Mathematical Model For Calculation Research Articles

A mathematical model of a liquid-loading vessel at the initial stages of design

To substantiate the main unknowns at the initial stages of design and, above all, during the re-search design, it is necessary to develop a mathematical model as sensitive as possible to changes in variable parameters, which can be any elements of the vessel or its subsystems. The need to ensure seaworthiness, such as buoyancy, stability, unsinkability, strength, seaworthiness and capacity requires the inclusion of these modules in modeling either in the form of calculation functions, such as determining precipitation from the equation of mass and buoyancy, or in the form of restrictions requiring, if not fulfilled, recalculation of the former. The paper describes a similar mathematical model in relation to an oil tanker of mixed (river-sea) navigation of the M-SP class of the Russian Classification Society. Its feature is the use of computer-aided design of the hull shape and the inclusion in the mathematical model of the actual calculation of the elements of buoyancy, initial stability and capacity, rather than using statistical dependencies for them, which significantly increases the adequacy of the final result.

Study on the structure parameters and design method optimization of blade-type screw steel pipe pile

The rationality of structure parameters of the blade-type screw steel pipe pile is the major factor in determining the safety, applicability, and economy of a pile foundation, but the existing design methods have not defined the specific approaches to calculating structure parameters of blades and steel pipes. To address this issue, an analysis of the strength theory was performed on spatial helical blades, revealing the ratio of blade width to steel pipe radius as the core index to do the structure parameters design of blade-type screw steel pipe pile and established a mathematical calculation model between the vertical bearing capacity of single pile and a. The rational value of a is 2.0–3.0 using numerical calculation. The correlation between blade thickness and wall thickness of steel pipes was determined using the force analysis based on the synergy between blades and steel pipes. Then the structure parameters design method of blade-type screw steel pipe pile with coordinated parameters was proposed. The rationality and superiority of this design method were verified by comparing the existing test data and the finite element simulative analysis. Based on this design method and the current specifications, such as the Technical Code for Building Pile Foundations, a safe, applicable, and economical optimization design method and flow of blade-type screw steel pipe piles were further proposed for engineering design reference.

Real-Time Monitoring of Cable Sag and Overhead Power Line Parameters Based on a Distributed Sensor Network and Implementation in a Web Server and IoT.

Based on the need for real-time sag monitoring of Overhead Power Lines (OPL) for electricity transmission, this article presents the implementation of a hardware and software system for online monitoring of OPL cables. The mathematical model based on differential equations and the methods of algorithmic calculation of OPL cable sag are presented. Considering that, based on the mathematical model presented, the calculation of cable sag can be done in different ways depending on the sensors used, and the presented application uses a variety of sensors. Therefore, a direct calculation is made using one of the different methods. Subsequently, the verification relations are highlighted directly, and in return, the calculation by the alternative method, which uses another group of sensors, generates both a verification of the calculation and the functionality of the sensors, thus obtaining a defect observer of the sensors. The hardware architecture of the OPL cable online monitoring application is presented, together with the main characteristics of the sensors and communication equipment used. The configurations required to transmit data using the ModBUS and ZigBee protocols are also presented. The main software modules of the OPL cable condition monitoring application are described, which ensure the monitoring of the main parameters of the power line and the visualisation of the results both on the electricity provider's intranet using a web server and MySQL database, and on the Internet using an Internet of Things (IoT) server. This categorisation of the data visualisation mode is done in such a way as to ensure a high level of cyber security. Also, the global accuracy of the entire OPL cable sag calculus system is estimated at 0.1%. Starting from the mathematical model of the OPL cable sag calculation, it goes through the stages of creating such a monitoring system, from the numerical simulations carried out using Matlab to the real-time implementation of this monitoring application using Laboratory Virtual Instrument Engineering Workbench (LabVIEW).

Mathematical Model of Calculation of the Surface Intensity of Feed of a Coolant in Aviation Extinguishing of Ground Forest Fires

Mathematical Model of Calculation of the Surface Intensity of Feed of a Coolant in Aviation Extinguishing of Ground Forest Fires

Research on Resistance Characteristics of Fire Zone of Mine Tunnel Fire and Construction of Calculation Model

