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To model advanced 3-D forming strategies for paper materials, the effects of environmental conditions on the mechanical behavior must be quantitatively and qualitatively understood. A tensile test method has been created, verified, and implemented to test paper at various moisture content and temperature levels. Testing results for one type of paper for moisture contents from 6.9 to 13.8 percent and temperatures from 23 to 168 degrees Celsius are presented and discussed. Coupled moisture and temperature effects have been discovered for maximum stress. Uncoupled effects have been discovered for elastic modulus, tangent modulus, hardening modulus, strain at break, tensile energy absorption (TEA), and approximate plastic strain. A hyperbolic tangent function is also utilized which captures the entire one-dimensional stress-strain response of paper. The effects of moisture and temperature on the three coefficients in the hyperbolic tangent function may be assumed to be uncoupled, which may simplify the development of moisture- and temperature-dependent constitutive models. All parameters were affected by both moisture and temperature with the exception of TEA, which was found to only be significantly dependent on temperature. [ABSTRACT FROM AUTHOR]

The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revised and improved versions of the top papers from the workshop on Mathematical Modeling and Problem Solving at PDPTA'23, the 29th International Conference on Parallel and Distributed Processing Techniques and Applications. Covering fundamental research in matrix operations and heuristic searches to real-world applications in computer vision and drug discovery, the issue underscores the crucial role of supercomputing and parallel and distributed computing infrastructure in research. Featuring nine key studies, this issue pushes forward computational technologies in mathematical modeling, refines techniques for analyzing images and time-series data, and introduces new methods in pharmaceutical and materials science, making significant contributions to these areas. [ABSTRACT FROM AUTHOR]

In the present paper, an improved mathematical model is developed based on a new refined sinusoidal shear deformation theory with only four unknown variables for static bending and dynamic analysis of functionally graded (FG) doubly-curved shell structures. The proposed higher-order shell theory yields an adequate distribution of the transverse shear strains through the thickness by satisfying the tensile-free boundary conditions at the top and bottom surfaces of the shell. The mechanical properties are supposed to change gradually through the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The shell equilibrium equations for this study are derived from Hamilton's variational principle and subsequently solved for simply supported boundary conditions by using the Navier solution methodology. However, this improved model is substantiated by several numerical results for the mechanical behavior of FG shell structures having different geometrical configurations, namely, cylindrical, spherical, hyperbolic paraboloid, and elliptical paraboloid shapes, which were compared, and successfully converged with the corresponding results found by alternative higher-order shear deformation models to validate the accuracy of the proposed theory. [ABSTRACT FROM AUTHOR]

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCozO2 (x ⩾ 0.8) (NMC) particles with poly(3,4-ethylenedioxythiophene) (PEDOT). The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion, and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport, promoting the lithium distribution across the secondary particles more homogeneously. Besides, the lower stiffness, higher ionic conductivity, and larger thickness of the coating layer improve the stress mitigation. This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels. [ABSTRACT FROM AUTHOR]

Nowadays, supply chain (SC) decentralised decision making is the most usual situation in SC operations planning. In this context, different companies can collaboratively plan to achieve a certain level of individual and SC performance. However in many cases, there is reluctance to collaborate because it is not known a priori which benefits will be reported. This paper aims to develop a mathematical programming-based methodology for the evaluation of different supply chain collaborative planning scenarios (MPM-SC-CP). It is assumed that different SC decision centres (DCs) make decisions based on mixed and integer linear programming models. Two main inputs feed the proposed MPM-SC-CP, a framework and associated methodology that support the integrated conceptual and analytical modeling of the SC-CP process in which several DCs make decisions according to spatio-temporal integration. Finally, an application to a real ceramic SC was conducted. [ABSTRACT FROM AUTHOR]

This paper proposes the Love Evolution Algorithm (LEA), a novel evolutionary algorithm inspired by the stimulus–value–role theory. The optimization process of the LEA includes three phases: stimulus, value, and role. Both partners evolve through these phases and benefit from them regardless of the outcome of the relationship. This inspiration is abstracted into mathematical models for global optimization. The efficiency of the LEA is validated through numerical experiments with CEC2017 benchmark functions, outperforming seven metaheuristic algorithms as evidenced by the Wilcoxon signed-rank test and the Friedman test. Further tests using the CEC2022 benchmark functions confirm the competitiveness of the LEA compared to seven state-of-the-art metaheuristics. Lastly, the study extends to real-world problems, demonstrating the performance of the LEA across eight diverse engineering problems. Source codes of the LEA are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/159101-love-evolution-algorithm. [ABSTRACT FROM AUTHOR]

This paper studies a mathematical model of the phase transition process as a moving boundary problem (MBP). An equation describing the temperature-dependent thermal conductivity and Robin-type boundary condition at the fixed boundary is used in the model. In order to solve the considered MBP, we propose an iterative-based Keller box method (KBM) for the numerical approximation and boundary immobilization method (BIM) to immobilize the moving boundary. In addition, KBM incorporates nonlinearities in thermal conductivity and boundary conditions. We study the stability and consistency and found out that the scheme is second-order accurate in both time and space. A specific case having a similarity solution has been considered to validate the numerical scheme. Our numerical results show that the KBM is in good agreement with the similarity solution. In addition, the rate of convergence of the KBM scheme is two. Different parameters and temperature-dependent thermal conductivity are studied to determine how these affect the position of the moving boundary. [ABSTRACT FROM AUTHOR]

