Mathematical Model Of Mechanism Research Articles

Atelectrauma can be avoided if expiration is sufficiently brief: evidence from inverse modeling and oscillometry during airway pressure release ventilation

BackgroundAirway 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.MethodsWe 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 E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${E}_{2}$$\\end{document} 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 (Rrs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{rs}$$\\end{document}).ResultsE2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${E}_{2}$$\\end{document}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 E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${E}_{2}$$\\end{document} was most depressed during inspiration in the higher-pressure group receiving the longer expiration, suggesting that E2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${E}_{2}$$\\end{document} reflects a balance between strain stiffening of the lung parenchyma and ongoing recruitment as lung volume increases. We also found in this group that Rrs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{rs}$$\\end{document} 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.ConclusionsThese 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.

Evaluation of cooling measures performance and thermal-humidity environment for ultra-high geothermal railway tunnel construction by using WBGT

High-geothermal damage is one of the major challenges in high-speed railway tunnel construction. Current studies have shortcomings in the formation mechanism of tunnel environment and the environment evaluation system. This may lead to an over-optimal environmental acceptability evaluation and jeopardize tunnel construction safety. This study established a mathematical model of the tunnel environment formation mechanism, proposed the wet-bulb globe temperature (WBGT) standard (26.49°C) for the tunnel construction, analysed the cooling efficiency of different environmental control measures. The results show that increasing the mechanical air supply volume can reduce tunnel temperature. Fog cannon can reduce the air temperature near the tunnel working face, the cooling range in front of the tunnel working face is 10.8 m. The cooling shield can control the WBGT below the standard. Under the 90°C rock temperature, the environmental acceptability of the tunnel under pure mechanical ventilation is 0%; the single fog cannon and double fog cannon (both cooperate with double-duct ventilation) are 22.85% and 54.29% respectively; the cooling shield with one fog cannon and double duct ventilation is 95.72%. This study improves the tunnel environment evaluation system during the construction stage, and provides design reference for temperature control measures in tunnel construction. Highlights: Tunnel environment under the impact of multi-physical coupling fields was analysed. Thermal radiation is taken into account in the formation of the tunnel environment. A new benchmark based on WBGT for high-geothermal tunnels construction was proposed. A tunnel environment assessment system was proposed. Cooling shield environmental-control measure was proposed for tunnel construction.

რისკების რაოდენობრივი შეფასების მაჩვენებელთა სისტემა და მათი ეკონომიკური ეფექტიანობის შეფასების მეთოდები

The mathematical models of the company's optimal risk management mechanism ensure the maximum efficiency of the activity at the level of risk acceptable to the enterprise. Classification of risks into operational risk and interest risk is given. One of the possible options for determining the tasks of optimal planning of the enterprise is presented, which includes restrictions on the values of operational effect (OE) (OR). The OE (two) indicator is considered as a limitation, the normative value of which can be considered as a given value during planning. It is a multidimensional linear optimal planning problem with linear constraints. Its size is determined by the number of product types in the enterprise. We have formulated original economic-mathematical models of the distribution type, which are used to create the optimal production plan of the enterprise. In order to minimize the interest risk, we have used the duration indicator analysis method. Duration represents the elasticity of the price of a financial instrument (in this case the present value of a stream of payments) with respect to the interest rate (discount rate) and is therefore a measure of the risk of the price of the instrument changing when the interest rate changes.

Implementation of multi-criteria decision making for the ranking of drugs used to treat bone-cancer

&lt;abstract&gt; &lt;p&gt;The concept of "topological index" refers to a numerical value determined by the structure of a chemical network. It serves to determine the physicochemical and biological properties of diverse medications, offering a more precise depiction of the theoretical properties of organic materials, this is achieved through the utilization of degree-based topological indices. Because of the development of resistance to existing treatments and the unpleasant side effects associated with some current drugs, the hunt for new drugs remains a priority. In drug discovery, QSPR approaches are widely used to predict, from a chemical structure, the biological activity of potential novel drugs. Researchers can prioritize compounds for synthesis and optimize them to improve potency, preference, and other desired attributes by establishing a correlation between chemical features and biological activity. Rational drug design approaches incorporate research methodologies such as quantitative structure-activity relationships (QSAR) and quantitative structure-property relationships (QSPR), along with decision-making strategies. The goal of these strategies is to improve the biological activity and physicochemical qualities of existing leads. This research includes mathematical modeling of drug mechanisms utilizing multiple-criteria decision analysis and QSPR analysis. Furthermore, using decision-making techniques, I can determine the order of production for various drugs used to treat bone cancer based on their examination using QSPR analysis and topological indices.&lt;/p&gt; &lt;/abstract&gt;

Mathematical model of shock-vibration mechanism.

