scholarly journals Mathematical Modeling of Coal Dust Screening by Means of Sieve Analysis and Coal Dust Combustion Based on New Methods of Piece-Linear Function Approximation

2021 ◽  
Vol 11 (4) ◽  
pp. 1609
Author(s):  
Sergei Aliukov ◽  
Konstantin Osintsev
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Particle Motion ◽  
Coal Dust ◽  
Continuous Functions ◽  
Linear Functions ◽  
Equivalent Diameter ◽  
Sieve Analysis ◽  
Fuel Production ◽  
Exchange Processes

This study focuses on the development of new methodological approaches to dust-preparation and burning of separated particles, including through the use of polyfractional ensembles. Coal dust screening by means of sieve analysis is described in standard methods. However, in order to further use the results obtained during mathematical modeling of particle motion in fuel-air mixture and exothermal reactions of oxidation while burning in a torch, it must be possible to differentiate and integrate continuous functions. The methodology is based on the continuity of particle motion in a mixture with air in the calculation of aerodynamic and heat-mass exchange processes in a torch. The paper employs new scientific approaches to transforming and normalizing a continuously differentiable function described by the Gauss curve. We propose to combine mathematical modeling of such functions with methods of approximation of piece-linear functions developed by Professor S. V. Aliukov. The implementation of such methods helps reduce calculation errors of particle size and deviations thereof from average equivalent diameter and to avoid the Gibbs effect while differentiating. The paper contains analytical calculations based on the proposed method and experimental data. Quantitative and qualitative results of comparing analytical and experimental data are also presented. We provide recommendations on the further use and extension of the range of the results obtained in a computer simulation of fuel production and burning processes in a torch.

Technological Features of the Liquid-Solid State of the Boundary Layer in the Processes of Bimetallic Products

2022 ◽  
Vol 1049 ◽  
pp. 53-61
Author(s):  
Valeriy Lykhoshva ◽  
Dmitry Glushkov ◽  
Elena Reintal ◽  
Valeriy V. Savin ◽  
Ludmila Alexeyevna Savina ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Boundary Layer ◽  
Solid State ◽  
Liquid Phase ◽  
Contact Zone ◽  
Thermal Field ◽  
Thermal State ◽  
Existence Time ◽  
Modeling Data

The hydrodynamic and thermal state in the contact zone of the layers of a bimetallic product obtained by pouring liquid iron onto a solid steel billet, which changes in time and is responsible for the strength of the diffusion joint and the geometric parameters of the transition layer, has been investigated. Simplified analytical dependences, mathematical modeling data and experimental results of the liquid phase existence time in the contact zone based on research of the melt velocities during pouring and changes in the thermal field are presented. It is shown that simplified calculations data coincide in order and are close in values ​​to the calculations of mathematical modeling and experimental data, which makes it possible to use them for preliminary rough estimates by technologists and metallurgists.

A Model for Otolith Dynamic Response with a Viscoelastic Gel Layer

1991 ◽  
Vol 1 (2) ◽  
pp. 139-151
Author(s):  
J.W. Grant ◽  
J.R. Cotton
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Equations Of Motion ◽  
Otolith Organs ◽  
Major Contributor ◽  
Viscoelastic Solid ◽  
Gel Layer ◽  
Element System ◽  
Experimental Data Analysis ◽  
Finite Difference Techniques

The otolith organs were modeled mathematically as a 3-element system consisting of a viscous endolymph fluid in contact with a rigid otoconial layer that is attached to the skull by a gel layer. The gel layer was considered to be a viscoelastic solid, and was modeled as a simple Kelvin material. The governing differential equations of motion were derived and nondimensionalized, yielding 3 nondimensional parameters: nondimensional density, nondimensional viscosity, and nondimensional elasticity. The equations were solved using finite difference techniques on a digital computer. By comparing the model’s response with previous experimental research, values for the nondimensional parameters were found. The results indicate that the inclusion of viscous and elastic effects in the gel layer are necessary for the model to produce otoconial layer deflections that are consistent with physiologic displacements. Future experimental data analysis and mathematical modeling effects should include viscoelastic gel layer effects, as this is a major contributor to system damping and response.

scholarly journals Weibull-like Model of Cancer Development in Aging

2010 ◽  
Vol 9 ◽  
pp. CIN.S5460 ◽  
Author(s):  
Tengiz Mdzinarishvili ◽  
Simon Sherman
Keyword(s):  
Mathematical Modeling ◽  
Hazard Function ◽  
White Men ◽  
Cancer Registries ◽  
Incidence Rates ◽  
Linear Functions ◽  
Cancer Development ◽  
Additional Parameter ◽  
Men And Women ◽  
Hazard Functions

