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In secondary lymphoid tissues, human immunodeficiency virus (HIV) can replicate in both the follicular and extrafollicular compartments. Yet, virus is concentrated in the follicular compartment in the absence of antiretroviral therapy, in part due to the lack of cytotoxic T lymphocyte (CTL)-mediated activity there. CTLs home to the extrafollicular compartment, where they can suppress virus load to relatively low levels. We use mathematical models to show that this compartmentalization can explain seemingly counter-intuitive observations. First, it can explain the observed constancy of the viral decline slope during antiviral therapy in the peripheral blood, irrespective of the presence of CTL in Simian Immunodeficiency Virus (SIV)-infected macaques, under the assumption that CTL-mediated lysis significantly contributes to virus suppression. Second, it can account for the relatively long times it takes for CTL escape mutants to emerge during chronic infection even if CTL-mediated lysis is responsible for virus suppression. The reason is the heterogeneity in CTL activity and the consequent heterogeneity in selection pressure between the follicular and extrafollicular compartments. Hence, to understand HIV dynamics more thoroughly, this analysis highlights the importance of measuring virus populations separately in the extrafollicular and follicular compartments rather than using virus load in peripheral blood as an observable; this hides the heterogeneity between compartments that might be responsible for the particular patterns seen in the dynamics and evolution of the HIV in vivo.

IntroductionCancer combination treatments involving immunotherapies with targeted radiation therapy are at the forefront of treating cancers. However, dosing and scheduling of these therapies pose a challenge. Mathematical models provide a unique way of optimizing these therapies.MethodsUsing a preclinical model of multiple myeloma as an example, we demonstrate the capability of a mathematical model to combine these therapies to achieve maximum response, defined as delay in tumor growth. Data from mice studies with targeted radionuclide therapy (TRT) and chimeric antigen receptor (CAR)-T cell monotherapies and combinations with different intervals between them was used to calibrate mathematical model parameters. The dependence of progression-free survival (PFS), overall survival (OS), and the time to minimum tumor burden on dosing and scheduling was evaluated. Different dosing and scheduling schemes were evaluated to maximize the PFS and optimize timings of TRT and CAR-T cell therapies.ResultsTherapy intervals that were too close or too far apart are shown to be detrimental to the therapeutic efficacy, as TRT too close to CAR-T cell therapy results in radiation related CAR-T cell killing while the therapies being too far apart result in tumor regrowth, negatively impacting tumor control and survival. We show that splitting a dose of TRT or CAR-T cells when administered in combination is advantageous only if the first therapy delivered can produce a significant benefit as a monotherapy.DiscussionMathematical models are crucial tools for optimizing the delivery of cancer combination therapy regimens with application along the lines of achieving cure, maximizing survival or minimizing toxicity.

This paper evaluates the nonlinear dynamics of a melanoma cancer model through the iterative technique of finding compact invariant sets (LMCIS). The objective is to discover equilibrium points, ascertain their stability qualities, and determine the presence of compact invariant sets within the model. For instance, this approach is assessed in a model demonstrating the interplay between four cellular populations and administrating interleukin-12 (IL-12) immunotherapy. Nevertheless, the mechanism by which this anti-cancer therapy operates has yet to be completely defined. The approach is evaluated using severe treatment situations to provide evidence for the presence of equilibrium points inside the iteratively confined zone and to assess its effectiveness. The outcomes derived from using this approach were then compared with a conventional iteration of Newton's method. Newton's approach extends to the resolution of the system of equations inside the model, facilitating the identification of the equilibrium points with a small tolerance error. While the iterations of the localization algorithm were set close to the results obtained by this method. Finally, the simulation outcomes are shown via the utilization of MATLAB R2020b. The findings demonstrate the temporal progression of the model under the effect of immunotherapy and without it. [ABSTRACT FROM AUTHOR]

Tight sandstone water-bearing gas reservoirs typically exhibit low porosity and low permeability, with reservoir rocks characterized by complex pore structures, often featuring micron-scale or smaller pore throats. This intricate reservoir structure significantly restricts fluid flow within the reservoir, necessitating a certain threshold pressure gradient (TPG) to be overcome before flow can commence. This study focuses on the Ordos Basin and explores the influence of high water content tight sandstone gas reservoirs on TPG under different water saturation and formation pressure conditions through experiments. A mathematical model of TPG is established using multiple linear regression method. The results show that TPG is primarily affected by water saturation, followed by formation pressure. As the water saturation increases, the TPG of the core decreases, and the change becomes more pronounced when the water saturation exceeds 50%. As formation pressure increases, the weakening of the slippage effect in gas molecules leads to TPG stabilization, especially when local pressure exceeds 25.0 MPa. The research also shows that low-permeability cores exhibit greater TPG variation with pressure changes, while high-permeability cores remain more stable. A mathematical model was developed and validated to predict TPG based on permeability, water saturation, and formation pressure. These findings highlight the need to monitor formation water content during tight sandstone gas reservoir development to optimize production strategies, providing valuable insights for improving reservoir management and guiding future research. [ABSTRACT FROM AUTHOR]

To reveal the velocity distribution law of a gas lift reverse circulation well washing flow field in drilling shaft sinking, a velocity mathematical model of well washing flow field is established. The theoretical analytical solutions and velocity distribution laws in the drill pipe and bottom hole were provided and validated through numerical simulations and similar model tests. Furthermore, this study explores the impacts of mud circulation, wind pressure, rock debris, and mud properties on the flow field distribution, presenting the sensitivity order of the factors. This study indicated the following findings. (1) The velocity theoretical model of well washing flow field was validated through numerical simulation and similar model tests, and the relative error ranged from 4.2 to 18.5%, demonstrating the high consistency. (2) The rock debris and mud experienced slight and consistent deceleration within the drill pipe. Upon reaching the gas input end, the axial upward return of the multiphase flow resulted in a "jumping" sharp increase. (3) The mud circulation, wind pressure, and void fraction positively correlated with the multiphase fluid velocity in the drill pipe, but negatively correlated with the mud density and slag content. The axial upward velocity of the rock debris decreased with increasing particle size and density. (4) The sensitivity of each factor to the discharge speed of rock debris was summarized as follows: air content > mud circulation > wind pressure > mud density > rock debris density > rock debris particle size > slag content. These findings could offer a theoretical basis for selecting well washing parameters and enhancing drilling and washing efficiency. [ABSTRACT FROM AUTHOR]

