scholarly journals Features of Adjusting the Frozen Soil Properties Using Borehole Temperature Measurements

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Mikhail Semin ◽  
Lev Levin ◽  
Aleksandr Bogomyagkov ◽  
Aleksei Pugin
Keyword(s):  
Mathematical Model ◽  
Survey Data ◽  
Frozen Soil ◽  
Temperature Measurements ◽  
Model Parameters ◽  
Processing Plant ◽  
Frozen Wall ◽  
Borehole Temperature ◽  
The Mathematical Model ◽  
Over Time

The paper examines the theoretical issues of using borehole temperature survey data to control a frozen wall formed around the sinking mine shafts of the Nezhinsk mining and processing plant potash mine. We consider adjusting the parameters of the mathematical model of the frozen soil based on temperature measurements in boreholes. Adjustment of the parameters of the mathematical model (thermophysical properties of the soil) is usually carried out by minimizing the discrepancy functional between the experimentally measured and model temperatures in the temperature control boreholes. An important question about the form of this functional and the existence of minima remained after the previous studies. The study aimed at this question included analysis of heat transfer in two horizontal layers (sand and chalk) for two shafts under construction using artificial ground freezing. It was shown that the discrepancy functional minimum under certain conditions moves over time or is nonunique. This phenomenon results in ambiguity in adjusting the mathematical model parameters in the frozen soil to fit the borehole temperature survey data. At the stage of the frozen wall growth, the effective thermal conductivity in the frozen zone can be determined ambiguously from the temperature measurements in the boreholes—its value can change over time. At the stage of maintaining the frozen wall, the solution turns out to be dependent on the ratio of effective thermal conductivities in the frozen and unfrozen zones.

Spectral characterization of ciliary beating: variations of frequency with time

1985 ◽  
Vol 249 (1) ◽  
pp. C160-C165 ◽  
Author(s):  
D. Eshel ◽  
Y. Grossman ◽  
Z. Priel
Keyword(s):  
Mathematical Model ◽  
Power Spectra ◽  
Ciliary Beating ◽  
Isolated Lung ◽  
Ciliary Cell ◽  
The Mathematical Model ◽  
Beating Frequency ◽  
Over Time ◽  
Dominant Frequencies

Ciliary beating frequency in tissue culture from frog palate and isolated lung was optically examined using instrumentation that was adjusted to measure a fraction of the surface area of a single ciliary cell. Consecutive 1-s segments of the analogue signal were fast Fourier transformed (FFT) to obtain a power spectrum. At room temperature, these power spectra changed over time from 1 s to the next. Each spectrum contained several dominant frequencies of similar intensities. Cooling the preparation resulted in a single-peak spectrum that was constant over time. A mathematical model is proposed to simulate these findings. The results and the mathematical model support the hypothesis that ciliary beating frequency fluctuates over short periods of time.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

scholarly journals The generation of a mathematical model of the biogas production process from organic municipal solid waste

2020 ◽  
Vol 180 ◽  
pp. 02019 ◽  
Author(s):  
Marzhan Temirbekova ◽  
Madina Aliyarova ◽  
Iliya Iliev ◽  
Aliya Yelemanova ◽  
Saule Sagintayeva
Keyword(s):  
Mathematical Model ◽  
Municipal Solid Waste ◽  
Solid Waste ◽  
Anaerobic Fermentation ◽  
Biogas Production ◽  
Biogas Plant ◽  
Model Parameters ◽  
Biochemical Processes ◽  
Biogas Plants ◽  
The Mathematical Model

This paper justifies the efficiency of the biogas collection and utilization at the MSW (municipal solid waste) landfill in Almaty with the installation of several modern biogas plants. The optimal mode of processes occurring in a biogas plant is determined by computer generated simulations. Mathematical model parameters were identified to describe biochemical processes occurring in a biogas plant. Two approaches are used to resolve the mathematical model: the finite-difference method for solving the system of differential equations and simulation modeling by using the Any Logic package. A program is written in the algorithmic language C ++. Numerous calculations were carried out, the results of which are presented in curves and their qualitative picture is consistent with the ongoing processes. The created computer program allows to make a preliminary forecast of anaerobic fermentation occurring in the bioreactor depending on volume of the substrate, methane microorganisms and temperature conditions.

