Analysis Of Mathematical Model Research Articles

Structural design and evaluation of bone remodeling effect of fracture internal fixation implants with time-varying stiffness

The stiffness of an ideal fracture internal fixation implant should have a time-varying performance, so that the fracture can generate reasonable mechanical stimulation at different healing stages, and biodegradable materials meet this performance. A topology optimization design method for composite structures of fracture internal fixation implants with time-varying stiffness is proposed, considering the time-dependent degradation process of materials. Using relative density and degradation residual rate to describe the distribution and degradation state of two materials with different degradation rates and elastic modulus, a coupled mathematical model of degradation simulation mechanical analysis was established. Biomaterial composite structures were designed based on variable density method to exhibit time-varying stiffness characteristics. Taking the bone plate used for the treatment of tibial fractures as an example, a composite structure bone plate with time-varying stiffness characteristics was designed using the proposed method. The optimization results showed that material 1 with high stiffness formed a columnar support structure, while material 2 with low stiffness was distributed at the degradation boundary and inside. Using a bone remodeling simulation model, the optimized bone plates were evaluated. After 11 months of remodeling, the average elastic modulus of callus using degradable time-varying stiffness plates, titanium alloy plates, and stainless steel plates were 8 634 MPa, 8 521 MPa, and 8 412 MPa, respectively, indicating that the use of degradable time-varying stiffness plates would result in better remodeling effects on the callus.

Study on indoor temperature and thermal performance of a novel solar coupled floor and Kang heating system

Coupled floor and Kang surface heating terminals have significant advantages in meeting the differentiated indoor thermal requirements of Northwest rural dwellings in winter. A novel solar coupling floor and Kang surface heating system is proposed, a mathematical analysis model of thermal performance is established, and experimental validation is carried out. The solar coupling floor and Kang surface heating systems can effectively meet the differing heating requirements of indoor and bedding thermal environment. The solar fraction can reach 59.4 %, showing good energy-saving capability. The solar coupled floor and Kang surface heating system were simulated and optimized. The more suitable scheme is a solar collector size of 7.0 m2 and a water tank capacity of 0.35 m3. This configuration better meets the differing heating requirements of indoor and bedding thermal environment when the nighttime water supplier temperature is inferior to the daytime water supplier temperature. The solar coupling floor and Kang surface heating system has a 20.4 % increase and can recover the payback period in 2.3 years compared with traditional solar heating system. The results of the study support the use of solar energy to enhance the indoor thermal demands of rural dwellings in Northwest China.

An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells

An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells

Improved FPA for aircraft conceptual design

Aircraft weight design is a key technology in aircraft conceptual design. The design of aircraft weight is directly related to many design parameters of the aircraft, and there are complex constraint relationships between these parameters. It is difficult to determine the design parameters in the process of aircraft conceptual design with an accurate mathematical analytical model, it is necessary to use an optimization algorithm. Firstly, to build the optimization object function, the aircraft weight function and some constrain functions are given out, thus, the aircraft weight design problem is transformed into a single objective multi-constraint optimization problem, aiming at the problem of parameter coupling, Aitken acceleration algorithm is proposed to solve the problem through iterative, thus, and a feasible solution of aircraft parameters are obtained; Secondly, considering the advantages of flower pollination algorithms in solving unconstrained problems, the flower pollination algorithm (FPA) combined with the Aitken acceleration algorithm is proposed for automatic global optimization, to avoid the FPA falling into the local optimal solution or missing optimal solution, propose improvements to the FPA algorithm from three aspects: adaptive conversion probability, adaptive step size adjustment, and adaptive reproduction probability generation. To use FPA, the multi-constraint optimization problem is transformed into a multi-parameter unconstrained optimization problem with a penalty term based on the penalty function method. Finally, a design example is given to verify the effectiveness of the algorithm, and the superiority of the improved algorithm is verified by comparing it with PSO and the fixed transition probability FPA.