Background: In Taiwan, the human immunodeficiency virus (HIV) is primarily transmitted among men who have sex with men (MSM). We believe that the primary source of heterogeneity influencing transmission is from whether the infected individuals engage in behaviors that promote transmission. Therefore, we differentiated and modeled the statuses of infected individuals, estimated parameters, and predicted future infection trends to better understand HIV transmission dynamics among MSM. Methods: We devised a computational approach to accurately estimate the number of infectious individuals during early surveillance years in Taiwan using monthly data of newly diagnosed patients with HIV from January 2005 to December 2006. Subsequently, using annual incident cases from 2005 to 2019, we estimated the susceptibility rate, transmission rates, and duration of risk and conducted short-term forecasts of HIV infection among MSM through mathematical modeling based on the susceptible-infected-removed model. Parameters and their values, such as HIV and acquired immunodeficiency syndrome (AIDS) transmission rates and removal rates, were also estimated. Results: A total of 850 infectious individuals with HIV were identified in 2005. From 2005 to 2019, approximately 0.68% (95% confidence interval: 0.64–0.71%) of Taiwan's male population were estimated to be susceptible to HIV infection via MSM. The transmission rate did not significantly differ between individuals with HIV and AIDS (0.0110 and 0.107 per 10,000 individuals, respectively). The average infection duration between infection and AIDS onset was 4.5 years and between AIDS onset and death was 2.1 years. In 2019, the proportion of infectious infected individuals continuously decreased. By 2026, only 11.85% and 10.21% of individuals with HIV and AIDS, respectively, will be infectious. Conclusions: Our study presents a new dynamic mathematical model for estimating infectious HIV cases among MSM in Taiwan. By accounting for the heterogeneity of infectious HIV/AIDS within the MSM population, we effectively estimated the number of infections during early surveillance years and implement concentrated measures, thereby reducing infectious HIV/AIDS cases, which contributes to the overall reduction in HIV/AIDS cases. With these estimations, identifying target populations and implementing effective intervention measures at appropriate times can be improved. [ABSTRACT FROM AUTHOR]

Cancer is a systemic heterogeneous disease involving complex molecular networks. Tumor formation involves an epithelial‐mesenchymal transition (EMT), which promotes both metastasis and plasticity of cancer cells. Recent experiments have proposed that cancer cells can be transformed into adipocytes via a combination of drugs. However, the underlying mechanisms for how these drugs work, from a molecular network perspective, remain elusive. To reveal the mechanism of cancer‐adipose conversion (CAC), this study adopts a systems biology approach by combing mathematical modeling and molecular experiments, based on underlying molecular regulatory networks. Four types of attractors are identified, corresponding to epithelial (E), mesenchymal (M), adipose (A) and partial/intermediate EMT (P) cell states on the CAC landscape. Landscape and transition path results illustrate that intermediate states play critical roles in the cancer to adipose transition. Through a landscape control approach, two new therapeutic strategies for drug combinations are identified, that promote CAC. These predictions are verified by molecular experiments in different cell lines. The combined computational and experimental approach provides a powerful tool to explore molecular mechanisms for cell fate transitions in cancer networks. The results reveal underlying mechanisms of intermediate cell states that govern the CAC, and identified new potential drug combinations to induce cancer adipogenesis. [ABSTRACT FROM AUTHOR]

In a fast-changing world, understanding how organisms adapt to their environment is a pressing necessity. Research has focused on genetic adaptation, while our understanding of non-genetic modes is still in its infancy. The host-associated microbiome can be considered a non-genetic mode of adaptation, which can strongly influence an organism's ability to cope with its environment. However, the role of the microbiome in host ecological dynamics is largely unexplored, particularly in animal communities. Here, we discuss the following hypothesis: invasive species may rapidly adapt to local conditions by adopting beneficial microbes from similar co-occurring native species. This occurs when the invader's fitness is influenced by adaptation to local conditions that is facilitated by microbes acquired from native microbiomes. We present a minimal mathematical model to explore this hypothesis and show that a delayed acquisition of native microbes may explain the occurrence of an invasion lag. Overall, our results contribute to broadening the conceptualization of rapid adaptation via microbiome transfer and offer insights towards designing early intervention strategies for invasive species management. [ABSTRACT FROM AUTHOR]

Introduction: Treating extensive burn injury requires an individually tailored resuscitation protocol that includes hourly-titrated intravenous fluid infusion to avert both hypovolemic shock and edema. Due to the complexity of burn pathophysiology and significant variability in treatment protocols, there is an ongoing effort to optimize burn resuscitation. The goal of this work is to contribute to this effort by developing a mathematical model of burn pathophysiology and resuscitation for in silico testing of burn resuscitation protocols and decision-support systems. Methods: In our previous work, we developed and validated a mathematical model consisting of volume kinetics, burn-induced perturbations, and kidney function. In this work, we expanded our previous mathematical model to incorporate novel mathematical models of cardiovascular system and hormonal system (renin-angiotensin-aldosterone (RAAS) system and antidiuretic hormone) which affect blood volume and pressure regulation. We also developed a detailed mathematical model of kidney function to regulate blood volume, pressure, and sodium levels, including components for glomerular filtration rate, reabsorption rates in nephron tubules, Tubuglomerular feedback, and myogenic mechanisms. We trained and validated the expanded mathematical model using experimental data from 15 pigs and 9 sheep with extensive burns to quantitatively evaluate its prediction accuracy for hematocrit, cardiac output, mean arterial pressure, central venous pressure, serum sodium levels, and urinary output. We then trained and tested the mathematical model using a clinical dataset of 233 human burn patients with demographic data and urinary output measurements. Results: The mathematical model could predict all tested variables very well, while internal variables and estimated parameters were consistent with the literature. Discussion: To the best of our knowledge, this is the first mathematical model of burn injury and resuscitation which is extensively validated to replicate actual burn patients. Hence, this in silico platform may complement large animal pre-clinical testing of burn resuscitation protocols. Beyond its primary purpose, the mathematical model can be used as a training tool for healthcare providers delivering insight into the pathophysiology of burn shock, and offering novel mathematical models of human physiology which can be independently used for other purposes and contexts. [ABSTRACT FROM AUTHOR]

This paper aims to investigate appropriate mathematical models devoted to the optimization of some cleaning processes related to pharmaceutical contaminant removal. In our recent works, we found the rehabilitation of the existing cleaning plants as a viable solution for the removal of this type of micropollutants from waters by introducing efficient techniques such as adsorption on granulated active carbon filters and micro-, nano-, or ultrafiltration. To have these processes under better control and to assure the transfer from small- to large-scale treatment stations, specific mathematical models are necessary. Starting from Navier–Stokes equations and imposing proper boundary conditions, some mathematical physics problems are obtained for which adequate solving methods via variational methods and surjectivity results are proposed. The importance of these solution characterizations consists in their continuation in adequate numerical methods and the possibility to visualize the result by using a CFD program. [ABSTRACT FROM AUTHOR]

The monitoring and diagnostic system has been suggested as a non-destructive diagnostic method. The structure and operation of the suggested system can be described by the concept of digital shadow (DS). One of the main DS subsystems is a set of sensors properly placed on the monitored object and coupled with a discrete data processing model created in Matlab/Simulink. The discrete model, as another important DS subsystem of the monitored facility, transfers information about its technical condition to the operator based on data recorded by the sensor system. The digital monitoring model processes the recorded data in the form of the object's response to actions caused by its operating conditions. This work formalized a mathematical model determining the coupling of the digital model with the sensors placed on the monitored object. The formulated method using DS, due to its sensitivity, enables the detection of the damage in the object at an early stage. The tests allowed for detecting the regularities enabling the determination of the area of damage to the shaft and its size. [ABSTRACT FROM AUTHOR]

