Analysis of Common Fixed Point Theorems in Diverse Spaces | Book Publisher International

Fixed Point (Fixed Point) Theory is a crucial and unexpectedly developing non-linear functional analysis subject matter. Outcomes describing the existence of fixed points are termed as fixed points theorems. Among all the functional parts of Mathematics, the theory of differential equations is of much importance. Its contribution towards Physics and Engineering cannot be neglected. Fixed-Point Theory guarantees the significant solution of these equations. A vast literature on fixed-point theory is available in journals of national and international repute and this is still growing. Fixed Point theorems are used to find solutions to many problems in various disciplines, which provide conditions under which a number of transformations have solutions. Fixed Point theory involves a very transparent and fundamental mathematical setting. This is primarily the logic that made us choose Fixed Point theory as the topic. This Fixed Point Theory is predominantly separated into the three following substantial theories:

·         Topological Fixed Point Theory

·         Metric Fixed Point Theory

·         Discrete Fixed Point Theory

Banach’s and Brouwer's fundamental Fixed Point theory led to the development of two of the scientific main and complementary elements, namely metrical Fixed Point theory and topological Fixed Point theory. The first Fixed Point outcome for a topological space was offered by Dutch mathematician Brouwer in 1912, which state that A continuous self-mapping explained on the closed unit ball in Euclidean space has at least one fixed point. Many authors have proved Fixed Point Theorems either by relaxing the domain or by the function definedon it. Banach in 1922 proved a Fixed Point Theory for contraction mapping, which was defined in complete Metric Space. The Banach theorem states that if it is a complete metric space and is a contraction, then it has a unique fixed point. According to the Brouwer theorem, there must be the closed unit ball in a Euclidean space. But in such a case, the set of all Fixed Points is not compulsorily a one-point set. The point is termed as Fixed Point if, on applying the transformation, the point stands untransformed. There are numerous mathematical issues involving various branches, which can be formulated into equivalent Fixed Point models. The major differentiation between two significant arms that is Topological Fixed Point Theory and Metric Space Set-Point Theory, of Fixed Point Theory is explained by Banach theorem and Brouwer theorem. Due to the wide variety of uses, the Fixed Point Theorems are avidly studied across a multitude of disciplines in the mathematical world. Due to the simplicity and usefulness of Banach's Fixed Point Theorem it came out as a contemporary instrument for the proof of existence and uniqueness of thrs in various boughs of mathematical analysis. In 1968, a contractive condition was introduced by Kannan that hold a unique fixed-point like Banach. However, unlike the Banach situation, a domain wise discontinuity of mappings with fixed points was proved by Kannan. Also, these mappings show a continuous nature at their Fixed Point.

The focus of chapter 2 is to find a fixed point that is common for a rationally contractive pair of mappings in the setting of a complete Complex Valued Metric Space. The result is the generalization of a variety of established theories. C´iri´c -Reich–Rus contraction mapping is described in complex valued Quasi Partial b Metric Space and presented Fixed Point theorem. in the context of complex valued quasi-partial b-metric space in chapter 3. In this study distinct explanation, definitions in addition to notations are used in the discussion of different subsequent. Cyclic C´iri´c-Reich-Rus contraction mapping has been used to show the existence and uniqueness of Common Fixed Point in the setting of complex valued Quasi Partial b Metric Space. The result is supported with suitable examples in this chapter 4.

Author(s) Details:

Arti Saxena,
School of Engineering and Technology, Manav Rachna International Institute of Research and Studies Faridabad, Haryana, India.

Poonam Rani,
Department of Humanities and Applied Sciences, Echelon Institute of Technology, Faridabad, Haryana, India.

Please see the link here: https://stm.bookpi.org/ACFPTDS/article/view/13166

Fortification of Foodstuffs (Food Material) with Moringa oleifera | Book Publisher International

This book examines sorghum, Bambara groundnut, and Moringa oleifera. It explores the nutritional value of these plants and the possible use of cutting-edge technologies such as pulse electric field and ultrasonication to extract bioactive compounds from these plants. While staples like sorghum and Bambara groundnut are high in nutrients, Moringa oleifera is notable for having numerous nutritional advantages and provides additional nutritional and antioxidant values to sorghum and Bambaras through fortification. The incorporation of these components into food systems is examined, emphasising the use of fermentation and malting. A detailed explanation of extracting bioactive compounds from Moringa oleifera using pulsed electric fields and ultrasonication is provided. The book consistently highlight the significance of additional investigation to fully realise the potential for improved nutrition and food security. This book also highlights the role that sorghum, Bambara groundnut, and Moringa oleifera play in addressing nutritional challenges while illuminating the transformative potential of these plants. The ability of the complex fermentation and malting processes to improve sorghum's nutritional profile is examined. Furthermore, the benefits of legumes for health are emphasised. The investigation reveals the varied and advantageous nature of Bambara groundnut and Sorghum metabolites. The book end with a call for more study and creativity, acknowledging the importance of pulsed electric fields and ultrasonication in the extraction of bioactive compounds.