The optimal construction of long-span ziplines represents a complex engineering and construction task, especially from a safety point of view. In contemporary literature and engineering practice, there are no appropriate theoretical bases, standards and recommendations directly related to this issue. The aim of this work is to try to define the appropriate theoretical and professional basis for the design of these devices. The paper describes the procedure for creating a mathematical model of a zipline, followed by experimental verification of the formed mathematical model on a particular zipline, and afterwards by an analysis of the influencing parameters. The beginning of the paper defines the theoretical background that is necessary for the mathematical model forming of descending a rider down a heavy rope that takes into account mechanical and aerodynamical resistances that occur during the descent, after which a description of formation of the model itself is given. The next part of the paper gives a detailed description of the zipline on which the measurements were made, and a complete description of the used measuring equipment. Then succeeding part contains measurement results, followed by verification of the mathematical model by comparing the measured and calculated values. In the end, the influence of relevant parameters are analyzed by using the mathematical model and adequate conclusions are drawn. [ABSTRACT FROM AUTHOR]

In this paper, the structural vibration control of short-period systems by a sliding model of a tuned liquid column damper (herein referred to as STLCD) is investigated from both theoretical and experimental points of view. The proposed STLCD is essentially composed of a U-tube container with liquid inside, which can slide on a linear guide rail and is connected to the structure by a spring-dashpot system. Unlike traditional fixed TLCDs, this type of arrangement allows the proposed STLCD to be tuned to short-period structural systems since the spring can be used for tuning while the dashpot provides additional damping. Details on the selection of the optimal design parameters of the STLCD are provided, and the validity of the introduced mathematical model is verified both in time and frequency domains through experimental tests conducted at the Laboratory of Experimental Dynamics at the University of Palermo, Italy. For the experimental tests, a scale model of an STLCD-controlled structure is considered, focusing on the reduction of the roof accelerations. Finally, for comparison purposes, the control performance of the proposed control strategy for the vibration suppression of stiff structures is evaluated by analyzing its structural responses in contrast with the corresponding uncontrolled structure under harmonic excitations. [ABSTRACT FROM AUTHOR]

Lighter-than-air (LTA) aerial vehicles such as airships and aerostats can be found in various strategic and commercial applications, primarily due to their capability to hover and stealth. The mathematical model of these vehicles helps in understanding their complex dynamics and designing and developing proper stabilisation systems for them. Stability derivatives have been used for developing mathematical models for heavier-than-air aerial vehicles since their introduction. This paper presents a methodology to develop a mathematical model of an aerostat based on stability derivatives. One of the major contributions of this study is the estimation of aerostat's added mass terms expressed as longitudinal stability derivatives due to acceleration of the longitudinal motion variables. A longitudinally decoupled linear mathematical model of a single-tethered aerostat using stability derivatives is investigated in this study. A computational fluid dynamics (CFD)-based analysis of the 3D model of the vehicle is used to obtain the stability derivatives. The methodology presented considers the aerostat and tether models separately before coupling them to create the full model. The stability derivative analysis is carried out using ANSYS Fluent, and the coupled tethered aerostat model is investigated using MATLAB 2020. The negative pitch angle of the aerostat is caused by the selection of the pitching centre as the aerostat centre of volume instead of the tether confluence point. The tension force on the tether, which is proportional to the wind velocity, and aerostat velocity components are found to be stabilised within 200–400 s. [ABSTRACT FROM AUTHOR]

Sustainability is an issue of worldwide concern. Twitter is one of the most popular social networks, which makes it particularly interesting for exploring opinions and characteristics related to issues of social preoccupation. This paper aims to gain a better understanding of the activity related to sustainability that takes place on twitter. In addition to building a mathematical model to identify account typologies (bot and human users), different behavioural patterns were detected using clustering analysis mainly in the mechanisms of posting tweets and retweets). The model took as explanatory variables, certain characteristics of the user's profile and her/his activity. A lexicon-based sentiment analysis in the period from 2006 to 2022 was also carried out in conjunction with a keyword study based on centrality metrics. We found that, in both bot and human users, messages showed mostly a positive sentiment. Bots had a higher percentage of neutral messages than human users. With respect to the used keywords certain commonalities but also slight differences between humans and bots were identified. [ABSTRACT FROM AUTHOR]