In recent years, due to the diversity of fire scenes in ports and ships, the problem of fire command is complicated. In the case of power failure, the original command platform and fire extinguishing system will not be able to be used normally, or the fire extinguishing resources carried by the ship when it is on fire cannot be used. In the traditional firefighting ability research, there is no clear measure of firefighting ability, resulting in inaccurate calculation results. By corresponding to the quantity and composition of resources for the study of fire extinguishing capability, the combination of the fire dynamics simulation software PyroSim2020 and a calculation model that converts its resources into the total amount and flow of fire extinguishing agent can be provided. Based on the analytic hierarchy process (AHP), a firefighting demand grade calculation and judgment model was established, which included five factors: fire scale, combustion material characteristics, foam extinguishing agent performance, firefighting object characteristics, and external factors. It concluded that the demand assignment values of each index element were 2, 5, 6, 9, and 10, and further proposed the grade judgment criteria for the calculation results of comprehensive fire demand. Through the quantitative simulation of firefighting demand based on the fire scenario and calculation model test of the consumption prediction of cooperative firefighting equipment, it can also provide a strategic reference for related cooperative fire rescue. [ABSTRACT FROM AUTHOR]

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The mathematical modeling of a combination of non-thermal technologies for E. coli inactivation is of great interest for describing the dynamic behavior of microorganisms in food, with the goal of process control, optimization, and prediction. This research focused on the design and implementation of a mathematical model to predict the effect of power ultrasound (US), high-pressure processing (HPP), and the combination of both non-thermal technologies on the inactivation kinetics of E. coli (DSM682) inoculated in orange juice. Samples were processed by US, HPP, and a combination of both technologies at varying process parameters, and a mathematical model for microbial inactivation was developed using a System Dynamics approach. The results showed that the combination of these technologies exhibited a synergistic effect, resulting in no detectable colony-forming units per mL of juice. The developed model accurately predicted the inactivation of E. coli following the combination of these technologies (R2 = 0.82) and can be used to predict microbial load reduction or optimize it based on process parameters. Additionally, combining both techniques offers a promising approach for extending the shelf life of fresh juices using non-thermal stabilization technology. [ABSTRACT FROM AUTHOR]

A universal mathematical model of an autonomous asynchronous generator with capacitor self-excitation in retarded phase coordinates is proposed, taking into account the electromagnetic connections between the windings of the stator and rotor phases, saturation of the main magnetic circuit, and active power losses in the magnetic circuit elements. The model provides an opportunity to analyze stable periodic modes and transient electromagnetic and electromechanical processes in autonomous power supply systems with arbitrary switching schemes of its elements and asynchronous generators. The model provides the possibility of taking into account the residual magnetization of the magnetic circuit of an asynchronous generator and the change in rotor speed during the course of the self-excitation process of an asynchronous generator with a grounded neutral of the stator winding and an asymmetric load. References 10, figures 2. [ABSTRACT FROM AUTHOR]

Background: Understanding how infectious disease transmission varies from person to person, including associations with age and contact behavior, can help design effective control strategies. Within households, transmission may be highly variable because of differing transmission risks by age, household size, and individual contagiousness. Our aim was to disentangle those factors by fitting mathematical models to SARS-CoV-2 household survey and serologic data. Methods: We surveyed members of 3,381 Utah households from January-April 2021 and performed SARS-CoV-2 antibody testing on all available members. We paired these data with a probabilistic model of household importation and transmission composed of a novel combination of transmission variability and age- and size-structured heterogeneity. We calculated maximum likelihood estimates of mean and variability of household transmission probability between household members in different age groups and different household sizes, simultaneously with importation probability and probabilities of false negative and false positive test results. Results: 12.8% of individual participants, residing in 17.4% of the participating households, showed serologic evidence of prior infection or reported a prior positive test on the survey. Serologically positive individuals in younger age groups were less likely than older adults to have tested positive during their infection according to our survey results. Our model results suggested that adolescents and young adults (ages 13–24) acquired SARS-CoV-2 infection outside the household at a rate substantially higher than younger children and older adults. Our estimate of the household secondary attack rate (HSAR) among adults aged 45 and older exceeded HSARs to and/or from younger age groups at a given household size. We found lower HSAR in households with more members, independent of age differences. The age-specific HSAR patterns we found could not be explained by age-dependent biological susceptibility and transmissibility alone, suggesting that age groups contacted each other at different rates within households. Conclusions: We disentangled several factors contributing to age-specific infection risk, including non-household exposure, within-household exposure to specific age groups, and household size. Within-household contact rate differences played a significant role in driving household transmission epidemiology. These findings provide nuanced insights for understanding community outbreak patterns and mechanisms of differential infection risk. [ABSTRACT FROM AUTHOR]

Summary Societal impact statement The European spruce bark‐beetle, Ips typographus, is a major pest of Norway spruce across mainland Europe; however, until 2018, it was considered absent from the United Kingdom (UK). The finding of a breeding population of I. typographus in Kent, England, in 2018 and subsequent findings in pheromone traps across the southeast of England, has led to an urgent need to improve understanding of environmental suitability across the UK. Two distinct published phenological models for I. typographus, developed in Sweden and Austria, were adapted for use in the UK and validated against pheromone trap data collected at the original site of infestation and in the surrounding area from 2019 to 2022. Both models captured some, but not all, of the within‐season variation in trap catches. One, the PHENIPS model, more accurately captured early season flight patterns. The climate in the southeast of England is mild enough to facilitate two generations of the beetle, while further north the pest is expected to be univoltine. At high altitude in Scotland, there is insufficient thermal warming within a season for the completion of one annual generation. Phenological modelling does not explain why the pest failed to establish in England prior to 2018 including when a large amount of infested material was imported to sawmills in the 1940s. Under 2 and 3°C global warming scenarios, we might expect to see an increase in potential voltinism across the UK in the next few decades, increasing the risk of large outbreaks of I. typographus were it allowed to establish. In 2018, a breeding population of the European spruce bark‐beetle, Ips typographus, was discovered in woodland in southeast England. Ips typographus is a major forest pest in continental Europe; however, despite previous findings at ports and sawmills, this was the first recorded infestation in the UK. The number of generations per year (voltinism) varies with latitude and altitude. Applying a phenological model, we find that the current climate in southern UK could support two generations, while temperature accumulation in parts of Scotland may be insufficient to support one generation. Global warming will increase voltinism and hence the risk of establishment. [ABSTRACT FROM AUTHOR]