To investigate resistance change in the fire area of a roadway caused by roadway fires, a mathematical calculation model for thermal resistance is developed. Theoretical research is conducted to analyze the factors influencing resistance change through theoretical derivation, revealing that temperature is a key factor contributing to the change in thermal resistance. By leveraging the correlation between changes in CO concentration and temperature on the downwind side of the roadway within the fire zone, researchers developed mathematical models to predict temperature increases at various points downwind of the fire source. These models were then used to determine the mathematical relationship governing the change in thermal resistance. The accuracy of the numerical simulation software was validated using Fluent numerical simulation software and scaled-down model experiments. Full-scale numerical simulation experiments were conducted to investigate the fire characteristics of roadway fires and validate the thermal resistance mathematical model. The results indicate that the thermal resistance in the numerical simulation is 7.55 Pa at 20m from the fire source and 5.54 Pa at the end of the roadway. The decrease in resistance is linear. The minimum error between the thermal resistance calculated by the mathematical model and the gradient of the pressure drop in the numerical simulation is 0.03 Pa, approximately 2.3%. Furthermore, the fitting degree of the pressure drop in each section is as high as 97.7%. The calculation model demonstrates high accuracy and offers a theoretical foundation for investigating fire resistance in tunnel fire.

Visiting experience of digital museum interior design based on virtual reality and sensor networks

China's computer technology and image sensor technology are both rapidly developing, and the related advantages of digital holography technology are gradually expanding. These technologies have been applied in many fields. For example, three-dimensional measurement, deformation measurement, and anti-counterfeiting fields. This article combines holographic technology and virtual reality technology, and applies them to the interior design of digital museums and the optimization of auxiliary visits. A corresponding mathematical calculation model is established for digital holographic images, and in-depth research is conducted on this mathematical calculation model. Relevant personnel have also conducted relevant research on commonly used digital holography technology, and provided a detailed introduction to the principles of virtual reality technology. They have also conducted in-depth research on the specific working principles of VR technology and the application technology of virtual reality systems. Finally, an analysis and research were conducted on the development of Chinese museums, and a new perspective was proposed on the indoor space of museums under the new digital concept, which has certain reference significance. Currently, Chinese museums are thriving, so deepening the interior space of museums is very important. This article hopes to provide some guidance and practical value for the development of Chinese museums.

DSFworld: A flexible and precise tool to analyze differential scanning fluorimetry data.

Differential scanning fluorimetry (DSF) is a method to determine the apparent melting temperature (Tma) of a purified protein. In DSF, the raw unfolding curves from which Tma is calculated vary widely in shape and complexity. However, the tools available for calculating Tma are only compatible with the simplest of DSF curves, hindering many otherwise straightforward applications of the technology. To overcome this limitation, we designed new mathematical models for Tma calculation that accommodate common forms of variation in DSF curves, including the number of transitions, the presence of high initial signal, and temperature-dependent signal decay. When tested these models against DSFbase, an open-source database of 6235 raw, real-life DSF curves, these models outperformed the existing standard approaches of sigmoid fitting and maximum of the first derivative. To make these models accessible, we created an open-source software and website, DSFworld (https://gestwickilab.shinyapps.io/dsfworld/). In addition to these improved fitting capabilities, DSFworld also includes features that overcome the practical limitations of many analysis workflows, including automatic reformatting of raw data exported from common qPCR instruments, labeling of data based on experimental variables, and flexible interactive plotting. We hope that DSFworld will enable more streamlined and accurate calculation of Tma values for DSF experiments.

Physical Model of Inclusions Removal at Static Steel-Slag Interface.

Inclusions are one of the important factors affecting the cleanliness of molten steel. The current optimization of inclusion removal methods mainly focuses on promoting inclusions to float to the slag-steel interface so that the inclusions can be absorbed and removed by the refining slag. However, the research on the floating removal of inclusions cannot be carried out directly in the ladle, so methods such as mathematical models and physical models were developed. This article uses silicone oil to simulate the slag layer; polypropylene particles; and aluminum oxide particles to simulate inclusions to establish a water model experiment. By changing the viscosity of silicone oil and the diameter of particles, the factors affecting the movement of inclusions at the slag-steel interface were explored. Based on the water model, a mathematical model of the floating behavior of inclusions at the slag-steel interface was constructed, and parameters such as particle diameter and interfacial tension in the water model experiment were studied by the mathematical model for calculation. Both the mathematical model and the water model experimental results show that after the viscosity of silicone oil increases from 0.048 Pa·s to 0.096 Pa·s, the dimensionless displacement and terminal velocity of the particles decreases. When the diameter of the same particle increases, the dimensionless displacement and terminal velocity increases. The dimensionless displacement of polypropylene particles of the same diameter is larger than that of aluminum oxide particles, and the terminal velocity is smaller than that of aluminum oxide particles. This is attributed to the better overall three-phase wettability of polypropylene particle. When the liquid level increases, the dimensionless displacement and terminal velocity of particles under the same conditions show only slight differences (less than 10%).

