Mathematical Model Research Articles

Mathematical Modeling and Analysis of the Freezing Process of Drainage Channels in Cold Region Tunnels

Mathematical Modeling and Analysis of the Freezing Process of Drainage Channels in Cold Region Tunnels

A mathematical model to study low-dose metronomic scheduling for chemotherapy

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient’s body.

A nonlocal photoacoustic effect with variable thermal conductivity of semiconductor material subjected to laser heat source

This study explores the behavior of laser-exposed photo-excited carriers, investigating the propagation of photoacoustic waves in the thermoelastic domain. It also delves into the theoretical generation of surface acoustic waves in semiconductors through photo-thermoelastic processes. The research considers the interaction between thermomechanical and acoustic waves in a nonlocal medium with temperature-dependent thermal conductivity. Unlike relying on electron–phonon or electron-hole thermalization processes, photoacoustic waves here result from thermoelastic stress induced by the laser-induced temperature increase. The investigation accounts for the optical, mechanical, and thermoelastic properties of nanoscale semiconductor materials. Predictions of photoacoustic signals are derived by solving a combined thermal diffusion issue and a thermoelastic problem, using Laplace and Fourier transforms in the mathematical model. Numerical solutions encompass various physical fields within the time domain using the inversion technique of Laplace and Fourier transforms, such as thermal, acoustic, mechanical, and carrier density diffusion. The study evaluates and compares the influences of thermal memory and thermal conductivity presenting visual representations.

Radiation Dose-Volume-Response Relationships for Adverse Events in Childhood Cancer Survivors: Introduction to the Scientific Issues in PENTEC

At its very core, radiation oncology involves a trade-off between the benefits and risks of exposing tumors and normal tissue to relatively high doses of ionizing radiation. This trade-off is particularly critical in childhood cancer survivors (CCS), in whom both benefits and risks can be hugely consequential due to the long life expectancy if the primary cancer is controlled. Estimating the normal tissue-related risks of a specific radiation therapy plan in an individual patient relies on predictive mathematical modeling of empirical data on adverse events. The Pediatric Normal-Tissue Effects in the Clinic (PENTEC) collaborative network was formed to summarize and, when possible, to synthesize dose-volume-response relationships for a range of adverse events incident in CCS based on the literature. Normal-tissue clinical radiation biology in children is particularly challenging for many reasons: (1) Childhood malignancies are relatively uncommon-constituting approximately 1% of new incident cancers in the United States-and biologically heterogeneous, leading to many small series in the literature and large variability within and between series. This creates challenges in synthesizing data across series. (2) CCS are at an elevated risk for a range of adverse health events that are not specific to radiation therapy. Thus, excess relative or absolute risk compared with a reference population becomes the appropriate metric. (3) Various study designs and quantities to express risk are found in the literature, and these are summarized. (4) Adverse effects in CCS often occur 30, 50, or more years after therapy. This limits the information content of series with even very extended follow-up, and lifetime risk estimates are typically extrapolations that become dependent on the mathematical model used. (5) The long latent period means that retrospective dosimetry is required, as individual computed tomography-based radiation therapy plans gradually became available after 1980. (6) Many individual patient-level factors affect outcomes, including age at exposure, attained age, lifestyle exposures, health behaviors, other treatment modalities, dose, fractionation, and dose distribution. (7) Prospective databases with individual patient-level data and radiation dosimetry are being built and will facilitate advances in dose-volume-response modeling. We discuss these challenges and attempts to overcome them in the setting of PENTEC.

Optimising power of PV module using modified MPPT for standalone load

The maximum power point tracking (MPPT) has been common terminology among the researchers for those who deal with solar energy. A lot of techniques involving MPPTs have been investigated, evolved and proposed by researchers. But those techniques have got some advantages and suffer from limitation to some extent. The gravity of limitations varies from case to case. In current work, it has been investigated the MPPT based Boost Converter without and with MPPT which is perturb and observe (P&O) type. After observing its limitation, this method of MPPT is modified so as to make it suitable for extracting the maximum power from PV unit at all different load conductance’s. In order to validate this concept, the mathematical model is developed using a MATLAB/Simulink environment and this Modified MPPT technique is implemented. The whole model is simulated and compared with conventional method. This concept is quite new and the proposed one exhibits better performance as compared to conventional methods.