Background: Heart rate is one of the most crucial vital signs and can be measured remotely using microwave Doppler radar. As the distance between the body and the Doppler radar sensor increases, the output signal weakens, making it difficult to extract heartbeat waveforms. In this study, we propose a new template-matching method that addresses this issue by simulating Doppler radar signals. This method extracts the heartbeat waveform with higher accuracy while the participant is naturally sitting in a chair. Methods: An extended triangular wave model was created as a mathematical representation of cardiac physiology, taking into account heart movements. The Doppler radar output signal was then simulated based on this model to automatically obtain a template for one cycle. The validity of the proposed method was confirmed by calculating the PPIs using the template and comparing their accuracy to the R-R intervals (RRIs) of the electrocardiogram for five participants and by analyzing the signals of eight participants in their natural state using the mathematical model of heart movements. All measurements were conducted from a distance of 500 mm. Results: The correlation coefficients between the RRIs of the electrocardiogram and the PPIs using the proposed method were examined for five participants. The correlation coefficients were 0.93 without breathing and 0.70 with breathing. This demonstrates a higher correlation considering the long distance of 500 mm, and the fact that body movements were not specifically restricted, suggesting that the proposed method can successfully estimate RRI. The average correlation coefficients, calculated between the Doppler output signals and the templates for each of the eight participants, exceeded 0.95. Overall, the proposed method showed higher correlation coefficients than those reported in previous studies, indicating that our method performed well in extracting heartbeat waveforms. Conclusions: Our results indicate that the proposed method of remote heart monitoring using microwave Doppler radar demonstrates higher accuracy in estimating the RRI of the electrocardiogram while at rest sitting in a chair, and the ability to extract the heartbeat waveforms from the measured Doppler output signal, eliminating the need to create templates in advance as required by conventional template matching methods. This approach offers more flexibility in the measurement environment than conventional methods. [ABSTRACT FROM AUTHOR]

It is important to examine and comprehend how HIV interacts with the immune system in order to manage the infection, enhance patient outcomes, advance medical research, and support global health and socioeconomic stability. In this study, we formulate the dynamics of HIV infection to investigate the intricate interactions between HIV and T-cells. The Atangana-Baleanu and Caputo-Fabrizio derivative frameworks are applied to comprehensively examine the phenomenon of HIV viral transmission. The basic concepts and results of fractional calculus are presented for the analysis of the model. In our work, we focus on the dynamical behavior of HIV and immune system. We introduce numerical schemes to elucidate the solution pathways of the recommended system of HIV. We have shown the influence of various input factors on the solution pathways of the recommended fractional system and highlighted the oscillatory behavior and chaotic nature of the dynamics. Our findings demonstrate the complexity of the system under study by revealing the existence of the chaotic and oscillatory nature in the dynamics of HIV. In order to quantitatively characterize HIV dynamics, a number of simulations are carried out, providing a visual representation of the effects of different input variables. It has been observed that the chaos and the oscillatory behaviour is strongly related to the nonlinearity of the system. The present study provides a basis for further initiatives that try to enhance interventions and policies to lessen the worldwide burden of infection. [ABSTRACT FROM AUTHOR]

To accurately characterize the geometric features in the repair of Ti-6Al-4 V alloy, a laser cladding mathematical model was developed and experimentally validated. The model employed a quartic polynomial function to analyze the geometric features of the clad layer, investigating correlations among deposition angle, clad layer width, melt pool depth, and clad layer area. Additionally, it utilized a quadratic polynomial function to characterize the geometric profile of the melt pool, establishing relationships involving clad layer width, melt pool depth, and melt pool area simultaneously. By means of the areas of the cladding layer and the melt pool, the value of the dilution rate can be obtained. Subsequently, the measured and predicted values of the clad layer, melt pool, and dilution rate were compared. The results demonstrated the mathematical model's capability to accurately forecast geometric features in laser cladding. Furthermore, an orthogonal experiment was conducted to investigate how process parameters—laser power, scanning speed, and powder feeding rate—affect the geometric dimensions (height, width, and melt pool depth) of single-pass, single-layer cladding, and to elucidate the underlying reasons. These investigations offered theoretical insights and practical guidelines for controlling the clad layer, melt pool, and dilution rate. [ABSTRACT FROM AUTHOR]

In this paper, the accelerated creep under uniaxial tension of hot fine-grained dense asphalt concrete at temperatures of 22–24 °C and stresses from 0.084 MPa to 0.596 MPa is experimentally investigated. The names and brief descriptions of the creep curve and accelerated creep characteristics are given. A mathematical model is proposed that has physical meaning and satisfactorily approximates the asphalt concrete accelerated creep. The model parameters are determined by the Levenberg–Marquardt method. The deformation and time characteristics of the accelerated creep of asphalt concrete are established and analyzed. [ABSTRACT FROM AUTHOR]

In rotating machinery, the condition of rolling bearings is paramount, directly influencing operational integrity. However, the literature on the fault evolution of rolling bearings in their nascent stages is notably limited. Addressing this gap, our study establishes an innovative nonlinear dynamic model for early fault evolution of rolling bearings based on collision impact. Firstly, considering the fault evolution characteristics, the influence of the rolling element and fault structure, the dynamic model of early fault evolution between the rolling element and the local fault is established. Secondly, according to the Hertzian contact deformation theory, a nonlinear dynamic model of rolling bearings expressed as mass-spring is established. Thirdly, the energy contribution method is used to integrate the fault evolution model and the nonlinear dynamic model of the rolling bearing. A nonlinear dynamic model of early fault evolution of the rolling bearing is proposed by using the Lagrangian equation. Comparing the simulation results of the nonlinear dynamic with the experimental results, it can be seen that the numerical model can effectively predict the evolution process and vibration characteristics of the fault evolution of rolling bearings in the early stage. [ABSTRACT FROM AUTHOR]

Background: Airway pressure release ventilation (APRV) has been shown to be protective against atelectrauma if expirations are brief. We hypothesize that this is protective because epithelial surfaces are not given enough time to come together and adhere during expiration, thereby avoiding their highly damaging forced separation during inspiration. Methods: We investigated this hypothesis in a porcine model of ARDS induced by Tween lavage. Animals were ventilated with APRV in 4 groups based on whether inspiratory pressure was 28 or 40 cmH2O, and whether expiration was terminated when end-expiratory flow reached either 75% (a shorter expiration) or 25% (a longer expiration) of its initial peak value. A mathematical model of respiratory system mechanics that included a volume-dependent elastance term characterized by the parameter E 2 was fit to airway pressure-flow data obtained each hour for 6 h post-Tween injury during both expiration and inspiration. We also measured respiratory system impedance between 5 and 19 Hz continuously through inspiration at the same time points from which we derived a time-course for respiratory system resistance ( R rs ). Results: E 2 during both expiration and inspiration was significantly different between the two longer expiration versus the two shorter expiration groups (ANOVA, p < 0.001). We found that E 2 was most depressed during inspiration in the higher-pressure group receiving the longer expiration, suggesting that E 2 reflects a balance between strain stiffening of the lung parenchyma and ongoing recruitment as lung volume increases. We also found in this group that R rs increased progressively during the first 0.5 s of inspiration and then began to decrease again as inspiration continued, which we interpret as corresponding to the point when continuing derecruitment was reversed by progressive lung inflation. Conclusions: These findings support the hypothesis that sufficiently short expiratory durations protect against atelectrauma because they do not give derecruitment enough time to manifest. This suggests a means for the personalized adjustment of mechanical ventilation. [ABSTRACT FROM AUTHOR]