Mathematical model of shock-vibration mechanism.

Justification of rational operating parameters of vibration disc-working engines of seeding units to improve energy-technological indicators

The article addresses the interaction of disc vibration working elements of a seed drill with soil to reduce traction resistance and energy consumption in soil processing. Regularities characterizing the impact of vibrations on the soil are identified, and a mechanical-mathematical model of soil cutting by the vibrational disc-working element of a seed drill is developed. Mathematical dependencies for determining the parameters of vibro-impact interaction of the cutting edge of the disc-working element with the soil are obtained. The efficiency conditions of the vibro-cutting process, in terms of reducing traction resistance and energy consumption, are established. A methodology for selecting rational parameters for vibro-cutting soil in the design and operation of the disc-working element of seeding equipment is developed. Experimental results of a prototype vibrational working equipment are presented, confirming theoretical findings and demonstrating the effectiveness and feasibility of vibrational soil cutting by the disc-working element for reducing traction resistance and energy costs. The research, the results of which are presented in this article, is funded by the Committee on Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant AP14869252 "Development of the universal sowing complex with increased productivity for the agro-industrial production of the Republic of Kazakhstan").

Mathematical modeling of small soil channel laboratory stand drive and evaluation of its energy state

The article presents data on improving the design of the Small Soil Channel research laboratory stand. The possibilities of experimental works on study of kinematic parameters and structural parameters, spatial dynamometering of working elements of tillage and sowing machines are described. The article considers the method for assessing the energy state of the laboratory stand small soil channel and studying the power distribution in its moving mechanisms. Based on the parameters obtained as a result of solving the equations of motion and energy state, using the full differential of the Hamelton function, the power distribution in the mechanisms under the action of external forces and the total mechanical energy of the stand are determined. The traction resistance of stand working body was determined using the Goryachkin formula. Based on the developed kinematic scheme, a mathematical model has been developed that imitates the movement of the belt transmission mechanism of the stand. Based on the developed mathematical model, calculation experiments were carried out using the Runge-Kutt numerical method, the results made it possible to find the motion parameters of the belt transmission mechanism of the stand. The results obtained when solving the mathematical model of the belt transmission mechanism of the stand made it possible to determine the parameters of movement of the stand engine and the drum. This article presents the results of determining the stiffness and elasticity coefficients of the belt, the moment of resistance of the drum, the driving moment of the driving pulley, angular speed, angular rooting, the moment of inertia of the driving and driven pulleys by compiling a mathematical model of the Laboratory Stand Small Soil Channel that imitates the working process of tillage and sowing machines.

Mechanical-Mathematical Modeling of the Shape of Dental Arches for Orthognathic Occlusion

Mechanical-Mathematical Modeling of the Shape of Dental Arches for Orthognathic Occlusion

A simulation Model of COVID-19 Epidemic Based on Vaccination and Treatment

This article presents a mathematical model of the COVID-19 transmission mechanism, considering therapeutic interventions like immunization and recovery or treatment. The model shows that the disease-free and endemic equilibriums are globally asymptotically stable when effective reproduction numbers are less than or larger than unity. The critical vaccination thresholddepends on the vaccine’s ability to prevent or cure the illness. The model predicts the effectiveness of vaccination based on factors like vaccination efficiency, scheduling, and relaxation of social measures. The subsiding of the epidemic as vaccination is implemented depends on the scale of relaxation of social measures.