Long-term performance analysis of operational efficiency of a grid-connected solar power plant under Mauritania climate

This work examines a solar power plant connected to the Nouakchott electricity grid in Mauritania. Operating since 2013, the 15 MWp plant's reliability and energy yield have been evaluated using a performance index. The assessment involves three phases. First, the plant's meteorological environment and technical indicators are presented. In the second phase, mathematical performance models specified by the International Energy Agency (IEA) are applied to calculate performance indices using data from the data acquisition system (SCADA). The third phase compares actual production data for 2015, 2017, and 2020 with results simulated for PVsyst for the same years. The obtained results are thoroughly analyzed to highlight relevant physical phenomena. The analysis focuses on the plant's 7-year operating period and its impact on performance indicators for electricity production fed into the grid. This study provides insights into the solar power plant's reliability and energy yield, aiding future operational enhancements. It underscores the importance of performance monitoring and assessment in optimizing solar power generation systems.

Drone direction estimation: phase method with two-channel direction finder

This scientific article presents a block diagram of a two-channel radio direction finder that effectively uses the phase method to determine the direction of the signal source. The main attention is paid to the mathematical model of the formation of the cardioid radiation pattern of biconical antennas, which have unique directivity characteristics. These features significantly affect the accuracy and reliability of the bearing determination process. The developed algorithm aims to accurately determine the direction of motion of an unmanned aerial vehicle, especially in the context of a two-channel radio receiver and a five-element antenna system. This antenna system provides unique capabilities for increased resolution and directional accuracy. The article also touches on the issue of software implementation of the developed algorithm, which is aimed at increasing the number of generated bearing estimates in conditions of limited time for observing an unmanned aerial vehicle. Thus, the proposed method is of interest in the field of precision direction finding in the context of small unmanned vehicles.

Survival modelling of infectious human norovirus and surrogates for high-pressure inactivation in strawberry puree

Berries contaminated with human norovirus (HuNoV) have been frequently identified as a cause of foodborne gastroenteritis. To prevent virus transmission while preserving sensory and quality parameters, non-thermal treatments, such as high-pressure processing (HPP), can be applied to the berries and products thereof. Here, strawberry purees contaminated with HuNoV genogroup I (GI.3[P13]) and II (GII.4 Sydney [P16]), along with murine norovirus (MNV) and Tulane virus (TV) serving as surrogates, were exposed to HPP at several pressure-time combinations. Virus inactivation was assessed by cell culture, including the novel human intestinal enteroids (HIE) model for HuNoVs. The infectivity results showed TV more resistant than MNV to HPP, as also confirmed by kinetic mathematical modelling. Results indicated that a holding pressure of 450 MPa and an exposure time of ≥5 min are reliable operational conditions for HPP process to successfully control viral contamination. In addition, the inactivation models deduced from MNV and TV viruses were challenged with experimental HuNoV GII.4 infectivity resulting in bias factors <1 for all treatment conditions. This finding validates the proposed models for the conservative estimation of HuNoV inactivation. Our work offers a blueprint for moving forward with inactivation studies using the HIE system, which provides useful practical information on optimum treatments for the best public health outcomes.

Speed control for traction motor of urban electrified train in field weakening region based on backstepping method

Tractor motors always operate in the speed region higher than rated speed, but is limited to the module of the stator current, stator voltage vectors. Additionally, mathematical model of traction motor has shown nonlinearity through the product of the state variables 𝑖𝑠𝑑, 𝑖𝑠𝑞 with the input variable 𝜔𝑠:𝜔𝑠𝑖𝑠𝑞, 𝜔𝑠𝑖𝑠𝑑. Therefore, this paper focuses on the study of speed control of traction motors in weakening field region while optimizing torque control, and choosing the backstepping method in designing speed–flux controller in order to solve the nonlinear structure. The simulation results of the responses: speed, torque, power, and flux performed on MATLAB/Simulink software with parameters collected from metro Nhon-Hanoi Station, Vietnam have proven the correctness in theoretical research.