Contemporary customers have increasingly heightened demands regarding their dietary preferences, favoring readily available and healthful ready-to-consume food and beverage alternatives. In order to fulfill this demand, the beverage industry has been exploring innovative products. Red beetroot juice (RBJ) is easily consumed and offers a beneficial advantage due to its betalain content. Both the traditional/spontaneous method and the industrial method are viable options for producing RBJ. The aim of this study was to examine the stability of betalains, the primary bioactive component in RBJ, throughout the fermentation process and during storage. The RBJ samples contained betalain pigments, as indicated by the infrared spectra. No decrease in betalain content was observed in either RBJ juice fermented by two different methods. The total betalain content of the RBJ samples was 594.068 and 535.152 mg/L at the beginning of fermentation through the spontaneous method and the method with the addition of Lacticaseibacillus paracasei 431 (Lc. paracasei), respectively, and 580.151 mg/L and 667.382 mg/L at the conclusion of fermentation, respectively. Mathematical models were employed to represent the degradation of betalains over time during storage. It was found that the sigmoidal model (R2 = 0.974) and other models (R2 = 0.957–0.969) demonstrated a greater potential to describe the degradation of betalains in RBJ samples produced by the spontaneous method compared to the first-order kinetics model (R2 = 0.932). The models used in the study were successful, with R2 values ranging between 0.927 and 0.932 in the RBJ samples produced with the addition of the probiotic Lc. paracasei for predicting betalain degradation. [ABSTRACT FROM AUTHOR]

Algal blooms pose a significant threat to the ecological integrity and biodiversity in aquatic ecosystems. In lakes, enriched with nutrients, these blooms result in overgrowth of periphyton, leading to biological clogging, oxygen depletion, and ultimately a decline in ecosystem's health and water quality. In this article, we presented a mathematical model centered around the role of aquatic species (specifically fish population) to alleviate algal blooms. The model analysis revealed significant shifts in dynamics, shedding light on the effectiveness of fish-mediated sustainability strategies to control algal proliferation. Notably, our study identified critical thresholds and regime transitions through the observation of saddle-node bifurcation within the proposed mathematical model. To validate our analytical findings, we have conducted numerical simulations, which provided robust evidence for the resilience of the ecosystem under different scenarios. [ABSTRACT FROM AUTHOR]

To facilitate a direct comparison of the differences in network resources among countries worldwide, this paper proposes a method for quantifying the relationship between autonomous systems and territorial networks from the perspective of network topology. Using global router-level network topology data as the foundational data for the network resources of various countries, we abstract the dual mapping information of router geographic distribution and operational ownership into a matrix-form mathematical model. By employing relevant indicators from both network scale and border connectivity, we compare matrix model data from different periods to quantitatively assess changes in the network structures of countries globally. The study results show that internet resources are concentrated in the United States, which owns 38.04% of the global routers, distributed across 87.88% of the countries, significantly impacting the global network. Compared to the average quantitative indicators of each country, 67.00% of the countries exhibit higher deployment consistency, 37.30% show higher border connection consistency, 23.81% perform prominently in terms of impact, and 46.20% have outstanding border node degrees. From a continental perspective, the analysis indicates that Asian and African countries have a closer relationship between AS and territorial networks, while Europe's connections are relatively sparse. Over time, we observe a slight decline in deployment consistency in Asia, Africa, and Europe, a slight increase in border connection consistency in Asia, Africa, and North America, and enhanced impact in Asia, Africa, Europe, and South America. These trends suggest that the integration between AS and territorial networks is intensifying in most countries. [ABSTRACT FROM AUTHOR]

Background: Several computational and mathematical models of protein synthesis have been explored to accomplish the quantitative analysis of protein synthesis components and polysome structure. The effect of gene sequence (coding and non-coding region) in protein synthesis, mutation in gene sequence, and functional model of ribosome needs to be explored to investigate the relationship among protein synthesis components further. Ribosomal computing is implemented by imitating the functional property of protein synthesis. Result: In the proposed work, a general framework of ribosomal computing is demonstrated by developing a computational model to present the relationship between biological details of protein synthesis and computing principles. Here, mathematical abstractions are chosen carefully without probing into intricate chemical details of the micro-operations of protein synthesis for ease of understanding. This model demonstrates the cause and effect of ribosome stalling during protein synthesis and the relationship between functional protein and gene sequence. Moreover, it also reveals the computing nature of ribosome molecules and other protein synthesis components. The effect of gene mutation on protein synthesis is also explored in this model. Conclusion: The computational model for ribosomal computing is implemented in this work. The proposed model demonstrates the relationship among gene sequences and protein synthesis components. This model also helps to implement a simulation environment (a simulator) for generating protein chains from gene sequences and can spot the problem during protein synthesis. Thus, this simulator can identify a disease that can happen due to a protein synthesis problem and suggest precautions for it. [ABSTRACT FROM AUTHOR]

Monkey pox causes a rash which can be uncomfortable, itchy, and painful and its early detection is vital to every control mechanisms. Hence, the objective of this paper was the development and simulation of a mathematical model for monkey-pox transmission disease in Nigeria using Ordinary Differential Equations. The feasible region of the model was verified and solutions positivity was shown. We achieved the disease free equilibrium and computed effective reproduction number, Re of the model system. We show the global stability of disease free equilibrium and we found that the disease free equilibrium of the model system is globally asymptotically stable if Re < 1 and G(X1, X2) = 0. The model system is considered mathematically and epidemiologically well posed. Furthermore, the simulations of the model shows that the average secondary cases of disease increases as exposed individual increases and rate of infection increases. Again, the effective reproduction number reduces as vaccination increases and it is observed that as exposed nonhuman transmits at low rate than symptomatic reduced, it reduces the secondary cases of the disease. [ABSTRACT FROM AUTHOR]

The aim of this research is to develop an electric motor simulator based on an electromechanical mathematical model, which can be used as a didactic tool for teaching courses in mechanical, electrical and electromechanical engineering laboratories. We used an analytical method to study the principles and elements of all parts of a DC motor and an experimental technique to collect the data; the Python programming language was used to perform the data analysis. In the validation of the model, a correlation of 0.775 was found for current; that is, the strength of association is high, and a correlation of 0.94 for velocity, which explains a very high strength of association. Furthermore, the root mean square error in current is 0.002, while the root mean square error in velocity is 1.189. The numerical results illustrate the robustness and stability of the mathematical model. The research has both academic and social contributions, it serves as a basis for future research work related to mathematical modeling in the field of mechanical, electrical, electromechanical, and control engineering. In future research, the goal is to model a number of motor types and subsequently develop an electric motor multisimulator for educational and economic purposes. [ABSTRACT FROM AUTHOR]

