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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]

This manuscript delves into the examination of the stochastic fractional derivative of Drinfel'd-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear wave phenomena. [ABSTRACT FROM AUTHOR]

The Electronic Personal Health Record (EPHR) provides an innovative service for citizens and professionals to manage health data, promoting patient-centred care. It enhances communication between patients and physicians and improves accessibility to documents for remote medical information management. The study aims to assess the prevalence of awareness and acceptance of the EPHR in northern Italy and define determinants and barriers to its implementation. In 2022, a region-wide cross-sectional study was carried out through a paper-based and online survey shared among adult citizens. Univariable and multivariable regression models analysed the association between the outcome variables (knowledge and attitudes toward the EPHR) and selected independent variables. Overall, 1634 people were surveyed, and two-thirds were aware of the EPHR. Among those unaware of the EPHR, a high prevalence of specific socio-demographic groups, such as foreign-born individuals and those with lower educational levels, was highlighted. Multivariable regression models showed a positive association between being aware of the EPHR and educational level, health literacy, and perceived poor health status, whereas age was negatively associated. A higher knowledge of the EPHR was associated with a higher attitude towards the EPHR. The current analysis confirms a lack of awareness regarding the existence of the EPHR, especially among certain disadvantaged demographic groups. This should serve as a driving force for a powerful campaign tailored to specific categories of citizens for enhancing knowledge and usage of the EPHR. Involving professionals in promoting this tool is crucial for helping patients and managing health data. [ABSTRACT FROM AUTHOR]

Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. We use Latent Neural Ordinary Differential Equations (LNODEs) to learn the pressure-volume dynamics of a heart failure patient. Our surrogate model is trained from 400 simulations while accounting for 43 parameters describing cell-to-organ cardiac electromechanics and cardiovascular hemodynamics. LNODEs provide a compact representation of the 3D-0D model in a latent space by means of an Artificial Neural Network that retains only 3 hidden layers with 13 neurons per layer and allows for numerical simulations of cardiac function on a single processor. We employ LNODEs to perform global sensitivity analysis and parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor. [ABSTRACT FROM AUTHOR]

Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia in pulmonary circulation, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19. [ABSTRACT FROM AUTHOR]

We consider a mathematical model of the initiation and development of atherosclerosis in the early stage, defined in different domains. The existence of nonnegative weak solutions is proved via studying an auxiliary system with absolute value terms and applying a novel semi-discrete, operator splitting numerical scheme. Numerical simulations were performed in an idealized two-dimensional geometry in order to verify our assumptions in model building and theoretical analysis. The framework we developed can also be used for nonlinear reaction–diffusion systems defined in other different domains with more complex coupling conditions. [ABSTRACT FROM AUTHOR]

A novel method is presented for explicitly solving inhomogeneous initial-boundary-value problems (IBVPs) on the half-line for a well-known coupled system of evolution partial differential equations. The so-called double-diffusion model, which is based on a simple, yet general, inhomogeneous diffusion configuration, describes accurately several important physical and mechanical processes and thus emerges in miscellaneous applications, ranging from materials science, heat-mass transport and solid–fluid dynamics, to petroleum and chemical engineering. For instance, it appears in nanotechnology and its inhomogeneous version has recently appeared in the area of lithium-ion rechargeable batteries. Our approach is based on the extension of the unified transform (also called the Fokas method), so that it can be applied to systems of coupled equations. First, we derive formally effective solution representations and then justify a posteriori their validity rigorously. This includes the reconstruction of the prescribed initial and boundary conditions, which requires careful analysis of the various integral terms appearing in the formulae, proving that they converge in a strictly defined sense. The novel solution formulae are also utilized to rigorously deduce the solution's regularity properties near the boundaries of the spatiotemporal domain. In particular, we prove uniform convergence of the solution to the data, its rapid decay at infinity as well as its smoothness up to (and beyond) the boundary axes, provided certain data compatibility conditions at the quarter-plane corner are satisfied. As a sample of important applications of our analysis and investigation of the boundary behavior of the solution and its derivatives, we both prove a novel uniqueness theorem and construct a 'non-uniqueness counterexample'. These supplement the preceding 'constructive existence' result, within the framework of well-posedness. Moreover, one of the advantages of the unified transform is that it yields representations which are defined on contours in the complex Fourier λ -plane, which exhibit exponential decay for large values of λ . This important characteristic of the solutions is expected to allow for an efficient numerical evaluation; this is envisaged in future numerical-analytic investigations. The new formulae and the findings reported herein are also expected to find utility in the study of questions pertaining to well-posedness for nonlinear counterparts too. In addition, our rigorous approach can be extended to IBVPs for other significant models of mathematical physics and potentially also to higher-dimensional and variable-coefficient cases. [ABSTRACT FROM AUTHOR]

Starting from a mesoscopic description of cell migration and intraspecific interactions, we obtain by upscaling an effective reaction–diffusion–taxis equation for the cell population density involving spatial nonlocalities in the source term and biasing its motility and growth behavior according to environmental acidity. We prove global existence, uniqueness, and boundedness of a nonnegative solution to a simplified version of the coupled system describing cell and acidity dynamics. A 1D study of pattern formation is performed. Numerical simulations illustrate the qualitative behavior of solutions. [ABSTRACT FROM AUTHOR]