A deterministic mathematical model with non-linear least squares method for investigating the transmission dynamics of lumpy skin disease

Lumpy skin disease (LSD) is an economically significant viral disease of cattle caused by the lumpy disease virus (LSDV) which is primarily spread mechanically by blood feeding vectors such as particular species in flies, mosquitoes and ticks. Despite efforts to control its spread, LSD has been expanding geographically, posing challenges for effective control measures. This study develops a Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model that incorporates cattle and vector populations to investigate LSD transmission dynamics. The model considers the waning rate of natural active immunity in recovered cattle, disease-induced mortality, and the biting rate. Using a standard dynamical system approach, we conducted a qualitative analysis of the model, defining the invariant region, establishing conditions for solution positivity, computing the basic reproduction number, and examining the stability of disease-free and endemic equilibria. We employ a non-linear least squares method for model calibration, fitting it to a synthetic dataset. We subsequently test it with actual infectious cases data. Results from the calibration and testing phases demonstrate the model’s validity and reliability for diverse settings. Local and global sensitivity analyses were conducted to determine the model’s robustness to parameter values. The biting rate emerged as the most significant parameter, followed by the probabilities of infection from either population and the recovery rate. Additionally, the waning rate of LSD infection-induced immunity gained positive significance in LSD prevalence from the beginning of the infectious period onward. Simulation results suggest reducing the biting rate as the most effective LSD control measure, which can be achieved by applying vector repellents in cattle farms/herds, thereby mitigating the disease’s prevalence in both cattle and vector populations and reducing the chances of infection from either population. Furthermore, measures aiming to boost LSD infection-induced immunity upon recovery are recommended to preserve the immune systems of the cattle population.

From Nash Q-learning to nash-MADDPG: Advancements in multiagent control for multiproduct flexible manufacturing systems

The emergence of flexible manufacturing systems (FMS) capable of processing multiple product types is a result of the growing demand for product customization and personalization. Such multiproduct systems are characterized by a higher level of uncertainty and variability when compared to traditional manufacturing systems. This paper proposes a Nash integrated multiagent deep deterministic policy gradient method (Nash-MADDPG) to control the mobile robots’ assignment in a multiproduct FMS to enable intelligent decision-making, interaction, and dynamic learning capabilities. A mathematical model of a multiproduct FMS from a previous study is described, and system dynamic property is characterized by permanent production loss (PPL). Then, by observing PPL of the system and market demand for each product type, the multi-agent control scheme is developed to assign mobile robots to load/unload various product types at various machines. First, a Nash game is developed among the mobile robots and to improve the cooperation, a collaboration cost is defined. This collaboration cost is then used in the reward function of the multiagent deep deterministic policy gradient (MADDPG) algorithm. Second, the actions are jointly defined based on the action values of MADDPG, and the mobile robots’ strategies in the Nash game, which update the environment to a new state. The performance of the proposed method is verified by comparing it with conventional Nash Q-learning, vanilla MADDPG, Q-learning based single agent reinforcement learning (SARL) and a first-come-first-serve (FCFS) based control. The results demonstrate that the multi-agent control scheme under the proposed Nash-MADDPG is effective in dealing with cooperative FMS environment that involves complicated dynamics and uncertainties.

