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1

On the stability analysis for a semi-analytical scheme for solving the fractional order blood ethanol concentration system using LVIM

Adel Mohamed, Sweilam Nasser H., Khader Mohamed M.

Journal of Applied Mathematics and Computational Mechanics

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2024

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Vol. 23, nr 1

7-18

EN

The purpose of this article is to present the Laplace variational iteration method, which combines the VIM with the Laplace transform approach (LVIM). This combination will result in a better and more quickly convergent sequence since nonlinear fractional differential equations (FDEs) cannot be solved using the Laplace transform. With the use of the fixed point theory, the stability analysis is specifically discussed and examined. The blood ethanol concentration system is solved numerically by using the suggested scheme. This model can be represented by a system of FDEs. The investigation will emploi the Caputo-Fabrizio fractional derivative. To provide a more in-depth study of this model, we have taken it in its fractional form so that we can more accurately follow the behavior of the solution in the future and history based on the memory effect of fractional derivatives. We determine the accuracy and efficiency of the provided process by evaluating the absolute errors, and a comparison with the existing published work. The results show that the approach is a useful tool for simulating this model.

2

Semi-analytical scheme with its stability analysis for solving the fractional-order predator-prey equations by using Laplace-VIM

Adel Mohamed, Sweilam Nasser H., Khader Mohamed M.

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 4

5-17

EN

The article’s goal is to implement a semi-analytical technique named, the Laplace variational iteration method (LVIM), which is the combination of VIM and Laplace transform method. Although both the Laplace transform method and VIM cannot be applied to some nonlinear fractional differential equations (FDEs) individually, this combination will give a fast-convergent solution to the problem under study. The proposed scheme is used to numerically solve a biodynamic system called the Lotka-Volterra system, i.e. Predator-Prey Equations (PPEs). The system of FDEs can be used to represent this scenario, as well as the Caputo-Fabrizio fractional derivative will be used throughout the study. By assessing the residual error function, we can confirm that the given procedure is effective and accurate. The outcomes demonstrate that the technique used is an effective tool for simulating such models.

3

Changes in Ti-Al-Mn alloy compositions during their smelting in a vacuum induction furnace

Blacha L., Oleksiak B., Smalcerz A., Matuła T.

Archives of Materials Science and Engineering

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2012

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Vol. 58, nr 1

28--32

EN

Purpose: Major problems with smelting of light titanium-based alloys are related to their strong reactivity in the liquid phase with virtually all melting pot materials. Another problem regarding titanium alloy smelting is an unfavourable process of alloy component evaporation due to high melting temperatures of the alloys and significant differences in vapour pressures of their individual components. In the present paper, results of a study on manganese evaporation from the OT4 alloy are presented. Design/methodology/approach: The OT4 alloy contained 94.29, 3.50 and 1.49 %mass of Ti, Al and Mn, respectively. The experiments were performed at 5 to 1000 Pa for 1973 K and 2023 K. During each smelting experiment, metal samples were collected and analysed for titanium, aluminium and manganese contents. Findings: During inductive OT4 alloy smelting from the Ti-Al-Mn system at reduced pressure, significant manganese losses from the alloy are observed as a result manganese evaporation. For manganese and titanium, the evaporation coefficient Ω Mn/Ti values were within 12421–42899, while for manganese and aluminium (Ω Mn/Al), they were within 34 to 52, suggesting that, thermodynamically, there is a potential for intense manganese evaporation from the investigated alloy .Research limitations/implications: The study findings may be a basis for a full kinetic analysis of Mn evaporation from the OT4 alloy which enables determination of process-controlling stages.Practical implications: The study results regarding changes in manganese content in the OT4 alloy during its smelting with the use of VIM technology suggest that one of conditions that may limit the unfavourable process of manganese evaporation is shortening the smelting time or performing the process at about 1000 Pa. Originality/value:In literature, there are no data regarding results of studies on manganese elimination from Ti-Al-Mn alloys during their smelting.

4

Analysis of experimental results obtained by ESR and VAR process for special steels

Zaman F., Iorga G., Ionescu M., Petrescu A., Carciumareasa D.

