound transitions expressed as discrete frequency dependence in the energy domain. The methods and discussion have general applicability, including both NAS and more complex systems, such as liquid water.

Collective cell migration due to guidance-by-followers is robust to multiple stimuli

Collective cell migration is an important process during biological development and tissue repair but may turn malignant during tumor invasion. Mathematical and computational models are essential to unravel the mechanisms of self-organization that underlie the emergence of collective migration from the interactions among individual cells. Recently, guidance-by-followers was identified as one such underlying mechanism of collective cell migration in the embryo of the zebrafish. This poses the question of how the guidance stimuli are integrated when multiple cells interact simultaneously. In this study, we extend a recent individual-based model by an integration step of the vectorial guidance stimuli and compare model predictions obtained for different variants of the mechanism (arithmetic mean of stimuli, dominance of stimulus with largest transmission interface, and dominance of most head-on stimulus). Simulations are carried out and quantified within the modeling and simulation framework Morpheus. Collective cell migration is found to be robust and qualitatively identical for all considered variants of stimulus integration. Moreover, this study highlights the role of individual-based modeling approaches for understanding collective phenomena at the population scale that emerge from cell-cell interactions.

One-piece knitted embedded hang-needle sensor for shoulder posture recognition

Wearable products have significant applications in medical assistance, posture correction, and humancomputer interaction. In this study, we present a knitting method for a one-piece knitted embedded hang-needle sensor. This method involves simultaneously knitting conductive yarn into the sensing zone while creating the monitoring garment in a seamless manner. By implementing a tight hanging needle structure in the sensing zone design and adjusting knitting parameters, the effect of pre-stretching on the sensor caused by the base garment is minimized. Furthermore, integrating the sensing area of the hang-needle structure with the monitoring garment eliminates the need for additional sensor integration steps and simplifies the preparation process, resulting in reduced time and material costs. Moreover, the monitoring garment offers a comfortable wearing experience without any foreign body sensation and accurately captures the initial shoulder posture of the wearer.

THREE-LAYER SCHEME FOR SOLVING THE RADIATION DIFFUSION EQUATION

A method has been developed for the numerical solution of a nonlinear equation describing the diffusion transfer of radiation energy. The method is based on the introduction of the second time derivative with a small parameter into the parabolic equation and an explicit difference scheme. Explicit approximation of the initial equation makes it possible to implement on its basis an algorithm that is effectively adapted to the architecture of high-performance computing systems. The new scheme provides, in comparison with the original scheme, a larger time integration step and a sufficiently high resolution quality of the solution structure, providing the second order of accuracy. A heuristic algorithm for choosing the parameters of a three-layer difference scheme is proposed. A promising field of application of the method can be problems of plasma physics and astrophysics.

Integrating AI Applications into Learning Management Systems to Enhance e-Learning

Artificial intelligence technologies have the potential to greatly enhance the organization of learning management systems and online learning experiences. In particular, the public release of OpenAI's GPT-3 model in December 2022 has given society a chance to learn more about the current status of artificial intelligence. There have been much research on the use of artificial intelligence in e-learning processes, but very few of them demonstrate how to integrate these applications step-by-step and with examples into learning management systems. This study intends to close this gap by demonstrating how artificial intelligence technologies are integrated into learning management systems using real-world examples. This study provides examples of practical applications as well as integration steps. Finally, GPT-3 plugins for Moodle are examined and sample JavaScript code is included for integrating Chat GPT into Moodle. By presenting a useful guide for integrating artificial intelligence technology into learning management systems, this work adds to the body of literature.

Software package «Integral» for modeling space constellations and space vehicles

The aim of the work was to create a software package for modeling the solution of target problems by multi-satellite constellations. The software consists of modules for the dynamics of the center of mass of the satellites, remote sensing of the Earth, satellite communications (including routing of messages over inter-satellite communications), space monitoring and others. The main feature of the implementation was the mathematical and computational optimization of calculations, which made it possible to carry them out on a conventional computer without involving additional computational power. In the course of the work, corrections to the Everhart method were proposed to improve the trajectory integration step. Parallel implementation also helped to significantly speed up the calculations. To illustrate the work, examples of solving two different problems are given: calculating the optimal orbit for the task of monitoring outer space and solving the problem of determining the minimum number of satellites needed to scan the border of the Russian Federation once every half an hour. A feature of the soft is the work with the constellation as an integral object at the level of setting tasks and the subsequent analytics of its solution, which is presented in the form of information on target tasks, subgroups of the constellation, spacecraft and the entire constellation.