Protective antigen (PA) is a protein produced by Bacillus anthracis. It forms part of the anthrax toxin and is a key immunogen in US and UK anthrax vaccines. In this study, we have conducted experiments to quantify PA in the supernatants of cultures of B. anthracis Sterne strain, which is the strain used in the manufacture of the UK anthrax vaccine. Then, for the first time, we quantify PA production and degradation via mathematical modelling and Bayesian statistical techniques, making use of this new experimental data as well as two other independent published data sets. We propose a single mathematical model, in terms of delay differential equations (DDEs), which can explain the in vitro dynamics of all three data sets. Since we did not heat activate the B. anthracis spores prior to inoculation, germination occurred much slower in our experiments, allowing us to calibrate two additional parameters with respect to the other data sets. Our model is able to distinguish between natural PA decay and that triggered by bacteria via proteases. There is promising consistency between the different independent data sets for most of the parameter estimates. The quantitative characterisation of B. anthracis PA production and degradation obtained here will contribute towards the ambition to include a realistic description of toxin dynamics, the host immune response, and anti-toxin treatments in future mechanistic models of anthrax infection. [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 review thoroughly explores numerous key areas contributing to sustainable health and well-being. It encompasses precision medicine, eco-friendly healthcare practices, digital health technologies, holistic well-being approaches, community health promotion, global health protection, and data-driven public health techniques, providing a roadmap for a greater resilient healthcare future. The study evaluates the effectiveness of mathematical modelling in predicting COVID-19 transmission patterns and variants. It starts by providing an overview of COVID-19 and its variants, which include their origins and modes of transmission, then delves into prediction techniques and mathematical modelling, focusing especially on the use of differential equations-based modelling to understand disease progression. The objective is to enhance scientific information of COVID-19 variants and their effect on public health by providing insights, situation analyses, and policy recommendations derived from mathematical modelling. This comprehensive review focuses on serving as a useful resource for researchers, policymakers, and healthcare experts in addressing the pandemic and its evolving variants. [ABSTRACT FROM AUTHOR]

Introduction: The efficiency of The International Classification of Headache Disorders (ICHD-3) in reflecting patients' disability has recently been questioned. This prompts consideration that clinical features beyond pain may more accurately indicate the extent of underlying brain impairment than the mere frequency of headache days. Important cognitive dysfunctions and psychological impairment have been reported in burdensome cases of migraine, and the presence of these alterations has been associated with biological changes in the nervous system. This study aimed to compare migraine-related disability within a specific patient group, classified using ICHD-3 criteria or classified based on findings from a neuropsychological evaluation using machine learning. Additionally, a complementary voxel-based morphometry (VBM) comparison was conducted to explore potential neuroanatomical differences between the resulting groups. Patients and methods: The study included episodic and chronic migraine patients seeking consultation at a specialized headache department. A neuropsychological evaluation protocol, encompassing validated standardized tests for cognition, anxiety, depression, perceived stress, and headache-related impact (HIT-6) and disability (MIDAS), was administered. Results from this evaluation were input into an automated K-means clustering algorithm, with a predefined K=2 for comparative purposes. A supplementary Voxel-based Morphometry (VBM) evaluation was conducted to investigate neuroanatomical contrasts between the two distinct grouping configurations. Results: The study involved 111 participants, with 49 having chronic migraine and 62 having episodic migraine. Seventy-four patients were assigned to cluster one, and 37 patients were assigned to cluster two. Cluster two exhibited significantly higher levels of depression, anxiety, and perceived stress, and performed worse in alternating and focalized attention tests. Differences in HIT-6 and MIDAS scores between episodic and chronic migraine patients did not reach statistical significance (HIT-6: 64.39 (±7,31) vs 62.92 (±11,61); p= 0. 42 / MIDAS: 73.63 (±68,61) vs 84.33 (±63,62); p=0.40). In contrast, patients in cluster two exhibited significantly higher HIT-6 (62.32 (±10,11) vs 66.57 (±7,21); p=0.03) and MIDAS (68.69 (±62,58) vs 97.68 (±70,31); p=0.03) scores than patients in cluster one. Furthermore, significant differences in grey matter volume between the two clusters were noted, particularly involving the precuneus, while differences between chronic and episodic migraine patients did not withstand correction for multiple comparisons. Conclusions: The classification of migraine patients based on neuropsychological characteristics demonstrates a more effective separation of groups in terms of disability compared to categorizing them based on the chronic or episodic diagnosis of ICHD-3. These findings could reveal biological changes that might explain differences in treatment responses among apparently similar patients. [ABSTRACT FROM AUTHOR]