Author(s) Details:

Abiodun Olukemi Famakinwa,
Department of Food Science and Technology, Faculty of Applied Sciences, Cape Peninsula University of Technology, Bellville 7535, Cape Town, South Africa.

Oluwafemi Omoniyi Oguntibeju,
Phytomedicine and Phytochemistry Group, Department of Biomedical Sciences, Faculty of Health and Wellness Sciences, Cape Peninsula University of Technology, Bellville 7535, South Africa.

Victoria Jideani,
Department of Food Science and Technology, Faculty of Applied Sciences, Cape Peninsula University of Technology, Bellville 7535, Cape Town, South Africa.

Jessy Van Wyk,
Department of Food Science and Technology, Faculty of Applied Sciences, Cape Peninsula University of Technology, Bellville 7535, Cape Town, South Africa.

Anthony Olusegun Obilana,
Department of Food Science and Technology, Faculty of Applied Sciences, Cape Peninsula University of Technology, Bellville 7535, Cape Town, South Africa.

Please see the link here: https://stm.bookpi.org/FFFMMO/article/view/13154

Living with Floods in Bangladesh’s Riverine Islands Understanding Vulnerability and Resilience | Book Publisher International

Flooding is a substantial and pervasive natural disaster in Bangladesh, severely impacting the nation's vulnerability to the effects of climate change. Due to its low-lying geography and close proximity to extensive river systems, the riverine islands, or chars, of Bangladesh are particularly susceptible to flood-related damage. This research aims to thoroughly evaluate the social vulnerability of riverine island inhabitants, examine the impacts of flood disasters on their lives, scrutinize their strategies for adaptation, and identify the challenges they encounter in acclimating to their environment.

The methodological approach of this study is primarily qualitative, supplemented by quantitative data, thereby adopting a mixed-methods framework to enhance the study's comprehensiveness and validity. Data collection was conducted using both primary and secondary methods. Primary data were meticulously gathered from individuals affected by flooding through a comprehensive strategy that included questionnaire surveys, focus group discussions, participatory observation, and interviews with key informants. Secondary data, on the other hand, were systematically sourced from a diverse range of published and unpublished materials, including academic journals, books, newspapers, magazines, documents from non-governmental organizations, annual reports, and institutional websites.

The study divulges that riverine island residents grapple with socio-economic vulnerabilities owing to their geographical location and limited facility access. Predominantly residing near the Jamuna River or its tributaries, these communities lack essential amenities such as schools, hospitals, and transportation, rendering them susceptible to floods. Additionally, patriarchal structures disproportionately place men under 30 at heightened risk. Compounded by low literacy rates and a lack of adaptation awareness, these vulnerabilities are exacerbated. The economic landscape is dominated by agriculture, supplemented by small businesses, day labor, and fishing. Monthly incomes vary from 3,000 to 6,000 BDT, with a notable 25.60% earning below 3,000 BDT and a mere 15.18% having savings. Access to clean water and sanitation is paramount; however, floods often contaminate wells, and numerous individuals resort to unhygienic Kutcha latrines. Housing types are reflective of socio-economic status, with many relying on inadequate flood shelters. The absence of modern energy sources further affects living standards, underscoring the need for comprehensive policy intervention.

The 2017 flood had a catastrophic impact on the socio-economic fabric of the selected study villages, leaving a trail of devastation that affected nearly every aspect of life. Almost every family had their homes damaged, forcing many to leave their ancestral homes. The agricultural sector was hit hard, with prolonged water stagnation leading to nearly 75% of respondents losing their crops, and most households suffering losses in livestock rearing. Half of the respondents lost their income and occupations, with the remaining having to adapt to new occupations, often earning less than before. This resulted in widespread unemployment and income loss. The flood also wreaked havoc on the quality of life, with almost all households experiencing damage to sanitary latrines and facing challenges in accessing clean drinking water and food, which led to various health issues. The education of children was disrupted, with many dropping out of school post-flood. Significant damage was also inflicted on social infrastructure, including embankments, schools, bridges, culverts, and roads.