A Numerical Study on Dust Control: Evaluating the Impact of Spray Angle and Airflow Speed in the Coalescence of Droplets and Dust

Spray dust reduction is one of the most economical and effective technologies for controlling coal dust in coal mining faces. We aimed to reproduce a spray dust reduction process in a simulation and investigate the mechanism by which the spray angle and airflow speed influence the dust reduction effect. Based on the DPM (discrete phase model) and the mixture model, we constructed a spray dust reduction evaluation model by considering two-way momentum coupling between the discrete phase and the continuous phase. The results showed that installing nozzles near the dust source (coal mining drum) significantly reduced the dust concentration at the coal mining face from 0.0005 kg/m3 to 0.0001 kg/m3. The increase in airflow speed and spray angle enhanced the horizontal transportation of droplets and dust, providing opportunities for the droplets to condense the dust; however, if the droplets have too large an angle, this will result in an insufficient concentration of droplets in the vicinity of the dust source. When the spray angle is 45°, increasing the airflow speed provides a better dust reduction effect. The nozzle position should also be set scientifically according to the airflow speed. Based on simulation results, a mathematical calculation model of spray dust reduction efficiency was constructed. These results can guide the key parameters of spray dust reduction systems, such as the installation position of the nozzle, the spray angle, and the airflow speed. This paper provides ideas for simulating spray dust reduction for other dust types.

Analysis the interaction of two cylindrical surfaces under shock impact load

The reactions of pipeline systems to shock impact load and the possibilities of the simulation and evaluation of dynamic processes are investigated in the paper. A heterogeneous system is composed of the elements with different properties, e.g. a pipeline with the sediment inside. Impact effect on it is one of the most effective methods to make substantial qualitative and quantitative changes in such system. The mathematical model for calculation of the elastically plastic displacements of the sediment was derived. It allows the analysis of dynamics of the change of the system’s specific state. The paper presents the calculation results of elastically plastic displacements of the substance caused by explosions in pipeline systems.

Modeling and control strategy optimizing of solar flux distribution in a four quadrant and adjustable focusing solar furnace

The solar furnace is key equipment for the thermochemical reaction research which uses focused solar energy to drive the reactor, and the solar flux distribution on the reactor surface plays a decisive role in the regulation of the thermochemical reaction process and formation of target products. In this paper, a reflective solar furnace with a thermal power of 30 kWth in Yanqing, Beijing, is taken as the research objective. Firstly, the Monte Carlo Ray Tracing (MCRT) method is used to establish the mathematical model for the optical calculation, and the distribution characteristics of solar flux are deeply analyzed. The accuracy of the model is verified through the comparison with the SolTrace software and experimental measurements respectively. Secondly, an improved four-quadrant and adjustable focusing solar furnace experimental equipment is developed, and a new solar flux distribution regulation strategy is proposed by using the inward crossover and outward expansion offset of the four-quadrant focusing points coupled with the heat-absorbing platform movement. The results show that the non-uniform factor and the peak value of the solar flux distribution in the set target area can be optimized by selecting an appropriate inward crossover offset and movement of the heat-absorbing platform, respectively. Moreover, when the DNI varies between 480 W/m2 and 800 W/m2, through the optimized control strategy, a non-uniformity factor with the value of less than 0.10 can be achieved in the target area of a square reactor surface with a side length of 10 cm, and the peak flux can also be controlled in the range from 3000 kW/m2 to 3300 kW/m2 with a fluctuation range of less than 10.0% as set by the thermochemical reaction. The optimized control strategy can effectively meet the uniformity and stability requirements of solar flux distribution in solar thermochemical reaction and finally achieve the goal of regulating the target products.

A linear mathematical optimization model for variable costs calculation in fertilizer production complex

A linear mathematical optimization model for variable costs calculation in fertilizer production complex

Rectifier load modeling and zero voltage switching design of inductive power transfer system with S‐type topology on the secondary side

SummaryRectifier load in inductive power transfer system has nonlinear characteristics. However, the traditional analysis method equates it to a pure resistor, which leads to a certain deviation between the theoretical analysis and the actual circuit. This will reduce the accuracy of the inductive power transfer (IPT) system model and affect the soft switching operation of the inverter. In this paper, the IPT system with S‐type topology on the secondary side is studied. Firstly, the resistance–inductance characteristics of the rectifier load are analyzed by simulation, and then a second‐order circuit response model is established to solve the time‐domain expression of voltage and current. Then, the fundamental component of voltage and current is extracted by Fourier transform to calculate the impedance value of the rectifier load, and the mathematical calculation model of the rectifier load is established. On this basis, the influence of the inductive component of the rectifier load on the input impedance of the IPT system is analyzed. Then, a parameter design method for zero voltage switching is proposed for S‐S and LCC‐S topologies. Finally, an experimental platform of S‐S and LCC‐S IPT system is built. The correctness and effectiveness of the theoretical analysis and the proposed parameter design method are verified by experiments.