Mathematical model for mesh analysis of gear pair in gear-shaft-bearing systems with localized failure on raceway

To investigate the influence of bearing failures on the mesh characteristics of gear pairs, this paper presents a mathematical model for gear-shaft-bearing systems. Within this simulation method, the model of defective bearings and the contact analysis methodology of gear pairs are integrated into the system equations. Additionally, the coupling mechanism between system components is determined by addressing the misaligned shafts induced by asynchronous bearing vibrations. Furthermore, the torsional deformation of gear teeth generated by uneven load distribution is considered, and a calculation method for mesh stiffness in complex environments is developed. By employing the comprehensive model, the effect of raceway failures on the mesh behavior is lucidly explained, the real-time distribution of contact stress and load on the tooth surface can be obtained, and the optimal modification strategies for gears are formulated. Finally, the proposed model is confirmed through the finite element (FE) model and experimental observation, which provides a potent tool for the performance optimization of gearboxes.

LattSAC: a software for the acoustic modelling of lattice sound absorbers

ABSTRACT The increasingly distressing problem of noise pollution prompts the rapid research and development of lattice-based acoustic materials for practical applications. These lattices boast excellent mechanical properties and unlimited design freedom made possible using additive manufacturing technologies. Currently, there is a lack of analytical mathematical models relating the lattice geometry to the acoustic models and the absence of software dedicated to the acoustic modelling of strut lattice-based sound absorbers. This work presents LattSAC, an acoustics calculator that takes in all the geometrical parameters of the lattice structure and outputs directly the sound absorption coefficients (SAC) and their statistics. Hidden within the code is the novel Multi-layered Micropore-Cavity (MMC) model with semi-empirical mathematical models well-trained using experimental data to output the SACs with excellent accuracies. This software aims to accelerate the research and development of lattice-based acoustic absorbers for actual applications. It also functions as a valuable tool for users looking to design sound-absorbing materials using lattice structures. The software installer may be downloaded for free from the following GitHub repository: https://github.com/JunWeiChua/LattSAC. If there are any suggestions or contributions, the user may write to zhaiweigroup@gmail.com.

Investment in vehicle-to-grid and distributed energy resources: Distributor versus prosumer perspectives and the impact of rate structures

Photovoltaic panels, electric vehicles, and vehicle-to-grid technologies are becoming more common and hold significant promises to improve the grid and foster the energy transition. However, significant questions remain unanswered with respect to who should invest in this equipment and what tariff should be used. This paper examines whether the distribution company or prosumer should invest in and manage Distributed Energy Resources (DER), the ideal combination of DER to utilize, and the appropriate tariff to implement. Central to this analysis is the assessment of different stakeholder objectives, particularly from the investor's perspective, where net present value is used as the primary criterion for evaluating the different investment scenarios. Additionally, the impact of these scenarios on the annual system cost is calculated. A mathematical scenario analysis model is developed to simulate the operation of DER and energy management systems. This model utilizes the Vermont electricity grid's real-world consumption, generation data, and cost structures. The results underscore the significance of incorporating vehicle-to-grid technology to enhance the profitability of DER investments. This inclusion of specific data sources and stakeholder criteria aims to provide insight into the complex dynamics of smart-home deployment.

Influence of Good Corporate Governance and Corporate Social Responbility To Company Value with Profitability as a Moderation Variable (Studies on Manufacturing Companies Listed on the Stock Exchange Indonesia Year 2017-2021)