Bending of a plate from a functionally heterogeneous material in the presence of large deformations

Details and elements of structures, which are made of functionally heterogeneous materials and have the property of shape memory and behave pseudo-elastically, may be under the influence of complex loads in the process of manufacturing and operation. Uneven heating of bodies in combination with force factors can lead to large deformations of the material and complex deformation processes. The existing models of the behavior of such elements do not take into account the nonlinearity of geometric relationships and are unsuitable for use with large deformations.&#x0D; The article deals with the bending of a plate of finite dimensions from a functionally heterogeneous material in the presence of large plastic deformations. The simulation of plate behavior is based on a nonlinear phenomenological model that describes the properties of shape memory alloys and the thermos-pseudo-plastic behavior of the material at a point. A diagram of a pseudo-elastic material consisting of three curved sections is used.&#x0D; The first feature of the formulation of the problem of specifying the area of geometric nonlinearity is the formulation of the boundary conditions around the support. If for a linear problem they are set only along the support line, then to refine the geometrically nonlinear solution, the zero vertical displacements of the plate points and, accordingly, the speed of movement were set in the vicinity of the area of contact with the support. The second feature of the refinement is a significant reduction in the number of coordinate integration steps (up to 5%). At the same time, in order to fulfill the condition of stability, a proportional reduction of the integration step over time is necessary. For a reliable comparison of results, it is necessary to increase the number of time integration steps while decreasing the integration steps by coordinates. This problem was solved using a sequence of numerical experiments. The third feature consists in solving the additional problem of interpolation of the required values in the nodes of the new finer grid by the corresponding value in the nodes of the main grid. This problem is solved using a two-dimensional spline function.

Fast and accurate adaptive collocation iteration method for orbit dynamic problems

For over half a century, numerical integration methods based on finite difference, such as the Runge-Kutta method and the Euler method, have been popular and widely used for solving orbit dynamic problems. In general, a small integration step size is always required to suppress the increase of the accumulated computation error, which leads to a relatively slow computation speed. Recently, a collocation iteration method, approximating the solutions of orbit dynamic problems iteratively, has been developed. This method achieves high computation accuracy with extremely large step size. Although efficient, the collocation iteration method suffers from two limitations: (A) the computational error limit of the approximate solution is not clear; (B) extensive trials and errors are always required in tuning parameters. To overcome these problems, the influence mechanism of how the dynamic problems and parameters affect the error limit of the collocation iteration method is explored. On this basis, a parameter adjustment method known as the “polishing method” is proposed to improve the computation speed. The method proposed is demonstrated in three typical orbit dynamic problems in aerospace engineering: a low Earth orbit propagation problem, a Molniya orbit propagation problem, and a geostationary orbit propagation problem. Numerical simulations show that the proposed polishing method is faster and more accurate than the finite-difference-based method and the most advanced collocation iteration method.

Questions of mathematical modelling in the study of acid retardation on ion–exchange resins

In this paper, the chemical equilibrium of a multicomponent solution is considered in detail as part of a dynamic model of the acid retardation method. A detailed study of the chemical equilibrium, represented as a system of nonlinear equations, is a key step for building an effective dynamic model in the case of a multicomponent solution. This paper presents an algorithm for efficient calculation of chemical equilibrium using extractive phosphoric acid as an example. This algorithm can be used in a dynamic model to calculate chemical equilibrium at each point of the spatial grid and at each integration step. Moreover, for the concentrations of substances in the experiment on the purification of extractive phosphoric acid, it is shown that the nonlinear system of equations of chemical equilibrium allows one to obtain simple algebraic relations for the connection of the concentration of molecules of the substance with the total concentration of substances of all elements in solution with good accuracy. In addition, it was shown that for each metal, only one type of salt sorption can be considered due to the low concentration of other types, which makes it possible to reduce the number of differential equations in the dynamic model of the acid retardation method.

