Mathematical modeling versus experimental data: how to interpret conflicting evidence?

2022 ◽  
Vol 132 (1) ◽  
pp. 220-221
Author(s):  
Bruno Grassi ◽  
Valentina Quaresima
2022 ◽  
Vol 1049 ◽  
pp. 53-61
Author(s):  
Valeriy Lykhoshva ◽  
Dmitry Glushkov ◽  
Elena Reintal ◽  
Valeriy V. Savin ◽  
Ludmila Alexeyevna Savina ◽  
...  

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.


1991 ◽  
Vol 1 (2) ◽  
pp. 139-151
Author(s):  
J.W. Grant ◽  
J.R. Cotton

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.


MRS Advances ◽  
2016 ◽  
Vol 1 (56) ◽  
pp. 3727-3733
Author(s):  
Scott A. Sinex ◽  
Theodore L. Chambers ◽  
Joshua B. Halpern

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.


2014 ◽  
Vol 687-691 ◽  
pp. 1385-1388
Author(s):  
Zhuo Wang ◽  
Bin Nie ◽  
Ri Yue Yu

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.


1995 ◽  
Vol 03 (02) ◽  
pp. 429-439 ◽  
Author(s):  
S. G. RUDNEV ◽  
A. A. ROMANYUKHA

Using ordinary differential equations, we propose a mathematical model describing an “averaged” dynamics of variables involved in which some parameters are shown to be important characteristics of lung resistance. The model consists of modified D.A. Lauffenburger’s mathematical model for inflammatory reaction in lungs, and the model of humoral immune response (G. I. Marchuk). Coefficients are identified against clinical and experimental data. We attempt to elucidate some disease characteristics in terms of sensitivity analysis of model solutions with respect to parameters variations.


2019 ◽  
Vol 316 (5) ◽  
pp. H941-H957 ◽  
Author(s):  
J. Skogestad ◽  
G. T. Lines ◽  
W. E. Louch ◽  
O. M. Sejersted ◽  
I. Sjaastad ◽  
...  

The intracellular Na+ concentration ([Na+]) regulates cardiac contractility. Previous studies have suggested that subsarcolemmal [Na+] is higher than cytosolic [Na+] in cardiac myocytes, but this concept remains controversial. Here, we used electrophysiological experiments and mathematical modeling to test whether there are subsarcolemmal pools with different [Na+] and dynamics compared with the bulk cytosol in rat ventricular myocytes. A Na+ dependency curve for Na+-K+-ATPase (NKA) current was recorded with symmetrical Na+ solutions, i.e., the same [Na+] in the superfusate and internal solution. This curve was used to estimate [Na+] sensed by NKA in other experiments. Three experimental observations suggested that [Na+] is higher near NKA than in the bulk cytosol: 1) when extracellular [Na+] was high, [Na+] sensed by NKA was ~6 mM higher than the internal solution in quiescent cells; 2) long trains of Na+ channel activation almost doubled this gradient; compared with an even intracellular distribution of Na+, the increase of [Na+] sensed by NKA was 10 times higher than expected, suggesting a local Na+ domain; and 3) accumulation of Na+ near NKA after trains of Na+ channel activation dissipated very slowly. Finally, mathematical models assuming heterogeneity of [Na+] between NKA and the Na+ channel better reproduced experimental data than the homogeneous model. In conclusion, our data suggest that NKA-sensed [Na+] is higher than [Na+] in the bulk cytosol and that there are differential Na+ pools in the subsarcolemmal space, which could be important for cardiac contractility and arrhythmogenesis. NEW & NOTEWORTHY Our data suggest that the Na+-K+-ATPase-sensed Na+ concentration is higher than the Na+ concentration in the bulk cytosol and that there are differential Na+ pools in the subsarcolemmal space, which could be important for cardiac contractility and arrhythmogenesis. Listen to this article’s corresponding podcast at https://ajpheart.podbean.com/e/heterogeneous-sodium-in-ventricular-myocytes/ .


Author(s):  
Yuelei Yang ◽  
Dan Zhang

This paper introduces a mathematical model which can be used to simulate the capillary pumping process of a micro heat engine. The micro heat engine has micron sized channels where the capillary pumping occurs. The classic Volume of Fluids (VOF) method is applied to obtain the velocity profiles of the fluids and to track the motions of the liquid-gas interfaces. The numerical results based this model have been compared with the experimental data and the initial retard of the pumping has been found and this phenomenon can be explained by the initial capillary pressure build-ups across the liquid-gas interfaces.


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