Groundwater contamination by dense nonaqueous phase liquids (DNAPLs) poses a severe environmental threat due to their persistence and toxicity. Modeling DNAPL contamination is essential for understanding their distribution, predicting contaminant spread, and developing effective remediation strategies, but it is also challenging due to their complex multiphase behavior. Over the past few decades, researchers have developed various models, including multiphase flow, mass transfer, and solute transport models, to simulate the distribution of DNAPLs. To understand the research trends in DNAPL modeling in groundwater, a bibliometric analysis was conducted using CiteSpace based on 614 publications from the WoS Core Collection database (1993–2023). The publications were statistically analyzed, and the research hotspots and trends were summarized. The statistical analysis of the publications indicates that the United States is leading the international research on DNAPL models, followed by China and Canada; the collaboration between countries and disciplines in this field needs to be strengthened. Keyword clustering and burst detection reveal that the current research hotspots focus on multiphase flow models, mass transfer models, back diffusion, and practical applications of the models; the research trends are centered on back diffusion mechanisms, the characterization of contamination source zones, and prediction of the contaminant distribution at real-world sites, as well as optimization of the remediation strategies. [ABSTRACT FROM AUTHOR]

The saline aquifer CCS is a crucial site for carbon storage. Safety monitoring is a key technology for saline aquifer CCS. Current CO2 leakage detection methods include microseismic, electromagnetic, and well-logging techniques. However, these methods face challenges, such as difficulties in determining CO2 migration fronts and predicting potential leakage events; as a result, the formulation of test timing and methods for these safety monitoring techniques are somewhat arbitrary. This study establishes a gas–water two-phase seepage model and solves it using a semi-analytical method to obtain the injection pressure and the derivative curve characteristics of the injection well. The pressure derivative curve can reflect the physical properties of the reservoir through which CO2 flows underground, and it can also be used to determine whether CO2 leakage has occurred, as well as the timing and amount of leakage, based on boundary responses. This study conducted sensitivity analyses on eight parameters to determine the impact of each parameter on the bottom-hole pressure and its derivatives, thereby obtaining the influence of its parameters on different flow stages. The research indicates that, when a steady-state flow characteristic appears at the outer boundary, CO2 leakage will occur. Additionally, the leakage location can be determined by calculating the distance from the injection well. This can guide the placement and measurement of safety monitoring methods for saline aquifer CCS. The method proposed in this paper can effectively monitor the timing, location, and amount of leakage, providing a technical safeguard for promoting CCS technology. [ABSTRACT FROM AUTHOR]

This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of Monkeypox virus spread across various regions, considering both human and animal hosts. We propose a comprehensive strategy that includes awareness campaigns, security measures, and health interventions in areas where the virus is prevalent. The goal is to reduce transmission between humans and animals, thereby decreasing human infections and eradicating the virus in animal populations. Our model, which integrates spatial variables, accurately reflects the geographical spread of the virus and the impact of interventions, followed by the implementation and analysis of an applicable optimal control problem. Optimal control theory methods are applied in this work to demonstrate the existence of optimal control and the necessary conditions for optimality. We conduct numerical simulations using MATLAB with the forward-backward sweep method, revealing the efficiency of strategies focused on protecting vulnerable populations, preventing contact with infected individuals and animals, and promoting the use of quarantine facilities as the most effective means to control the spread of the Monkeypox virus. Additionally, the study examines the socio-economic impacts of the virus and the benefits of timely intervention. This approach provides valuable insights for policymakers and public health officials in managing and controlling the spread of Monkeypox. [ABSTRACT FROM AUTHOR]

Small-strain shear modulus (G) is an essential parameter for many geotechnical analyses. Most of shallow foundations are constructed in an unsaturated soil and the shear modulus of the unsaturated soil fluctuates because of the precipitation, evaporation, and rising of ground water table. In this paper, a new mathematical model is proposed for the estimation of the shear modulus function, Gunsat, which defines the relationship between small-strain modulus of unsaturated soil and matric suction. In the proposed model, the soil-water characteristic curve in the form of the degree of saturation is used as the input information. There are additional two parameters named n and C, which can be calibrated with the experimental data, are adopted in the proposed model. The estimated results show good agreement with the experimental data from literature. The proposed method can be used to track the tendency of Gunsat and minimize the data points from the laboratory tests. [ABSTRACT FROM AUTHOR]

Background: Evidence shows that motivational practices focused on utility, importance, and autonomy shape university students' motivational orientation toward learning. On the other hand, the relationship between these variables and motivational orientation toward learning is not linear and requires models that describe their behavior over time. Method: In this study, mathematical modeling based on system dynamics methodology is used to simulate in health students the temporal dynamics of the motivational orientation toward learning based on the behavior of these variables in different scenarios. Results: The results indicate that a) Mastery is sensitive to changes in frequency when importance and autonomy practices are performed; b) the development of Mastery is critical in the first three semesters of academic life, but its loss is hardly recoverable even when practices are incorporated in subsequent semesters; c) Utility-focused motivational practices have no significant effect on the development of learning-oriented motivation. Conclusion: These findings have significant practical implications for higher education. Understanding the critical role of Mastery in the early stages of academic life and the limited potential for recovery if lost can help raise awareness of the importance of early implementation of motivational practices focused on relevance and autonomy. [ABSTRACT FROM AUTHOR]

The study establishes two mathematical formulations to predict the pressure drop in a solid–liquid slurry flowing through a straight pipe. Employing the Eulerian–Eulerian RNG k-ε model, the computational investigation uses water as the carrier fluid and glass beads as solid particles. The analysis spans various particle sizes (d50 = 75–175 μm), volumetric concentrations (Cvf = 10–50%), and velocities (Vm = 1–5 m/s). The first model, developed using the MATLAB curve-fitting tool, is complemented by a second empirical equation derived through non-polynomial mathematical formulation. Results from both models are validated against existing experimental and computational data, demonstrating accurate predictions for d50 = 75–175 µm particles within a Reynolds number range of 20,000 ≤ Re ≤ 320,000. [ABSTRACT FROM AUTHOR]

The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data. [ABSTRACT FROM AUTHOR]

This article uses a high-temperature sintering imaging instrument to test the flowability of borosilicate glass melt doped with Cr 2 O 3 , and establishes a mathematical model for high-temperature glass melt spreading. Discuss the glass melt from a thermodynamic perspective by combining model interpretation with experimental characterization. The results indicate that the thermodynamic judgment formula for high-temperature flow spreading of borosilicate glass is: Q ≥ ρ [ A 0 exp (− T / k 0) + S 0 ] − M · δ [ A 0 exp (− T / k 0) + S 0 ] 1 / 2 . To improve the high-temperature flow ability of borosilicate glass, it is necessary to increase the spreading activation energy Q. On the other hand, it is necessary to reduce the spreading coefficients A 0 、 k 0 and S 0. As a refractory metal oxide and active oxide, Cr 2 O 3 plays a role in reducing the spreading coefficient of glass systems. [ABSTRACT FROM AUTHOR]