Communities in Bangladesh's flood-prone regions employ various adaptive mechanisms to mitigate the impacts of recurrent flooding. These adaptations include early warning systems, public education, elevated housing, diversified livelihoods, modified agricultural practices, livestock protection, food and water management, financial strategies, health precautions, and institutional support. Local knowledge and early warning indicators are utilized in the absence of modern forecasting technologies. Educational initiatives and awareness campaigns are pivotal for community flood preparedness. Elevated housing and community shelters offer protection, while boats provide essential transportation during floods. Agriculture adapts through flood-resistant and fast-growing crops. Livestock protection involves relocation and elevated shelters. Food and water management include purification and storage techniques. Financial coping strategies encompass asset liquidation and loans. Health adaptations involve traditional healing practices and raised tube-wells. Furthermore, government and non-governmental organizations play a crucial role in providing support ranging from immediate relief to long-term rehabilitation, ensuring community resilience against floods.

The study also investigates the complex challenges faced by inhabitants of Bangladesh's riverine islands, particularly in char regions, amidst recurrent flooding. Financial constraints significantly impede the adaptive capacities of these historically resilient communities. The 2017 flood revealed significant shortcomings in their communication infrastructure, which is crucial for timely emergency responses and development initiatives. Dependence on obsolete agricultural practices, such as monocultures, heightens their vulnerability to food scarcity and economic instability during floods. A pervasive lack of formal education impedes their ability to comprehend and respond to the complexities of flooding and climate shifts. Moreover, institutional support is marred by mismanagement, corruption, and delayed services, further complicating their situation. Limited access to advanced early warning and communication systems also undermines their resilience.

The findings underscore the urgent need for comprehensive strategies to strengthen resilience and adaptive capacities and address these challenges, in order to improve the sustainability and quality of life for these vulnerable communities.

Author(s) Details:

Babul Hossain,
Management Science and Engineering, Hohai University, Nanjing-210000, China.

Guoqing Shi,
National Research Center for Resettlement, Hohai University, Nanjing-210000, China.

Md. Nazirul Islam Sarker,
School of Social Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia.

Please see the link here: https://stm.bookpi.org/LFBRIUVR/article/view/13170

Development of a New Magnetic Stirring Facility and Efficient Method for Refinement of Solidified Grain Structure | Chapter 10 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

This work aimed to develop an efficient stirring facility and method with magnetic induction. Because the stirring by Rotation Magnetic Field (RMF) often produces strong macrosegregation, the Traveling Magnetic Field (TMF) was chosen for the stirring. The construction of this TMF twin-inductor is significantly different from the traditional magnetic stirrers, and it has a closed magnetic circuit. Three different magnetic fields can be produced with the developed twin-inductor to investigate the stirring effect. The inductor develops strong shearing stress at the flow perpendicular to the solidification front by flowing a part of metallic-melt layers touching each other in a direction opposite. The TMF twin inductor was combined with a solidification facility for the unidirectional solidification of different alloys.

 

The effect on the grain structure of the three different magnetic fields was compared using Al-7%Si-1% and Al-10%Si-0,2%Fe alloys. It has demonstrated that the most efficient mixing occurs when the magnetic fields in the two inductors move opposite each other.

Author(s) Details:

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Mária Svéda,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13086

Periodically Changing Rod Distance in Unidirectional Solidified Al-Al3Ni Eutectic | Chapter 9 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

The microstructure of eutectics is frequently lamellar or rod-like, depending on the phase fractions of the constituent phases. The effect of melt flow on eutectic microstructures has been investigated by several research groups, especially since the availability of solidification processing under microgravity conditions. This chapter discusses the periodically changing rod distance in unidirectional solidified Al - Al3Ni eutectic.

 

Eutectic Al-5.6 wt% Ni was directionally solidified with and without magnetic stirring, and the eutectic rod-like microstructures were characterised. The research aims to study the effect of a rotating magnetic field on the microstructure of the eutectic composition alloy. Rod-like eutectics are generally described by rod distance and the number of the nearest neighbours. More than the commonly used average values are required for complete characterisation of the microstructure because placing the rods is not homogenous. We measured the parameters above along straight lines and found a previously unknown phenomenon. In the case of intensive melt flow, the spacings between rods show a significant periodic inhomogeneity. This inhomogeneity can be explained by the formation of vortices in the melt at the solidification front. It is concluded that the rod spacing in the eutectic microstructure changed periodically.

Author(s) Details:

Zsolt Veres,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary and HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Arnold Rónaföldi,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary and HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Jeno Kovacs,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Andras Roosz,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary and HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13085

Detailed Study on the Effect of Forced Melt Flow on Al–Si Eutectic-alloy Microstructures | Chapter 8 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

