Mathematical Model Research Articles

The Inversion Method of Shale Gas Effective Fracture Network Volume Based on Flow Back Data—A Case Study of Southern Sichuan Basin Shale

Fracture network fracturing is pivotal for achieving the economical and efficient development of shale gas, with the connectivity among fracture networks playing a crucial role in reservoir stimulation effectiveness. However, flow back data that reflect fracture network connectivity information are often ignored, resulting in an inaccurate prediction of the effective fracture network volume (EFNV). The accurate calculation of the EFNV has become a key and difficult issue in the field of shale fracturing. For this reason, the accurate shale gas effective fracture network volume inversion method needs to be improved. Based on the flow back characteristics of fracturing fluids, a tree-shaped fractal fracture flow back mathematical model for inversion of EFNV was established and combined with fractal theory. A genetic algorithm workflow suitable for EFNV inversion of shale gas was constructed based on the flow back data after fracturing, and the fracture wells in southern Sichuan were used as an example to carry out the EFNV inversion. The reliability of the inversion model was verified by testing production, cumulative gas production, and microseismic results. The field application showed that the inversion method proposed in this paper can obtain tree-shaped fractal fracture network structure parameters, fracture system original pressure, matrix gas breakthrough pressure, fracture compressibility coefficient, reverse imbibition index, equivalent main fracture half length, and effective initial fracture volume (EIFV). The calculated results of the model belong to the same order of magnitude as those of the HD model and Alkouh model, and the model has stronger applicability. This research has important theoretical guiding significance and field application value for improving the accuracy of the EFNV calculation.

Evaluation of the Potential of a Biocoagulant Produced from Prickly Pear Peel Waste Valorization for Wastewater Treatment

This study evaluated the potential of a biocoagulant produced from prickly pear peel waste valorization and its use as a biocoagulant aid mixed with aluminum sulfate to remove turbidity in domestic wastewater. A central composite design (CCD) and a simplex lattice design (SLD) of two components (biocoagulant and aluminum sulfate) were developed to determine the optimal doses and pH of the biocoagulant and optimal mixing proportions. Both designs optimized the coagulation process from an analysis of variance to fit the experimental data to mathematical models and an optimization analysis to obtain the highest percentage of turbidity removal. The results showed that a water pH of 4 and a biocoagulant dose of 100 mg/L are optimal conditions for a turbidity removal of 76.1%. The potential decreases to 51.7% when the wastewater pH is maintained at 7.8 and a dose of 250 mg/L is used. This efficiency could be increased to 58.2% by using a mixture with optimal proportions of 30% biocoagulant and 70% aluminum sulfate. The experimental data were fitted to two quadratic models, estimating model prediction errors of 0.42% and 2.34%, respectively. Therefore, these results support the valorization of prickly pear peel waste to produce a biocoagulant, which could be used in acid and alkaline wastewater or as a biocoagulant aid mixed with aluminum sulfate.

A Methodology for Post-Necking Analysis in Isotropic Metals

Metallic materials are commonly characterized through tensile tests. For ductile metals, a consistent part of the test occurs after the necking onset. A first estimate of the post-necking behavior could be obtained by extrapolating the mathematical model that fits the pre-necking law. However, as well known, the accuracy of the predictions would not be guaranteed. Therefore, over the past decades many efforts have been devoted to dealing with the necking phenomenon. The most popular correction formula proposed by Bridgman is an analytical method based on the neck geometry. Despite being widely used, it may not be accurate at large strains due to the assumption of uniform distribution of the equivalent stress and equivalent strain in the specimen minimum cross-section. Starting from Bridgman’s idea and in order to overcome its limitations, the present paper develops an efficient method to calibrate the hardening law of isotropic metallic materials at large strains. The proposed method requires to record the outer contour of the necking zone during the test and to build a dataset of necking deformed shapes. Experimental quasi-static tensile tests were analyzed with the proposed approach, which appears promising when critically compared with other methods.