Since the discovery and the development of many technological instruments such as modern communication and communication technologies, digital media has served widely from the technology, and thus intersected quasi all life's domains, by providing news, information, and also discussions of quasi all subjects. In social sciences, for example, a major part of digital media sites discusses the well-being of both individuals, and societies, especially with the presence of many challenging phenomena like pandemics, wars, and financial crises. A major concern for QoL index for example resides in whether it is a uniform stable index or on the contrary a non-uniform index depending strongly and point-wisely on the time scale. This motivates the consideration of a non-uniform QoL index based on non-uniform wavelets to take into account the influence of many factors issued from political, social, environmental, economic effects according to the time scale. The model developed is tested on Saudi Arabia QoL index case. Recall that the Kingdom of Saudi Arabia has fixed many aims in its 2030-vision plan including the quality of life as a major goal. For example, the KSA worldwide NEOM project necessitates surely a supportive environment to be realized. The second purpose of our paper is also to study the impact of digital media such as social one on the QoL. Therefore, the data collected is basically issued from a set of conversations on social media platforms. To obtain a suitable time series, we developed a backward-forward non-uniform wavelet forecasting model to extend the data sample suitably. The whole time series is by the next applied for the QoL index dynamics and interpretations. The findings showed that effectively, the QoL index is never a stable single index on the whole year, but on the contrary, the dependence on the time scale is non-uniform. Moreover, to interpret suitably and for a correct policy, the non-uniform behavior should be considered adequately. [ABSTRACT FROM AUTHOR]

The study discussed the effects of different mineral incorporations and the curing time on the strength of modified magnesium phosphate cement (MPC) mortars through mechanical tests, mathematical model analysis and microstructure characterization. Fly ash (FA), silica fume (SF), and metakaolin (MK), which exhibit excellent durability and bonding properties, were used to modify the MPC. A quantitative relationship was established between the strength of modified MPC mortars and the mineral incorporation and curing time. First, the strength of each mineral-modified MPC mortar cured in air with different mineral incorporations and curing durations was evaluated. The strengths of MPC mortars containing 10% fly ash, 15% silica fume, and 10% metakaolin—which perform best in their incorporations—were compared to analyze the function of the three minerals. To establish the relationship between strength and mineral incorporation and curing time, three mathematical models, linear model, general nonlinear model, and data distribution shape nonlinear model (DDSNM), are commonly used for material property analysis based on statistics. DDSNM best describes the trend of strength change among the three models and the error is small for three minerals. Based on DDSNM, the influence of various minerals on the strength of MPC mortar was quantitatively evaluated by calculating the variable partial derivatives, and verified by scanning electron microscopy and X-ray diffraction. MK performs the best in improving the flexural strength performance of MPC, while SF performs the best in the compressive strength. FA-MPC has low sensitivity to dosage fluctuations and is easy to prepare. [ABSTRACT FROM AUTHOR]

Despite artificial intelligence (AI) technology progresses at unprecedented rate, our ability to translate these advancements into clinical value and adoption at the bedside remains comparatively limited. This paper reviews the current use of implementation outcomes in randomized controlled trials evaluating AI-based clinical decision support and found limited adoption. To advance trust and clinical adoption of AI, there is a need to bridge the gap between traditional quantitative metrics and implementation outcomes to better grasp the reasons behind the success or failure of AI systems and improve their translation into clinical value. [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]

Recently, industry, suppliers, distributors, academia, governments, and even consumers have focused on agri-food supply chain sustainability, environmental concerns, and managing energy and other resources essential for human survival. A supply chain model is a network of facilities and operations involving processes related to procuring raw materials from suppliers, producing and developing products on production sites, and ultimately distributing products at final consumption destinations. This study aims to propose a multi-stage model for sustainable supply chain network design. After an overview of operations research methods for sustainable supply chain network design, this study proposed a hybrid method based on multi-criteria decision-making (MCDM) and optimization techniques in operations research. The criteria extracted from library resources were selected using the Delphi method in the first step. Then, the criteria for selecting suppliers, transformer sites, and critical distribution hubs were weighted using the best–worst method. After weighing the criteria using the Complex Proportional Assessment of alternatives (COPRAS) technique, eight raw material suppliers, three potential transformer sites, and five main distribution hubs were selected for supply chain network design. The second part presented a multi-objective mixed-integer linear programming model to optimize the designed supply chain network. All three sustainability dimensions, i.e., economic, social, and environmental, were considered in developing the supply chain network. In the economic dimension, we sought to minimize total costs consisting of transportation costs, the cost of construction, maintenance, and closure of transformer and distribution sites, the cost of the capacity change of transformer and distribution sites, and the cost of production. In the social dimension, we sought to maximize the number of job opportunities created in each facility. We sought to minimize carbon and nitrous oxide footprints and water consumption in the environmental dimension. Furthermore, a fourth objective function was presented to minimize product delivery time in addition to the three dimensions of sustainability. Then the proposed mathematical programming model was solved using the LP-metric method, and the necessary comparisons were made between the results. Finally, agri-food industry executives were given a decision-making tool by generating Pareto frontier graphs. [ABSTRACT FROM AUTHOR]

In the traditional tobacco drying process, there is often a problem of uneven drying, which is closely related to drying conditions such as air velocity and temperature. To better understand the drying characteristics of tobacco, its drying kinetic performance were experimentally studied and predicted in this paper. In the drying experiment, the range of air temperature and velocity is 20–60℃ and 0.95–4.93 m/s, respectively. The results show that the effective diffusion coefficient increases with the increase of air temperature and decreases with the increase of air velocity. The effective moisture diffusivity( D eff ) ranges from 2.077 × 10–7 to 9.136 × 10–7 m2/s. Additionally, the activation energy (Ea) is between 14.292 and 21.032 kJ/mol according to Arrhenius law. Among the six commonly used empirical correlations, the logarithmic model has higher prediction accuracy, but it has a prediction deviation of more than 20% in the later stage of drying. Based on the logarithmic model and the two models, a new prediction model of tobacco drying characteristics was proposed with a maximum relative deviation error of less than 1%. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference and show that it converges to a stochastic process in distribution on the Skorokhod space. [ABSTRACT FROM AUTHOR]