NUMERICAL TREATMENT OF LINEAR VOLTERRA INTEGRO DIFFERENTIAL EQUATIONS USING VARIATIONAL ITERATION ALGORITHM WITH COLLOCATION

To numerically solve the linear Volterra integro-differential equation, this study employs fourth-kind Chebyshev polynomials and the variational iteration algorithm with collocation, which is a combination of the variational iteration strategy and collocation technique. By applying fourth-kind Chebyshev polynomials to the variational iteration method with collocation for solving Volterra integro-differential equations, mathematical problems with a broad range of multidisciplinary applications are addressed, and numerical techniques that produce more accurate and efficient results are developed. The recommended method is then used, and the fourth-kind Chebyshev polynomials generated for the given integro-differential equation serve as the trial functions for the approximation. As a result, the suggested method's significance probably goes beyond a particular equation or application, as it contributes to the larger field of mathematical modeling and numerical analysis. Research methods employing a variational iteration algorithm with collocation aim to provide general techniques that can be applied to a wide range of problems. Additionally, numerical examples were provided to highlight the applicability and dependability of the proposed methodology. The mathematical computations were carried out using the Maple 18 software.

An innovative dry-lab test rig for mechanical-hydraulic power take-off of wave energy conversion system

A dry-lab test rig is a powerful means to reduce costs in the design process of a wave energy conversion system (WECs). A dry-lab test rig technique allows the use of real components inside a simulation of a mathematical model. This paper presents the development of an innovative dry-lab test rig for the mechanicalhydraulic power take-off (MHPTO) unit of WECs. The development of a drylab test rig of MHPTO involves several processes, such as three-dimension (3D) modelling, component purchasing, structure fabrication, component installation, and operational testing. The developed dry-lab test rig consists of two main parts, such as the simulated wave emulator plant and the real MHPTO unit plant. The simulated wave emulator plant was developed in this test rig to replicate the interaction motion between the ocean wave motion and the wave absorber device. The developed dry-lab test rig was tested using five different irregular wave input conditions to ensure it could perform under the five different wave input conditions. The overall results demonstrate that the developed dry-lab test rig was successfully performed in all sea states. From the results, the profile of electrical power produced by the real MHPTO unit can be clearly obtained in each sea state.

DSFworld: A flexible and precise tool to analyze differential scanning fluorimetry data.

Differential scanning fluorimetry (DSF) is a method to determine the apparent melting temperature (Tma) of a purified protein. In DSF, the raw unfolding curves from which Tma is calculated vary widely in shape and complexity. However, the tools available for calculating Tma are only compatible with the simplest of DSF curves, hindering many otherwise straightforward applications of the technology. To overcome this limitation, we designed new mathematical models for Tma calculation that accommodate common forms of variation in DSF curves, including the number of transitions, the presence of high initial signal, and temperature-dependent signal decay. When tested these models against DSFbase, an open-source database of 6235 raw, real-life DSF curves, these models outperformed the existing standard approaches of sigmoid fitting and maximum of the first derivative. To make these models accessible, we created an open-source software and website, DSFworld (https://gestwickilab.shinyapps.io/dsfworld/). In addition to these improved fitting capabilities, DSFworld also includes features that overcome the practical limitations of many analysis workflows, including automatic reformatting of raw data exported from common qPCR instruments, labeling of data based on experimental variables, and flexible interactive plotting. We hope that DSFworld will enable more streamlined and accurate calculation of Tma values for DSF experiments.

A Mamdani fuzzy inference system with trapezoidal membership functions for investigating fishery production

Seas, marine ecosystems, and coastal regions are crucial components of our environment. Numerous scientific strategies have been adopted to boost fisheries and aquaculture productivity. This study proposes a fuzzy-logic-based model to produce fisheries in India, which ranks fourth worldwide for fisheries production. Five input variables, such as fish seed, export, post-harvesting, released fund, and temperature, are considered inputs, and the production of fisheries is taken as the output variable. A Mamdani-type fuzzy inference system with trapezoidal membership functions is prepared with 243 rules in the IF-THEN format. This mathematical model investigates the impacts of input parameters on the production of Indian fisheries. We fit the model with the real-world data and show that fish seed, export, released fund, and post-harvesting facilities positively impact fisheries production. However, a very high temperature is unsuitable for high production, even if all other parameters lie at their desired level.