Al–Si eutectic alloys are industrially important; they play a significant role in the casting-manufacturing of most materials. The Al–Si alloys used therein are eutectic; the two phases of Al and Si grow simultaneously from a liquid state at a constant temperature. In 1966, Jackson and Hunt developed the most comprehensive model for eutectic-structure formation. The properties of the materials are governed by their microstructure, which can be tuned by adjusting the solidification process parameters. Herein, the effect of forced melt flow on the microstructure of an Al-Si eutectic alloy during unidirectional solidification was investigated experimentally. Al–12.6-wt%-Si alloy samples were solidified in a vertical Bridgman-type furnace equipped with a rotating magnetic inductor to induce flow in the melt. The samples were subjected to different magnetic induction conditions during the solidification experiments. The diameter of the samples was 8 mm, and their length was 120 mm. The eutectic alloy samples were solidified unidirectionally at a growth rate of v  ≈ 0.1 mm/s and a temperature gradient of G  ≈ 6 K/mm. The inter-lamellar distances (λ), lengths, and orientation angles of the Si lamellae were investigated using new measurement methods. The experimental results reveal that applying the rotating magnetic field (RMF) during the solidification has a distinct effect on the microstructure of Al-Si eutectic alloys. Indeed, the RMF re-fines the eutectic structure, reduces the interlamellar distances, and increases the diversity of the Si lamella angle`s orientations. However, the successive stirring process has a negligible effect on the lengths and angles of Si lamellae.

 

In general, the flow enriches the center area with the alloying element (Si), which results in the solidification of the eutectic structure in the center area and primary Al at the edges of the sample.

Author(s) Details:

Kassab Al-Omari,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13084

Macrosegregation Evolution in Eutectic Al-Si Alloy under the Influence of a Rotational Magnetic Field | Chapter 7 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

Macrosegregation is a phenomenon that affects the quality of industrial castings and therefore attracted many research groups for several decades. Using magnetic stirring during solidification provides a good opportunity to control the microstructure of the alloys, thus controlling their physical properties. However, magnetic stirring is often accompanied by a change in local concentrations, and new structures form, which could harm the physical properties This chapter highlights the effect of forced melt flow by a rotating magnetic field (RMF) on the macrostructure of an Al-Si eutectic alloy. To serve this purpose, Al-12.6wt% Si alloy samples were solidified in a vertical Bridgman-type furnace equipped with a rotating magnetic inductor to induce the flow in the melt. The diameter and length of the sample are 8 mm and 120 mm, respectively. The solidification parameters are; The temperature gradient (G) of 6 K/m, and the solid/liquid front velocity (v) of 0.1 mm/s. These samples were divided into parts during the solidification process, where some of these parts were solidified under the effect of RMF stirring while others were solidified without stirring.

The structure obtained after solidification showed a distinct impact of stirring by RMF; new phases have been solidified which are not originally present in the structure before stirring. Besides the eutectic structure, the new phases are the primary aluminum and the primary silicon. The Si concentration and the volume fraction of each phase were measured using EDS and new image processing techniques. The experimental results reveal that applying the RMF during the solidification has a distinct effect on the macrostructure of Al-Si eutectic alloys.

Indeed, the RMF provokes macro-segregation, reduces the amount of eutectic structure, and changes the sample’s Si concentration distribution.

Finally, it is concluded that The RMF destroys the coupled growth of the α-Al and Si eutectic phases at the edges and alters the leading phase from the Si to the α-Al phase.

Author(s) Details:

Kassab Al-Omari,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

András Roósz,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary and HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Arnold Rónaföldi,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary and HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Mária Svéda,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Zsolt Veres,
Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary and HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13082

Dynamical and Empirical Simulation Methods of Secondary Dendrite Arm Coarsening: A Comparative Approach | Chapter 6 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

This chapter evaluate a comparative approach of Dynamical and Empirical Simulation Methods of Secondary Dendrite Arm Coarsening.  The secondary dendritic arm spacing (SDAS) has a significant influence on the mechanical and physical characteristics of an alloy that has been dendritically solidified completely (wrought alloys) or partially (cast alloys). A practical yet straightforward approach for calculating the SDAS during and after solidification as a function of cooling rate is required for both the solidification simulation and casting practice. Based on many solidification experiments, a simple equation to calculate the SDAS (empirical method) is known to use the local solidification time, which can be obtained from the measured cooling curves (equiaxed solidification), or can be calculated from the temperature gradient and front velocity (directional solidification). In the present work, first, we show the effect of the curvature of the solid/liquid interface on the equilibrium concentrations and then the different processes of SDA coarsening. In our earlier paper, we demonstrated that using the empirical method, the final SDAS can be calculated with acceptable correctness in the case of four unidirectional solidification experiments of Al-7wt%Si alloy. The current study demonstrates that the known cooling curve was utilized in the numerical integration of Kirkwood's equations, allowing for the calculation of the SDAS both during and after solidification in good agreement with the experimental findings. We claimed that the approaches' accuracy is comparable to the two calculation methods. The equilibrium concentration in the liquid phase on the solid phase’s surface depends on the curvature of the solid phase. Consequently, diffusion in the liquid phase from high to low solute regions will result in the coarsening of the SDA. Still, the results of the solidification simulation (the microsegregation) will be more correct using the dynamical method. It is also shown that with the dynamical method, the SDAS can be calculated from any type of cooling curve, and using the dynamical method, it is proved that some different SDASs could belong to the same local solidification time.