The aerospace industry is pivotal for global transportation and is a cornerstone of high-tech industry growth in both developed and developing nations. Ensuring the integrity of aircraft products and components, maintenance, repair, and overhaul (MRO) operations is critical to the sector's success. This paper presents a linear programming model for scheduling aircraft C-check and D-check maintenance operations with multiple component treatment options: replacement, repair, and remanufacturing. Risk of component failure before the next maintenance is integrated into the model. The objective is to minimize maintenance cost while adhering to safety standards. The model also incorporates allocation of maintenance resources including labor and machinery capacities. Scenario analyses are conducted to assess varying parameters such as resource availability, unplanned maintenance costs, and penalty on the model solutions. The potential for remanufacturing to reduce maintenance expenses in MRO operations is evaluated. The main contribution of this work lies in its novel approach to integrating risk assessment with resource optimization in MRO scheduling with remanufacturing and in providing a comprehensive framework to enhance decision-making for MRO maintenance operations. [ABSTRACT FROM AUTHOR]

Purpose: The mounted stationary sensor on the ring casing has become a widely accepted way to monitor the planetary gear condition and one challenging aspect of this method is the modulation effect caused by the moving planet gears. It is valuable to study the modulation effect caused by the moving planet gears. Method: Different window functions have been proposed to model this modulation phenomenon and there are several drawbacks: the selection of the window function parameters is often arbitrary and subjective instead of basing on the planetary gear physical parameter; the current window function is hard to reflect the impact from the ring gear boundary conditions. Therefore, this paper simulated this modulation phenomenon as moving load dynamic problem to overcome these drawbacks, where the ring casing has been modelled as an axisymmetric flexible structure and the internal meshing forces have been modelled as spatially varying moving loads. Based on the improved hamming window function, this paper related the window function parameters with the planetary gear physical properties and operation conditions and then, quantified the modulation effect with the consideration of moving load speed as well as the ring gear boundary condition. Results: For the planetary gear carrier arm rotation speed, the result suggested that the moving speed mainly affect the parameter β and the corresponding value showed a nonlinear decreasing trend when the moving speed increased. For the ring gear rim thickness, similarly, parameter β increased significantly with the increase of the rim value. For the radial support stiffness, parameter β has also been affected most and it shows a decreasing trend when the support stiffness increased. For the sensor location, both parameter α and β shows a periodical change around the ring casing. Conclusion: The results suggested that both parameters have been impacted by the rotation speed and boundary conditions, among which parameter β has been impacted most. [ABSTRACT FROM AUTHOR]

Hybrid ion exchange (IX) and biological processes have been developed for various water and wastewater treatment applications. These hybrid systems integrate multiple physical, chemical, biological, hydrodynamics, and substrate transport processes to improve the treatment efficiencies and system stability. The mathematical description of the individual process has been well established previously; however, there is a lack of a holistic review and guidelines to develop hybrid models for different treatment systems. In this paper, we summarize the applications of hybrid IX and biological systems, critically review the representative individual process models, and propose the framework to integrate these models for the hybrid process. Additionally, we provide a comprehensive review of the equilibrium, kinetic, and thermodynamic models for the IX process and the key biological process models, along with their applied scenarios. Advanced data-driven modelling and its combination with mechanistic models are also discussed to overcome the drawbacks in conventional modeling approach. We highlight emerging techniques that would lead to higher fidelity models. This review provides a comprehensive guideline for the model development of hybrid systems and presents future research directions to build robust systems. [ABSTRACT FROM AUTHOR]

The penetration coefficient can represent the relationship between force and depth in the rock drilling process, but its understanding is limited. Therefore, based on the rock drilling theory with a hydraulic breaking hammer, a mathematical model of the penetration coefficient is established in this paper, and the main influencing factors of the penetration coefficient are determined. The discrete element method is used to establish a rock simulation model that can represent the real characteristics, and the variation law of the penetration coefficient under cyclic impact is studied. In addition, the drilling processes of drill bits with different impact velocities, shapes, and angles are simulated to evaluate the effects of operational parameters on the penetration coefficient. The results show that cyclic impact will change the rock cohesion and affect the change in the penetration coefficient. With an increase in impact times by the same drill bit, the penetration coefficient first increases and tends to be stable, and then decreases. Regarding operational parameters, the impact velocity has little effect on the penetration coefficient, while the shape and angle of the drill bit have a significant effect on the penetration coefficient, and a drill bit with a smaller angle is accompanied by more rock debris. Highlights: A theoretical model of the penetration coefficient is established. DEM simulation reveals the rock drilling mechanism under cyclic impact. The effect law and significance of operation parameters are obtained. [ABSTRACT FROM AUTHOR]

