Mathematical Modeling Approach Research Articles

Propagation of solitary waves in origami-inspired metamaterials

We propose a design strategy for creating origami-like mechanical metamaterials with diverse non-linear mechanical properties and capable of remote actuation. The proposed triangulated cylindrical origami (TCO)-inspired metamaterials enable the highly desirable strain-softening/hardening and snap-through behaviors via a multi-material and highly deformable hinge design. Moreover, we couple these novel non-linear mechanical properties of the TCO origami-inspired metamaterials with the transformative ability of hard-magnetic active materials, allowing for untethered shape- and property-actuation in the developed metamaterials. We develop a mathematical modeling framework for the proposed TCO origami-inspired metamaterials, building on approximating the highly deformable hinges as a combination of longitudinal and rotational springs. We validate the accuracy of the developed mathematical modeling approach by comparing the analytically predicted compressive response of a unit cell structure with the corresponding numerical and experimental results. Using the developed mathematical modeling framework, we investigate the magnetic field-induced large deformation and superimposed solitary wave propagation in the TCO origami-inspired metamaterial system. We show that the proposed metamaterial allows us to tune the key characteristics of the enabled non-linear solitary waves, including their characteristic width and amplitude. The proposed design strategy for readily manufacturable origami-inspired metamaterial systems paves a novel path for practical engineering applications. Our studies also underscore the potential of magneto-mechanical interaction in the design of reconfigurable metamaterial systems with superior non-linear mechanical and elastic wave properties.

A Comparative Study on Various ANN Optimization Algorithms for Magnetorheological Elastomer Carbonyl Iron Particle Concentration Estimation

Estimation particle composition such as particle shape, size, and concentration are crucial prior to the fabrication process of magnetorheological elastomer (MRE) to avoid process repetition due to inaccurate formulation. Currently, most of MRE prediction model were purposely used to predict the rheological properties such as shear stress and dynamic modulus, known as forward model. Nonetheless, very few studies have been reported to be capable able of predicting particle composition particularly in MR materials, which known as inverse model. Therefore, this paper proposed a carbonyl iron particle (CIP) concentration based MRE prediction model using neural network algorithm. Neural network-based machine learning model is more approachable compared to conventional mathematical modelling approach due to easily identify trends and pattern while handling multi-variety data. Various optimization algorithms have been employed such as Adam, RMSprop, SGD, AdaGrad, and Nadam throughout the modelling process. As the results, given shear strain amplitude, magnetic flux density, storage modulus, and loss factor as model input, SGD gave the maximum prediction accuracy with 0.95 and 3.038 MPa of R2 and RMSE, respectively. Hence, this model can be the basis to the MRE material and devices development particularly as the tool to reduce costing and time consuming.

Assessing the impact of information-induced self-protection on Zika transmission: A mathematical modeling approach

Abstract As per the World Health Organization’s (WHO’s) suggestions, personal protection via adopting precautionary measures is one of the most effective control aspects to avoid Zika infection in the absence of suitable medical treatment. This personal protection further can be enhanced and explored by propagating information about disease prevalence. Therefore, in this study, we wish to see the effect of information on Zika transmission by formulating a compartmental mathematical model that quantifies the effect of an individual’s behavioral response as self-protection due to information. Furthermore, the basic reproduction number was calculated using the next-generation matrix technique. The model analysis was carried out to determine the local and global stability properties of equilibrium points. In addition, the model shows the occurrence of forward bifurcation when the reproduction number crosses unity. To understand the impact of various model parameters, we conducted a sensitivity analysis using both the normalized sensitivity index and the partial rank correlation coefficient methods. Moreover, we performed numerical simulations to assess the influence of important parameters on the model’s behavior for Zika prevalence. Our study accentuates that as information-induced self-protection increases, the prevalence of Zika infection will be at a very minimum level, and this observation is in line with WHO suggestions.