A new optimal strategy for energy minimization in wireless sensor networks

In recent years, evolutionary and metaheuristic algorithms have emerged as crucial tools for optimization in the field of artificial intelligence. These algorithms have the potential to revolutionize various aspects of our lives by leveraging the multidisciplinary nature of wireless sensor networks (WSNs). This study aims to introduce genetic and simulated annealing algorithms as effective solutions for enhancing WSN performance. Our contribution entails two main phases. Firstly, we establish mathematical models and formulate objectives as a nonlinear constrained optimization problem. Secondly, we develop two algorithmic solutions to address the formulated optimization problem. The obtained results from multiple simulations demonstrate the positive impact of the proposed strategies on improving network performance in terms of energy consumption.

Mathematical model for IL-2-based cancer immunotherapy

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD4+ T cells, the relative death rate of CD8+ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD4+ T cells die out. However, in cases where CD4+ and CD8+ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD4+ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD4+ T cells, while high doses for a short period of time over several days transiently increase the population of CD8+ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.

BimodalPS: Causes and Corrections for Bimodal Multi-Path in Phase-Shifting Structured Light Scanners.

Structured light illumination is an active 3D scanning technique based on projecting and capturing a set of striped patterns and measuring the warping of the patterns as they reflect off a target object's surface. As designed, each pixel in the camera sees exactly one pixel from the projector; however, there are multi-path situations where a camera pixel sees light from multiple projector positions. In the case of bimodal multi-path, the camera pixel receives light from exactly two positions, which occurs along a step edge where the edge slices through a pixel which, therefore, sees both a foreground and background surface. In this paper, we present a general mathematical model to address this bimodal multi-path issue in a phase-shifting or so-called phase-measuring-profilometry scanner to measure the constructive and destructive interference between the two light paths, and by taking advantage of this interference, separate the paths and make two decoupled depth measurements. We validate our algorithm with both simulations and a number of challenging real-world scenarios, significantly outperforming the state-of-the-art methods.

Empowering geological data analysis with specialized software GIS modules

This research is devoted to the development of a geographic information system (GIS) for the analysis of geological data. It presents two specialized software modules designed to solve complex geological problems related to potential progress to disturbed masses and magnetotelluric sounding. These modules are integrated into the QGIS environment, offering efficient data processing and analysis capabilities, contributing to a deeper understanding of geological structures. The study presents a mathematical model for the problem of magnetotelluric sounding (MTS) and the continuation of potentials towards the perturbed masses, demonstrating numerical results using the developed algorithm. To confirm the accuracy of the model, a comparative analysis was carried out with empirical data for various chemical elements, which showed high accuracy, especially at shallow depths, with an error rate of less than 2%. In addition, the study highlights the importance of powerful GIS for the analysis and interpretation of geological data, including geochemical, geophysical and remote sensing information. The advanced functionality of QGIS simplifies data processing and visualization, which makes it an invaluable tool for geologists and researchers.

Experimental investigation of the small-scale prototype of the dew point water recovery system

The article presents experimental investigation of the Dew Point Water Recovery (DPWR) system designed for clean water recovery using the dew point cooling phenomenon. The technology is a novel distillation process which allows for highly efficient water recovery. It is a first distillation technology which allows for water distillation through direct contact with atmospheric air. The authors designed, built, and tested an original prototype of a laboratory-scale DPWR system to verify its basic operating principles and perform performance analysis. It was shown that on average 10 × 10−6 m3 of clean water could be recovered from each cubic meter of the supply air with an average GOR of 1.9. Although the operation of the DPWR system requires electricity to drive fans, pumps and other associated equipment, the actual driving force of the system is thermal energy. The average thermal energy demand of the DPWR system was 370 kWh/m3, and more than half of this energy was based on the thermodynamic potential of the supply air. Based on experimental data, the mathematical model of the DPWR system was verified and it was found that the average relative discrepancy in predicting air temperature did not exceed 8%, and in predicting air humidity: 5%. The conducted experiments confirmed that the proposed DPWR system is feasible and has the potential to fill the technological gap in terms of a low-energy and easily accessible water recovery method.