Purpose: The study added profitability as a moderating variable, predicting that the higher the profitability a firm has achieved, the more valuable it will be. Companies that can survive over the long term are reflected in further improvements in corporate value. Theoretical framework: Agency theory focuses on two individuals, namely the principal and the agent. The principal delegates responsibility for decision making to agents. Both principals and agents are assumed to be rational economic people who are solely motivated by self-interest, but they have difficulty differentiating respect for preferences, beliefs and information. Material and Method: This study uses a kind of quantitative research. The audit committee, board size, excellent corporate governance, and corporate social responsibility are the study's independent variables. Tobin's Q-ratio is the dependent variable in this investigation. The moderator variable for this study is profitability. The study uses secondary data, i.e. data from financial reports. The survey was conducted on all manufacturing companies listed on the Indonesian Stock Exchange. A quantitative approach was used using mathematical models for collection and analysis using statistical formulas. The sampling technique of the data collection method used in this study is literature review. internet media. The study population is manufacturing companies listed on the Indonesian Stock Exchange (IDX) between 2017 and 2021. The sample size for this study is 40 companies he listed on IDX between 2017 and 2021. The results show that the size of a company's board of directors has a significant impact on corporate value in the IDX-listed manufacturing industries from 2017 to 2021. Findings: The results show that audit committees will not have a significant impact on the enterprise values of manufacturers listed on the IDX from 2017 to 2021. Findings show that corporate social responsibility (CSR) does not have a significant impact on corporate value for manufacturers listed in the IDX 2017-2021. Research practical & Social Implication: Based on the research, the results of this study also show that the size of a company's board of directors helps increase shareholder value. Originality/value: This is evidenced by her MRA test results in the previous chapter, where profitability amplifies the effect of a company's board size on its value. After all, the more profitable a company is, the more the board will be happy to work and the more valuable the company will be.

The Impact of the Fluid-Solid Coupling Behavior of Macro and Microstructures in the Spiral Cochlea on Hearing.

The cilia of the outer hair cells (OHCs) are the key microstructures involved in cochlear acoustic function, and their interactions with lymph in the cochlea involve complex, highly nonlinear, coupled motion and energy conversions, including macroscopic fluid-solid coupling. Recent optical measurements have shown that the frequency selectivity of the cochlea at high sound levels is entirely mechanical and is determined by the interactions of the hair bundles with the surrounding fluid. In this paper, an analytical mathematical model of the spiral cochlea containing macro- and micromeasurements was developed to investigate how the phonosensitive function of OHCs' motions is influenced by the macrostructural and microstructural fluid-solid coupling in the spiral cochlea. The results showed that the macrostructural and microstructural fluid-solid coupling exerted the radial forces of OHCs through the flow field, deflecting the cilia and generating frequency-selective properties of the microstructures. This finding showed that microstructural frequency selectivity arises from the radial motions of stereocilia hair bundles and enhances the hearing of sound signals at specific frequencies. It also implied that the macrostructural and microstructural fluid-solid couplings influence the OHCs' radial forces and that this is a key factor in the excitation of ion channels that enables their activity in helping the brain to detect sound.

Mathematical modelling of quantifying bioethanol fuel production from pineapple waste

Lack of confidence in potential bioenergy production and net benefit hinders rapid implementations of such sustainable energy productions from different waste sources. With the aim of accelerating real-life implementations of more bioenergy productions, this paper presents development of a simple mathematical model, which can be used to evaluate potential bioethanol production capacity from pineapple waste under different input conditions. Based on an earlier experimental study, the mathematical model was developed depending on three contributing factors; pH, temperature and substrate concentration as considered in the earlier experimental study. Results from the developed mathematical formulation were compared with the experimental data from the earlier original study. It is found that the developed model is quite capable to estimate potential bioethanol productions from pineapple waste. Model estimated results are having a coefficient of correlation of 0.84 with the measured data. Standard errors of the model’s estimations are also quite low; RMSE = 0.49, MAE = 0.39 and RAE = 0.06. To facilitate a wider industrial generation, a basic mathematical model framework for economic analysis is proposed involving evaluation of net present values of expected future yields, as well as costs (initial and maintenance). Such mathematical model of economic analysis will help stakeholders on selecting optimum input parameters in achieving targeted benefit through optimised energy consumption.

Business investment decision-making based on mathematical model and risk analysis

Business investments are prone to market risks, so pre-analysis is mandatory. The type of risk, its period, sustainability, and economic impact are the analyzable features for preventing loss and downfall. In recent years, mathematical models have been used for representing business cycles and analyzing the impacting risks. This article introduces a Decisive Risk Analytical Model (DRAM) for identifying spur defects in business investments. The proposed risk analytical model exploits the investments, returns, and influencing factors over the various market periods. The risk model is tuned for identifying the influencing factors across various small and large investment periods. The model is tuned to adapt to different economic periods split into a single financial year. In the process of tuning and training the mathematical analysis model, deep learning is used. The learning paradigm trains the risks and modifying features from expert opinion and previous predictions. Based on these three factors, the risk for the current investment is forecasted. The forecast aids in improving the new investment feasibilities with minimal risks and model modifications. The frequent market status is identified for preventing unnecessary risk-oriented forecasts using the training performed. Therefore, the proposed model is reliable in identifying risks and providing better investment recommendations.

