scholarly journals On the correct use of mathematical constructions in physical models

2020 ◽  
pp. 7-27
Author(s):  
M. Belevich
Keyword(s):  
Mathematical Models ◽  
Physical Meaning ◽  
Fluid Model ◽  
Model Development ◽  
Physical Models ◽  
Model Modification ◽  
First Case ◽  
Viscous Fluid Model ◽  
Model Equations ◽  
Physical Phenomena

The physical limitations of the mathematical constructions used in developing or modifying mathematical models are discussed. All reasonings are illustrated by examples from fluid mechanics. The following topics are considered: means of description; correct approach to model modification and the physical meaning of model development stages. In the first case, the method of describing physical objects using numbers as well as corresponding restrictions are investigated, followed by developing general recommendations on procedures for modifying mathematical models of fluid dynamics. The well-known procedure of averaging the viscous fluid model equations to obtain the turbulent fluid model is used as an illustration. Since we are considering the models of physical phenomena, it is natural to provide physical interpretation for each stage of model development. Unfortunately, some of the transformations used are often treated as purely technical tricks, therefore denoting the lack of the physical meaning in such cases, which does not make a mathematical procedure unacceptable, but does mark out the model's place which requires reasonable interpretation. In this paper, we are considering two variants of this kind of interpretation, namely the case of using imaginary quantities, and the case of applying integral transformations. Meanwhile, all the above-mentioned restrictions are not always given due attention. Sometimes this leads to various undesirable consequences, including excessive task complication, implicit substitution of a declared problem with another one, or, finally, lack of solution to the formulated problem.

scholarly journals Viscosity Model for Nanoparticulate Suspensions Based on Surface Interactions

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2752
Author(s):  
Benedikt Finke ◽  
Clara Sangrós Sangrós Giménez ◽  
Arno Kwade ◽  
Carsten Schilde
Keyword(s):  
Mechanistic Model ◽  
Model Development ◽  
Rheological Behaviour ◽  
Hybrid Modelling ◽  
Shear Rates ◽  
Drag Forces ◽  
Boehmite Nanoparticles ◽  
Data Points ◽  
Two Parameters ◽  
Physical Phenomena

In this paper, a widely mechanistic model was developed to depict the rheological behaviour of nanoparticulate suspensions with solids contents up to 20 wt.%, based on the increase in shear stress caused by surface interaction forces among particles. The rheological behaviour is connected to drag forces arising from an altered particle movement with respect to the surrounding fluid. In order to represent this relationship and to model the viscosity, a hybrid modelling approach was followed, in which mechanistic relationships were paired with heuristic expressions. A genetic algorithm was utilized during model development, by enabling the algorithm to choose among several hard-to-assess model options. By the combination of the newly developed model with existing models for the various physical phenomena affecting viscosity, it can be applied to model the viscosity over a broad range of solids contents, shear rates, temperatures and particle sizes. Due to its mechanistic nature, the model even allows an extrapolation beyond the limits of the data points used for calibration, allowing a prediction of the viscosity in this area. Only two parameters are required for this purpose. Experimental data of an epoxy resin filled with boehmite nanoparticles were used for calibration and comparison with modelled values.

The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Samer Hassan ◽  
Masahiro Kawaji
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Particle Motion ◽  
Fluid Model ◽  
Resonance Phenomenon ◽  
Fluid Viscosity ◽  
Mass Force ◽  
Amplitude Data ◽  
Viscous Fluid Model ◽  
Fluid Cell

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities (58.0cP and 945cP), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5cP and 945cP. While there is a resonance frequency corresponding to the particle peak amplitude for oil (58.0cP), this phenomenon disappeared for glycerol (945cP). This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals Using Model Performance to Assess the Representativeness of Data for Model Development and Calibration in Financial Institutions

Risks ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 204
Author(s):  
Chamay Kruger ◽  
Willem Daniel Schutte ◽  
Tanja Verster
Keyword(s):  
Case Studies ◽  
Model Development ◽  
Model Performance ◽  
Data Set ◽  
Pooled Data ◽  
External Data ◽  
First Case ◽  
Multivariate Prediction ◽  
Credit Data

This paper proposes a methodology that utilises model performance as a metric to assess the representativeness of external or pooled data when it is used by banks in regulatory model development and calibration. There is currently no formal methodology to assess representativeness. The paper provides a review of existing regulatory literature on the requirements of assessing representativeness and emphasises that both qualitative and quantitative aspects need to be considered. We present a novel methodology and apply it to two case studies. We compared our methodology with the Multivariate Prediction Accuracy Index. The first case study investigates whether a pooled data source from Global Credit Data (GCD) is representative when considering the enrichment of internal data with pooled data in the development of a regulatory loss given default (LGD) model. The second case study differs from the first by illustrating which other countries in the pooled data set could be representative when enriching internal data during the development of a LGD model. Using these case studies as examples, our proposed methodology provides users with a generalised framework to identify subsets of the external data that are representative of their Country’s or bank’s data, making the results general and universally applicable.