Flywheel energy storage systems (FESSs) are widely used for power regulation in wind farms as they can balance the wind farms' output power and improve the wind power grid connection rate. Due to the complex environment of wind farms, it is costly and time-consuming to repeatedly debug the system on-site. To save research costs and shorten research cycles, a hardware-in-the-loop (HIL) testing system was built to provide a convenient testing environment for the research of FESSs on wind farms. The focus of this study is the construction of mathematical models in the HIL testing system. Firstly, a mathematical model of the FESS main circuit is established using a hierarchical method. Secondly, the principle of the permanent magnet synchronous motor (PMSM) is analyzed, and a nonlinear dq mathematical model of the PMSM is established by referring to the relationship among d-axis inductance, q-axis inductance, and permanent magnet flux change with respect to the motor's current. Then, the power grid and wind farm test models are established. Finally, the established mathematical models are applied to the HIL testing system. The experimental results indicated that the HIL testing system can provide a convenient testing environment for the optimization of FESS control algorithms. [ABSTRACT FROM AUTHOR]

Background: Tumor-immune interactions shape a developing tumor and its tumor immune microenvironment (TIME) resulting in either well-infiltrated, immunologically inflamed tumor beds, or immune deserts with low levels of infiltration. The pre-treatment immune make-up of the TIME is associated with treatment outcome; immunologically inflamed tumors generally exhibit better responses to radio- and immunotherapy than non-inflamed tumors. However, radiotherapy is known to induce opposing immunological consequences, resulting in both immunostimulatory and inhibitory responses. In fact, it is thought that the radiation-induced tumoricidal immune response is curtailed by subsequent applications of radiation. It is thus conceivable that spatially fractionated radiotherapy (SFRT), administered through GRID blocks (SFRT-GRID) or lattice radiotherapy to create areas of low or high dose exposure, may create protective reservoirs of the tumor immune microenvironment, thereby preserving anti-tumor immune responses that are pivotal for radiation success. Methods: We have developed an agent-based model (ABM) of tumor-immune interactions to investigate the immunological consequences and clinical outcomes after 2 Gy × 35 whole tumor radiation therapy (WTRT) and SFRT-GRID. The ABM is conceptually calibrated such that untreated tumors escape immune surveillance and grow to clinical detection. Individual ABM simulations are initialized from four distinct multiplex immunohistochemistry (mIHC) slides, and immune related parameter rates are generated using Latin Hypercube Sampling. Results: In silico simulations suggest that radiation-induced cancer cell death alone is insufficient to clear a tumor with WTRT. However, explicit consideration of radiation-induced anti-tumor immunity synergizes with radiation cytotoxicity to eradicate tumors. Similarly, SFRT-GRID is successful with radiation-induced anti-tumor immunity, and, for some pre-treatment TIME compositions and modeling parameters, SFRT-GRID might be superior to WTRT in providing tumor control. Conclusion: This study demonstrates the pivotal role of the radiation-induced anti-tumor immunity. Prolonged fractionated treatment schedules may counteract early immune recruitment, which may be protected by SFRT-facilitated immune reservoirs. Different biological responses and treatment outcomes are observed based on pre-treatment TIME composition and model parameters. A rigorous analysis and model calibration for different tumor types and immune infiltration states is required before any conclusions can be drawn for clinical translation. [ABSTRACT FROM AUTHOR]

Physical adsorption takes place inside narrow pores where the attractive interaction between the surface of the adsorbent and the contaminant molecules is strong enough to retain the molecules. Adsorption columns involve a range of mass-transport mechanisms: advection through the free spaces between the adsorbent pellets, diffusion through the macro/mesopores of the adsorbent, and adsorption at the surface, where the micropores exist. The adsorbent specifications along with its assembly within the sorption column are key factors when optimizing the filtration of pollutants. In this work we present a mathematical model based on advection–diffusion equations coupled with Langmuir kinetics that accounts for a geometrical approach to the porosity structure inside the adsorbent, formed by a radial lattice of cylinders, and the channels through which the fluid flows surrounding the cylindrical pellets. The model is tested using typical lab-scale values based on VOC adsorption, and we use it to identify optimal macro/mesopore size and column porosity for energetic considerations. [ABSTRACT FROM AUTHOR]

Summary Plant chemodiversity, the diversity of plant‐specialized metabolites, is an important dimension of biodiversity. However, there are so far few mathematical models to test verbal hypotheses on how chemodiversity evolved. Here, we develop such a model to test predictions of five hypotheses: the ‘fluctuating selection hypothesis’, the ‘dominance reversal hypothesis’, the interaction diversity hypothesis, the synergy hypothesis, and the screening hypothesis. We build a population genetic model of a plant population attacked by herbivore species whose occurrence fluctuates over time. We study the model using mathematical analysis and individual‐based simulations. As predicted by the ‘dominance reversal hypothesis’, chemodiversity can be maintained if alleles conferring a defense metabolite are dominant with respect to the benefits, but recessive with respect to costs. However, even smaller changes in dominance can maintain polymorphism. Moreover, our results underpin and elaborate predictions of the synergy and interaction diversity hypotheses, and, to the extent that our model can address it, the screening hypotheses. By contrast, we found only partial support for the ‘fluctuating selection hypothesis’. In summary, we have developed a flexible model and tested various verbal models for the evolution of chemodiversity. Next, more mechanistic models are needed that explicitly consider the organization of metabolic pathways. [ABSTRACT FROM AUTHOR]

In the face of ongoing challenges posed by the COVID-19 and the persistent threat of human immunodeficiency virus (HIV), the emergence of co-infections such as COVID-19 and HIV has heightened complexities in disease management. This study aims to identify effective control strategies to mitigate COVID-19 and HIV co-infection, which aggravates the existing challenges posed by these two diseases. To achieve this, we formulated a co-infection model that describes the transmission dynamics of COVID-19 and HIV. Under certain circumstances, we established that HIV infection may facilitate COVID-19 transmission, highlighting the need to identify and implement effective interventions to mitigate COVID-19 and HIV co-infection. As a result, we incorporated four time-dependent control strategies in the co-infection model: HIV prevention, HIV treatment, COVID-19 vaccination, and COVID-19 treatment. Numerical simulations were conducted to support and clarify the analytical results and to show how preventative efforts affect the co-infected population. Simulations confirm that applying any of the study's strategies will reduce the number of co-infection cases. However, the implementation of these strategies is constrained by limited resources. Therefore, a comprehensive cost-effectiveness analysis was conducted to identify the most economically viable strategy. The analysis concludes that implementing a combined approach of vaccination and treatment for COVID-19 emerges as the most cost-effective measure for preventing the spread of COVID-19 and HIV. These findings provide crucial guidance for decision-makers in adopting precise preventive strategies, ultimately aiming to reduce mortality rates among HIV patients. [ABSTRACT FROM AUTHOR]