Energy harvesting using lead-free multilayer piezo stacks based on 0.95(Bi0.5Na0.5)TiO3-0.05(BaTiO3) piezoceramics through the addition of ZrO2

This paper explores the feasibility of utilizing lead-free multilayer piezo stacks, particularly focusing on Zr-doped 0.95(Bi0.5Na0.5)TiO3-0.05(BaTiO3) piezoceramics, for energy harvesting. Various lead-free BNT-BT disk samples with different Zr concentrations undergo structural, microstructural, and electrical characterizations. The results illustrate that Zr-doping improves piezoelectric constitutive parameters, notably at a 2.0 mol% concentration. Electromechanical tests were conducted on multilayer piezo stacks, involving variations in electric load, mechanical load, frequency, and number of stacked disks. These tests demonstrate the ability of the multilayer transducer to produce up to 1.5 V (peak) under particular conditions: a 250 Hz frequency, a 10 N mechanical load, and an open circuit electric load, utilizing a stack comprising 5 disks. Employing an analytical mathematical model, an effective d33eff of the system is determined, yielding values ranging from 588 to 625 pC/N for a stack composed of 5 disks. These findings highlight the considerable potential of lead-free multilayer piezo stacks in energy harvesting applications, offering crucial insights for the development of sustainable and eco-friendly energy solutions.

Viability of low‐grade heat conversion using liquid piston Stirling engines

AbstractLiquid piston Stirling engines (LPSEs) are low‐cost, simple, maintenance‐free, and flexible external combustion engines with the potential to operate from low‐grade heat sources. This study reviews the major components, operations, and variants of LPSEs along with the mathematical models to assess their performance, which have been developed since the inception of LPSEs. Consequently, the technical feasibility of LPSEs in different applications is deduced from this complete systematic review, especially useful for both theoretical and applied researchers. The operation is based on a four‐stage Stirling cycle with most engines having three main components as per the findings of this study: the displacer columns, the regenerator, and tuning columns. The two main variants categorized by this study are the dry operating fluidyne and the wet operating thermofluidic. The accurate analyses of these engines are mostly within the spheres of experimental and numerical techniques since analytical mathematical models are difficult to develop owing to the complexity of the operating thermo‐physics. Pumping, cooling, and the direct generation of electricity are frequent applications of these engines reported in the literature. However, since their inception in 1969, these engines are yet to be commercialized owing to their low energy efficiency, power density, and reliability. The findings of this research conclude that LPSEs are essential for environment‐friendly pumping applications using low‐grade heat, especially in the irrigation sector of remote regions with limited access to electricity grids. Additionally, by replacing the electricity‐consuming status quo pumps, LPSEs ensure sustainability with minimal greenhouse gas emissions.This article is categorized under: Energy and Power Systems > Energy Management Sustainable Development > Energy‐Water‐Food Nexus Energy and Power Systems > Distributed Generation Sustainable Development > Goals

Stochastic simulation of magnetically controlled convection in porous media with random porosity via Karhunen-Loève expansion and intrusive polynomial chaos expansion

Understanding and quantifying uncertainty factors are crucial for accurately predicting thermomagnetic convection phenomena. This study presented a mathematical model and algorithm framework for uncertainty analysis of thermomagnetic convection in porous media with random porosity. The proposed method combined Karhunen-Loève expansion and intrusive polynomial chaos expansion to represent the input random parameters and output response, respectively. The Galerkin projection method was employed to decouple the stochastic governing equations of thermomagnetic convection into deterministic governing equations that can be efficiently solved using the finite volume method. By solving the polynomial chaos expansion of the output response and employing the stochastic projection method to solve the associated decoupled governing equations, the temporal evolution and statistical characteristics of the output response were obtained. The study revealed that porosity uncertainty in the porous medium affects the thermomagnetic convection of paramagnetic fluid, exhibiting significant chaos effects. Monte Carlo simulations were performed to validate the accuracy of the proposed approach and demonstrate its computational efficiency compared to traditional Monte Carlo methods. This research provides valuable insights into the uncertainty analysis of thermomagnetic convection and offers a promising methodology for analyzing heat transfer in various porous media applications.