The Scott bond test method has been used extensively in the paper industry over the years as a means to assess the bond strength of paper. The method has been a subject of some controversy lately since it does not always correlate to the sensitivity of the material to fracture by delamination. To gain some further insight into which parameters govern the fracture process in a Scott bond test a simplified approach has been chosen in order to formulate an analytical mathematical/mechanical model of the test. The model is dynamic in the sense that inertia effects are included. The material model utilised is a simple cohesive theory that assumes a linear behaviour between stress and crack opening when the material has started to degrade. This choice of material model makes the mathematical model very nonlinear. In fact, a system of three coupled nonlinear second order partial differential equations have to be solved and adjusted to the correct initial conditions. The material parameters needed for the model are the elastic modulus in the thickness direction, the transverse shear (elastic) modulus, the tensile strength (in the thickness direction) and the fracture work (per unit area) for a delamination crack. To investigate the ability of the model, a Scott bond testing apparatus have been equipped with a piezoelectric load sensor. The load cell was mounted on the apparatus’ pendulum so that the load acting on the sample holder could be recorded during the whole impact stage. This was done for a number of different initial velocities of the pendulum and it is found that the model gives a fair prediction of the contact load. [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem modeling spherically symmetric tumor growth with angiogenesis and a periodic supply of nutrients. The mathematical model is a free boundary problem since the external radius of the tumor denoted by R (t) changes with time. The characteristic of this model is the consideration of both angiogenesis and periodic external nutrient supply. The cells inside the tumor absorb nutrient u (r , t) through blood vessels and attracts blood vessels at a rate proportional to α. Thus on the boundary, we have u r (r , t) + α (u (r , t) − ψ (t)) = 0 , r = R (t) , t > 0 , where ψ (t) is the nutrient concentration provided externally. Considering that the nutrient provided externally to the tumor are generally provided periodically, in this paper, we assume that ψ (t) is a periodic function. Sufficient conditions for a tumor to disappear are given. We investigate the existence, uniqueness, and stability of solutions. The results show that when the nutrient concentration exceeds a certain value and c is sufficiently small, the solutions of the model can be arbitrarily close to the unique periodic function as t → ∞ . [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem modeling spherically symmetric tumor growth with angiogenesis and a periodic supply of nutrients. The mathematical model is a free boundary problem since the external radius of the tumor denoted by R (t) changes with time. The characteristic of this model is the consideration of both angiogenesis and periodic external nutrient supply. The cells inside the tumor absorb nutrient u (r , t) through blood vessels and attracts blood vessels at a rate proportional to α. Thus on the boundary, we have u r (r , t) + α (u (r , t) − ψ (t)) = 0 , r = R (t) , t > 0 , where ψ (t) is the nutrient concentration provided externally. Considering that the nutrient provided externally to the tumor are generally provided periodically, in this paper, we assume that ψ (t) is a periodic function. Sufficient conditions for a tumor to disappear are given. We investigate the existence, uniqueness, and stability of solutions. The results show that when the nutrient concentration exceeds a certain value and c is sufficiently small, the solutions of the model can be arbitrarily close to the unique periodic function as t → ∞ . [ABSTRACT FROM AUTHOR]

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. While current methods can identify such equations, they often require extensive manual hyperparameter tuning, limiting their applicability. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques to smooth the signal, sparse regression to identify the relevant parameters, and bootstrap confidence intervals to quantify the uncertainty of the estimates. We evaluate our method on well-known ordinary differential equations with an ensemble of random initial conditions, time series of increasing length, and varying signal-to-noise ratios. Our algorithm consistently identifies three-dimensional systems, given moderately-sized time series and high levels of signal quality relative to background noise. By accurately discovering dynamical systems automatically, our methodology has the potential to impact the understanding of complex systems, especially in fields where data are abundant, but developing mathematical models demands considerable effort. Discovering nonlinear differential equations from empirical data is a significant challenge, often requiring manual parameter tuning. This paper introduces a machine learning method integrating denoising techniques, sparse regression, and bootstrap confidence intervals, which shows consistent accuracy in identifying 3D dynamical systems with moderate data size and high signal quality. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

The polyaneuploid cancer cell (PACC) state promotes cancer lethality by contributing to survival in extreme conditions and metastasis. Recent experimental evidence suggests that post-therapy PACC-derived recurrent populations display cross-resistance to classes of therapies with independent mechanisms of action. We hypothesize that this can occur through PACC memory, whereby cancer cells that have undergone a polyaneuploid transition (PAT) reenter the PACC state more quickly or have higher levels of innate resistance. In this paper, we build on our prior mathematical models of the eco-evolutionary dynamics of cells in the 2N+ and PACC states to investigate these two hypotheses. We show that although an increase in innate resistance is more effective at promoting cross-resistance, this trend can also be produced via PACC memory. We also find that resensitization of cells that acquire increased innate resistance through the PAT have a considerable impact on eco-evolutionary dynamics and extinction probabilities. This study, though theoretical in nature, can help inspire future experimentation to tease apart hypotheses surrounding how cross-resistance in structured cancer populations arises. [ABSTRACT FROM AUTHOR]

The presented work is a continuation of the development of a computational and experimental method for determining the thermophysical characteristics (TPC) of the stator coils of a generator operating with the use of the phenomenon of high-temperature superconductivity (HTSC). The paper considers algorithms for identifying heat transfer models in the composite material of the stator coil winding. Using the discovered thermophysical properties, it is planned to study the electrothermal interaction in a high-temperature superconductor before its transition to a superconducting state. There is a significant variety of methods for solving the problems of identifying mathematical models of heat transfer, in particular, of determining the thermophysical characteristics of composite materials. As a result of the analysis of alternative methods for solving the identification problem, the iterative regularization method is used in this work. [ABSTRACT FROM AUTHOR]

Cellular networks have been widely deployed and are under ever-growing pressure from increasing energy consumption. Identifying the spatio-temporal properties of network traffic is crucial to effectively manage large-scale cellular networks and to optimize energy control strategies. However, traditional methods need to construct complex mathematical models to describe the properties of traffic, making the process inefficient and not automatic. Recent methods based on deep learning techniques are unexplainable and untraceable. In this paper, we propose a novel modeling and analysis approach by applying the spatio-temporal model checking technique to the identification of network traffic properties. First, we model the spatial structure of the cellular network by a closure space and the temporal structure of network traffic by the Kripke structure. Second, we provide logical characterizations of the spatio-temporal properties of network traffic by suitable spatio-temporal logic of closure space (STLCS) formulas. Third, we use model checking algorithms to detect the spatio-temporal properties of network traffic and to visualize the results. The experiments are illustrated with the Milan network traffic dataset and indicate that our approach can automatically and effectively detect desirable spatio-temporal properties of cellular network traffic. [ABSTRACT FROM AUTHOR]