Combinatorial optimization methods for yarn dyeing planning

AbstractManaging yarn dyeing processes is one of the most challenging problems in the textile industry due to its computational complexity. This process combines characteristics of multidimensional knapsack, bin packing, and unrelated parallel machine scheduling problems. Multiple customer orders need to be combined as batches and assigned to different shifts of a limited number of machines. However, several practical factors such as physical attributes of customer orders, dyeing machine eligibility conditions like flotte, color type, chemical recipe, and volume capacity of dye make this problem significantly unique. Furthermore, alongside its economic aspects, minimizing the waste of natural resources during the machine changeover and energy are sustainability concerns of the problem. The contradictory nature of these two makes the planning problem multi-objective, which adds another complexity for planners. Hence, in this paper, we first propose a novel mathematical model for this scientifically highly challenging yet very practical problem from the textile industry. Then we propose Adaptive Large Neighbourhood Search (ALNS) algorithms to solve industrial-size instances of the problem. Our computational results show that the proposed algorithm provides near-optimal solutions in very short computational times. This paper provides significant contributions to flexible manufacturing research, including a mixed-integer programming model for a novel industrial problem, providing an effective and efficient adaptive large neighborhood search algorithm for delivering high-quality solutions quickly, and addressing the inefficiencies of manual scheduling in textile companies; reducing a time-consuming planning task from hours to minutes.

Diverse misinformation: impacts of human biases on detection of deepfakes on networks

Social media platforms often assume that users can self-correct against misinformation. However, social media users are not equally susceptible to all misinformation as their biases influence what types of misinformation might thrive and who might be at risk. We call “diverse misinformation” the complex relationships between human biases and demographics represented in misinformation. To investigate how users’ biases impact their susceptibility and their ability to correct each other, we analyze classification of deepfakes as a type of diverse misinformation. We chose deepfakes as a case study for three reasons: (1) their classification as misinformation is more objective; (2) we can control the demographics of the personas presented; (3) deepfakes are a real-world concern with associated harms that must be better understood. Our paper presents an observational survey (N = 2016) where participants are exposed to videos and asked questions about their attributes, not knowing some might be deepfakes. Our analysis investigates the extent to which different users are duped and which perceived demographics of deepfake personas tend to mislead. We find that accuracy varies by demographics, and participants are generally better at classifying videos that match them. We extrapolate from these results to understand the potential population-level impacts of these biases using a mathematical model of the interplay between diverse misinformation and crowd correction. Our model suggests that diverse contacts might provide “herd correction” where friends can protect each other. Altogether, human biases and the attributes of misinformation matter greatly, but having a diverse social group may help reduce susceptibility to misinformation.

Mathematical Models of Wound Healing and Tissue Regeneration: Insights with Numerical Solution

Understanding and forecasting the dynamics of wound healing processes heavily relies on mathematical modeling. Researchers can understand the complicated connections between cells, tissues, and biochemical components involved in wound healing by using mathematical equations and computational simulations. One such mathematical model that has seeks the interest of researchers in exploring wound healing phenomenon is Fisher’s equation. In the present work, the equation is solved using differential quadrature method with trigonometric tension B-spline (TTBs) basis function. The obtained results are compared with the results obtained from earlier studies and the results are presented in form of tables and figures. The implementation of the particle swarm optimization algorithm has removes the dilemma of unknown parameter involvement in the TTBs and hence resulted in a novel technique to find the numerical results.

Mathematical model of cancer with radiotherapy and chemotherapy treatments

The typical treatment for tumor involves a combination of radiation therapy and chemotherapy. In this study, we explore a mathematical model based on proliferation and diffusion, considering the impacts of both radiotherapeutic and chemotherapeutic treatments. The mathematical model is formulated as a system of partial differential equations, accompanied by initial, boundary, and free boundary conditions. Existence and uniqueness of this mathematical problem are obtained by developing an iteration algorithm in this paper.

