scholarly journals Modeling and calculation of SC currents for alternative group grounding system for the dc contact line supports

2021 ◽  
Vol 2131 (4) ◽  
pp. 042067
Author(s):  
V A Osipov ◽  
A I Osipova
Keyword(s):  
Mathematical Model ◽  
Contact Line ◽  
Calculation Error ◽  
Model Quality ◽  
Grounding System

Abstract The problem of creating a mathematical model of the group grounding system of the contact line supports is considered. The paper considers an alternative way of organizing group grounding. For such a method of grounding, a model of a section of a DC railroad is proposed, which makes it possible to calculate the SC current. An analysis of the constructed model quality is carried out, an assessment of the calculation error according to the proposed method is given.

Identification of the Mathematical Model of a Gas Turbine Engine Taking Into Account the Uncertainty of the Initial Data

2021 ◽  
Author(s):  
Oleg Baturin ◽  
Grigorii Popov ◽  
Paúl Nicolalde ◽  
Anastasia Korneeva
Keyword(s):  
Mathematical Model ◽  
Probability Distribution ◽  
Initial Data ◽  
Mathematical Models ◽  
Gas Turbine ◽  
Gas Turbine Engine ◽  
Bivariate Distribution ◽  
Calculation Error ◽  
Turbine Engine ◽  
The Mathematical Model

Abstract The article describes the method developed by the authors and tested on the example of the AI-25 engine. The study was focused on determining the probability distribution of the output parameters of a gas turbine engine mathematical model. The distribution was obtained considering the uncertainty of the initial data. The paper describes the identified problems and possible ways to solve them. In particular, it was found that it is not possible to study the influence of more than 7..8 input parameters on the probability distribution of output parameters with the current level of development of computer technology even using simple mathematical models. For this reason, a method has been developed to obtain reliable results while reducing the number of considered input data based on sensitivity analysis. The paper also proposed a way of comparing stochastic experimental and computational data with each other using a bivariate distribution. This method allows a precise characterisation of the calculation error using 4 numerical values. The experience obtained in the work has shown that taking into account the uncertainty of the initial data dramatically changes the process of interpreting the results. It should be noted that the obtained results are universal and can be used with other mathematical models in various industries although they were developed on the example of the mathematical model of a gas turbine engine.

Moving contact lines in liquid/liquid/solid systems

1997 ◽  
Vol 334 ◽  
pp. 211-249 ◽  
Author(s):  
YULII D. SHIKHMURZAEV
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Contact Angle ◽  
Flow Field ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Three Phase

A general mathematical model which describes the motion of an interface between immiscible viscous fluids along a smooth homogeneous solid surface is examined in the case of small capillary and Reynolds numbers. The model stems from a conclusion that the Young equation, σ1 cos θ = σ2 − σ3, which expresses the balance of tangential projection of the forces acting on the three-phase contact line in terms of the surface tensions σi and the contact angle θ, together with the well-established experimental fact that the dynamic contact angle deviates from the static one, imply that the surface tensions of contacting interfaces in the immediate vicinity of the contact line deviate from their equilibrium values when the contact line is moving. The same conclusion also follows from the experimentally observed kinematics of the flow, which indicates that liquid particles belonging to interfaces traverse the three-phase interaction zone (i.e. the ‘contact line’) in a finite time and become elements of another interface – hence their surface properties have to relax to new equilibrium values giving rise to the surface tension gradients in the neighbourhood of the moving contact line. The kinematic picture of the flow also suggests that the contact-line motion is only a particular case of a more general phenomenon – the process of interface formation or disappearance – and the corresponding mathematical model should be derived from first principles for this general process and then applied to wetting as well as to other relevant flows. In the present paper, the simplest theory which uses this approach is formulated and applied to the moving contact-line problem. The model describes the true kinematics of the flow so that it allows for the ‘splitting’ of the free surface at the contact line, the appearance of the surface tension gradients near the contact line and their influence upon the contact angle and the flow field. An analytical expression for the dependence of the dynamic contact angle on the contact-line speed and parameters characterizing properties of contacting media is derived and examined. The role of a ‘thin’ microscopic residual film formed by adsorbed molecules of the receding fluid is considered. The flow field in the vicinity of the contact line is analysed. The results are compared with experimental data obtained for different fluid/liquid/solid systems.

Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters

1998 ◽  
Vol 120 (1) ◽  
pp. 92-99 ◽  
Author(s):  
Shinn-Liang Chang ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Contact Line ◽  
Relative Velocity ◽  
Tooth Profile ◽  
Gear Pair ◽  
Line Method ◽  
Envelope Method ◽  
Noncircular Gears

Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method, but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally, modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied, and to investigate the phenomenon of tooth undercutting.

scholarly journals Modeling the bacterial self-organization in a circular container along the contact line as detected by bioluminescence imaging

2011 ◽  
Vol 16 (3) ◽  
pp. 270-282 ◽  
Author(s):  
Romas Baronas ◽  
Remigijus Šimkus
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Contact Line ◽  
Bioluminescence Imaging ◽  
Reaction Diffusion ◽  
Growth Function ◽  
Model Parameters ◽  
One Dimensional ◽  
The Mathematical Model ◽  
Autocatalytic Growth

This paper presents a one-dimensional-in-space mathematical model of a bacterial selforganization in a circular container along the contact line as detected by quasi-one-dimensional bioluminescence imaging. The pattern formation in a luminous Escherichia coli colony was modeled by the nonlinear reaction-diffusion-chemotaxis equations in which the reaction term for the cells is a logistic (autocatalytic) growth function. By varying the input parameters the output results were analyzed with a special emphasis on the influence of the model parameters on the pattern formation. The numerical simulation at transition conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data.

The computation of ungulate age (mortality) profiles from dental crown heights

Paleobiology ◽  
1983 ◽  
Vol 9 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Richard G. Klein ◽  
Kathryn Cruz-Uribe
Keyword(s):  
Mathematical Model ◽  
Basic Program ◽  
Calculation Error ◽  
Crown Height ◽  
Age Classes ◽  
The Individual ◽  
Number Of Individuals ◽  
Potential Objection ◽  
Bone Accumulation ◽  
Dental Crown

The age (mortality) profiles of ungulate species in a fossil fauna are useful for reconstructing modes of death and of bone accumulation. Crown height measurements probably provide the most practical means of obtaining age profiles in most fossil samples. Reliable, interpretable profiles will result when individual age is estimated from crown height using a mathematical model first suggested by C. A. Spinage and when the individual ages are grouped into relatively broad age classes. One potential objection to the model is that it requires tedious calculation and there is a strong possibility of calculation error when many crown heights are involved. This problem may be circumvented by the use of an interactive BASIC program appended to this paper. The user supplies the raw crown heights in a fossil sample, together with estimates of initial unworn crown height, ages of dental shedding and eruption, and maximum possible individual age. The program then tabulates the number of individuals in successive 10%-of-potential-lifespan intervals.

scholarly journals Economic and mathematical modeling as an effective tool of the analysis of economic processes in industry

2019 ◽  
Vol 12 (3) ◽  
pp. 316-322
Author(s):  
A. S. Kulyasova ◽  
A. R. Esina ◽  
V. D. Svirchevskiy
Keyword(s):  
Mathematical Model ◽  
Resource Allocation ◽  
Foreign Currency ◽  
High Tech ◽  
Calculation Error ◽  
Allocation Mechanism ◽  
Industrial Enterprises ◽  
Statistical Regularities ◽  
Cost Of Materials ◽  
The Cost

In conditions of market volatility, an important issue for industrial enterprises is the issue of creating an efficient resource allocation mechanism. The article gives an example about using of individually adapted economic and mathematical model for forecasting the cost of materials and purchased products, that takes into account both internal and external factors affecting the planning figures. In order to create an effective predictive model, an analysis was conducted of statistical data for the period from 2009 to 2016, data was represented by high-tech enterprises of the radioelectronic industry. As a result of analysis it was revealed the presence of statistical regularities in the nature of the distribution of the analyzed data.On the basis of the calculated distribution parameters, a prediction procedure was performed using the exponential smoothing method and the total projected cost of materials and purchased products was obtained. The use of elements of probability theory and mathematical statistics, as well as methods for forecasting time series as basic methods of the model allows to take into account probabilistic economic factors, such as, for example, a change in the exchange rate of a foreign currency, as well as the presence of defects in the production process. Application of a special mathematical apparatus provides an ability to create a flexible, individually-adapted forecasting model. As a result of application of the model intended for forecasting the cost of materials and purchased products at one of industry enterprises it was revealed that the developed model has lover calculation error than the method that is used at the enterprise at present. Thus economic and mathematical model allows increasing the efficiency of the enterprise’s planned system and ensuring a rational resource allocation by increasing the accuracy of the forecasting process.

Theory of Cylindrical Gas Film Seal

2014 ◽  
Vol 602-605 ◽  
pp. 375-378
Author(s):  
Tao Chen ◽  
Mei Hong Liu
Keyword(s):  
Mathematical Model ◽  
Calculation Error ◽  
Film Pressure ◽  
Related Theory ◽  
The Mathematical Model

This paper mainly introduces the related theory and method of cylindrical gas film seal, the structure and principle of the cylindrical gas film seal, and solving the mathematical model, introduces several methods commonly used for solving the gas film pressure, and compare these methods, get the applicable conditions and calculation error of these methods.

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