In this paper, we take the four-way shuttle system as the research object and establish the mathematical model of scheduling optimization based on the minimum time for the in/out operation optimization and path optimization scheduling problems of the four-way shuttle system. An improved genetic algorithm is used to solve the task planning, and an improved A* algorithm is used to solve the path optimization within the shelf level. The conflicts generated by the parallel operation of the four-way shuttle system are classified, and the improved A* algorithm based on the time window method is constructed for path optimization through the dynamic graph theory method to seek safe conflict-free paths. Through simulation example analysis, it is verified that the improved A* algorithm proposed in this paper has obvious optimization effect on the model of this paper. [ABSTRACT FROM AUTHOR]

The principal target of this work is to compute the optimal tilt angle (OTA) for Photovoltaic (PV) panels. To perform this task, comprehensive simulations are done starting from altering the tilt angle (TA) daily, to use one fixed TA for all the year. The mathematical models for extra-terrestrial radiation (ETR) of both horizontal and inclined surfaces are presented firstly. At a later stage, the optimization formulation for the maximizing the solar radiation (SR) is adapted, and then the daily, monthly, seasonally, half-yearly and optimal fixed TAs are obtained. Although, the daily OTA produces the maximum SR, it is costly and impractical. It is found that altering the TA twice a year at optimal values that are computed as 5° and 50° for Suez city, gives the best results that are very near to the daily altering of the OTA. The difference between the two methods is 1.56% which is very small. Also, the two OTAs has SR better than that of the fixed OTA which is 28° by 7.77%. Also, it is found that the yearly fixed OTA (28°) is nearly equal to the latitude angle of Suez city which is 30°. The two OTAs method of this paper is different from the commonly used method that suggests two TAs. The first TA is used for winter months which is obtained by adding 15° to the latitude angle while the second TA is obtained by subtracting 15° from the latitude angle for the summer months. This commonly used method produces lesser SR than the two OTAs method of this paper. The theoretical work has been proved by an experimental work on two PV systems constructed at 25° and 30° TAs. The results of the experimental work agree with the theoretical results. [ABSTRACT FROM AUTHOR]

Numerous studies on project scheduling only consider a single factor, which fails to reflect the actual environment of project operations. In light of this issue, the article synthesizes multiple perspectives and proposes a multi-skill resource-based multi-modal project scheduling problem (MRCMPSP). This problem is described, modeled, and solved using the resource capability matrix and other constraints to minimize the project duration. To effectively solve MRCMPSP and enrich scheduling algorithms, the paper selects the hybrid quantum algorithm (HQPSO) based on the quantum particle swarm algorithm (QPSO). The HQPSO introduces various improvements such as the JAYA optimization search to improve the algorithm's performance. In order to verify the generality, superiority, and effectiveness of the algorithm, independent operation comparison experiments and practical application experiments of the algorithm are designed based on different case sizes and resource quantities. The experimental results demonstrate that the proposed algorithm has superior convergence performance and solution accuracy and can provide an effective scheduling solution for real cases. Additionally, the article provides targeted management suggestions based on the research findings. Overall, this study contributes a novel mathematical model, solution algorithm, optimization strategies, and managerial insights, advancing the field of project management research. [ABSTRACT FROM AUTHOR]

An efficient finite difference approach is adopted to analyze the solution of a novel fractional-order mathematical model to control the co-circulation of double strains of dengue and COVID-19. The model is primarily built on a non-integer Caputo fractional derivative. The famous fixed-point theorem developed by Banach is employed to ensure that the solution of the formulated model exists and is ultimately unique. The model is examined for stability around the infection-free equilibrium point analysis, and it was observed that it is stable (asymptotically) when the maximum reproduction number is strictly below unity. Furthermore, global stability analysis of the disease-present equilibrium is conducted via the direct Lyapunov method. The non-standard finite difference (NSFD) approach is adopted to solve the formulated model. Furthermore, numerical experiments on the model reveal that the trajectories of the infected compartments converge to the disease-present equilibrium when the basic reproduction number ( R 0 ) is greater than one and disease-free equilibrium when the basic reproduction number is less than one respectively. This convergence is independent of the fractional orders and assumed initial conditions. The paper equally emphasized the outcome of altering the fractional orders, infection and recovery rates on the disease patterns. Similarly, we also remarked the importance of some key control measures to curtail the co-spread of double strains of dengue and COVID-19. [ABSTRACT FROM AUTHOR]