Exact solutions have been constructed for some problems on thawing frozen soil in the process of water seeping into it as a result of the melting of underground ice and the associated violation of the mechanical integrity of the soil (thermokarst). Factors of thermokarst in frozen soil, determined by the specifics of heat and mass transfer in it, have been identified. The influence of the porosity of rocks, which changes during their melting, on the course of the thermokarst formation as a whole has been studied. An analytical solution to the problem of thermokarst is constructed. An expression was obtained for the rate of thermokarst formation in frozen soil. [ABSTRACT FROM AUTHOR]

A physical description is given of the formation of corrosion product deposits on the surfaces of pipelines of heat supply systems, and an investigation has been made into the effects of various factors on this process. An analysis has been made of the existing models of formation of corrosion deposites. A mathematical model has been developed for the formation of corrosion product deposites in the liquid's motion through pipelines of heat supply systems in the region of linear velocity of the growth of deposits at a constant temperature of the heat transfer agent. The model is based on equations of conservation of the mass of dissolved depolarizer and solid particles suspended in the solution. The parametric calculations performed on the basis of the developed mathematical model have shown a possibility for the existence of a maximum in the thickness of the corrosion product deposit layer through the pipe length. [ABSTRACT FROM AUTHOR]

We introduce the notion of positive strong amalgamation property and we investigate some universal forms and properties of this notion. Considering the close relationship between the amalgamation property and the notion of complete theories, we explore the fundamental properties of positively complete theories, and we illustrate the behaviour of this notion by bringing changes to the language of the theory through the groups theory. [ABSTRACT FROM AUTHOR]

The article examines the relevance of piezoceramic spherical shell actuators, which provide a high level of accuracy and stability in the generation of vibrational oscillations over a wide range of amplitude-frequency characteristics. The spherical shape of these actuators is chosen because it allows for uniform distribution of mechanical stresses across the actuator's surface, thereby enhancing its durability and efficiency compared to traditional flat or cylindrical designs. The study presents analytically derived mathematical models and formulas for determining the electrical impedance of piezoelectric elements and analyzes the dependence of the amplitude of electrical impedance on frequency and the charge ratio on the polarized surfaces of the spherical piezoceramic element. The proposed model enables the determination of electrical impedance as a function of cyclic frequency and various parameters (geometric, physical and mechanical, electrical) of the actuators. The study establishes that spherical shell actuators exhibit a higher quality factor (2-2.5 times greater than disk actuators and 1.4-1.8 times greater than cylindrical actuators) and a significant reduction in impedance (2.5-7 times lower) at electromechanical resonance frequencies around 2.4 kHz. Furthermore, spherical actuators demonstrate 20-30 % better resistance to deformation and 15-25 % lower susceptibility to local resonances compared to other actuator shapes, which enhances operational stability and vibration generation accuracy. [ABSTRACT FROM AUTHOR]

The paper aims to analyze the improved design of an in-pipe vibration-driven robot, which is equipped with a self-locking mechanism, electromagnetic exciter, and size-adapting devices. The study focuses on examining the robot's locomotion conditions at different working regimes. The research methodology contains four main stages: analysis of the design peculiarities of the enhanced wheeled in-pipe vibration-driven robot; developing a simplified dynamic diagram and deriving the differential equations to describe its locomotion conditions; carrying out numerical modeling with the help of Mathematica software to analyze the robot's basic dynamic parameters; conducting virtual experiments and testing the robot locomotion characteristics by means of the computer simulation in SolidWorks Motion software. The results obtained include the time-based data on the robot's displacement, speed, acceleration, and consumed power under different operating conditions, such as varying forced frequencies and excitation force amplitudes. The novelty of this investigation lies in identifying efficient working regimes for the improved wheeled vibration-driven robot intended for moving inside the pipelines. Future research will focus on developing a full-scale experimental prototype of the robot and conducting laboratory investigations at different working regimes. The findings of this research are valuable for scientists and engineers involved in the study and design of similar vibration-driven locomotion systems. [ABSTRACT FROM AUTHOR]

The crank-type vibration exciters represent innovative and promising actuators for a variety of vibratory technological equipment. Extensive research has demonstrated their potential for generating specific trajectories of the working components of various technological machines. This study builds upon previous investigations of the authors, focusing on the kinematics and dynamics of crank-type vibration exciters, with a specific emphasis on analyzing the forces, moments, and torques acting on the elements of the twin crank-type actuating mechanism. The research methodology involves the development of a simplified dynamic diagram of the mechanism and derivation of the analytical expressions to describe its force parameters. Mathematical modeling and computer simulation are then conducted to analyze the forces, moments, and torques experienced by the mechanism during its motion under different operational conditions and design parameters. The results obtained provide time-dependent profiles of these parameters across various conditions and design configurations of the twin crank-type mechanism. A key scientific contribution of this paper consists in the development of the theoretical basis for creating novel techniques of dynamic and strength analysis and optimization of design and operational parameters of enhanced vibration exciters equipped with twin crank-type mechanisms. The research findings offer valuable insights for engineers involved in the development and enhancement of vibratory technological machines equipped with crank-type vibration exciters. [ABSTRACT FROM AUTHOR]

This study aims to characterize ramie-low melt polyester nonwoven fabrics treated with low-temperature plasma and to analyze 3-D images based on object-depth mapping (ODM) using the MATLAB® R2022a software. We examined the low-temperature plasma treatment of nonwoven ramie fabrics using a plasma generator with 30 kV output power, six-minute treatment times, and a 4.5 cm distance between electrodes. The fabric's chemical properties and surface topography were investigated using scanning electron microscopy (SEM) and infrared spectroscopy (FTIR). An analysis of the SEM images was performed using a statistical approach and image processing to determine the level of surface roughness. FTIR analysis revealed that fabrics exposed for six minutes differed from those that were not. Our findings indicated that plasma treatment caused the following: 1) Ramie fabrics to become more hydrophilic, as shown by their increased T% in the FTIR of hydrophilic functional groups such as hydroxyl (O-H), carboxyl (-COOH), and carbonyl (C=O); 2) A higher surface roughness was observed in nonwoven fabric during SEM testing and image processing; 3) Plasma treatment of fabrics resulted in a higher coefficient of variation (CV) than untreated fabrics; 4) Nonwoven fabric mass reduction. Based on this study, we found the relationship between plasma-treated ramie fabric and textiles in biomechanics. Plasma treatment reduced the mass of ramie fabric by 0.11 %, according to our findings. We found that the greater the mass reduction, the greater the surface roughness value. The novelty of this study is the use of 3-D images based on object-depth mapping (ODM) using the MATLAB® R2022a software in SEM to observe surface roughness to the physical properties of ramie fabric for the first time. [ABSTRACT FROM AUTHOR]

In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the general fractional derivative to analyze the impact. The Laplace decomposition technique is employed to obtain the numerical outcomes of the model. In order to observe the effect of the diffusion component in the SIR model, graphical solutions are also displayed. [ABSTRACT FROM AUTHOR]