Theoretical and experimental study on lubrication and friction of slipper pair of valve distribution piston pump based on FVM-TRD coupling method

To study the dynamic characteristics of the slipper pair with the complex surface structure of the valve distribution piston pump, the Least Square Method was combined with the TRD(Trust Region Dogleg) optimization method, and then dynamically coupled with the FVM(Finite Volume Method) and introduced into the solution of the slipper pair lubrication model. Then the mathematical analytical model of lubrication and friction of single-support belt and multi-support belt slipper pair of the valve distribution piston pump based on the FVM-TRD coupling method was established. The lubrication performance of slipper pairs was analyzed by combining the proposed slipper overturning rate and Efficiency Reference Value. Finally, relevant experimental research was conducted. The results show that the oil film dynamic pressure effect of the slipper with multi-support belt is stronger. The influence laws of working condition parameters on the three types of slipper pairs is basically the same, and the slippers are more prone to overturning wear in the low pressure area. Besides, the anti-overturning performance of S3 slipper is the best, S1 is slightly worse, and S2 is the worst. However, the power efficiency of S3 slipper is the lowest, followed by S2, and S1 is the highest. The accuracy of theoretical calculation is verified by experiments.The research results lay a theoretical and technical foundation for the optimal design of slipper pairs of valve distribution piston pump.

Modeling of assessment criteria of physical fitness of sports radio direction finders at the stage of specialized basic training

The purpose of the article: to determine the dynamics of constructed mathematical models of indicators of physical fitness of sports radio direction finders at the stage of specialized basic training based on the results of pedagogical control. The methodology of the process of developing evaluation criteria of physical fitness of athletes from radio direction finding is based on the use of mathematical models for analysis, description and forecasting of their parameters. The process of modeling the evaluation criteria of physical fitness included the following stages: definition of the goal and tasks; selection of motor tests; choice of methods; building a model; checking its effectiveness; optimization and correction of the model; terms of use. The scientific novelty consists in the development of means and methods of physical training, the determination of data on the dynamics of the development of general and special motor qualities, the construction of models for evaluating the results of motor testing of young radio direction finders based on regression analysis, which allows modeling the relationship between the dependent variable (Y – evaluation points on the DCOLIFK scale and independent variables (X₁, X₂, ... Xn – quantitative results of motor testing). Assessment of the adequacy of the built models during the pedagogical experiment was carried out according to the coefficient of determination (R2). Conclusion. Constructed models of the dependence of the score on the DCOLIFK scale and the quantitative indicators of motor testing allowed for their interpretation, which includes the consideration of each regression coefficient and the assessment of their influence on the dependent variable, the optimization of the constructed models was carried out in order to determine the influence of each independent variable on Y, forecasting the level physical training based on the results of motor testing.

Investigation of recent advances related to AI in mathematics education

The integration of mathematics and Artificial Intelligence (AI) is an immensely promising field, making a comprehensive overview in this domain highly essential. This article provides an overview of two methodologies: Sofia and ITS. Sofia is an AI mathematical analysis model that engages in dialogues with multiple components and robots, performing calculations by processing sentences through Unix file system paths. ITS, on the other hand, is an intelligent tutoring system, comprising domain, student, tutor, and interface components, facilitating interactions within the teaching and learning processes. This article intricately delineates the implementation and functionalities of these two methodologies, encompassing their constituents, applications, and limitations. The applications of these methodologies are far-reaching in both mathematics and AI domains. For instance, in the realm of education, ITS can furnish personalized learning experiences by offering feedback and suggestions tailored to students' knowledge and behaviors. In the arena of mathematical analysis, Sofia can aid in analyzing and solving intricate mathematical problems, rendering support and guidance to students and professionals alike. In conclusion, this article offers a comprehensive overview of the amalgamation of mathematics and AI, introducing the implementations and applications of the Sofia and ITS methodologies. These approaches hold substantial potential within the fields of mathematics and AI, providing valuable references for future research and applications.