The Study of Arc Teethed Automotive Synchronous Belt's Transmission Stability

2014 ◽  
Vol 915-916 ◽  
pp. 277-280
Author(s):  
Yao Chen Shi ◽  
Zhan Guo Li ◽  
Xiu Guang Yang
Keyword(s):  
Mathematical Model ◽  
Rotation Speed ◽  
Longitudinal Vibration ◽  
Dynamic Measurement ◽  
Frequency Change ◽  
Measurement Device ◽  
Transmission Process ◽  
Belt Transmission ◽  
The Mathematical Model ◽  
Over Time

The vibration of belt affected the transmission stability of automotive synchronous belt. The mathematical model of longitudinal vibration was established through analyzing the longitudinal vibration of automotive synchronous belt. Developed the vibration dynamic measurement device, aiming at RU style arc teethed synchronous belt transmission process, measured the variety of amplitude over time at the middle of the belt span obtained the rules of amplitude and frequency change along with the rotation speed. It is of certain importance to improving the transmission stability of arc teethed synchronous belt.

Study on the Dynamic Models of Systems Biology from the View of Engineering

2012 ◽  
Vol 220-223 ◽  
pp. 952-957
Author(s):  
Chen Liu ◽  
Xiao Yan Liu
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Dynamic Process ◽  
Biological System ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Biochemical Pathway ◽  
The Right ◽  
The Mathematical Model

From the view of engineering, based on expatiating the features of systems biology, the paper discusses the workflows and the research emphasis of systems biology. It also explains how to model and analyze the dynamic process of signal transmitting network for a biological system by an example. Based on the complexity and uncertainty of the mathematical model, the right methods are chosen to realize the effective estimation of state variables and model parameters for the biochemical pathway.

Drying of solids; estimation of the mathematical model parameters

2010 ◽  
pp. n/a-n/a ◽  
Author(s):  
Aleksandra Sander ◽  
Jasna Prlić Kardum ◽  
Antun Glasnović
Keyword(s):  
Mathematical Model ◽  
Model Parameters ◽  
The Mathematical Model

Research on the Simulation of the Charge Mathematical Model of the Vehicle Starting Battery

2013 ◽  
Vol 680 ◽  
pp. 479-483
Author(s):  
Pei Ying Li ◽  
Yu Tian Pan
Keyword(s):  
Mathematical Model ◽  
Battery Life ◽  
Model Parameters ◽  
Analysis Method ◽  
Lead Acid Battery ◽  
Battery Charge ◽  
Charge Model ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Lead Acid

In order to meet the demands of practical, convenient and quick charge requirements, a mathematical model of a certain type of vehicle starting lead-acid battery is established. Using the method of circuit analysis, the model parameters are identified by the known test data. In addition, battery charge model is simulated in each charge stage using the intelligent three-stage charge method, simulation waveform and test waveform fit very well, absolute errors between them reach to 10-6. Simulation results show that the mathematical model and its analysis method is proper for the charge characteristics of vehicle starting lead-acid battery. This has a good guidance to design intelligent charger and extend the battery life.

scholarly journals Determining the width of the ship’s course using a mathematical model to ensure the safety of the ship’s navigation

2021 ◽  
Vol 2131 (3) ◽  
pp. 032034
Author(s):  
O Lebedev ◽  
I Lipatov
Keyword(s):  
Mathematical Model ◽  
Time Interval ◽  
Safe Operation ◽  
Drift Angle ◽  
Model Experiments ◽  
Urgent Task ◽  
The Mathematical Model ◽  
Over Time ◽  
Shift Angle

Abstract Determination of the ship’s course width necessary for the ships safe operation is an urgent task due to the increase in the modern ships’ dimensions. The existing methods for assessing the fairway are calculated with a full re-positioning of the propulsion-rudder complex, according to the maximum drift angle. The vessel movement is considered to be steady, that is, the speed, the drift angles do not depend on time. The relevance of this study is associated with the assessment of determining the width of the fairway at any time interval. This is due to the fact that when passing the river sections, the vessels perform maneuvering with the rudder gear shifted for short periods of time and not at the maximum shift angle. Determination of the parameters of the ship’s movement over time when the navigator manipulates the ship’s controls (control of the rudder device, changing the parameters of the main engines) can be determined by the mathematical model of the ship’s movement. This article discusses the issues of creating a model that adequately describe the processes of vessel movement, including in the conditions of vessel movement along a limited ship’s course. The adequacy of the model was verified using the data of field and model experiments. According to the compiled mathematical model, the calculations were made for various projects of dry cargo ships.

scholarly journals Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

2021 ◽  
Author(s):  
S. Yu Martynov ◽  
V. L. Poliakov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Underground Water ◽  
Model Parameters ◽  
Kinetic Coefficients ◽  
Transfer Equations ◽  
The Mathematical Model ◽  
Autocatalytic Effect ◽  
Forms Of Iron

Abstract The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

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