Author(s) Details:

András Roósz,
HUN REN - University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Arnold Rónaföldi,
HUN REN - University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Mária Svéda,
HUN REN - University of Miskolc, Materials Science Research Group, Hungary.

Zsolt Veres,
HUN REN - University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13081

The Effect of Rotating Magnetic Field Induced Melt Flow on the Meso and Microstructure of Unidirectionally Solidified Al – 7wt% Si Alloy | Chapter 5 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

During the last two decades, many algorithms have been developed to simulate solidification processing for different casting methods, such as the continuous casting of steel and the direct chill cast of aluminium. Experiments performed in well-known conditions and the detailed knowledge of meso- and microstructures are necessary to validate these simulations. The primary aim of this chapter is to examine the effect of melt flow on the meso- and microstructure of the Al-7wt% Si binary alloy. When developing simulations describing solidification, it is complicated to consider melt flow and its effect on the emerging meso and microstructure. Several experiments are in the literature in which melt probably flowed during solidification. Still, the exact parameters of the experiment and the meso and microstructure formed during solidification are unknown. In this chapter, we present a well - defined experiment and its results, which can be used to validate a simulation that also considers melt flow.

 

Unidirectional solidification experiments were performed using a rotating magnetic field (RMF) to study the effect of melt flow on the solidified meso- and microstructure of the Al-7wt% Si binary alloy. The samples' first and third 1/3 parts were solidified without magnetic stirring, and the second (middle) 1/3 part was solidified using magnetic stirring. The magnetic induction was 10 mT, the temperature gradient was ~7 K/mm, and the sample movement velocity was 0.1 mm/s. On the longitudinal section of the Sample, the columnar/equiaxed transition (CET), the equiaxed/columnar transition (ECT), the secondary dendrite arm spacing (SDAS), and the macrosegregation (concentration distribution and the amount of eutectic) were investigated. The primary dendrite arm spacing (PDAS) and the grain structure were studied on the cross-section after colour etching. Finally, it is concluded that progressive columnar/equiaxed transition (CET) caused by the magnetic stirring developed between the non-stirred and the stirred part of the sample.

Author(s) Details:

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Anna Sycheva,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Mária Svéda,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13080

Effect of Solidification Parameters on the Amount of Eutectic and Secondary Arm Spacing of Al–7wt%Si Alloy Solidified under Microgravity: An Experimental Analysis | Chapter 4 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

This chapter highlights the effect of G and v on the secondary dendrite arm spacing (SDAS) in purely diffusion circumstances, analysed the thermal data of the experiments in detail, and take into account the macrosegregation caused by the diffusion of Si from the initial mushy zone during the homogenization step of experiments. During the solidification of hypoeutectic alloy (like Al-7% Si), density difference develops in the melt generated by concentration and temperature difference. On Earth, as an effect of this density difference, the melt can flow due to gravity affecting the solidified microstructure. The developing meso- and micro-structures are also significantly affected by the melt flow occurring during the solidification processes in different casting technologies. This melt flow can be eliminated in a microgravity environment, which then makes it possible to examine the solidification process under conditions of pure diffusion. In the Materials Science Lab (MSL) on board the International Space Station (ISS), four solidification experiments were conducted on grain refined and non-grain refined Al-7wt% Si alloy to investigate the effects of the solidification parameters  (solid/liquid front velocity v, temperature gradient G) on the dendritic microstructures and the grain structure. A detailed analysis of the grain structure was conducted in a few previous articles. The macrosegregation was calculated by the Finite Different Method. Because the steady-state solidification conditions were never reached, the solidification process was characterized by the average front velocity and temperature gradient. It is shown that steady-state solidification conditions are never reached. At a given sample position, the velocity of the solid/liquid S/L) and the eutectic/liquid (E/L) fronts and the temperature gradient at the two fronts are different. Then, the solidification process can be characterized by the average front velocity and average temperature gradient.

Author(s) Details:

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Yuze Li,
School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an, 710100, China.

Nathalie Mangelinck-Noël,
Aix Marseille University, Université de Toulon, CNRS, IM2NP, 13013 Marseille, France.

Gerherd Zimmermann,
ACCESS e.V., Intzestrasse 5, Aachen, Germany.

Henri Nguyen-Thi,
Aix Marseille University, Université de Toulon, CNRS, IM2NP, 13013 Marseille, France.