Elite sports contexts are highly pressurised and frequently enforce a win-at-all-costs approach. This narrow focus on performance outcomes can potentially contribute in negative ways to the mental health of those within these environments. In this Current Opinion paper, we propose a model that outlines how key elements contributing to psychologically safe or unsafe environments may contribute to better or worse mental health outcomes, respectively. In an environment in which individuals feel safe to show their authentic selves rather than 'wear a mask', different experiences of mental health are likely to be normalised, help-seeking behaviour increased, and thus, mental health outcomes enhanced. We outline how sports teams and organisations can contribute to this through the creation of appropriate policies and procedures, in addition to leaders modelling and reinforcing positive cultural norms. It is intended that the theoretical model can inform stakeholders in elite sport as well as future research directions. [ABSTRACT FROM AUTHOR]

Clinical abbreviation disambiguation is a crucial task in the biomedical domain, as the accurate identification of the intended meanings or expansions of abbreviations in clinical texts is vital for medical information retrieval and analysis. Existing approaches have shown promising results, but challenges such as limited instances and ambiguous interpretations persist. In this paper, we propose an approach to address these challenges and enhance the performance of clinical abbreviation disambiguation. Our objective is to leverage the power of Large Language Models (LLMs) and employ a Generative Model (GM) to augment the dataset with contextually relevant instances, enabling more accurate disambiguation across diverse clinical contexts. We integrate the contextual understanding of LLMs, represented by BlueBERT and Transformers, with data augmentation using a Generative Model, called Biomedical Generative Pre-trained Transformer (BIOGPT), that is pretrained on an extensive corpus of biomedical literature to capture the intricacies of medical terminology and context. By providing the BIOGPT with relevant medical terms and sense information, we generate diverse instances of clinical text that accurately represent the intended meanings of abbreviations. We evaluate our approach on the widely recognized CASI dataset, carefully partitioned into training, validation, and test sets. The incorporation of data augmentation with the GM improves the model's performance, particularly for senses with limited instances, effectively addressing dataset imbalance and challenges posed by similar concepts. The results demonstrate the efficacy of our proposed method, showcasing the significance of LLMs and generative techniques in clinical abbreviation disambiguation. Our model achieves a good accuracy on the test set, outperforming previous methods. [ABSTRACT FROM AUTHOR]

Vaccinating young children against rotavirus (RV) is a promising preventive strategy against rotavirus gastroenteritis (RVGE). We evaluated the relative risk reduction of RVGE induced by universal vaccination in Vietnam through dynamic model analysis. We developed an age-stratified dynamic Vaccinated-Susceptible-Infectious-Recovered-Susceptible model to analyze RV transmission and assess vaccine effectiveness (VE). We assumed 3 different vaccine efficacies: 55%, 70%, and 85%. For model calibration, we used a database of patients under 5 years of age admitted to Ho Chi Minh No.1 Hospital with RVGE between January 2013 and December 2018. Assuming a vaccination rate of 95%, the number of RVGE hospitalizations after 5 years from universal RV vaccination decreased from 92,502 cases to 45,626 with 85% efficacy, to 54,576 cases with 70% efficacy, and to 63,209 cases with 55% efficacy. Additionally, RVGE hospitalizations after 10 years decreased from 177,950 to 89,517 with 85% efficacy and to 121,832 cases with 55% efficacy. The relative risk reductions of RVGE after 10 years were 49.7% with 85% efficacy, 40.6% with 70% efficacy, and 31.5% with 55% efficacy. The VE was 1.10 times (95% CI, 1.01–1.22) higher in the 4-months to 1-year-old age group than in the other age groups (P = 0.038), when applying 85% efficacy with 95% coverage. In conclusion, despite its relatively lower efficacy compared to high-income countries, RV vaccination remains an effective intervention in Southwestern Vietnam. In particular, implementing universal RV vaccination with higher coverage would result in a decrease in RVGE hospitalizations among Vietnamese children under 5 years of age. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) presents a severe and urgent threat to global health. In response to the COVID-19 pandemic, many countries have implemented nonpharmaceutical interventions (NPIs), including national workplace and school closures, personal protection, social distancing, contact tracing, testing, home quarantine, and isolation. To evaluate the effectiveness of these NPIs in mitigating the spread of early COVID-19 and predict the epidemic trend in the United Kingdom, we developed a compartmental model to mimic the transmission with time-varying transmission rate, contact rate, disease-induced mortality rate, proportion of quarantined close contacts, and hospitalization rate. The model was fitted to the number of confirmed new cases and daily number of deaths in five stages with a Markov Chain Monte Carlo method. We quantified the effectiveness of NPIs and found that if the transmission rate, contact rate, and hospitalization rate were approximately equal to those in the second stage of the most strict NPIs, and the proportion of quarantined close contacts increased by 3%, then the epidemic would die out as early as January 12, 2021, with around 1,533,000 final cumulative number of confirmed cases, and around 55,610 final cumulative number of deaths. [ABSTRACT FROM AUTHOR]