A Model Validatory Approach in Determining Solar Panel Tilting Angles and Orientations at the Brikama Environment of The Gambia

This paper determines the solar panel optimal tilt angle and orientations at the Brikama environment of The Gambia. This was achieved by comparing mathematical model results with experimental data collected using a PV module (Model AP-120) manufactured by AstroPower, USA, and a single-axis tracker technology at the same location and months of the year. The experimental tilt angles obtained range from 5.1°-28.2° with an average angle of 14.8° while the mathematical model approach obtained the tilt angle to be within the range of 9.1°-22.3° with a mean value of 15.5°. The generated power analysis revealed that the peak power produced by the solar panel was recorded at an angle of 30° due South and the mean power gain from the orientation of the PV panel ranged from 3.6-48.1W. The mean power result suggests that, in comparison to a horizontal position, solar collecting efficiency is higher at the optimal tilt angle.

ESTIMATION OF THE POSTMORTEM INTERVAL BY CRANIOENCEPHALIC THERMOMETRY WITH A SINGLE DISCRETE DECREASE IN AMBIENT TEMPERATURE

Aim– development of a method implemented in the format of a computer program for determining the postmortem interval (PMI) by cranioencephalic temperature (CT) of a corpse under conditions of cooling with a single discrete decrease in ambient temperature. Material and methods. Analytical and finite element modeling of CT dynamics with a single discrete decrease in ambient temperature is performed. Results. A mathematical model has been developed for determining the PMI and the uncertainty of its estimates with a single discrete decrease in the ambient temperature. The values of the constants of the model equation and their variances are determined on the basis of finite element modeling of CT dynamics under the specified cooling conditions. The computational algorithm of the specified method for determining PMI and contraindications to its use are implemented in the C# language in the form of the Warm Bodies DSC program. Conclusion. The developed method and the application implementing it are recommended for use in forensic medical practice to determine the PMI with a single discrete decrease in ambient temperature.

A two-dimensional elastic contact problem with unilateral constraints

We consider a mathematical model which describes the equilibrium of two elastic membranes fixed on their boundary and attached to an adhesive body, say a glue. The variational formulation of the model is in a form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the model, and then we state and prove a convergence result, for which we provide the corresponding mechanical interpretation. Next, we consider two associated optimization problems for which we provide existence results. Finally, we the present numerical simulation which validates our convergence result. We end this paper with some concluding remarks and an Appendix, in which we present the preliminary material needed in this paper.

ДИНАМІЧНІ ВИПРОБУВАННЯ МОСТІВ. ЗАГАЛЬНИЙ ОГЛЯД МЕТОДІВ

Introduction. This article deals with the issue of relevance of dynamic testing of bridges in Ukraine, an overview of dynamic testing methods and the prospects for the development of this type of bridge testing. Problem statement. Monitoring the technical condition of bridges is an urgent problem for maintenance services and requires the use of the most advanced methods to quickly identify possible defects and damage in their structures. Dynamic testing is one of such methods, the development and implementation of which requires joint efforts of engineers and the scientific community. Objective. The main purpose of the article is to evaluate and analyze existing approaches to dynamic testing of bridges to diagnose their condition. This study aims to highlight the need to apply these methods to improve the reliability and safety of bridges, as well as to improve strategies for the maintenance and repair of bridge structures. Materials and methods. The material for the article is the experience of performing dynamic tests of bridges in Ukraine, including an example of testing a 420-meter-long reinforced concrete road bridge located in the Western Ukraine. The following research methods were used: analysis of data from scientific sources, analysis of regulatory documents, practical results of using the «Spectrum» software package, mathematical modeling, and general methods of theoretical research.

Complex fracture description and quasi-elastic energy development mathematical model for shale oil reservoirs

Reservoir numerical simulation is an important tool and method for the reasonable and efficient development of shale reservoirs. Accurate description of three-dimensional fractures in shale reservoir development is a necessary and sufficient condition to improve the accuracy and robustness of shale reservoir numerical simulation. This paper achieves precise characterization of complex fracture shapes and oil, gas and water flow by establishing an embedded discrete fracture model based on a non-structural network, which has advantages in the fine characterization of complex morphological fractures in the reservoir and the grid division of the reservoir. In the large matrix solution method, the Newton-Raphson method is used to linearize the nonlinear equations, the Jacobian matrix is ​​constructed, the ILU method is used for preprocessing, the conjugate gradient method is used to solve the linear equations, and the shale oil quasi-elasticity is established A fully implicit solution method for mathematical models of energy development.

