scholarly journals A method for estimating the statistical error of the solution in the inverse spectroscopy problem

2021 ◽  
Vol 58 ◽  
pp. 3-17
Author(s):  
T.M. Bannikova ◽  
V.M. Nemtsov ◽  
N.A. Baranova ◽  
G.N. Konygin ◽  
O.M. Nemtsova
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Stable Solution ◽  
Statistical Error ◽  
Computer Processing ◽  
Error Evaluation ◽  
Distribution Law ◽  
Spectral Components ◽  
Real Experimental Data ◽  
Smooth Functional

A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.

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.

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.

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.

MATHEMATICAL MODELING OF IMMUNE-INFLAMMATORY REACTION IN ACUTE PNEUMONIA

1995 ◽  
Vol 03 (02) ◽  
pp. 429-439 ◽  
Author(s):  
S. G. RUDNEV ◽  
A. A. ROMANYUKHA
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Sensitivity Analysis ◽  
Inflammatory Reaction ◽  
Humoral Immune ◽  
Disease Characteristics ◽  
Acute Pneumonia ◽  
Lung Resistance

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.

scholarly journals Evidence for heterogeneous subsarcolemmal Na+ levels in rat ventricular myocytes

2019 ◽  
Vol 316 (5) ◽  
pp. H941-H957 ◽  
Author(s):  
J. Skogestad ◽  
G. T. Lines ◽  
W. E. Louch ◽  
O. M. Sejersted ◽  
I. Sjaastad ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Cardiac Myocytes ◽  
Ventricular Myocytes ◽  
Homogeneous Model ◽  
Cardiac Contractility ◽  
Channel Activation ◽  
Internal Solution ◽  
Rat Ventricular Myocytes ◽  
Quiescent Cells

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/ .

scholarly journals Detection and Positioning of Pipes and Columns with Autonomous Multicopter Drones

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Edmundo Guerra ◽  
Rodrigo Munguía ◽  
Yolanda Bolea ◽  
Antoni Grau
Keyword(s):  
Experimental Data ◽  
Multiple Solutions ◽  
Parametric Method ◽  
Vision Sensors ◽  
Pose Recovery ◽  
Combined Solution ◽  
Real Experimental Data

A multimodal sensory array to accurately position aerial multicopter drones with respect to pipes has been studied, and a solution exploiting both LiDAR and vision sensors has been proposed. Several challenges, including detection of pipes and other cylindrical elements in sensor space and validation of the elements detected, have been studied. A probabilistic parametric method has been applied to segment and position cylinders with LIDAR, while several vision-based techniques have been tested to find the contours of the pipe, combined with conic estimation cylinder pose recovery. Multiple solutions have been studied and analyzed, evaluating their results. This allowed proposing an approach that combines both LiDAR and vision to produce robust and accurate pipe detection. This combined solution is validated with real experimental data.

Sign in / Sign up

Export Citation Format

Share Document