Research on large-scale clean energy optimal scheduling method based on multi-source data-driven

With the large-scale growth and grid connection of intermittent renewable energy such as wind and solar, the problem of increasing renewable energy curtailment rate and system backup flexibility has become increasingly prominent. In order to solve the problem of high proportion of renewable energy scientific consumption and flexible and stable operation of energy system. We propose a flexible and economical dispatch method based on data-driven multi-regional power system. For the problem of economic dispatch of multi-area power system, a mathematical calculation model is established to satisfy the constraints of unit output, system power balance, unit ramp rate, and valve point effect, and to consider the requirement of minimizing the cost of multi-area power load comprehensively. Based on data-driven, this paper adopts an improved fruit fly optimization algorithm to quickly find the global optimal solution. The calculations are performed by IEEE6 simulation test system, and the results verify the feasibility of the proposed algorithm. The improved fruit fly optimization algorithm is compared and analyzed with other algorithms considering the quality of the obtained solutions. The results show the effectiveness and superiority of the proposed algorithm in solving multi-area economic dispatching problems in real power systems.

Research on the evacuation of people from a road tunnel fire based on a mathematical model

A mathematical model for the evacuation of people from a road tunnel is created, taking into account various factors such as the speed at which people move, the density of the flow of people, and the outcome of the fire. This model allows for the precise calculation of the evacuation time and the optimization of the evacuation route in a fire scenario. The constructed mathematical model was used to determine how long it would take for people to evacuate this road tunnel, and the findings of the Pathfinder simulation were compared. The findings demonstrate a relationship between the model's evacuation time and the human flow density, movement velocity, and fire product characteristics. The evacuation time is closer to the outcome of the actual fire scene when the impact of the fire environment on the speed of evacuation is quantified. The mathematical model of human evacuation's calculation of the evacuation time is essentially accurate when compared to the Pathfinder simulation's calculation, with an error of only 0.77 %. The model provides recommendations for optimizing the evacuation of people from a road tunnel in the case of a fire by not only predicting where the crowding would occur but also by calculating the duration of the crowding.

Investigation of the Application of Complex Function Theory in Underground Mine Design: A Case Study

This study, with the engineering background of the design of a stope involving a sublevel mining method in a certain underground metal mine, explored the application of stress-solving methods based on the complex variable function theory in actual engineering. Three mathematical calculation models based on the functions of a complex variable were established. Through triangle interpolation, mapping functions of a plane with a roadway section and a plane with the stope section were determined. An improved Schwarz alternating method was adopted to study the stability of the roadway and the influence of an adjacent roadway from the perspective of the stress field. In addition, in light of the distribution characteristics of a gangue in the stope, the design parameters of a pillar were optimized, with the pillar’s optimal dimensions determined. The results showed that when the magnitudes of two far-field principal stresses in the rock mass are relatively close, the distribution of the surrounding rock stress around the roadway is more uniform, and tensile stress is less likely to occur. The excavation of a neighboring roadway exacerbates to some extent the side stress of the other roadway, especially the compressive stress concentration on the side closer to the neighboring roadway. However, when the distance between the two roadways is significantly larger than the roadway size, this effect is not pronounced. In the engineering case studied in this research, the thickness of the pillar is approximately linearly positively correlated with the safety factor of the pillar approximately linearly negatively correlated with the recovery rate. Overall, this research explored the application of the complex variable function theory in an underground mine design, demonstrating its accuracy and practicality.

МОДЕЛІ УПРАВЛІННЯ РИЗИКАМИ З ВИКОРИСТАННЯМ СУЧАСНИХ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ

Risk management requires the use of a number of mathematical models for calculation. To use these models, it is necessary to form large databases on the quantitative characteristics of both the studied objects/processes/systems and the surrounding environment and conditions of the task. Implementation of this program requires the use of modern information technologies. The article analyzes the methodology for the formation of quantitative risk values, which allows for the formation of approaches to a certain standard for performing risk analysis for complex situations. A system of mathematical models and methods is proposed that allow building a system of quantitative modeling of risk situations for a wide class of objects/processes/systems. The article provides a comparative analysis of deterministic and stochastic risk management models, analyzes the riskiness model of risk stratification and the model for detecting differences from white noise. For the latter, a comparison of the experimental and theoretical concepts of the models was made. Information technologies that help organizations effectively identify, analyze and manage various types of risks, while providing a reliable protection mechanism against possible threats, such as ERM Systems, GRC Platforms, IRM Solutions, Cybersecurity Risk Management, Project Risk Management and Data Risk, are highlighted and analyzed Management.