Parkinson's disease (PD) and essential tremor (ET) are prevalent movement disorders that mainly affect elderly people, presenting diagnostic challenges due to shared clinical features. While both disorders exhibit distinct speech patterns—hypokinetic dysarthria in PD and hyperkinetic dysarthria in ET—the efficacy of speech assessment for differentiation remains unexplored. Developing technology for automatic discrimination could enable early diagnosis and continuous monitoring. However, the lack of data for investigating speech behavior in these patients has inhibited the development of a framework for diagnostic support. In addition, phonetic variability across languages poses practical challenges in establishing a universal speech assessment system. Therefore, it is necessary to develop models robust to the phonetic variability present in different languages worldwide. We propose a method based on Gaussian mixture models to assess domain adaptation from models trained in German and Spanish to classify PD and ET patients in Czech. We modeled three different speech dimensions: articulation, phonation, and prosody and evaluated the models' performance in both bi-class and tri-class classification scenarios (with the addition of healthy controls). Our results show that a fusion of the three speech dimensions achieved optimal results in binary classification, with accuracies up to 81.4 and 86.2% for monologue and /pa-ta-ka/ tasks, respectively. In tri-class scenarios, incorporating healthy speech signals resulted in accuracies of 63.3 and 71.6% for monologue and /pa-ta-ka/ tasks, respectively. Our findings suggest that automated speech analysis, combined with machine learning is robust, accurate, and can be adapted to different languages to distinguish between PD and ET patients. [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 photovoltaic (PV) cell behavior is characterized by its current–voltage relationship. This relationship is dependent on the PV cell's equivalent circuit parameters. Accurate estimation of such parameters is essential to study and analyze the PV system performance in terms of many aspects such as modeling and control. The main purpose of this paper is to develop mathematical models for the parameters of the single-diode poly and monocrystalline PV cells. The models are formulated using Eureqa software by utilizing training data collected from simulating thousands of PV modules available in Simulink library. The developed models can be easily and instantly executed by only using information available from module datasheet under standard test conditions (STC). The models are then validated using four different assessments by considering testing data, commercial PV modules, and experimental data, in addition to benchmarking with other reported algorithms. As an overall evaluation, the assessments have shown that the developed models are efficient in estimating the PV cell equivalent circuit parameters and can consequently predict the I–V curves for any poly or monocrystalline PV modules, under any weather conditions, with a high degree of accuracy. [ABSTRACT FROM AUTHOR]

This letter to the editor responds to a paper that compares different mathematical models for describing the relationship between exercise intensity and duration before task failure. The authors argue that a power law model is a better fit for a wide range of intensities and durations compared to the commonly used hyperbolic model. However, they also acknowledge that the hyperbolic model has physiological significance, particularly in terms of the critical power (CP) and work prime (W') parameters. The authors suggest that incorporating durability as a parameter may improve the accuracy of mathematical models for endurance performance. Overall, the letter emphasizes the importance of considering the physiological significance of parameters when choosing a mathematical model. [Extracted from the article]

Through System Identification techniques, it is possible to obtain a mathematical model for a dynamic system from its input/output data. Due to their intrinsic dynamic behavior and simple and fast training procedure, the use of echo state networks (ESNs), a kind of neural network, for System Identification is advantageous. However, ESNs have global parameters that should be tuned in order to improve their performance in a determined task. Besides, a random reservoir may not be ideal in terms of performance. Due to their theoretical ability to obtain good solutions with few evaluations, the Real Coded Quantum-Inspired Evolutionary Algorithm (QIEA-R) and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) represent efficient alternatives of evolutionary algorithms for optimizing ESN global parameters and weights. Thus, this work proposes a neuro-evolutionary method that automatically defines an ESN for System Identification problems. The method initially focuses on finding the best ESN global parameters by using the QIEA-R or the CMA-ES then, in sequence, selecting its best reservoir, which can be done by a second optimization focused on some reservoir weights or by doing a simple choice based on networks with random reservoirs. The method was applied to seven benchmark problems in System Identification produced good results when compared to traditional methods. [ABSTRACT FROM AUTHOR]

This article devoted the mathematical model of the plasticization process for the injection molding processes in a cylindrical domain influenced from the main thermodynamic characteristics: particle velocity, pressure distribution, particle flow density, and melting temperature. Here is determined a thermodynamic relationship between the particle velocity vector and the scalar pressure function in which the particle velocity is defined by the three-dimensional Maxwell distribution satisfying the energy conservation law. The presented mathematical model has been described via the initial-boundary value problem for second-order parabolic equations in a cylindrical domain. Here the three-dimensional energy conservation law regulates the pressure instability effect according to the particle velocity vector in a turbulent flow. It is a new issue for defining the processing pressure distribution that is provided proofing the theorem of existence and uniqueness of their classical parameters. This result as Maxwell distribution of the particle velocity has great opportunity for studying the transient particle flows in multiscale modeling the thermodynamic diffusivity for the injection moldings processes. In the previous author's research was investigated a weak formulation of the Navier–Stokes problem. [ABSTRACT FROM AUTHOR]

Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion. In this paper, we develop a framework to model plastic and mutational mechanisms of acquiring resistance in a continuous gradual fashion. We use this framework to examine ways in which cancer and bacterial populations can respond to stress and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution. [ABSTRACT FROM AUTHOR]

Recovering three-dimensional structure from images is one of the important researches in computer vision. The quality of feature matching is one of the keys to obtaining more accurate results. However, as different objects or different surfaces of objects have similar images with the same elements and different typography, the camera pose estimation will be wrong and the task will fail. This paper proposes a new mismatch elimination algorithm based on global topology consistency. We first formulate the matching task as a mathematical model based on the global constraints, then convert the feature matching into grid matching, calculate the confidence of the grids according to the changes in the angle and displacement between correspondence grid vectors, and remove the mismatches with low confidence. The experiments have demonstrated that our proposed method performs better than the state-of-the-art feature matching methods to accomplish outlier match rejection in the task of similar image matching and could be helped to obtain the correct camera pose to reconstruct more complete and more accurate object models. [ABSTRACT FROM AUTHOR]

