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A fractional study of mhd casson fluid motion with thermal radiative flux and heat injection/suction mechanism under ramped wall condition: application of rabotnov exponential kernel

Rehman Aziz Ur, Jarad Fahd, Riaz Muhammad Bilal

Acta Mechanica et Automatica

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2024

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Vol. 18, no. 1

84--92

EN

The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as 𝑢0. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as 𝛼, 𝛽, 𝑃𝑟, 𝑄, 𝐺𝑟, 𝑀, 𝑁𝑟 and 𝐾, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.

2

Optymalizacja parametrów systemu odometrii wizyjnej RGB-D metodami populacyjnymi

Kostusiak A., Skrzypczyński P.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2018

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z. 196

461--470

PL

Dokładna lokalizacja jest bardzo ważna w wielu praktycznych zagadnieniach robotyki mobilnej. Często korzysta się z odometrii wizyjnej, obecnie powszechnie wykorzystującej kamery (sensory) RGB-D. W niniejszym artykule badana jest możliwość automatycznego doboru optymalnych parametrów prostego systemu odometrii wizyjnej RGB-D. Wykorzystano i porównano dwie metody optymalizacji oparte na populacji rozwiązań: algorytm genetyczny oraz algorytm roju cząstek. Zbadano wpływ poszczególnych parametrów na dokładność otrzymywanych estymat trajektorii sensora. Na tej podstawie wyciągnięto wnioski zarówno co do skuteczności i efektywności zastosowanych metod optymalizacji, jak i co do wpływu poszczególnych parametrów na dokładność estymat. Eksperymenty przeprowadzono przy wykorzystaniu publicznie dostępnych zestawów danych, aby zapewnić weryfikowalność prezentowanych wyników.

EN

In this paper, we investigate two population-based optimization methods as the means for optimization of the selected parameters in a visual odometry system using RGB-D data. One of the simplest and most used approaches to localization with RGB-D data is feature-based visual odometry that computes frame-to-frame rigid transformations of the sensor upon a sparse set of features and then concatenates these transformations into an estimate of the trajectory. This approach, yet simple, requires careful tuning of a number of parameters that control both the behavior of the feature detector, and the frame-to-frame rota-translation estimation algorithm. Therefore, we propose to employ robust and efficient soft computing optimization methods to find the best parameters for an exemplary RGB-D visual odometry system. We investigate and compare two approaches: the simple to implement particle swarm optimization algorithm, and a more complicated variant of the genetic algorithm. We seek a set of parameters that not only provide good results in terms of the estimated trajectory residual errors but are also applicable to different RGB-D datasets. Moreover, the optimization experiments make it possible to draw more general conclusions as to the role of particular building blocks of the visual odometry system (e.g. RANSAC) in achieving accurate trajectory estimates.

3

Wyznaczanie parametrów linii produkcyjnej z dwoma typami zgłoszeń

Szostek R.

Elektronika : konstrukcje, technologie, zastosowania

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2014

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Vol. 55, nr 12

53-55

PL

W pracy została przedstawiona metoda modelowania oraz wyznaczania parametrów wycinka linii produkcyjnej zawierającego bufor. W modelowanym wycinku linii produkcyjnej występują dwa rodzaje obiektów, które pojawiają się w ciągu produkcyjnym w sposób niedeterministyczny i różnią się czasem dalszego przetwarzania. Dla rozważanego modelu, uwzględniającego różny charakter naprzemienności tych obiektów, wyznaczona została wydajność linii produkcyjnej. Zastosowany model jest niedeterministyczny.

EN

This paper was presented method of modeling and determining the parameters of the fragment of the production line containing buffer. In the modeled segment of the production line there are two types of objects that appear in the production in a non-deterministic and a different time for further processing. For a given model, taking into account the different nature of these objects alternans was assigned production line efficiency. The model used is non-deterministic.

4

Strategies evaluation on the attempts to gain access to a service system (the second problem of an impatient customer)

Szostek R.

Electronics and Telecommunications Quarterly

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2008

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Vol. 54, No 2

135-147

EN

The paper introduces the solution of the optimization problem consisting in choosing a more efficient strategy while accessing a service system. To solve the problem a method of queuing systems analysis by included Markov chains [1] [4] was used. The examined system is described by non-Markovian model. The presented issue was called the second problem of an impatient customer. The first problem of an impatient customer was discussed in paper [5]. Author's comprehensive study formulates and solves an original task of the second problem of an impatient customer.

5

Optimization of time between the attemps to gain acces to a service system (a generalized problem of an impatient customer)

Szostek R.

Electronics and Telecommunications Quarterly

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2008

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Vol. 54, No 1

67-79

EN

The purpose of the paper is to solve an optimization problem consisting in finding the optimal time between the attempts to access a service system. To obtain a solution the method of queueing systems analysis with the aid of Markov chain was used [1][4]. It allows to solve a problem which is presented by non Markovian model. The discussed task is called a generalized problem of an impatient customer. The basic problem of an impatient customer is presented in [5]. The author formulates and solves the problem of an impatient customer in this paper.