Assessing botanical compatibility in gin production: A mathematical model and network analysis approach

This study introduces a novel methodology for evaluating volatile-compound-based compatibility in 160 botanicals essential for gin production. It establishes a comprehensive botanical pairing system through network analysis, mathematical modeling, and indicator development. Key findings include the benefits of strategic botanical inclusions to recipes for compatibility improvement and a numerical compatibility assessment, revealing an average indicator of 1.78 across thirty validated gin recipes, with a significant threshold at 1.36 indicating superior compatibility. Additionally, two distinct indicators were formulated—one focusing on the percentage of shared compounds due to a specific botanical and another on the botanical’s representation in the recipe. A visual network analysis replaces the traditional aroma classification wheel, offering a comprehensive view of aromatic profiles. This research transforms gin formulation, supported by an extensive database and validated methods.

A Deep Neural Network-Fused Mathematical Modeling Approach for Reliable Flight Control of Small Unmanned Aerial Vehicles

In order to ensure the flight safety of small unmanned aerial vehicles (UAVs), a deep neural network-fused mathematical modeling approach is put up for reliable flight control of small UAVs. First, engine torque, thrust eccentricity and initial stop angle are taken into full consideration. A six-degree-of-freedom nonlinear model is formulated for small UAVs, concerning both ground taxiing and air flight status. Then, the model was linearized using the principle of small disturbances. The linearized model expressions for both ground taxiing and air flight were provided. In addition, radial basis function neural networks are used for online approximation to address the nonlinearity and uncertainty caused by changes in aircraft aerodynamic parameters. At the same time, to compensate for the external disturbance and the approximation error of the neural network, the system robustness is improved by selecting reasonable design parameters. This helps the whole flight control system obtain better tracking control performance. At last, some simulation experiments are carried out to evaluate the performance of the proposed mathematical modeling framework. The simulation results show that the proposal has stronger convergence ability, smaller prediction error, and better performance. Thus, proper proactivity can be acknowledged.

Novel mathematical modelling approaches and a new lower bounding scheme for multi-manned assembly line balancing problems with walking workers

This article suggests two novel mathematical modelling approaches and a lower bound calculation method for the number of workstations to balance multi-manned assembly lines with walking workers. While new formulations include more variables, they require fewer constraints than the existing one. The performances of all formulations are compared each other using benchmark test instances from the literature as well as the instances produced in this study. Comparison results showed that one of novel modelling approaches exhibits superior performance than the existing one in all aspects. It has been demonstrated that the proposed model can be applied to practical-sized instances of the problem. Also, the advantages of the proposed lower bounding scheme have been shown.

Hydrodynamic Modeling of Water Renewal Time and Potential Dissolved Matter Using TELEMAC: Applications to Shediac Bay (New Brunswick, Canada)

This study examines the hydrodynamic regimes in Shediac Bay, located in New Brunswick, Canada, with a focus on the breach in the Grande-Digue sand spit. The breach, which was developed in the mid-1980s, has raised concerns about its potential impacts on water renewal time and water quality in the inner bay. The aims of this study, using mathematical modeling approaches, were to evaluate the flow regimes passing through the breach and influences on the distribution of dissolved matter, providing insights into whether the breach should be allowed to naturally evolve or be artificially infilled to prevent contaminant stagnancy in the bay. The study considered three simulation scenarios to comprehend the water renewal time and the role of the breach in the environmental management of Shediac Bay. Results indicated that completely closing the breach would significantly increase the water renewal time in the inner bay, although the spatial extent of this increase is limited. However, the study identified some limitations, including the need to better define the concentration limit for considering water as renewed and the lack of consideration of dynamic factors such as wind and wave effects.

Exploring factors shaping antibiotic resistance patterns in Streptococcus pneumoniae during the 2020 COVID-19 pandemic.

