scholarly journals On the selection of fractional-differential model of convective diffusion with mass exchange

2020 ◽  
pp. 7-10
Author(s):  
Vsevolod Bohaienko ◽  
Anatolij Gladky
Keyword(s):  
Decision Making ◽  
Mass Exchange ◽  
Caputo Derivative ◽  
Heuristic Algorithms ◽  
Convective Diffusion ◽  
Concentration Field ◽  
Model Parameters ◽  
Differential Model ◽  
Fractional Differential

The paper considers two fractional-differential models of convective diffusion with mass exchange and proposes a decision-making algorithm for determining the optimal model at the time of concentration field observation. As for soils of fractal structure, direct experimental determination of model parameters’ values and type of mass exchange process is in many cases impossible, calibration and determination of the most adequate models is performed mainly solving inverse problems by, in particular, meta-heuristic algorithms that are computationally complex. In order to reduce the computational complexity, we study the qualitative differences between diffusion processes described by fractional-differential models with non-local mass exchange on the base of the Caputo derivative and local non-linear mass exchange based on the non-equilibrium sorption equation that corresponds to the description by the Caputo-Fabrizio derivative. We determine under which conditions both models within a given accuracy describe the same set of measurements at a certain moment of time. When the solutions are close at a certain initial stage of process development, the model with the Caputo derivative describes its faster approach to a steady state. Based on the obtained estimates of differences in solutions, a decision-making algorithm is proposed to determine the most accurate model and the values of its parameters concurrently with the acquisition of measurements. This algorithm’s usage reduces the time spent on solving inverse calibration problems.

scholarly journals Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative

2018 ◽  
Vol 2 (4) ◽  
pp. 28 ◽  
Author(s):  
Vsevolod Bohaienko ◽  
Volodymyr Bulavatsky
Keyword(s):  
Caputo Derivative ◽  
Numerical Experiments ◽  
Convective Diffusion ◽  
Time Lag ◽  
Time Variable ◽  
Industrial Wastes ◽  
Diffusion Field ◽  
One Dimensional ◽  
Fractional Differential ◽  
Field Formation

Within the framework of a new mathematical model of convective diffusion with the k-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corresponding filtration scheme, we consider the scheme for the spread of pollution from rivers, canals, or storages of industrial wastes. On the base of a locally one-dimensional finite-difference scheme, we develop a numerical method for obtaining solutions of boundary value problem for fractional differential equation with k-Caputo derivative with respect to the time variable that describes the convective diffusion of salt solution. The results of numerical experiments on modeling the dynamics of the considered process are presented. The results that show an existence of a time lag in the process of diffusion field formation are presented.

PROBABILISTIC DETERMINATION OF STABILITY FOR A DELAY-DIFFERENTIAL MODEL OF THE GLUCOSE-INSULIN DYNAMICAL SYSTEM

1999 ◽  
Vol 07 (02) ◽  
pp. 131-144 ◽  
Author(s):  
A. DE GAETANO ◽  
O. ARINO
Keyword(s):  
Dynamical System ◽  
Equilibrium Point ◽  
Stability Criterion ◽  
Model Parameters ◽  
Qualitative Behavior ◽  
System Modelling ◽  
Differential Model ◽  
The Stability ◽  
Delay Differential

Some of the questions involved in the formulation of a new model for a physiological phenomenon, when the model represents a dynamical system, concern its qualitative behavior. The determination of the stability of a particular dynamical system is usually made analytically, from a linearization of the system around an equilibrium point. This analytic proof may often be complicated or impossible, leading to the imposition of conditions on the relative magnitude of the model structural parameters or to other partial results. We discuss a general technique whereby a probabilistic judgement is made on the stability of a dynamical system, and we apply it to the study of a particular delay differential system modelling the relationship between insulin secretion and glucose uptake. This technique is applicable in case experimental material is available: a stability criterion is obtained via the usual linearization around an equilibrium point and its distribution is approximated from the estimated dispersion of the model parameters. The probability that the stability criterion is such as to make the model stable can then be computed directly. While the conclusion is probabilistic in nature, it is generally applicable to a vast class of models.

IMPLEMENTASI MANAJEMEN PEMBELAJARAN TAHFIDZUL QUR’AN DI MI ISTIQOMAH SAMBAS PURBALINGGA

2018 ◽  
Vol 19 (2) ◽  
pp. 104-120
Author(s):  
Maulana Khusen
Keyword(s):  
Decision Making ◽  
Teacher Performance ◽  
Learning Program ◽  
Target Class ◽  
Class 1 ◽  
Second Year ◽  
Learning Management ◽  
Coordination Meeting

Abstract: The results of the study show that: (1) Tahfidzul Qur'an learning planning is done through the preparation of memorization targets and the determination of effective weeks and days in each semester; (2) Organizing is carried out through the division of tasks and responsibilities as well as the construction of the structure of the tutoring teacher; (3) The mobilization is carried out through the coordination meeting of the Tahfidz coordinator as a shering forum for decision making and direction of the Tahfidzul Qur'an learning program and the implementation of learning is carried out every Monday-Friday; and (4) Supervision is carried out through assessing teacher performance at the end of December and June. The highest achievement target for the second year of the implementation of the Tahfidzul Qur'an's 2017/2018 year program is juz 29 and 30, the lowest target for class 1 is juz 30 to Surat al Ghosyiyyah. For class 1, 85% of the target is achieved and 11% of students exceed the target. Class 2 targets reached 19%. Class 3, 10.86% reached the target and 0.35% of students exceeded the target. Class 4 tarjet reached 12.44%. Class 5 targets reached 4.24%, and the last grade 6 target reached 13.79% and 1.5% of students exceeded the target. Keywords: Learning Management, Tahfidzul Qur'an.

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

scholarly journals A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1554
Author(s):  
Dragiša Stanujkić ◽  
Darjan Karabašević ◽  
Gabrijela Popović ◽  
Predrag S. Stanimirović ◽  
Muzafer Saračević ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Criteria Decision Making ◽  
Grey System Theory ◽  
Multiple Criteria ◽  
Decision Making Process ◽  
Grey System ◽  
Criteria Weights

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.

Experience with the IMMa tyre test bench for the determination of tyre model parameters using genetic techniques

2005 ◽  
Vol 43 (sup1) ◽  
pp. 253-266 ◽  
Author(s):  
J. A. Cabrera ◽  
A. Ortiz ◽  
E. Carabias ◽  
A. Simón
Keyword(s):  
Test Bench ◽  
Model Parameters ◽  
Tyre Model ◽  
Genetic Techniques
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