Assessment and Health Risks of Glyphosate Residues and Traces Metals Elements in Groundwater Arround Abidjan Region, Côte d’Ivoire

Hydraulic networks from groundwater are the resources most exploited by the population for their daily needs. These water tables are constantly under pressure from pollution caused by human activities. In the tropical zone, more particularly in Ivory Coast, very few studies have been carried out on glyphosate, aminomethylphosphonic acid (AMPA), glufosinate and metallic trace elements (ETM) in groundwater. This study aims to determine the level of vulnerability of groundwater by these compounds. The study covered the waters of thirteen boreholes with an average depth of 69.26 meters near the Abidjan region (5°25'0" N / 4°1'60" W ) and the analyzes were carried out using the chromatographic method with detection by spectrophotometry. The results revealed the presence of glyphosate in all the samples analyzed at average concentrations of: 0.12±0.02 µg/L (minimum) and 1.9 ±0.1 µg/L (maximum), all higher than the water potability threshold value (0.1 µg/L) defined by the WHO. As for ETM, they are present in these boreholes at high concentrations of: 39±2 µg/L (As), 130±3 µg/L (Pb), 80±1 µg/L (Cu), 73±3 µg /L (Ni), 200±3 µg/L (Zn) at FILTISSAC, 20±2 µg/L (Cr) at Vridi and 21000 ±200 µg/L (S) in the Koumassi borehole. The health risk linked to the consumption of groundwater by the population, according to the mathematical calculation model used, is not acceptable. This study deserves to be conducted throughout the national territory.

Studying the influence of transport model parameters on the results of passenger traffic calculations (using the case of St. Petersburg)

This study focuses on the development of mathematical modelling methods for transport and urban planning. The current research focuses on an innovative mathematical model for simultaneous calculation of passenger and transport flow intensity in urban agglomerations using a common transport graph. An assessment of the model limitation impact on the parameters of individual and public transportation systems in a city (urban agglomeration) is conducted. To verify the model, several experimental calculations are performed for the transport system of the St. Petersburg agglomeration. The model presented by the authors can be used in scientific research in urban and transport planning and in the development of design solutions in cities.

Use of heat recovery technology to increase thermal efficiency of rotary furnaces

The article considers the problem of increasing the energy efficiency of rotary kilns, which are used in various industries for thermal processing of materials, such as metallurgical, chemical, construction, electrode and others. The source of heat for the kilns is gaseous fuel, which is supplied through special burners located at one end of the cylinder. The material for processing is loaded at the opposite end and moves towards the burner due to the force of gravity and rotation of the kiln. One of the important aspects of operating rotary kilns is energy efficiency, which depends on many factors and generally characterizes the degree of use of heat from fuel for heating the material. However, a significant part of the heat from fuel is lost through the kiln shell, which leads to an increase in fuel consumption and a decrease in kiln productivity. Therefore, it is necessary to look for ways to reduce heat losses and use part of the heat for other purposes. In this context, heating secondary air can be one of the important methods for increasing the thermal efficiency of rotary kilns, especially for kilns that operate in a mode for pyrolysis firing of materials such as coal, wood, peat, etc. The aim of the work is to increase the energy efficiency of a rotary kiln using a spiral heat exchanger, using the heat from the external shell of the kiln to heat secondary air. The paper proposes the use of a sectional heat exchanger, which can perform the functions of a cooler, a thermal insulator and a regulator of temperature regimes of the kiln. The heat exchanger consists of several sections that are attached to the outer surface of the kiln shell and have channels for air passage. The air is heated by contact with the hot shell and then supplied to the burner as secondary air. Thus, the heat exchanger allows to reduce the temperature of the shell and provide an additional source of hot air. A mathematical model for numerical calculation of a spiral heat exchanger has been developed, which allows to evaluate its thermal and temperature characteristics. It is shown that by using the heat from the shell it is possible to heat secondary air to a temperature of 270 °C in an amount sufficient to ensure the operation of the burner. An analysis of the location of the heat exchanger and the use of insulation coating has been carried out, which made it possible to significantly reduce its size without changing the total thermal effect compared to a heat exchanger installed along the entire length of the kiln shell. The effectiveness of using thermal insulation has been shown, which makes it possible to increase the temperature of air by 50 °C with its thickness 7 mm. The obtained results can be useful for further development and optimization of projects aimed at improving heat exchange systems and efficient use of thermal resources in rotary kilns.