Archives of Metallurgy and Materials

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2008

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Vol. 53, iss. 2

629-632

EN

The paper presents the results regarding quality of special steels for aero industry, obtained by two different processes: Electro Slag Remelting (ESR) and Vacuum Arc Remelting (VAR) on pilot experiments. The main object of these trials was obtaining super clean steels (oxygen <20 ppm, hydrogen <1 ppm, nitrogen <20 ppm, sulphur <50 ppm, phosphorus <100 ppm) and a controlled solidificated structure of steel semis. The experiments took off the benefits of vacuum arc remelting process, for decreasing gaseous content of steels versus electro slag remelting process which can improve the decreasing of sulphur content of steel. In order to analyse the influence of a double vacuum process VIM – VAR (Vacuum Induction Melting and Vacuum Arc Remelting) on quality of steel, some trials were also performed.

PL

Artykuł przedstawia wyniki dotyczące jakości stali specjalnych stosowanych w przemyśle lotniczym, uzyskane z dwóch różnych procesów: elektrożużlowego przetapiania stali i przetapiania w próżni na podstawie badań pilotażowych. Głównym przedmiotem badań było uzyskanie super czystych stali (tlen <20 ppm, wodór <1 ppm, azot <20 ppm, siarka <50 ppm, fosfor <100 ppm) i kontrola struktury bliźniaków w krzepnącej stali. W doświadczeniach wykorzystano korzyści płynące z odgazowania stali w procesie próżniowym, naprzeciw możliwościom elektrożużlowego przetapiania, które poprawia odsiarczanie stali. Wykonane zostało również kilka prób, aby przeanalizować wpływ procesu VIM – VAR na jakość stali.

5

Cost reduction of TiAl by alternative production and integration of TiAl scrap recycling - concepts and vacuum-metallurgical equipment

Lochbichler C., Friedrich B., Jarczyk G., Scholz H.

Advances in Materials Science

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2008

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Vol. 8, nr 1(15)

67-74

EN

Due to high corrosion resistance and low density titanium alum in ides show a great potential as material for structural applications in the aerospace and automotive industry. However the high actual production costs for semi-finished products slow down a break through to mass production of TiAl. Current research projects at IME, Aachen funded by AIF "Otto von Guericke" and BMBF aim on cost reduced production methods of TiAl and on the minimisation of downgrading TiAl scrap. This article presents firstly the state of the art of TiAl production by vacuum arc (re)melting (V AR) or induction skull melting (ISM). A comparison of new process routes under special consideration of recycling issues will follow. Innovative processing and equipment concepts are shown by intelligent combination of well known vacuum melting and remelting processes such as vacuum induction melting, specialized using ceramic lining and deoxidisation with e.g. electro slag remelting (ESR). For each process step and accordingly equipment the metallurgical opportunities are pointed out and the way to make use of them within the process route is described. Requirements on input material and final metal quality addicted to the processing route and refining techniques with their adjustment in respect to TiAl are mentioned. Selected results of laboratory and pilot scale experiments done at IME in Aachen and equipment needs therefore are shown.

6

Cost reduction of TiAl by alternative production and integration of TiAl scrap recycling - concepts and vacuum-metallurgical equipment

Lochbichler C., Friedrich B., Jarczyk G., Scholz H.

Advances in Materials Science

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2007

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Vol. 7, nr 4(14)

81-88

EN

Due to high corrosion resistance and low density titanium aluminides show a great potential as material for structural applications in the aerospace and automotive industry. However the high actual production costs for semi-finished products slow down a break through to mass production of TiAl. Current research projects at IME, Aachen funded by AIF "Otto von Guericke" and BMBF aim on cost reduced production methods of TiAl and on the minimisation of downgrading TiAl scrap. This article presents firstly the state of the art of TiAl production by vacuum arc (re)melting (VAR) or induction skull melting (ISM). A comparison of new process routes under special consideration of recycling issues will follow. Innovative processing and equipment concepts are shown by intelligent combination of well known vacuum melting and remelting processes such as vacuum induction melting, specialized using ceramic lining and deoxidisation with e.g. electro slag re-melting (ESR). For each process step and accordingly equipment the metallurgical opportunities are pointed out and the way to make use of them within the process route is described. Requirements on input material and final metal quality addicted to the processing route and refining techniques with their adjustment in respect to TiAl are mentioned. Selected results of laboratory and pilot scale experiments done at IME in Aachen and equipment needs therefore are shown.