Building Information Modelling for Application in Geotechnical Engineering

BIM (Building Information Modelling) is used to create and manage data during design, construction, and operation. It helps to effectively manage resources and optimize processes in the construction industry. Geotechnical engineering is one of the complex disciplines that may require BIM integration. Various data types must be provided in a timely manner and require real-time feedback, fast processing, and construction guidance. The first problem presented in the paper is the use of the traditional 2D-based method used by engineers for a particular task. It seems to be impractical when some adjustments are included. Another issue is the lack of communication between the workers. It poses the problem of information exchange and misunderstanding during the interpretation of technical data. This paper aims to find different integration techniques and steps for integrating geotechnical data into the BIM process. Methods used to examine the topic are qualitative research, literature review, and case studies. These methods were useful for studying the problems and introducing the soil information into the BIM application. Firstly, a case study with I-BIM was considered, and the BIM–FEM–BIM interaction was applied to introduce geotechnical information with Plaxis 3D. The results have shown that further development of BIM in infrastructure is needed. Another case study explored the present state of the geotechnical design in BIM and potential solutions. The new frameworks were recreated: many boreholes were imported to the BIM, and a 3D geometric model of the entire hill was created for the hill fortification structure with soil clogging. The last two studies in Malaysia modeled a 3D subsurface and used two geotechnical formats, AGS and CVS. The first includes more information than the second; however, the second can be used for a more generalized model. Overall, BIM–FEM interaction can be used as a geometric model for data transfer. However, the open data format of the Industry Foundation Class (IFC) or geotechnical data format of the AGS and CVS were suggested to be used for greater flexibility. It was also found that excessive information makes the model loaded and complex. Therefore, it was recommended that big data be summarized properly with minimal loss of necessary data. Further research is needed to understand data transmission schemes of geotechnical information better. Moreover, it is recommended to put all the strategies directly into practice to create a geotechnical design.

A multi-GPU and CUDA-aware MPI-based spectral element formulation for ultrasonic wave propagation in solid media

In this paper, we introduce a new multi-GPU-based spectral element (SE) formulation for simulating ultrasonic wave propagation in solids. To maximize communication efficiency, we purposely developed, based on CUDA-aware MPI, two novel message exchange strategies which allow the common nodal forces of different subdomains to be shared between different GPUs in a direct manner, as opposed to via CPU hosts, during central difference-based time integration steps. The new multi-GPU and CUDA-aware MPI-based formulation is benchmarked against a multi-CPU core and classical MPI-based counterpart, demonstrating a remarkable acceleration in each and every stage of the computation of ultrasonic wave propagation, namely matrix assembly, time integration and message exchange. More importantly, both the computational efficiency and the degree-of-freedom limit of the new formulation are actually scalable with the number of GPUs used, potentially allowing larger structures to be computed and higher computational speeds to be realized. Finally, the new formulation was used to simulate the interaction between Lamb waves and randomly shaped thickness loss defects on plates, showing its potential to become an efficient, accurate and robust technique for addressing the propagation of ultrasonic waves in realistic engineering structures.

A MS-feature-based medicinal plant database-driven strategy for ingredient identification of Chinese medicine prescriptions

Identification of the individual herbs that constitute the Chinese medicine prescription (CMP) is a key step to control the quality and ensure the efficacy of traditional Chinese medicine (TCM), but also a challenging task for analysts from all over the world. In this study, a MS-feature-based medicinal plant database-driven strategy was proposed for quick and automatic interpretation of CMP ingredients. The single herb database consisting of stable ions of sixty-one common TCM medicinal herbs was first constructed. And then, the data of CMP was imported into a self-built searching program to achieve quick and automatic identification with four steps including level 1 candidate herb screening based on stable ions (step 1), level 2 candidate herb screening based on unique ions (step 2), difficult-to-distinguish herb differentiation (step 3) and results integration (step 4). The identification model was optimized and validated with homemade Shaoyaogancao Decoction, Mahuang Decoction, Banxiaxiexin Decoction, and their related negative prescriptions and homemade fakes. Another nine batches of homemade and commercial CMPs were applied to this new approach and most of composed herbs in the corresponding CMPs were correctly identified. This work provided a promising and universal strategy for the clarification of CMP ingredients.