Mathematical modeling of cancer development is aimed at assessing the risk factors leading to cancer. Aging is a common risk factor for all adult cancers. The risk of getting cancer in aging is presented by a hazard function that can be estimated from the observed incidence rates collected in cancer registries. Recent analyses of the SEER database show that the cancer hazard function initially increases with the age, and then it turns over and falls at the end of the lifetime. Such behavior of the hazard function is poorly modeled by the exponential or compound exponential-linear functions mainly utilized for the modeling. In this work, for mathematical modeling of cancer hazards, we proposed to use the Weibull-like function, derived from the Armitage-Doll multistage concept of carcinogenesis and an assumption that number of clones at age t developed from mutated cells follows the Poisson distribution. This function is characterized by three parameters, two of which ( r and λ) are the conventional parameters of the Weibull probability distribution function, and an additional parameter ( C0) that adjusts the model to the observational data. Biological meanings of these parameters are: r—the number of stages in carcinogenesis, λ—an average number of clones developed from the mutated cells during the first year of carcinogenesis, and C0—a data adjustment parameter that characterizes a fraction of the age-specific population that will get this cancer in their lifetime. To test the validity of the proposed model, the nonlinear regression analysis was performed for the lung cancer (LC) data, collected in the SEER 9 database for white men and women during 1975–2004. Obtained results suggest that: (i) modeling can be improved by the use of another parameter A- the age at the beginning of carcinogenesis; and (ii) in white men and women, the processes of LC carcinogenesis vary by A and C0, while the corresponding values of r and λ are nearly the same. Overall, the proposed Weibull-like model provides an excellent fit of the estimates of the LC hazard function in aging. It is expected that the Weibull-like model can be applicable to fit estimates of hazard functions of other adult cancers as well.

Inspiring Online Collaborative STEM Learning

MRS Advances ◽  
2016 ◽  
Vol 1 (56) ◽  
pp. 3727-3733
Author(s):  
Scott A. Sinex ◽  
Theodore L. Chambers ◽  
Joshua B. Halpern
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
General Chemistry ◽  
High School Teachers ◽  
Informal Education ◽  
Student Feedback ◽  
Stem Learning ◽  
School Teachers ◽  
Undergraduate Level ◽  
Collaborative Skills

ABSTRACTEducators are advocating a variety of 21st century technologies to increase student engagement and prepare them for the modern workplace. As part of this effort this paper describes the development of several introductory laboratory activities which enhance online collaborative skills in the context of group collaborations. The experiments mostly deal with measurement and error in the context of mathematical modeling. They inculcate online collaborative skills including group writing, collection of experimental data, student feedback, and assessment using forms, spreadsheets with data pooling, real-time graphing/computations, and discussions using chat. These are all available in Google Drive, a free cloudbased application. We have also introduced student collaborative-pair computational spreadsheet assignments, and results of two projects in general chemistry are presented. Building formative assessment into these activities allows for immediate adjustment to instruction. This approach could be used from middle school through the undergraduate level. It can be implemented both in informal education or formal classroom settings by enhancing interactions with remote partners. Student evaluations have been very positive for the variety of activities, as well as from workshop feedback from high school teachers.

scholarly journals Equilibria and Systemic Risk in Saturated Networks

2021 ◽  
Author(s):  
Leonardo Massai ◽  
Giacomo Como ◽  
Fabio Fagnani
Keyword(s):  
Systemic Risk ◽  
Nash Equilibria ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Linear Functions ◽  
Shock Propagation ◽  
Fundamental Study ◽  
Network Games ◽  
Bifurcation Phenomenon

We undertake a fundamental study of network equilibria modeled as solutions of fixed-point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk in networks of financial institutions interconnected by mutual obligations. It is one of the simplest continuous models accounting for shock propagation phenomena and cascading failure effects. This model also characterizes Nash equilibria of constrained quadratic network games with strategic complementarities. We first derive explicit expressions for network equilibria and prove necessary and sufficient conditions for their uniqueness, encompassing and generalizing results available in the literature. Then, we study jump discontinuities of the network equilibria when the exogenous flows cross certain regions of measure 0 representable as graphs of continuous functions. Finally, we discuss some implications of our results in the two main motivating applications. In financial networks, this bifurcation phenomenon is responsible for how small shocks in the assets of a few nodes can trigger major aggregate losses to the system and cause the default of several agents. In constrained quadratic network games, it induces a blow-up behavior of the sensitivity of Nash equilibria with respect to the individual benefits.

Data Mining and Optimize TCM Prescription Compatibility Based on WDS-PLS

2014 ◽  
Vol 687-691 ◽  
pp. 1385-1388
Author(s):  
Zhuo Wang ◽  
Bin Nie ◽  
Ri Yue Yu
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Data Mining ◽  
Regression Coefficient ◽  
Uniform Design ◽  
Herbal Medicines ◽  
Data Standardization ◽  
Modeling Data ◽  
Pls Method ◽  
Original Formula

Data mining and optimize traditional Chinese medicine (TCM) prescription compatibility based on wavelet denoise spectral and partial least squares (WDS-PLS). Method: First of all, experimental design: with reference to the original formula, the herbal medicines in a prescription designed nine formula based on mixing uniform design; Secondly, obtain experimental data and data standardization; Finally, mathematical modeling, data mining and optimize TCM prescription compatibility base on WDS-PLS.Results: gain the regression coefficient and equation, VIP sorting, loadings Bi plot, and seek out the optimized direction of the prescription. Conclusion: the method data mining and optimize the compatibility of the dachengqi decoction is feasible and effective.

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