Mária Svéda,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13079

Microstructure Analysis of Al-7 wt%Si Alloy Solidified on Earth Compared to Similar Experiments in Microgravity: An Update | Chapter 3 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

 This chapter highlights a comparative overview of the grain structure (especial the CET) and the type of the coarsening process of the secondary dendrite arm (especially the kinetic constant n) of the samples solidified in space and the Earth to get information on the effect of buoyancy flow. During ground-based solidification, buoyancy flow can develop by the density difference in the hypoeutectic type of the alloy, such as Al-7 wt% Si alloy. Buoyancy flow can affect the thermal field, solute distribution in the melt, and the position and amount of the new grains. Under microgravity conditions, natural convection does not exist or is strongly damped due to the absence of the buoyancy force. Therefore, experiments in microgravity conditions provide unique benchmark data for pure diffusive solidification conditions. Compared to the results of the ground-based and microgravity ( µ g) experiments, it is possible to get information on the effect of gravity (buoyancy force). In the framework of the CETSOL project, four microgravity solidification experiments were performed on grain-refined (GF) and non-grain refined Al-7 wt% Si alloy onboard the International Space Station in the Materials Science Laboratory. Four ground-based (GB) experiments were performed under Earth -like conditions with the same (similar) solidification parameters in a vertical Bridgman-type furnace. A detailed analysis of the grain structure and amount of eutectic and secondary dendrite arm spacing (SDAS) for different process conditions is reported and compared with the results of the microgravity experiments. GB experiments showed that the microstructure was columnar in the samples that do not contain GF material or in case the solid/liquid (vSL front velocity was slow (0.02 mm/s)). In contrast, in the GF material sample, progressive columnar/equiaxed transition (PCET) was observed at vSL = 0.077 mm/s and GSL = 3.9 K/mm. The secondary (SDAS) dendrite arm spacing follows the well-known power law, SADS = K[ t0 ]1/3  where K is a constant, and t0 is the local solidification time for both GB and µg experiments. The experiments in microgravity conditions provide unique benchmark data for pure diffusive solidification conditions. Compared to the results of the ground-based and microgravity experiments, it is possible to get information on the effect of gravity (buoyancy force).

Author(s) Details:

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Yuze Li,
School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an, 710100, China.

Nathalie Mangelinck-Noël,
Aix Marseille University, Université de Toulon, CNRS, IM2NP, 13013 Marseille, France.

Gerhard Zimmermann,
ACCESS e.V., Intzestrasse 5, D-52072, Aachen, Germany.

Henri Nguyen-Thi,
Aix Marseille University, Université de Toulon, CNRS, IM2NP, 13013 Marseille, France.

Mária Svéda,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13078

Effect of Crucible Wall Roughness on the Laminar/Turbulent Flow Transition of the Ga75In25 alloy Stirred by a Rotating Magnetic Field | Chapter 2 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

This chapter highlights the effect using extremely different wall roughness values. As the experiments were performed at room temperature, the Ga75In25 alloy was used from the usually used low melting temperature metals and alloys. The critical magnetic induction (Bcr) values of a melt flow produced by a rotating magnetic field (RMF), remaining laminar or turbulent, are essential in different solidification processes. In an earlier paper [1], we showed that Bcr depends on the crucible radius (R) and frequency of the magnetic field (f). The pressure of the melt changes if the melt is rotated without a free surface, that is, in a closed tank. However, the pressure could be measured directly along the radius. Using ten different wall materials, we determined the angular frequency ( w ) and Reynolds number (Re) as a function of the magnetic induction (B) and f using two different measuring methods (pressure compensation method, PCM; height measuring method, HMM). Many different crucible materials were used in the solidification experiments to study the effect of magnetic stirring on the solidified microstructure. The experiments were performed at room temperature; therefore, the Ga75wt%In25wt% alloy was chosen for the experiments. Based on the measured and calculated results, a simple relationship was determined between Bcr and Re*, f, R, and W.R., where the constants K1, K2, K3, and K4 depended on the physical properties of the melt and wall material:

BCR( Re* , f , R , WR ) = Re*/R2 (K1 f-K2  + K3 f-k4 WR)

Author(s) Details:

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Mária Svéda,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary.

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13077

Determination of Laminar/Turbulent Flow Transition Using Pressure Compensation Method for Ga75In25 Alloy Stirred by RMF | Chapter 1 | Effect of Microgravity and Magnetic Steering on the Melt Flow and the Microstructure of Solidified Alloys

Melt flow has a very significant influence on the microstructure formed during solidification. Due to the formation of vortices, turbulent flow significantly affects the formation of macro-segregation than laminar flow, for example, in continuous steel casting, where magnetic stirring is an industrial practice. Several software programs have recently been developed to simulate solidification processes, where melt flow induced by magnetic stirring is also considered. However, in practical cases, it is almost impossible to prove by experiments what the type of melt flow was; at most, it can be deduced somewhat from the microstructure.