Non-pharmaceutical interventions implemented to block SARS-CoV-2 transmission in early 2020 led to global reductions in the incidence of invasive pneumococcal disease (IPD). By contrast, most European countries reported an increase in antibiotic resistance among invasive Streptococcus pneumoniae isolates from 2019 to 2020, while an increasing number of studies reported stable pneumococcal carriage prevalence over the same period. To disentangle the impacts of the COVID-19 pandemic on pneumococcal epidemiology in the community setting, we propose a mathematical model formalizing simultaneous transmission of SARS-CoV-2 and antibiotic-sensitive and -resistant strains of S. pneumoniae. To test hypotheses underlying these trends five mechanisms were built into the model and examined: (1) a population-wide reduction of antibiotic prescriptions in the community, (2) lockdown effect on pneumococcal transmission, (3) a reduced risk of developing an IPD due to the absence of common respiratory viruses, (4) community azithromycin use in COVID-19 infected individuals, (5) and a longer carriage duration of antibiotic-resistant pneumococcal strains. Among 31 possible pandemic scenarios involving mechanisms individually or in combination, model simulations surprisingly identified only two scenarios that reproduced the reported trends in the general population. They included factors (1), (3), and (4). These scenarios replicated a nearly 50% reduction in annual IPD, and an increase in antibiotic resistance from 20% to 22%, all while maintaining a relatively stable pneumococcal carriage. Exploring further, higher SARS-CoV-2 R0 values and synergistic within-host virus-bacteria interaction mechanisms could have additionally contributed to the observed antibiotic resistance increase. Our work demonstrates the utility of the mathematical modeling approach in unraveling the complex effects of the COVID-19 pandemic responses on AMR dynamics.

Evaluation of Banana Sale Drying Performance Using a Tray Dryer with Mathematics Modeling

The drying process of Banana Sale involves two mathematical modeling approaches: the Newton model and the Henderson-Pabis model. The bananas are sliced and dried for 220 minutes at a temperature of 60°C with a drying rate of 4.5 m/s, and observations are made every 20 minutes. The research includes the analysis of moisture content, texture, and mass changes in banana chips. The modeling using the Newton and Henderson-Pabis models shows significant results. The drying rate coefficient (k) in both models is 0.00335, and the R2 values for both models are 0.98961 and 0.98967. These results indicate that both models are theoretically suitable for explaining the banana chips drying process, providing essential insights for understanding and optimizing this process.

Dynamic interactions of HSV-2 and HIV/AIDS: A mathematical modeling approach

To enhance my research, I would like to share my knowledge of Herpes simplex virus-2 (HSV-2) and HIV/AIDS (Acquired Immunodeficiency Syndrome) through a mathematical model. The study’s objective is to develop and examine the co-disease model for the modern era using mathematical modeling. Based on their modes of transmission, HSV-2 and HIV/AIDS are currently the leading causes of death from infectious and severe chronic diseases. Depending on the severity of HIV-2’s chronic disease, the model is divided into five phases: the first two HIV-2 stages and the remaining three HIV stages. Ordinary differential equations (ODEs) are arranged differently by each individual. Investigations into the mathematical equation model have revealed the points of equilibrium between the free and endemic models. A study of the developed model was conducted using the basic reproduction numbers [R0] of HSV-2 and HIV. The results demonstrate that if R0<1, the free equilibrium of disease is asymptotically locally stable. When R0>1, equilibrium endemic states are regarded as existing. Finally, MATLAB software was used to simulate the numerical equations of the model.

A Review of Research on Supply Chain Resilience Evaluation Indicator System and Evaluation Methods

In the context of intensifying globalization and escalating supply chain risks, the study of supply chain resilience has increasingly attracted significant scholarly attention globally. This paper provides a comprehensive review of the current research landscape on the definition of supply chain resilience, its evaluation metric systems, and assessment methodologies, with an in-depth analysis of pertinent literature from both domestic and international sources. The extant research reveals a lack of consensus on the precise definition of supply chain resilience. The predominant evaluation methodologies encompass index weighting methods, mathematical modeling approaches, and simulation techniques, each possessing distinct advantages and limitations. This paper underscores the necessity for future research to emphasize the contextual variability in supply chain complexity, bolster the inherent resilience of supply chains, and develop more objective and versatile evaluation models. Furthermore, the integration of emerging technologies such as big data, artificial intelligence, and blockchain is anticipated to play a pivotal role in enhancing supply chain resilience. The deployment of these advanced technologies not only offers novel avenues for theoretical exploration but also furnishes crucial tools and methodologies for practical supply chain management.