We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]

This study focuses on improving the accuracy of assessing liver damage and early detection for improved treatment strategies. In this study, we examine the human liver using a modified Atangana-Baleanu fractional derivative based on the mathematical model to understand and predict the behavior of the human liver. The iteration method and fixed-point theory are used to investigate the presence of a unique solution in the new model. Furthermore, the homotopy analysis transform method, whose convergence is also examined, implements the mathematical model. Finally, numerical testing is performed to demonstrate the findings better. According to real clinical data comparison, the new fractional model outperforms the classical integer-order model with coherent temporal derivatives. [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]

Mathematical models are increasingly being developed and calibrated in tandem with data collection, empowering scientists to intervene in real time based on quantitative model predictions. Well-designed experiments can help augment the predictive power of a mathematical model but the question of when to collect data to maximize its utility for a model is non-trivial. Here we define data as model-informative if it results in a unique parametrization, assessed through the lens of practical identifiability. The framework we propose identifies an optimal experimental design (how much data to collect and when to collect it) that ensures parameter identifiability (permitting confidence in model predictions), while minimizing experimental time and costs. We demonstrate the power of the method by applying it to a modified version of a classic site-of-action pharmacokinetic/pharmacodynamic model that describes distribution of a drug into the tumor microenvironment (TME), where its efficacy is dependent on the level of target occupancy in the TME. In this context, we identify a minimal set of time points when data needs to be collected that robustly ensures practical identifiability of model parameters. The proposed methodology can be applied broadly to any mathematical model, allowing for the identification of a minimally sufficient experimental design that collects the most informative data. [ABSTRACT FROM AUTHOR]

A non-linear mathematical model of underactuated airship is derived in this paper based on Euler-Newton approach. The model is linearized with small disturbance theory, producing a linear time varying (LTV) model. The LTV model is verified by comparing its output response with the result of the nonlinear model for a given input signal. The verified LTV model is used in designing the LQT controller. The controller is designed to minimize the error between the output and required states response with acceptable control signals using a weighted cost function. Two LQT controllers are presented in this work based on two different costates transformations used in solving the differential Riccati equation (DRE). The first proposed assumption of costates transformation has a good tracking performance, but it is sensitive to the change of trajectory profile, whereas the second one overcomes this problem due to considering the trajectory dynamics. Therefore, the first assumption is performed across the whole trajectory tracking except for parts of trajectory profile changes where the second assumption is applied. The hybrid LQT controller is used and tested on circular, helical, and bowed trajectories. The simulation assured that the introduced hybrid controller results in improving airship performance. [ABSTRACT FROM AUTHOR]

In recent years, path dependence has gained increasing scientific attention in many disciplines, leading to various new concepts and notations, such as path creation or path plasticity. However, if mathematical arguments are used, they are based on the early works by Brian W. Arthur and Paul A. David, usually referring to the mathematical concept of ergodicity. We extend their mathematical framework and develop a graphical representation of systems that allows for a metaphorical discussion of system behaviors beyond the original cases, especially in evolving systems, and the inclusion of the recently developed concepts within path dependence. Visualizations are used to explain the definition and characteristics of seven types of path dependence: lock-in, path-breaking, path-furrowing, path plasticity, path formation, path creation, and path selection. Although these visualizations are explained verbally and can be understood without a mathematical expertise, a mathematical model is used to generate them. The deduction of the metaphorical concept from a mathematical model guarantees the completeness of the identified processes and the rigor in their categorization as well as the identification of respective characteristics for their distinction. However, the aim of the paper is to provide an illustrative concept that allows researchers to classify and structure the various path-dependent processes they observe in their application. While five of the identified processes are in line with concepts from the literature and are defined accordingly, we also detect a sixth process that is new to the literature so far: path-furrowing. Moreover, slightly deviating from the literature, we define path selection as the possibility to choose a path intentionally, thereby focusing on the mindful choice of options. [ABSTRACT FROM AUTHOR]

The paper considers the problem of variational assimilation of observational data in order to reconstruct the initial state and heat fluxes for the mathematical model of sea thermodynamics developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences. The sensitivity of the functionals of the solution to the input data on the heat flux on the sea surface in the considered variational assimilation problem is studied, and the results of numerical experiments for the Black Sea dynamics model are presented. [ABSTRACT FROM AUTHOR]