An efficient finite difference approach is adopted to analyze the solution of a novel fractional-order mathematical model to control the co-circulation of double strains of dengue and COVID-19. The model is primarily built on a non-integer Caputo fractional derivative. The famous fixed-point theorem developed by Banach is employed to ensure that the solution of the formulated model exists and is ultimately unique. The model is examined for stability around the infection-free equilibrium point analysis, and it was observed that it is stable (asymptotically) when the maximum reproduction number is strictly below unity. Furthermore, global stability analysis of the disease-present equilibrium is conducted via the direct Lyapunov method. The non-standard finite difference (NSFD) approach is adopted to solve the formulated model. Furthermore, numerical experiments on the model reveal that the trajectories of the infected compartments converge to the disease-present equilibrium when the basic reproduction number ( R 0 ) is greater than one and disease-free equilibrium when the basic reproduction number is less than one respectively. This convergence is independent of the fractional orders and assumed initial conditions. The paper equally emphasized the outcome of altering the fractional orders, infection and recovery rates on the disease patterns. Similarly, we also remarked the importance of some key control measures to curtail the co-spread of double strains of dengue and COVID-19. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier–Stokes–Darcy model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework. [ABSTRACT FROM AUTHOR]

Nowadays, with the increasing demands for quality and precision in microelectronic packaging, the study and prediction of droplet parameters before packaging have become increasingly important. This paper aims to derive a predictive formula for droplet volume dispensing to improve packaging quality, optimize process parameters, reduce resource waste, enhance process control, and enhance product quality and reliability. Based on the needle transfer method for ultra-microdroplet dispensing, a droplet dispensing device that meets packaging requirements is established, and precise control of droplet volume is achieved by changing the factors that affect droplet formation. The droplets obtained from experiments are analyzed using pixel extraction, and a numerical fitting method is employed to establish a droplet volume model. It is found that the pixel method is a practical approach for determining droplet volume, with an average deviation of approximately 1.85%. By conducting droplet dispensing experiments with varying initial distances, the smallest droplet volume achieved is 24.33 pL, and it is concluded that larger initial distances result in smaller droplet volumes and reduced droplet contact area. Based on the droplet dispensing experimental data obtained by varying the initial distance, mathematical predictive models for droplet volume and droplet contact area are derived. The results show that the average difference rate between predicted and actual volumes is 0.51%, and the average difference rate between predicted and actual contact areas is 0.56%. [ABSTRACT FROM AUTHOR]

Chemical graph theory is a well-established discipline within chemistry that employs discrete mathematics to represent the physical and biological characteristics of chemical substances. In the realm of chemical compounds, graph theory-based topological indices are commonly employed to depict their geometric structure. The main aim of this paper is to investigate the degree-based topological indices of dominating David derived networks (DDDN) and assess their effectiveness. DDDNs are widely used in analyzing the structural and functional characteristics of complex networks in various fields such as biology, social sciences, and computer science. We considered the FN*, M 2 ∗ , and HM N topological indices for DDDNs. Our computations' findings provide a clear understanding of the topology of networks that have received limited study. These computed indices exhibit a high level of accuracy when applied to the investigation of QSPRs and QSARs, as they demonstrate the strongest correlation with the acentric factor and entropy. [ABSTRACT FROM AUTHOR]

The polyaneuploid cancer cell (PACC) state promotes cancer lethality by contributing to survival in extreme conditions and metastasis. Recent experimental evidence suggests that post-therapy PACC-derived recurrent populations display cross-resistance to classes of therapies with independent mechanisms of action. We hypothesize that this can occur through PACC memory, whereby cancer cells that have undergone a polyaneuploid transition (PAT) reenter the PACC state more quickly or have higher levels of innate resistance. In this paper, we build on our prior mathematical models of the eco-evolutionary dynamics of cells in the 2N+ and PACC states to investigate these two hypotheses. We show that although an increase in innate resistance is more effective at promoting cross-resistance, this trend can also be produced via PACC memory. We also find that resensitization of cells that acquire increased innate resistance through the PAT have a considerable impact on eco-evolutionary dynamics and extinction probabilities. This study, though theoretical in nature, can help inspire future experimentation to tease apart hypotheses surrounding how cross-resistance in structured cancer populations arises. [ABSTRACT FROM AUTHOR]

This work is devoted to the development of a procedure for the calculation and experimental determination of the thermophysical characteristics of the stator coils of a generator operating using the phenomenon of high-temperature superconductivity. To realize the conditions close to operational ones, temperature regimes of cooling down the coil from 300 to 78 K with subsequent heating to 300 K were implemented during the experiment. The values of the thermophysical characteristics were calculated from the data of temperature measurements at the internal points of the samples. The paper presents a description of the experimental technique. [ABSTRACT FROM AUTHOR]

This paper discusses the results of profile lattice construction using an analytical method based on ovoid transformation. To implement the proposed mathematical model, an algorithm, and a package of applied subroutines (modules) based on the algorithm, were developed. This study presents basic original calculation dependencies. Analytical and constructive elaborations of the profile include the conversion of ovoid images into profile images, calculation of their geometric characteristics, construction of a midline, and determination of the maximum thickness of the profile, lattice, and interblade channel layout. The proposed mathematical model can be considered an independent system or a subsystem (software module) of computer-aided design. [ABSTRACT FROM AUTHOR]

This is a review on models for dynamic analyses of various drilling systems suitable for application in oil and gas industry. The rotary and also rotary–percussive drilling systems, vertical, horizontal and inclined, are physically and mathematically modeled. The basic physical model for analysis of the drilling system is the Timoshenko beam. Torsional, axial, transversal and combined vibrations of the drill string are considered. Special attention is given to bit–rock interaction models. Various mathematical expressions for bit–rock torque and force are suggested. Inclusion of these mathematical models in the drilling system consideration is expected in the future. In the paper advantages and disadvantages of drilling systems are also discussed. Finally, the aim of this review is to give direction for future research and improvement in drilling systems. [ABSTRACT FROM AUTHOR]