Autoignition Problem in Homogeneous Combustion Systems: GQL versus QSSA Combined with DRG

The global quasi-linearization (GQL) is used as a method to study and to reduce the complexity of mathematical models of mechanisms of chemical kinetics. Similar to standard methodologies, such as the quasi-steady-state assumption (QSSA), the GQL method defines the fast and slow invariant subspaces and uses slow manifolds to gain a reduced representation. It does not require empirical inputs and is based on the eigenvalue and eigenvector decomposition of a linear map approximating the nonlinear vector field of the original system. In the present work, the GQL-based slow/fast decomposition is applied for different combustion systems. The results are compared with the standard QSSA approach. For this, an implicit implementation strategy described by differential algebraic equations (DAEs) systems is suggested and used, which allows for treating both approaches within the same computational framework. Hydrogen–air (with 9 species) and ethanol–air (with 57 species) combustion systems are considered representative examples to illustrate and verify the GQL. The results show that 4D GQL for hydrogen–air and 14D GQL ethanol–air slow manifolds outperform the standard QSSA approach based on a DAE-based reduced computation model.

Comprehensive energy efficiency analysis of ultra-supercritical thermal power units

At present, ultra-supercritical power plant is the most advanced technology, which can achieve ultra-low pollutant emissions and greatly improve the energy efficiency of power plant. In this paper, the key factors affecting the energy efficiency of thermal power unit are analyzed. Moreover, the way in which these factors affect the energy efficiency of thermal power unit is obtained. Besides, this study lay a solid foundation for subsequent improvements in the energy efficiency of thermal power unit. First, a mathematical mechanism model of ultra-supercritical thermal power units is established. In addition, Aspen Plus software is used to build a full process simulation model of thermal power unit. In addition, a methodology for energy efficiency analysis based on the exergy balance theory is presented, and energy efficiency evaluation indicators are defined. Finally, the TOPSIS method was used to rank the key factors affecting the energy efficiency of thermal power unit. Based on experimental analysis, this study found that in comparison to general unit, the ultra-supercritical thermal power units has improved boiler efficiency by approximately 2%, power generation efficiency by approximately 6.77%, carbon emissions by approximately 0.027 t/h and the exergy efficiency by approximately 2.91%, providing better energy efficiency and lower carbon emissions.

Toward computational neuroconstructivism: a framework for developmental systems neuroscience.

Brain development is underpinned by complex interactions between neural assemblies, driving structural and functional change. This neuroconstructivism (the notion that neural functions are shaped by these interactions) is core to some developmental theories. However, due to their complexity, understanding underlying developmental mechanisms is challenging. Elsewhere in neurobiology, a computational revolution has shown that mathematical models of hidden biological mechanisms can bridge observations with theory building. Can we build a similar computational framework yielding mechanistic insights for brain development? Here, we outline the conceptual and technical challenges of addressing this theory gap, and demonstrate that there is great potential in specifying brain development as mathematically defined processes operating within physical constraints. We provide examples, alongside broader ingredients needed, as the field explores computational explanations of system-wide development.

Lissajous confocal fluorescent endomicroscopy with a lever mechanism and a frequency separation by an asymmetric polymer tube

We present a confocal fluorescent endomicroscopic system with a Lissajous scan using an asymmetric polymer tube and piezoelectric (PZT) tube actuator. The fiber cantilever’s scanning part is often inside the PZT tube actuator to reduce the scanner’s rigid length and enhance the beam deflection via a lever mechanism. Here, the mathematical model of the PZT tube actuator-based lever mechanism is first proposed by considering the piezoelectric parameters of the actuator and Euler-Bernoulli beam deflection, showing a good agreement with experimental data. In addition, an elliptical polymer tube is used to divide the resonant frequencies of the fiber cantilever, allowing enough scanning amplitudes and alleviating the inherent cross-coupling issue of a PZT tube actuator. The design optimization is performed by selecting the optimal lever length and the shape of the PFA tube. The implemented endomicroscopic probe could successfully acquire imaging results from both a lens-cleaning tissue and an ex-vivo mouse colon.