scholarly journals LabVIEW Interface for Controlling a Test Bench for Photovoltaic Modules and Extraction of Various Parameters

2015 ◽  
Vol 6 (3) ◽  
pp. 498 ◽  
Author(s):  
Abderrezak Guenounou ◽  
Ali Malek ◽  
Michel Aillerie ◽  
Achour Mahrane
Keyword(s):  
Numerical Simulation ◽  
Mathematical Models ◽  
Energy Production ◽  
Test Bench ◽  
Graphical Interface ◽  
Detailed Report ◽  
Photovoltaic Modules ◽  
Pv Modules ◽  
Computer Controlled ◽  
Physical Phenomena

Numerical simulation using mathematical models that take into account physical phenomena governing the operation of solar cells is a powerful tool to predict the energy production of photovoltaic modules prior to installation in a given site. These models require some parameters that manufacturers do not generally give. In addition, the availability of a tool for the control and the monitoring of performances of PV modules is of great importance for researchers, manufacturers and distributors of PV solutions. In this paper, a test and characterization protocol of PV modules is presented. It consists of an outdoor computer controlled test bench using a LabVIEW graphical interface. In addition to the measuring of the IV characteristics, it provides all the parameters of PV modules with the possibility to display and print a detailed report for each test. After the presentation of the test bench and the developed graphical interface, the obtained results based on an experimental example are presented.

scholarly journals APPLICATION OF COMPUTER MODELING POSSIBILITIES IN THE STUDY OF PHYSICAL MODELS

2021 ◽  
pp. 25-34
Author(s):  
Pavlo Kindrat ◽  
Ihor Voitovych ◽  
Vladimir Mashchenko
Keyword(s):  
Physics Education ◽  
Mathematical Problem ◽  
Computer Models ◽  
Ideal Gas ◽  
Educational Process ◽  
Physical Models ◽  
Professional Activities ◽  
Advantages And Disadvantages ◽  
Virtual Laboratories ◽  
Physical Phenomena

The advantages and disadvantages of using a virtual laboratory and computer models in the educational process in physics are identified. The expediency of using virtual laboratories and computer models in the context of mixed physics education is substantiated. To teach future physics teachers to create and use computer models of physical phenomena and processes is carried out in a professionally oriented author's course "Methods of using computer technology in professional activities." The stages of development of a physical model for the formulation of a mathematical problem are described and the implementation on the example of development and use of the program "Dynamic model of an ideal gas" is shown.

Development of mathematical models to predict calcium, magnesium and selenium excretion from lactating Holstein cows

2018 ◽  
Vol 58 (3) ◽  
pp. 489 ◽  
Author(s):  
K. Taylor ◽  
J. A. D. Ranga Niroshan Appuhamy ◽  
J. Dijkstra ◽  
E. Kebreab
Keyword(s):  
Mathematical Models ◽  
Dairy Cows ◽  
Protein Content ◽  
Milk Yield ◽  
Milk Fat ◽  
Meta Analysis ◽  
Model Development ◽  
Dietary Factors ◽  
Mineral Excretion ◽  
Lactating Dairy Cows

The aim of this study was to develop and evaluate mathematical models that predict mineral excretion, particularly calcium (Ca), magnesium (Mg) and selenium (Se), from lactating dairy cows. Mineral excretion can be affected by several dietary factors. A deficiency in Ca or Mg application to pasture, among other factors, can contribute to grass tetany or wheat pasture poisoning in cows, whereas an excess can cause runoff into water supplies. Manure application with high Se concentration can also result in runoff, causing the bioaccumulation of selenium in aquatic ecosystems, wetland habitats and estuaries, leading to toxic levels in fish. A database composed of studies relating to mineral utilisation in lactating dairy cows conducted after and including the year 2000 was compiled. A meta-analysis was conducted with the aim of creating multiple empirical equations to predict Ca, Mg and Se excretion from lactating dairy cows. Calcium intake, feed Ca content, milk yield, milk protein content and acid detergent fibre content in diet were positively and linearly related to Ca excretion. Dietary crude protein content and milk fat content were negatively related to Ca excretion. Magnesium intake, feed Mg content and milk yield were positively and linearly related to Mg excretion. Selenium content of diet and dry matter intake were linearly and positively related to Se excretion. Two sets of models were developed using or excluding the intake variable and both sets of models were evaluated with independent data originating from commercial herd or individual animals. In general, intake measurements improved prediction when evaluated with independent datasets (root mean square prediction error = 8% to 19% vs 14% to 26% of the average observed value). There were substantial mean biases, particularly those evaluated with data from a commercial farm, perhaps due to inaccurate feed intake measurements. Although there was generally good agreement between predicted and observed mineral excretion, model development and evaluation would benefit from an expanded database.

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