This study delves into the realm of solving Einstein's field equations within the framework of general relativity. In this paper, we present an exact solution derived through the vanishing complexity approach and offer a comparative analysis with the established embedding class one approach. This exploration sheds light on the efficacy and validity of these methods in generating solutions for Einstein's field equations. Our study involves a comprehensive exploration of several key parameters, encompassing thermodynamic factors, causality conditions, stability evaluations, as well as analyses of the mass function. Based on our findings, it can be suggested that the vanishing complexity approach could serve as a viable alternative method to the embedding class one approach for the derivation of exact solutions of Einstein's field equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier–Stokes–Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework. [ABSTRACT FROM AUTHOR]

There is a trend to deploy neural network on edge devices in recent years. While the mainstream of research often concerns with single edge device processing and edge-cloud two-layer neural network collaborative computing, in this paper, we propose partitioning multi-layer edge network for neural network collaborative computing. With the proposed method, sub-models of neural network are deployed on multi-layer edge devices along the communication path from end users to cloud. Firstly, we propose an optimal path selection method to form a neural network collaborative computing path with lowest communication overhead. Secondly, we establish a time-delay optimization mathematical model to evaluate the effects of different partitioning solutions. To find the optimal partition solution, an ordered elitist genetic algorithm (OEGA) is proposed. The experimental results show that, compared with traditional cloud computing, single-device edge computing and edge-cloud collaborative computing, the proposed multi-layer edge network collaborative computing has a smaller runtime delay with limited bandwidth resources, and because of the pipeline computing characteristics, the proposed method has a better response speed when processing large number of requests. Meanwhile, the OEGA algorithm has better performance than conventional methods, and the optimized partitioning method outperforms other methods like random and evenly partition. [ABSTRACT FROM AUTHOR]

The performance growth in processors has been continuing toward increasing the number of processing cores on the chip and scaling the feature size of transistors. However, in the nanoera, side effects of the scaling, such as induced heterogeneities in the performance, power, and soft error rate of identically designed cores, prevent the potential performance from being fully utilized. In this paper, we harness the mentioned side effects in shared-memory multicore processors with unknown workloads by a dynamic heuristic scheduling algorithm called HDSAP. HDSAP aims to maximize performance, i.e., the average response time, under power and reliability constraints in presence of induced heterogeneities. In this regard, we use a mathematical model to quantify task to core assignments based on performance variation. We also consider the variation in power to change selected cores when the power constraint is missed. To meet the reliability constraint, we use N-modular redundancy while being aware of the variation in the soft error rate of cores to prevent under/over reliability estimation. To evaluate HDSAP, we run SPLASH benchmark suite on Sniper and MACPat simulators. As a result, the response time of HDSAP reduces by 6%, 8%, and 25% in comparison with similar algorithms under the same power and reliability constraints. [ABSTRACT FROM AUTHOR]

Correlated shape features involving nearby objects often contain important anatomic information. However, it is difficult to capture shape information within and between objects for a joint analysis of multi-object complexes. This paper proposes (1) capturing between-object shape based on an explicit mathematical model called a linking structure, (2) capturing shape features that are invariant to rigid transformation using local affine frames and (3) capturing Correlation of Within- and Between-Object (CoWBO) shape features using a statistical method called NEUJIVE. The resulting correlated shape features give comprehensive understanding of multi-object complexes from various perspectives. First, these features explicitly account for the positional and geometric relations between objects that can be anatomically important. Second, the local affine frames give rise to rich interior geometric features that are invariant to global alignment. Third, the joint analysis of within- and between-object shape yields robust and useful features. To demonstrate the proposed methods, we classify individuals with autism and controls using the extracted shape features of two functionally related brain structures, the hippocampus and the caudate. We found that the CoWBO features give the best classification performance among various choices of shape features. Moreover, the group difference is statistically significant in the feature space formed by the proposed methods. [ABSTRACT FROM AUTHOR]

This paper describes the study of a problem of thermocapillary convection in a flat bounded region filled with liquid and gas in contact along the interfacial interface under weak evaporation. It is proposed to investigate the heat and mass transfer processes and the parameters of phase transitions during local heating using a two-sided mathematical model based on the Oberbeck–Boussinesq equations. The characteristics of mass transfer through a thermocapillary interface due to evaporation and vapor content in the gas layer are analyzed with account for the influence of the Soret and Dufour effects. The results of a numerical study of the evolution of the interface and unsteady flows in a cell are presented. The calculation of the main characteristics of the liquid — gas system and the position of the interface at each time is carried out using a specially developed numerical algorithm. The model presented in this study makes it possible to describe the formation of characteristic thermal and concentration structures and the transition modes of cellular convection with a complex configuration of flows in layers. [ABSTRACT FROM AUTHOR]