An Influence of Spatial Harmonics on an Electromagnetic Torque of a Symmetrical Six-Phase Induction Machine

The analyses of the influence of spatial harmonics on the electromagnetic torque of the multi-phase induction machine and reducing this influence are important tasks to ensure the high efficiency of the induction machine. Designing the machine to consider the influence of spatial harmonics is essential to ensure the desired mechanical and energy characteristics. In the case of the sinusoidal winding supply of the induction machine, the magnetomotive force has high spatial harmonics, which are caused by the machine-winding design. The interaction between the 5th, 7th, 11th and 13th spatial harmonics of the winding function and the first time-harmonic of the winding supply causes the appearance of the 6th and 12th harmonics in the electromagnetic torque of the machine. A prototype of the symmetrical six-phase induction machine and the experimental study for the influence of spatial harmonics on the harmonic content of the stator currents in different machine modes are given in this paper. The mathematical model of the six-phase induction machine has been developed using the average voltages in integration step method. The introduction of the harmonic components into the magnetization inductance in the mathematical model of the six-phase induction machine for taking into account the spatial harmonics of the machine-winding function is proposed in this paper. The adequacy of the mathematical model was confirmed by comparing the simulation and experimental results. The harmonic content of the electromagnetic torque, which is caused by spatial harmonic influence, is analyzed.

Spectral Properties of Exact Polarobreathers in Semiclassical Systems

In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable.

An International Study of Factors Affecting Variability of Dosimetry Calculations, Part 2: Overall Variabilities in Absorbed Dose.

Dosimetry for personalized radiopharmaceutical therapy has gained considerable attention. Many methods, tools, and workflows have been developed to estimate absorbed dose (AD). However, standardization is still required to reduce variability of AD estimates across centers. One effort for standardization is the Society of Nuclear Medicine and Molecular Imaging 177Lu Dosimetry Challenge, which comprised 5 tasks (T1-T5) designed to assess dose estimate variability associated with the imaging protocol (T1 vs. T2 vs. T3), segmentation (T1 vs. T4), time integration (T4 vs. T5), and dose calculation (T5) steps of the dosimetry workflow. The aim of this work was to assess the overall variability in AD calculations for the different tasks. Methods: Anonymized datasets consisting of serial planar and quantitative SPECT/CT scans, organ and lesion contours, and time-integrated activity maps of 2 patients treated with 177Lu-DOTATATE were made available globally for participants to perform dosimetry calculations and submit their results in standardized submission spreadsheets. The data were carefully curated for formal mistakes and methodologic errors. General descriptive statistics for ADs were calculated, and statistical analysis was performed to compare the results of different tasks. Variability in ADs was measured using the quartile coefficient of dispersion. Results: ADs to organs estimated from planar imaging protocols (T2) were lower by about 60% than those from pure SPECT/CT (T1), and the differences were statistically significant. Importantly, the average differences in dose estimates when at least 1 SPECT/CT acquisition was available (T1, T3, T4, T5) were within ±10%, and the differences with respect to T1 were not statistically significant for most organs and lesions. When serial SPECT/CT images were used, the quartile coefficients of dispersion of ADs for organs and lesions were on average less than 20% and 26%, respectively, for T1; 20% and 18%, respectively, for T4 (segmentations provided); and 10% and 5%, respectively, for T5 (segmentation and time-integrated activity images provided). Conclusion: Variability in ADs was reduced as segmentation and time-integration data were provided to participants. Our results suggest that SPECT/CT-based imaging protocols generate more consistent and less variable results than planar imaging methods. Effort at standardizing segmentation and fitting should be made, as this may substantially reduce variability in ADs.