Mathematical Modeling Approach for Compact Objects: A New Metric Potential in the Spherically Symmetric System with Schwarzchild’s Coordinates

Mathematical Modeling Approach for Compact Objects: A New Metric Potential in the Spherically Symmetric System with Schwarzchild’s Coordinates

Integrated algorithm evaluation of a scalable digital power management innovation model

Maintaining contemporary society’s steady progress depends on the reliable functioning of the electrical grid. The complexity and nonlinearity of today’s power networks make it difficult to manage them using conventional mathematical modeling approaches. To get around these problems, researchers have started using machine learning methods, such transient stability evaluation that is based on machine learning. This research suggests a way to evaluate the transient stability of power systems by making use of the complex feature extraction capabilities of multi-layer perceptron (MLP) networks. Another approach is to suggest an ensemble learning model that uses the easy-ensemble undersampling technique to deal with power system transient stability data that is unbalanced. This method preserves unstable power system samples, performs multiple undersampling on stable samples and combines unstable and undersampling samples into multiple new balanced training sets for MLP model training. The final ensemble model is obtained through voting integration strategy. Through conducting a comparative evaluation of individual models and ensemble models, this paper discovers that the ensemble learning models exhibit superior sensitivity and accuracy in effectively addressing system instability.

The Development of a Transient Analysis Platform of Near-Critical CO2 Thermodynamic Systems via an Enthalpy-Based Implicit Continuous Eulerian Approach

This work presents the development and validation of an enthalpy-based implicit continuous Eulerian (ICE) solver, termed the near-critical ICE solver (NICES), for the analysis of near-critical CO2 thermodynamic systems. Traditional approaches relying on pressure and temperature as main inputs for the analysis have limitations in handling CO2 near the critical point, which exhibits unique characteristics and frequent phase changes. To overcome these limitations, this study proposes using enthalpy as a more suitable mathematical modeling approach. The NICES methodology employs the homogeneous equilibrium model and the Span and Wagner equations of state for CO2. This solver demonstrates improved numerical stability and computational speed compared to explicit calculation methods, as validated by frictionless heated pipe scenarios involving phase transitions near the critical point. The enthalpy-based NICES platform can predict thermohydraulics, including multiphase flows, without requiring specialized two-phase flow models.

Thiophene Stability in Photodynamic Therapy: A Mathematical Model Approach.

Thiophene-containing photosensitizers are gaining recognition for their role in photodynamic therapy (PDT). However, the inherent reactivity of the thiophene moiety toward singlet oxygen threatens the stability and efficiency of these photosensitizers. This study presents a novel mathematical model capable of predicting the reactivity of thiophene toward singlet oxygen in PDT, using Conceptual Density Functional Theory (CDFT) and genetic programming. The research combines advanced computational methods, including various DFT techniques and symbolic regression, and is validated with experimental data. The findings underscore the capacity of the model to classify photosensitizers based on their photodynamic efficiency and safety, particularly noting that photosensitizers with a constant rate 1000 times lower than that of unmodified thiophene retain their photodynamic performance without substantial singlet oxygen quenching. Additionally, the research offers insights into the impact of electronic effects on thiophene reactivity. Finally, this study significantly advances thiophene-based photosensitizer design, paving the way for therapeutic agents that achieve a desirable balance between efficiency and safety in PDT.

Mitochondria and MICOS- function and modeling.

An extensive review is presented on mitochondrial structure and function, mitochondrial proteins, the outer and inner membranes, cristae, the role of F1FO-ATP synthase, the mitochondrial contact site and cristae organizing system (MICOS), the sorting and assembly machinery morphology and function, and phospholipids, in particular cardiolipin. Aspects of mitochondrial regulation under physiological and pathological conditions are outlined, in particular the role of dysregulated MICOS protein subunit Mic60 in Parkinson's disease, the relations between mitochondrial quality control and proteins, and mitochondria assignaling organelles. A mathematical modeling approach of cristae and MICOS using mechanical beam theory is introduced and outlined. The proposed modeling is based on the premise that an optimization framework can be used for a better understanding of critical mitochondrial function and also to better map certain experiments and clinical interventions.