In this paper the formulation of hybrid-Trefftz displacement finite elements for transient problems in three-dimensional elastic media is derived. The mathematical model is derived from the classical theory of elasticity. The governing domain and boundary equations are discretized in time using a wavelet basis expansion to yield a series of spectral problems which only depend on space. Displacements are the main approximation in the domain of the element (displacement model) and tractions are approximated on the essential boundaries (hybrid formulation). The displacement trial functions are constrained to satisfy exactly the domain equations (Trefftz constraint), and consist of one family of compression waves and two families of shear waves. The problem is reduced to solving an algebraic system whose unknowns are the weights of the displacement bases. Strains and stresses are derived from the displacement approximations through the compatibility and elasticity equations. The formulation is implemented as a new module in FreeHyTE, an open-source and user-friendly Trefftz platform. Numerical tests have been carried out with the new 3D FreeHyTE module implemented with the functions derived in this paper and the results are satisfactory. [ABSTRACT FROM AUTHOR]

The pressure relief door (PRD) is a vital structure to ensure the safety and reliability of the engine. This paper established a zero-dimensional transient simulation mathematical model to study the plenum compartment pressure threshold and maximum opening angle effects on the nacelle pressure relief process under different opening modes. Then, a computational fluid dynamics model verified by experimental literature data was used to simulate the nacelle pressure relief process and to determine the influence of two different opening modes on the force and discharge characteristics of the PRD. The results of this study show that different opening modes strongly impact the nacelle pressure relief process. Reducing the nacelle compartment pressure threshold of the PRD opening can reduce the time required for the pressure relief process to reach the equilibrium stage. Reducing the maximum opening angle may increase the nacelle compartment pressure during the equilibrium stage. In addition, under the same nacelle compartment pressure thresholds and maximum opening angles, the pressure relief process under the vertical opening mode can reach a lower nacelle compartment pressure during the pressure relief equilibrium stage compared to that under the horizontal opening mode. Therefore, the vertical opening mode is better than the horizontal opening mode. This paper provides two lower calculation costs and high accuracy research models for studying the nacelle pressure relief process. [ABSTRACT FROM AUTHOR]

With the rapid development of precision micro-manufacturing technology, the connection and assembly processes of precision micro-devices have placed higher demands on the volume and precision of micro-dispensing technology. In the dispensing process, the adhesive dispensing volume is crucial to the bonding quality. In this paper, based on the analysis of the composition of critical contact force and the mechanism of action, a method was proposed to control the ultra-micro-adhesive dispensing volume at pL level. Firstly, a mathematical model describing the change of droplet size and critical contact force during the extrusion of adhesive was established, which provided a theoretical basis for analyzing the mapping relationship between contact force and adhesive dispensing volume. Then, the mathematical models describing the droplet initial volume, dispensing volume, and transfer ratio were derived. Based on this, a mechanism and method to control the volume of dispensing to the substrate by contact force control to trigger the liquid bridge pull-off action was developed. The critical contact force was detected in real time to determine the changing state of the process of adhesive contacting the substrate, and used as the basis for triggering the stretching stage of the liquid bridge, and then achieved the prediction and control of the adhesive dispensing volume. In this paper, a series of experimental studies were conducted on the method of controlling the adhesive dispensing volume through contact force by embedding a micro-force sensor with high resolution into the dispensing system. The experiments were conducted with the critical contact force in the range of 0.5–4.5 mN. The results showed that the increase of the critical contact force was approximately linear with the increase of the adhesive dispensing volume. The deviation rate of the dispensing volume under the same critical contact force was less than 1.7%, and the average deviation rate of the overall adhesive dispensing volume was about 0.6%, so it was basically possible to precisely control the adhesive dispensing volume at the pL level by changing the contact force. This study revealed the composition and variation mechanism of contact force, and the proposed method for controlling the adhesive dispensing volume have significant value and potential in the micro-assembly of viscous ultra-microfluids and other applications. [ABSTRACT FROM AUTHOR]

This paper presents a physical and mathematical model and the results of evaluation calculations of the process of gas release from structural materials located inside a nonpressurized instrument compartment (NPIC) of a high-orbital spacecraft. Also presented is a model of the dynamics of the pressure drop of the residual gas inside the NPIC, after passing through the active phase of the flight and entering the calculated orbit. It is shown that the main reason for the significant (2–3 week) duration of the process of gas-pressure reduction of an NPIC to a value that allows the inclusion of high-frequency and -voltage equipment is the process of gas evolution from structural and paintwork materials located inside the NPIC. The intensity of outgassing, in turn, depends on the diffusion processes of outgassing substances within the materials themselves. An analysis of the influence of the geometry of the ventilation openings on the duration of the decrease in pressure inside the NPIC to the required level indicated the insignificance of this influence. The physical and mathematical models presented in the paper make it possible to estimate the characteristic time for reducing the pressure inside the NPIC to the required level and, thereby, select the materials inside the NPIC in order to reduce the period of reaching the allowable pressure inside the NPIC. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established. [ABSTRACT FROM AUTHOR]

This paper is devoted to the guaranteeing estimation method with application to the calibration problem of a gyro unit. Mathematical models are constructed to describe the kinematics of the gyro unit on a test bench. The applicability limits and errors of the models are investigated. A numerical solution procedure is developed for guaranteeing estimation problems based on their reduction to l1-approximation problems. [ABSTRACT FROM AUTHOR]