Temperature control research for laser-induction hybrid strengthening process

ABSTRACT A comprehensive control methodology has been developed to address challenges such as temperature fluctuations, inconsistent depth penetration, and compositional integrity variations during laser-induction hybrid strengthening performed with consistent power parameters. This approach synergistically integrates a fuzzy controller and a decoupling compensator. In the initial part of this study, a temperature field model was utilized to investigate the effects of different process factors on temperature profiles. The analysis of step response data facilitated the development of mathematical models that delineate the correlation between the input factors and output responses. Subsequently, a decoupling compensation technique was used to reduce the coupling effects between temperature and its rate of change. A fuzzy controller was then developed to reduce the system's reliance on mathematical models, hence improving the accuracy of the control strategy. The results indicate that the application of fuzzy PI control and the implementation of decoupling compensation, the control strategy successfully improves the performance of the controller by minimizing parameter interactions. This strategy also incorporates real-time adjustment of PI parameters. Compared to conventional PI control, this method offers improved response speed and reduced overshoot. The laser-induction hybrid strengthening technique ensures superior temperature control, maintaining steady-state temperature precision within a 1% tolerance.

Performance Analysis of Feeding System in Sugar Mill with Consideration of Bagasse Jamming

Objectives: The sugar industry comprises various units, including feeding, crushing, evaporation, refining, and crystallization. The feeding system is the most crucial aspect of the sugar mill as the sugar-making process starts from here. So faults which occur here are divided into four categories minor, major, cease faults and walkout faults. This paper sets out to showcase a comprehensive analysis of the system's performance, availability, and profit. The study takes into account how minor, major, and cease faults can potentially impact the system's overall effectiveness. The findings of this research hold significant importance for sugar mills that prioritize optimal performance and profit. Methods: Primary data regarding various failures is collected from Ch. Devilal Co-Operative Sugar Mills Limited, Ahulana, Gohana. To find MTSF, Reliability, Availability, Profit etc., a mathematical model has been created. This model is based on the Semi-Markov process and Regenerative Point Technique and equations are drawn using exponential distribution and solved with Cremer’s rule and Laplace ­- Stieltjes transformation. Findings: A fault, Bagasse Jamming is considered a cease fault which occurs very frequently in the feeding system. Therefore, it is found that cease faults and major faults have more adverse impacts on the system's performance and availability than minor faults. MTSF, Availability and Profit are inversely proportional to these faults. When a major fault is 0.0035 and the cease fault is 0.0042, MTSF is nearly 100. So, to gain more profit we have to pay more attention to these faults. Novelty: The paper's results will aid in fault removal, increase availability, and optimize maintenance tactics in the sugar industry. Keywords: MTSF, Performance Analysis, Availability, Reliability, Minor, Major, Cease Faults

Geometric potential in nano/microelectromechanical systems: Part I Mathematical model

Geometric potential in nano/microelectromechanical systems: Part I Mathematical model

Investigation of design methodology for doubly-fed bearingless flux reversal motor

This article integrates the technology of bearingless motors with the basic theory of magnetic flux reverse motors, proposes a doubly fed bearingless magnetic flux reverse motor, and conducts research on its structural design, operating mechanism, electromagnetic performance analysis, mathematical model, control method, digital control system, and other aspects. The basic structure of a new type of doubly fed bearingless magnetic flux reverse motor is designed, and the principle of radial suspension force generation is studied. The performance related to torque and radial suspension force is analyzed. A mathematical model of torque and radial suspension force is established, including magnetic field distribution, no-load permanent magnet flux, and no-load back electromotive force. A doubly fed bearingless magnetic flux reverse motor system is designed and constructed, and inductance experiments are conducted.