Wave Energy Conversion through Oscillating Water Columns: A Review

An oscillating water column (OWC) is designed for the extraction and conversion of wave energy into usable electrical power, rather than being a standalone renewable energy source. This review paper presents a comprehensive analysis of the mathematical modeling approaches employed in OWC systems, aiming to provide an in-depth understanding of the underlying principles and challenges associated with this innovative technology. A prominent classification within the realm of wave energy devices comprises OWC systems, which exhibit either fixed or floating configurations. OWC devices constitute a significant proportion of the wave energy converter prototypes currently operational offshore. Within an OWC system, a hollow structure, either permanently fixed or floating, extends below the water’s surface, creating an enclosed chamber where air is captured over the submerged inner free surface. This comprehensive study offers a thorough assessment of OWC technology in conjunction with air turbines. Additionally, the investigation delves into theoretical, computational, and experimental modeling techniques employed for analyzing OWC converters. Moreover, this review scrutinizes theoretical, computational, and experimental modeling methodologies, providing a holistic understanding of OWC converters. Ultimately, this work contributes a thorough assessment of OWC technology’s current state, accentuating its potential for efficient wave energy extraction and suggesting future research avenues.

Decoding cardiac reinnervation from cardiac autonomic markers: A mathematical model approach

BackgroundAlthough cardiac autonomic markers are commonly used to assess cardiac reinnervation in heart transplant patients (HTx), their relationship to the degree of sympathetic and vagal cardiac reinnervation is not well understood yet. To study this relationship, we applied a mathematical model of the cardiovascular system and its autonomic control. MethodsBy simulating varying levels of sympathetic and vagal efferent sinoatrial reinnervation, we analyzed the induced changes in cardiac autonomic markers including resting heart rate (HR), bradycardic and tachycardic HR response to Valsalva Maneuver, root mean square of successive differences between normal heartbeats (RMSSD), low-frequency- (LF), high-frequency- (HF), and total spectral power. ResultsThe results suggest that for assessment of vagal cardiac reinnervation levels >20%, resting HR (ρ=0.99, p<0.05), RMSSD (ρ=0.97, p<0.05), and total spectral power (ρ=0.96, p<0.05) may be equally suitable as the commonly used measure of HF-power (ρ=0.97, p<0.05). To assess sympathetic reinnervation, our results suggest that the LF/HF-ratio (ρ=0.87, p<0.05) and tachycardic response to Valsalva maneuver (ρ=0.9, p<0.05) may be more suitable than the regularly used measure of LF-power (ρ=0.77, p<0.05). ConclusionsOur model reports, for the first time, mechanistic relationships between the cardiac autonomic markers and the level of efferent autonomic sinoatrial reinnervation. The results indicate differences in the suitability of these markers to assess vagal and sympathetic reinnervation. Although our analysis is purely conceptual yet, the developed mathematical model can help to gain important insights into the genesis of cardiac autonomic markers and their relationship to efferent sinoatrial reinnervation and, thus, provide indications for clinical study evaluation.

A Model for Membrane Degradation Using a Gelatin Invadopodia Assay.

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.

Working with an instructional video on mathematical modeling: upper-secondary students’ perceived advantages and challenges

Many instructional videos in mathematics education target knowledge of procedures and algorithms. To design instructional videos that support students in a non-algorithmic domain, such as mathematical modeling, we developed a framework based on research on heuristic worked examples and instructional videos. Because students’ perceptions play an important role in whether they will engage with a learning resource, our research questions focus on the advantages and challenges students perceive when they work with an instructional video on mathematical modeling and solve a subsequent related modeling problem. Using a video based on the developed framework, we conducted an interview study with 14 pairs of upper-secondary students. The results of the qualitative text analysis showed that the perceived advantages and challenges were related to certain design features and to the processes of self-regulated learning with the video. The students experienced challenges regarding the video’s duration, the transfer to a subsequent related modeling problem, the absence of a teacher, and self-discipline. Hence, further learner support is necessary to guide the transition from working with a video to autonomous modeling, such as combining the video with strategic instruments and teacher support. In addition, interactive video features may be essential, as the students enjoyed how those features involved them in the process of watching the video. Overall, the results indicate that instructional videos are promising for providing heuristic worked examples, offering an innovative approach for teaching and learning mathematical modeling.