 

The effect of melt-flow on the microstructure has been investigated by performing several unidirectional solidification experiments where the melt has been flown in a rotating magnetic field. It is well-known that the angular frequency of the melt cylinder always differs from the angular frequency of the magnetic field. However, it proved to be very difficult to determine during the experiments. In our present study, the magnetic Taylor number and the Reynolds number were determined as a function of the radius of the melt cylinder, the magnetic induction, and the angular frequency of the magnetic field using the real angular frequency defined by the so-called pressure -compensation method developed earlier in the case of Ga75In25 alloy. The simulations developed for performing similar experiments can be checked, and the different experiments can be compared correctly using the obtained measurement results. By knowing the critical Reynolds number belonging to the laminar/turbulent flow transition, the value of critical magnetic induction belonging to the transition has been determined as a function of the radius of the melt cylinder. With the described experimental method, it has been possible to determine at what magnetic induction the flow would be turbulent. The results can be used to validate the software, and then validated software has a good chance of characterizing the flow of practical technologies.

Author(s) Details:

Arnold Rónaföldi,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Zsolt Veres,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

András Roósz,
HUN REN- University of Miskolc, Materials Science Research Group, Hungary and Institute of Physical Metallurgy, Metal Forming, and Nanotechnology, University of Miskolc, Hungary.

Please see the link here: https://stm.bookpi.org/EMMSMFMSA/article/view/13076

Optimal Partial Diallel Cross Plan and Its Constructions | Chapter 9 | Research and Applications Towards Mathematics and Computer Science Vol. 8

In this chapter, a new method of constructing a partial diallel cross plan using the two blocked (equal block) and unblocked (unequal block) balanced incomplete block designs d1 and d2, and each design has two sets of parameters m1, m2, and n1, n2, where S0 ≥6 with parameters v,b,r,k and λ, is proposed. In plant breeding operations, diallel crossings are employed to explore the genetic characteristics of inbred lines. Using the linear model, estimated only the general combining ability effects. The crosses were taken based on the design parameters, and each cross occurred only once in constructing the partial diallel cross plan. When the number of lines (v) increases, the efficiency factor (Ep) and efficiency factor (E*) per cross will increase. The constructed method is also illustrated with a suitable example. The MS-optimality criterion is significantly more straightforward than traditional criteria since it allows for algebraic findings in an area where different criteria are typically only evaluated numerically, design by design.

Author(s) Details:

Rajarathinam, A.,
Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli – 627 012, India.

Please see the link here: https://stm.bookpi.org/RATMCS-V8/article/view/13122

A Brief Overview on Memory Management and Reuse Mechanism for Virtual Machine in Cloud Computing to Minimize Energy Consumption | Chapter 8 | Research and Applications Towards Mathematics and Computer Science Vol. 8

In this paper, a propose technique that reduces the size of memory image stored on source host before migration. Cloud computing is an emerging computing technology for large data centers that maintains computational resources through the internet, rather than on local computers. The ultimate goal of efficient resource utilization in cloud computing is to maximize the profit for cloud providers and to minimize the cost for cloud consumers. Virtual Machine (VM) migration provides the capability to balance the load, system maintenance and fault tolerance, etc. However, existing migration techniques, used to migrate virtual machines keeping memory images of VMs in host and skipping transfer of unchanged memory pages to reduce the amount of transfer data during migration, if number of migrations increases, number of memory images stored on host are also increased, this causes memory starvation. When a VM migrates to other host, memory images of VM is kept in the source host after removing unwanted data according to the Probability factor. When the VM migrates back to the original host later, the kept memory image will be “reused”, i.e. data which are identical to the kept data will not be transferred and comparative to existing system the size of memory image is small. To validate this approach, evaluate the results using different threshold levels and probability factor of change in data. Proposed system required less memory to store the memory image and allow more VMs to be hosted. Specifically, proposed work is used to improve resource efficiency throughout by reducing the size of memory image that is stored on source host. The current work focuses on efficient memory management for source host and will reduce the memory requirement while migration. The main idea behind this concept is, whenever a VM is ready for migration from one host to another, its current state is stored on source host for future use to reduce the data transfer when it come back from the destination host after processing.

Author(s) Details:

Sandeep Kaur,
Department of Computer Science and Engineering, Punjab Institute of Technology (PTU Main Campus), PTU University, Punjab, India.