Analysis and Design of the High Current Rising Rate Hybrid DC Current Limiting Circuit Breaker

To solve the problem of the high rising rate and large peak value of the expected current of the short-circuit current in marine DC power system faults, a hybrid DC current limiting circuit breaker scheme based on a high-speed electromagnetic repulsion mechanism is proposed. A parameter selection model is constructed by comprehensively considering the short-time withstand of the thyristor, the volume of the commutation circuit, and capacitor energy, and the optimal value of the commutation circuit parameters at a certain voltage level is obtained. The finite element mathematical model of the high-speed electromagnetic repulsion mechanism is established by coupling the electromagnetic force field, which enables the deformation process of the mechanism under the condition of high acceleration to be considered. The von Mises yield criterion is adopted as the mechanical boundary condition in the design of a high-speed electromagnetic repulsion mechanism, which solves the problem of the long inherent time of opening. The experiment platform is built, and the experiment under the fault condition with a current rising rate of 20 A/μs is completed. The arcing time, commutation time, zero-voltage recovery time, and contact movement characteristics are obtained, which meet the design requirements, verify the effectiveness of the analysis, and lay a solid foundation for further research and development of the current limiting circuit breakers for medium voltage DC systems.

Design of 4UM-120D Electric Leafy Vegetable Harvester Cutter Height off the Ground Automatic Control System Based on Incremental PID

In this study, a 4UM-120D electric leafy vegetable harvester was employed as the research object. An automatic control system was created to maintain the cutter’s height above the ground within ±2% of the desired value. The intention was to reduce the operators’ work intensity while improving the leafy vegetable harvester’s working quality. The automatic control system for the cutter height from the ground was explained, along with its structure and operating philosophy. MATLAB was used to establish the two-phase hybrid stepper motor’s mathematical electrical equation and mechanical equation models. An analysis was carried out on the fundamentals and differences between position PID and incremental PID control algorithms. Utilizing incremental PID in combination, the control strategy for the harvester cutter height from the ground was built, and an automatic control system was produced under the corresponding control strategy. The stability, accuracy, and rapidity of the automatic control system of the cutter height from the ground under the incremental PID control strategy were analyzed by simulating different actual working conditions with MATLAB/Simulink and taking the steady-state transition time as the evaluation index. The test results show that when the deviation between the current value and the set value was greater than 2%—that is, when the harvester was in the condition of suddenly crossing the ditch or suddenly climbing the slope—the automatic control system based on the incremental PID control strategy had a good dynamic response performance and stability. This resulted in the automatic control function of the harvester cutter height off the ground being achieved. When the rotation angle PID control algorithm’s proportional coefficient is Kp = 4.665, the rotation speed PID control algorithm’s proportional coefficient is Kp = 5.65 and its integral coefficient is Ki = 3.86, and the current PID control algorithm’s proportional coefficient is Kp = 0.5455 and its integral coefficient is Ki = 30.4578. The harvester abruptly crossed a ditch while operating steadily, and the automatic control system’s steady-state transition time for the height of the cutter off the ground was 1.0811 s. The harvester abruptly climbed a slope while operating steadily, and the automatic control system’s steady-state transition time for the height of the cutter off the ground was 1.1185 s. Data from the field tests revealed a degree of reliability in the simulation test results. The study offered a strategy for raising the harvester quality for leafy vegetables while lowering the operator workload.

A mathematical model for mechanical activation and compound action potential generation by the utricle in response to sound and vibration.

Calyx bearing vestibular afferent neurons innervating type I hair cells in the striolar region of the utricle are exquisitely sensitive to auditory-frequency air conducted sound (ACS) and bone conducted vibration (BCV). Here, we present experimental data and a mathematical model of utricular mechanics and vestibular compound action potential generation (vCAP) in response to clinically relevant levels of ACS and BCV. Vibration of the otoconial layer relative to the sensory epithelium was simulated using a Newtonian two-degree-of-freedom spring-mass-damper system, action potential timing was simulated using an empirical model, and vCAPs were simulated by convolving responses of the population of sensitive neurons with an empirical extracellular voltage kernel. The model was validated by comparison to macular vibration and vCAPs recorded in the guinea pig, in vivo. Transient stimuli evoked short-latency vCAPs that scaled in magnitude and timing with hair bundle mechanical shear rate for both ACS and BCV. For pulse BCV stimuli with durations <0.8 ms, the vCAP magnitude increased in proportion to temporal bone acceleration, but for pulse durations >0.9 ms the magnitude increased in proportion to temporal bone jerk. Once validated using ACS and BCV data, the model was applied to predict blast-induced hair bundle shear, with results predicting acute mechanical damage to bundles immediately upon exposure. Results demonstrate the switch from linear acceleration to linear jerk as the adequate stimulus arises entirely from mechanical factors controlling the dynamics of sensory hair bundle deflection. The model describes the switch in terms of the mechanical natural frequencies of vibration, which vary between species based on morphology and mechanical factors.