Role of volatility and thermal properties in droplet spreading: a generalisation to Tanner's law

Droplet spreading is ubiquitous and plays a significant role in liquid-based energy systems, thermal management devices and microfluidics. While the spreading of non-volatile droplets is quantitatively understood, the spreading and flow transition in volatile droplets remains elusive due to the complexity added by interfacial phase change and non-equilibrium thermal transport. Here we show, using both mathematical modelling and experiments, that the wetting dynamics of volatile droplets can be scaled by the spatial–temporal interplay between capillary, evaporation and thermal Marangoni effects. We elucidate and quantify these complex interactions using phase diagrams based on systematic theoretical and experimental investigations. A spreading law of evaporative droplets is derived by extending Tanner's law (valid for non-volatile liquids) to a full range of liquids with saturation vapour pressure spanning from $10^1$ to $10^4$ Pa and on substrates with thermal conductivity from $10^{-1}$ to $10^3\ {\rm W}\ {\rm m}^{-1}\ {\rm K}^{-1}$ . In addition to its importance in fluid-based industries, the conclusions also enable a unifying explanation to a series of individual works including the criterion of flow reversal and the state of dynamic wetting, making it possible to control liquid transport in diverse application scenarios.

Coupling of neurons favors the bursting behavior and the predominance of the tripod gait

In nature, it has been observed that the dominant locomotor pattern of hexapod insects is often the tripod gait. Our analysis of a Central Pattern Generator (CPG) of the insect movement gives reasons for this dominance: the mathematical CPG model presents the tripod pattern with bursting dynamics in a parametric region where an isolated neuron has a simpler behavior. That is, we show how the coupling of small networks of neurons makes the system to continue having bursting dynamics even when an isolated neuron would be spiking. Moreover, in parametric regions where a neuron shows chaotic dynamics, the CPG exhibits a chaotic synchronization phenomenon: the chaotic tripod gait. In other words, coupling loves bursting… and tripod gait. The hyperchaotic phenomenon is also present and we locate regions where up to four Lyapunov exponents are positive.

Policy, practice, and prediction: model-based approaches to evaluating N. gonorrhoeae antibiotic susceptibility test uptake in Australia.

Antimicrobial resistance (AMR) represents a significant threat to global health with Neisseria gonorrhoea emerging as a key pathogen of concern. In Australia, the Australian Gonococcal Surveillance Program (AGSP) plays a critical role in monitoring resistance patterns. However, antibiotic susceptibility test (AST) uptake - a crucial component for effective resistance surveillance - remains to be a limiting factor. The study aims to model the processes involved in generating AST tests for N. gonorrhoea isolates within the Australian healthcare system and assess the potential impact of systematic and policy-level changes. Two models were developed. The first model was a mathematical stochastic health systems model (SHSM) and a Bayesian Belief Network (BBN) to simulate the clinician-patient dynamics influencing AST initiation. Key variables were identified through systematic literature review to inform the construction of both models. Scenario analyses were conducted with the modification of model parameters. The SHSM and BBN highlighted clinician education and the use of clinical support tools as effective strategies to improve AST. Scenario analysis further identified adherence to guidelines and changes in patient-level factors, such as persistence of symptoms and high-risk behaviours, as significant determinants. Both models supported the notion of mandated testing to achieve higher AST initiation rates but with considerations necessary regarding practicality, laboratory constraints, and culture failure rate. The study fundamentally demonstrates a novel approach to conceptualising the patient-clinician dynamic within AMR testing utilising a model-based approach. It suggests targeted interventions to educational, support tools, and legislative framework as feasible strategies to improve AST initiation rates. However, the research fundamentally highlights substantial research gaps in the underlying understanding of AMR.

Per-Subject Oculomotor Plant Mathematical Models and the Reliability of Their Parameters

The practical value of oculomotor plant mathematical models (OPMMs) has been demonstrated across various domains, including biometrics and eye movement prediction. To further enhance their utilization, new optimization approaches are commonly developed and introduced within the research community. In this study, we demonstrate a new integration of a previously developed per-subject optimization procedure for an Enderle OPMM and introduce methods to evaluate the reliability of OPMM parameters using the intraclass correlation coefficient (ICC) and Kendall's Coefficient of Concordance (KCC). We evaluated two per-subject OPMM models, Bahill and Enderle, using the 'GazeBase' eye movement dataset. The models differed in accuracy, expressed as the per-sample error in degrees of visual angle, based on the differences between the actual and predicted saccade trajectories. We found that some of the parameter estimates for both models were quite unreliable. We discuss the importance of addressing low-reliability issues and suggest methods to modify the models to enhance reliability and performance.