The paper proposes a methodology for mathematical modeling of the phased development of nodes and transport routes in a hierarchical network with multicommodity discrete flows of correspondences based on solving the problems of optimizing its structure and distribution of flows. As a rule, such networks consist of a decentralized mainline network and networks in the internal service areas of mainline nodes. In a multicommodity network, each node can exchange correspondence (products, goods, cargo, messages) with the other nodes. Correspondence is characterized by a source node, a sink node, and a quantity, which for data transmission networks is given by the number of bytes, kilobytes, etc., and for transport networks by the number of cargo units in a package of uniform size. In the mainline network, all correspondences are transmitted via communication channels or transported by vehicles in transport units of a given size (capacity, volume). The authors considered the main postulates of generating a mathematical model of the perspective development of mainline network. They presented a method of mathematical modeling of the phased development of nodes and transport routes, which includes, for each stage of development, the forecasting of data and network parameters, solving the problem of packing correspondence and choosing the structure of the network, and solving the problem of distribution and routing of transport unit flows. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a qualitative approach to the theory of conceptual spaces, in contrast to the usual metric framework. This requires qualitative notions of similarity, simple concepts, prototypes and conceptual categorisation. For this purpose, I will introduce three mathematical models for conceptual spaces. The first one is topological and has been proposed by Mormann. The other two are new and are based on atomistic orders and similarity relations. I will discuss how each of them deals with the Design Principles proposed by Douven and Gärdenfors and with further Adequacy Conditions. Despite being apparently different, I will show that these three models are mathematically equivalent. Finally, I will address three objections to the present approach. The first one says that the qualitative notion of a prototype is a bad analogue of the metric one. The second one suggests that, in contrast to the Voronoi construction, the function qualitatively representing the conceptual categorisation process is arbitrary. The last one appeals to Goodman's companionship and imperfect community problems to show that there is a flaw in defining simple concepts from similarity relations. [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]

Purpose: Scholarship on the social and structural determinants of intimate partner violence (IPV) rarely differentiates between Johnson's types in examining pathways to violent outcomes. This study applies Bronfenbrenner's model to consider the etiology of Johnson's types at multiple social-ecological levels. Method: To test the hypothesis that pathways from local social and structural conditions to IPV differ by type of IPV, I reanalyzed longitudinal data from a recent study that explored the role of factors at multiple social-ecological levels on physical IPV in a highly vulnerable sample: 1,112 different-sex couples in which the male partner had recently returned from prison. Results: In fitted structural equation models, local social and structural conditions predict both situational couple violence (SCV) and coercive controlling violence (CCV). However, the influence of local conditions on each type of IPV occurs via different proximal factors. Local conditions predict SCV via hopelessness and predict CCV via post-traumatic stress and dysfunctional conflict. Conclusions: These exploratory findings indicate that local social and structural conditions could promote both SCV and CCV, but via different proximal processes. They suggest that IPV research has much to gain from integrating the distinct theoretical and methodological contributions of scholarship on Johnson's typology and ongoing inquiry into the broader social ecology of IPV. [ABSTRACT FROM AUTHOR]

Purpose: Brake squeal as a dynamic instability phenomenon is a major comfort problem observed in automotive disc brake systems. Thus, it is aimed to investigate the effects of certain operational parameters on squeal initiation. Methods: The problem is investigated both experimentally and mathematically from the perspective of system stability. Experimentally, a mass-sliding belt experiment is designed and built, with a focus on three key operational parameters. Experiments are conducted at a wide range of these operational parameters. Furthermore, the contact stiffness at the mass and sliding belt contact interface is evaluated via modal tests. Mathematically, a nonlinear mathematical model of the experiment is developed. The model is then linearized through certain assumptions, and the stability of the system is assessed through the linearized mathematical model via complex eigenvalue solution. Results: Data measured from the experiments are processed in time and frequency domains. Time domain results reveal local dynamic amplifications in time histories of certain operational parameters, which lead to the emergence of super-harmonics in frequency domain. Furthermore, Stribeck type friction characteristic is observed at the mass and sliding belt contact interface. The critical values of dynamic friction coefficient and motor angular speed are obtained for the validation of predictions with experimental data. Conclusion: A good correlation between the model predictions and experiments is achieved, thus the stability analysis based on linearized model is validated with the experimental data. An extensive understanding about the effects of key operational parameters on system stability is obtained. [ABSTRACT FROM AUTHOR]

Purpose: In the work there are presented results of the synthesis and additional validation of previously developed mathematical models of two different mechanical oscillators with 1 degree of freedom and harmonic excitation: (i) with magnetically modified elasticity generating a double symmetrical minimum of potential; (ii) with linear mechanical springs and with a one-sided limiter of motion. Methods: In the first case, original mathematical models of non-linear magnetic springs were developed, allowing for effective and fast numerical simulations of the bifurcation dynamics of a real mechanical oscillator with Duffing type stiffness. In the second system, various models of impact were proposed and tested: continuous models based on the generalized Hunt–Crossley model and original discontinuous versions of this model based on the restitution coefficient and with a finite duration of the collision. In the frame of the present work, a system consisting of magnetic springs used in the first system and obstacles from the second oscillator was built and investigated. The system was built as a new configuration of a special universal stand used in the earlier studies mentioned here. Results and Conclusion: In the current study, the parameters of the models identified in previous studies on two different systems were used, the synthesis of which is the current work. A very good agreement was obtained between numerical simulations and experimental data, thus demonstrating the correctness and effectiveness of the adopted mathematical models. [ABSTRACT FROM AUTHOR]

The paper presents a brief analytical review of the current state of research in the field of recovery and its modeling in order to predict the structure and properties, as well as a review of experimental research methods and mathematical models of the processes of structure formation during annealing of cold-rolled steels. The paper also presents the results of an experimental study of the recovery process in cold-rolled automotive steels using various techniques and describes a mathematical model for calculating the kinetics of this process depending on the temperature and chemical composition of steels. [ABSTRACT FROM AUTHOR]