Due to gravity, a change in the welding position will significantly affect the flow of the molten pool, thus affecting the weld bead shape. An all-position welding process of low-power pulsed laser-MAG (metal active gas) hybrid welding was proposed to improve the welding efficiency and quality of all-position welding. This paper used the response surface method (RSM) to develop the weld bead geometry mathematical model. The analysis of variance confirmed the significance and accuracy of the model. The results show that the models can accurately predict the weld geometry, percentage errors for any models are less than 8.1%. Then, the effects of welding parameters and welding position on weld width, weld reinforcement, and weld penetration were analyzed. Finally, the optimal welding parameters at five positions of 0°, 45°, 90°, 135°, and 180° were obtained by numerical optimization with RSM. The study results can provide a reference for applying laser-MAG hybrid welding in all-position welding. [ABSTRACT FROM AUTHOR]

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders. [ABSTRACT FROM AUTHOR]

The flexible and cost-effective service provided by cloud computing has led to the development of a vast array of applications in smart cities. Nevertheless, their traditional security approaches presented the concept of a static target for attacks, leading to an asymmetric situation between defenders and attackers. Adaptive cyber defense (ACD) has, therefore, recently emerged as a game-changer to reverse this asymmetry by reconfiguring the system according to the network scenario. Analyzing and quantifying the effectiveness of these ACDs are of high importance. Previous research on ACD analysis focused more on either studying the system properties using experiment-based approaches or on evaluating its effectiveness by different mathematical modeling approaches. However, little effort has been made to overcome the problems of isolated solutions. In this paper, we described the defensive process as a racing game between the attacker and the defender. On this basis, we conducted a thorough ACD effectiveness evaluation and suggested a comparison strategy using three methods, namely semi-Markov, stochastic reward net, and experimental methods. The obtained simulation results were approximate, and the error rate was less than 3.36% reflecting the reliability of the proposed methods. Based on the assessments, we finally summarized the features of these methods to specify and deduce different scenarios and their corresponding suitable evaluation method. [ABSTRACT FROM AUTHOR]

Electromagnetic clinching (EMC) is a high-speed connection technology that combines electromagnetic forming and mechanical clinching. The die structure significantly affects the mechanical properties of the joint. In this paper, an optimal method based on response surface methodology (RSM) and particle swarm optimization algorithm (PSO) is proposed to improve the mechanical properties of joints clinched by EMC. The mathematical models of die geometrical parameters and cross-sectional parameters of the joint are obtained by RSM and numerical simulation. Then, the die structure is optimized through PSO. Finally, the experiments are carried out using the optimized and standardized die. The results show small errors between the simulation and the experiment. The joint strength using a standardized die is 878 N, and energy absorption is 0.758 J. The joint strength using the optimized die is 1322 N, and energy absorption is 1.335 J. Compared with the standardized die, the joint strength and energy absorption of parts obtained by the optimized die are increased by 50.5% and 76.1%, respectively. [ABSTRACT FROM AUTHOR]

The present paper deals with the analytical study of Love-type wave propagation in a fiber-reinforced viscoelastic layer sandwiched between an orthotropic viscoelastic layer of finite thickness and an inhomogeneous viscoelastic half-space. A dispersion equation for Love-type wave propagation has been obtained using suitable boundary conditions. Some particular cases have also been calculated, and it is seen that the dispersion equation is reduced to the classical Love wave equation, which validates the present mathematical model. Numerical computations were carried out for involved parameters and illustrated with the help of graphs. The effects of viscoelastic parameters, thickness ratio, reinforced parameters, inhomogeneity parameters, and order of the depth variation in the dispersion curves are highlighted. The present study may be beneficial in geophysical applications and earthquake engineering to understand the nature of seismic wave propagation. [ABSTRACT FROM AUTHOR]

This paper proposes mathematical modelling of photovoltaic (PV) array under partial shading condition. The proposed mathematical modelling is capable of predicting the output characteristics of PV array of any dimension, made of any kind of PV modules, having any number of bypass diodes, and for any shading pattern (irradiance and temperature) by utilizing only the values of the parameters of PV module provided in the manufacturer's datasheets. Although the proposed modelling can be implemented by any software tool, in this paper, it has been implemented using MATLAB programming. The proposed modelling has been validated on two PV arrays ((i) PV array made of four WS-330 PV modules configured in SP configuration and (ii) PV array made of four HSTBF24265P PV modules configured in TCT configuration) for in total of five test cases to establish its robustness. The test cases cover situations ranging from the most probable to least probable shading scenarios. The results generated by MATLAB programming of the proposed equations of PV array under uniform irradiance condition and partial shading condition have been validated by the results obtained by MATLAB simulation. The proposed modelling has also been experimentally validated on the aforementioned PV arrays. [ABSTRACT FROM AUTHOR]

Wood chipping is a critical component part of many pulp and paper making processes. In order to study the damage mechanisms, when wood chips are created through the wood chipping process, it is crucial to have access to an experimental equipment in which chips can be produced under realistic conditions. In this paper, a laboratory chipper is presented, which has been developed to admit chipping at rates that can be varied in a large interval, i.e. at rates ranging from 0 to 50 m/s. The chipper also makes it possible to study e.g. the influence of different cutting angles on the chip geometry. The knife used to cut the chips is mounted on a knife holder, which is instrumented in such a way that forces in three orthogonal directions can be measured. One reason for measuring the forces acting on the knife during chipping is that the average force in the cutting direction will give information about the wear of the knife over time. Since the actual force and the measured force differ due to inertia effects, a simple mathematical model is developed and used to evaluate the force acting on the knife. The results from the force measurements are presented and it is concluded that the laboratory chipper is a versatile tool in the process of increasing the understanding of the chipping process. [ABSTRACT FROM AUTHOR]