Designing a Computer Simulation Model to Study the Failure Mechanism in Rotating Shaft

The phenomenon of the failure of rotating mechanical structures is considered one of the dangerous phenomena that researchers are trying to study to find effective ways to avoid it. Many mathematical models describing the mechanism of crack formation in structures and the occurrence of failure in them have been adopted. In this paper, a computer simulation model of the failure mechanism in the intermediate conduction shaft of the ship's propeller (oil shuttle tanker) was designed based on the mathematical model that describes the stages of failure according to the number of revolutions that the shaft bears and the dimensions of fatigue cracks in it. In the beginning, a detailed mathematical model of the crack propagation mechanism was deduced as an initial stage, through which the differential equations that express the failure of the shaft were described. In the second stage, numerical simulations were implemented using the Euler and Rung-Kutta numerical methods used in solving ordinary differential equations. Also, for both methods using the Matlab language to reach the results and accurate graphs and analyze them. In this way it is possible to predict the number of cycles that the column will bear before the collapse, and this will reduce the occurrence of sudden collapses and save time, effort, and costs.

Stability of equilibrium points of equation of regulatory mechanisms of cardiac activity

The article presents a mathematical model of regulatory mechanisms of cardiac activity in the form of system of functional-differential equations with delay arguments. With the use of reduction and scaling methods, the system of equations is reduced to the form of a functional-differential equation with delay argument. The equation was qualitatively analyzed. Equilibrium points are revealed and their stability is analyzed. As a result of a qualitative analysis, it was revealed that the mathematical model can reflect various modes of regulatory mechanisms of cardiac activity in normal conditions and in case of anomalies, the modes such as stationary, auto-oscillating, dynamic chaos, “black hole” and falling state.

STUDY OF THE STRESS-STRAIN STATE OF THE MAXILLA DURING ORTHODONTIC TREATMENT OF DENTOGNATHIC DEFORMATIONS IN CHILDREN WITH CONGENITAL CLEFT LIP AND PALATE.

The aim: To create a three-dimensional simulation mechanical-mathematical model of the biomechanical system "Orthodontic appliance-maxilla", to study peculiarities of the stress-strained state of the maxilla. Materials and methods: A simulation model of the biomechanical system "Orthodontic appliance-maxilla" was created using computed tomography (CBCT) data. Mathematical modeling was used to determine the stress-strain state of the simulation model. Results: The patterns of changes in the stress state were determined and the values of deformation displacements in the structural elements of the biome-chanical system "Orthodontic appliance-maxilla" were determined under a force stress of the orthodontic device with an amplitude of 50 N. Conclusions: Simulation computer modeling of the stress-strain state of the "Orthodontic appliance-maxilla" system showed that activation of the kinematic mechanism of the appliance with a force of 50 N causes the emergence of a complex stress-strain state of bones. When the orthodontic appliance is activated, there is an asymmetry in the distribution of stresses by Mises between the right and left sides both for the appliance itself and for the maxillary bone tissue.

Numerical modeling of crack formation and propagation using contact elements

The work is devoted to modeling the process of formation, development and propagation of cracks. Currently, there is a large number of physical and mechanical-mathematical models describing the process of destruction of various materials. In addition to the fracture criteria, it is also important to correctly take into account changes in the rheology of the fractured material, including the contact interaction between the surfaces of cracks and fragments. This paper proposes a numerical approach to solving the problems of contact interaction and brittle fracture of elastically deformable bodies. Crack bank interactions, including frictional forces and contact pressures, is modeled by the means of frame-type contact finite elements (CFE) using a stepwise analysis method. Various contact conditions – separation, clutch, friction-sliding, as well as rheological properties of crack surfaces and fragments – contact layer pliability, adhesion strength, etc. are modeled with the help of CFE. The proposed approach was used in the numerical modeling of bone damage under the penetrating action of a rigid indenter. The conducted numerical studies have shown a good correspondence of the calculated and experimental results, despite the substantial approximation of the used calculation schemes.