Please see the link here: https://stm.bookpi.org/RATMCS-V8/article/view/13121

Analysis of Sales Pattern Predictions on New Segment Norms Using Linear Regression | Chapter 7 | Research and Applications Towards Mathematics and Computer Science Vol. 8

This work aims to create a system that identifies the different factors and predicts the most accurate sales for a particular region with the help of history in that particular history. This is to resolve all the challenges and problems that occur while making orders daily. Building this tool will increase the overall sales of the country by aiming at the potential areas of growth which will directly lead to an increase in sales. The Revenue Growth Management analysis generates a sales prediction basedonvarious factors which will help in targeting manufacturing and so on. The aim is to generate a system that predicts accurate sales so least of the products are being manufactured with no use. This will help in targeting the niche market of buyers who are potential buyers.

Author(s) Details:

Logeswari Saranya R.,
Department of AI&DS, RMK Engineering College, Thiruvallur-601206, India.

Please see the link here: https://stm.bookpi.org/RATMCS-V8/article/view/13120

Computer Integration within Problem Solving Process | Chapter 6 | Research and Applications Towards Mathematics and Computer Science Vol. 8

The complexity of current software tools increases with the complexity of problem solving tasks they are designed to assist and are mainly dedicated to computer educated people. On the other hand current computer technology is deeply involved in people's everyday life. This gap deepens and stresses software technology and computer education. By computational emancipation the natural language becomes a family of non-ambiguous languages. This means that every problem solver uses a non-ambiguous natural language, termed here as Domain Algorithmic Language, DAL. Here we show how to develop software tools dedicated to the problem domain and illustrate the methodology we propose with the software tools required by teaching high school algebra.

Author(s) Details:

Teodor Rus,
Department of Computer Science, The University of Iowa, Iowa City, USA.

Please see the link here: https://stm.bookpi.org/RATMCS-V8/article/view/13075

SpaceConnect: A Framework for Modelling and Managing Behavioral States of Evolutive Agents | Chapter 5 | Research and Applications Towards Mathematics and Computer Science Vol. 8

In the natural world, all objects and entities (agents) evolves and changes their state continually e.g. a village may become "Town". To capture and depict the evolution of agents, a commonly used approach is the utilization of a multi-dimensional model. This model is used in most of traditional and highly powerful analytical systems which data are being represented in multi-dimensional data structure, enabling efficient data tracking and monitoring. Such systems are popular in organizations and institutions that store and interpret historical cumulative data for forecasting and decision-making purposes, such as data warehousing. However, when dealing with unconventional evolutionary spaces, handling and representing the agent’s evolution using a multi-dimensional model becomes challenging. One of the key challenges lies in managing reactive and dynamic data, which are being more specified and solicited, and may include and stimulate a massive amount of knowledge. In this chapter, a meticulous/methodical framework is proposed for modeling and managing of evolving agents or structural entities (metaphors, e.g. Restaurants, Hospitals, Factories, etc.). These agents can exist within the same or different spaces (as organizational structures); they evolve, interact and transit. They are inter-dependent, and have analytical state-full characteristics (so far, seen as expressive dimensions). The framework provides solutions for analysis and prediction, along with an analytical methodology support that shows; how agents evolve, how evolutions propagate, how evolutions stimulate the evolution of other agents etc. The chapter extensively discusses the fundamental features, principles, and foundations that illustrated in preceding work “hyper-space navigational framework renovated with SpaceConnect”, and also experimented with an indicative case study.

Author(s) Details:

Mohamed Dbouk,
Faculty of Sciences (I), Lebanese University, Beirut, Lebanon.

Hamid Mcheick,
Université du Québec à Chicoutimi, Québec, Canada.

Ebrahim Al-Almani,
Doctoral School of Science and Technology, Lebanese University, Beirut, Lebanon and Faculty of Science & Engineering, The National University, Sana’a, Yemen.

Please see the link here: https://stm.bookpi.org/RATMCS-V8/article/view/13074

Construction of Partial Diallel Cross Plan and its Operations | Chapter 4 | Research and Applications Towards Mathematics and Computer Science Vol. 8

In this chapter, a new method of constructing a partial diallel cross plan using the cubic lattice partially balanced incomplete block designs of three associated classes with parameters v = s3 , b = 2 s3 , r = 4 , k = 2, λ1 = 1, λ2  and λ 3 = 1, where S ≥ 2 is proposed. Diallel crosses are used to investigate the genetic features of inbred lines in plant breeding operations. Only the effects of the general combining ability were estimated in the linear model, and the crosses were chosen based on the association scheme. Each cross occurs a maximum of one time in the construction of a partial diallel cross plan, and as the number of lines (v) increases, the efficiency (Ep) decreases and efficiency factor ( E*) per cross increases. The Cubic Lattice PBIB design with three associate class were used to construct the partial diallel cross plans to estimate the GCA effects and the efficiency Ep decreases and the efficiency factor E* per cross increases, provided v is large.

Author(s) Details:

Rajarathinam, A.,
Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli – 627 012, India.

Please see the link here: https://stm.bookpi.org/RATMCS-V8/article/view/13072