Sensory omics combined with mathematical modeling for integrated analysis of retronasal Muscat flavor in table grapes

This study focused on analyzing the aroma formation mechanism of retronasal muscat flavor in table grapes. The sensory characteristics and fragrance components of table grape juice with different intensities of Muscat were investigated using GC-Quadrupole-MS, quantitative descriptive analysis and three-alternate forced choice. Free monoterpenoids were the main contributors to the retronasal Muscat flavor. The contribution of Muscat compounds to this flavor was quantified by Stevens coefficient, the most and the least sensitive compounds to concentration changes were citronellol and linalool, respectively. To predict the Muscat flavor intensity by mathematical modeling, established a model between Muscat flavor intensity and monoterpenoids concentration, and an optimal partial least squares regression model with a linear relationship between natural logarithms was obtained. These findings provide reference for understanding the formation mechanism of specific aromas in fruits and provide a basis for the development and quality control of processed products such as Muscat flavor grape juice.

Mathematical Modeling for Non-Linear Behaviorial Analysis of Job Embeddedness on Organization with Improved Statistical Tools

This research endeavors to enhance our understanding of job embeddedness within organizations by employing advanced mathematical modeling and statistical tools to analyze its non-linear behavioral dynamics. Job embeddedness refers to the extent to which an individual feels deeply connected to their job, colleagues, and the organization, which has significant implications for employee retention, performance, and organizational success. Our study applies cutting-edge statistical techniques, such as nonlinear regression models, machine learning algorithms, and network analysis, to decipher the complex interplay of factors that contribute to job embeddedness. By examining various intrinsic and extrinsic factors, including job satisfaction, organizational culture, social networks, and employee engagement, our mathematical models aim to provide a comprehensive perspective on the phenomenon. Through a rigorous analysis of large-scale organizational datasets, we uncover hidden patterns, nonlinear relationships, and critical tipping points that influence job embeddedness. This research not only contributes to a deeper theoretical understanding of job embeddedness but also offers practical insights for organizational leaders and human resource professionals to design targeted strategies for fostering employee commitment and reducing turnover. Ultimately, our mathematical modeling approach improves the accuracy of predicting and managing job embeddedness within organizations, thereby assisting businesses in creating more engaged, satisfied, and embedded workforces.

Design, Analysis, and Optimization of Off-Highway Rear Dump Truck Chassis Frame Rail Profile Using Design Exploration and Finite Element Analysis Technique

<div>During mining material hauling, the chassis frame structure of rear dump trucks is subjected to fatigue loading due to uneven road conditions. This loading often leads to crack propagation in the frame rails, necessitating the determination of stresses in the critical zone during the design stage to ensure structural integrity. In this study, a computer-aided engineering (CAE) methodology is employed to size and select the rectangular profile cross section of the chassis frame rail. A detailed design investigation of the chassis frame is conducted to assess its load resistance, structural flexibility, and weld joint fatigue life under critical stresses arising from combined bending and torsion loads. The optimization process aims to determine the optimal rail size and material thickness, striking a balance between minimizing mass and maximizing structural reliability. By achieving this, the risk of major structural failures during the transportation of large payloads can be significantly reduced. To address the demand for extended structural life and reduced chassis frame weight, the frame rail cross section is optimized using a multi-objective genetic algorithm (MOGA) implemented within the ANSYS software package. This optimization process is facilitated by utilizing design exploration studies and finite element analysis (FEA) techniques to understand how stress affects the chassis frame of a vehicle when it is subjected to combined bending and torsion load case. To do this, the research study used a combination of analytical calculations, mathematical modeling, and design exploration studies.</div> <div>The research findings highlight the effectiveness of combining empirical approaches with modern CAE tools, enabling engineers to design and analyze complex structures with optimized sizes and weights suitable for off-highway mining applications.</div> <div>Through the utilization of this integrated approach, significant advancements can be made in enhancing the structural performance and efficiency of chassis frame structures in the demanding off-highway mining industry.</div>