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Mathematics
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Mathematical Modelling in Applied Sciences
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Mathematical Modelling in Applied Sciences

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 23 November 2024 | Viewed by 27981

Special Issue Editor

Prof. Dr. Stefan Balint

E-Mail Website
Guest Editor
Department of Computer Science, West University of Timisoara, Bulv. V. Parvan 4, 300223 Timisoara, Romania
Interests: fractional derivatives; mathematical physics and mechanics; computational fluid dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

A mathematical description of a real-world phenomenon is objective if it is independent of the observer. That is, it is possible to reconcile observation of phenomena with a single coherent description of it. This requirement was highlighted by Galileo Galilee (1564–1642), Isaac Newton (1643–1727), and Albert Einstein (1879–1955) in the context of the mathematical description of mechanical movement: “The mechanical event is independent of the observer”.

The majority of mathematical descriptions reported in the literature are objective. However, there are also descriptions that are nonobjective. For example, descriptions that use Caputo or Riemann-Liouville fractional order derivatives, have integral representation on a finite interval, and describe a constitutive law, elastic phenomena, wave propagation, fluid flow, or molecular diffusion are nonobjective.

The goal of this Special Issue is to publish contributions revealing nonobjective mathematical descriptions in mechanics and explaining how the reported results have to be interpreted by the reader.

Prof. Stefan Balint
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical description
  • objective description
  • nonobjective description in mechanics
  • integer order differential equations
  • fractional order differential equations.

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Published Papers (7 papers)

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Research

14 pages, 2333 KiB  
Article
Hybrid Nanofluid Flow and Heat Transfer Past an Inclined Surface
by Sumayyah Alabdulhadi, Iskandar Waini, Sameh E. Ahmed and Anuar Ishak
Mathematics 2021, 9(24), 3176; https://doi.org/10.3390/math9243176 - 9 Dec 2021
Cited by 26 | Viewed by 3168
Abstract
This paper examines the hybrid nanoparticles and the magnetic field impacts on the mixed convection boundary layer flow and heat transfer caused by an inclined shrinking–stretching surface in a hybrid nanofluid. Silver (Ag) is added into a MgO–water nanofluid to form Ag-MgO–water hybrid [...] Read more.
This paper examines the hybrid nanoparticles and the magnetic field impacts on the mixed convection boundary layer flow and heat transfer caused by an inclined shrinking–stretching surface in a hybrid nanofluid. Silver (Ag) is added into a MgO–water nanofluid to form Ag-MgO–water hybrid nanofluid. By making use of proper similarity transformations, the governing equations are transformed to ordinary differential equations. The problem is numerically solved with the help of the MATLAB function bvp4c. The influences of the chosen parameters on the temperature, velocity, heat transfer rate and the skin friction coefficient are addressed and graphically illustrated. The results show that increasing the magnetic parameter substantially improves the heat transfer rate and increases the skin friction coefficient. The findings also suggest that increasing the nanoparticle volume fraction φ2 (Ag) improves the skin friction coefficient while decreasing the heat transfer rate. For both stretching and shrinking instances, non-unique (dual) solutions are discovered. Only the first solution is stable, according to the temporal stability analysis of the dual solutions. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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30 pages, 12579 KiB  
Article
Generation of 3D Turbine Blades for Automotive Organic Rankine Cycles: Mathematical and Computational Perspectives
by Fuhaid Alshammari, Apostolos Pesyridis and Mohamed Elashmawy
Mathematics 2021, 9(1), 50; https://doi.org/10.3390/math9010050 - 29 Dec 2020
Cited by 4 | Viewed by 2361
Abstract
Organic Rankine cycle technology is gaining increasing interest as one of potent future waste heat recovery potential from internal combustion engines. The turbine is the component where power production takes place. Therefore, careful attention to the turbine design through mathematical and numerical simulations [...] Read more.
Organic Rankine cycle technology is gaining increasing interest as one of potent future waste heat recovery potential from internal combustion engines. The turbine is the component where power production takes place. Therefore, careful attention to the turbine design through mathematical and numerical simulations is required. As the rotor is the main component of the turbine, the generation of the 3D shape of the rotor blades and stator vanes is of great importance. Although several types of commercial software have been developed, such types are still expensive and time-consuming. In this study, detailed mathematical modelling was presented. To account for real gas properties, REFPROP software was used. Moreover, a detailed 3D CFD numerical analysis was presented to examine the nature of the flow after generating the 3D shapes of the turbine. Moreover, finite element analysis was performed using various types of materials to obtain best-fit material for the current application. As the turbine is part of a larger system (i.e., ORC system), the effects of its performance on the whole ORC system were discussed. The results showed that the flow was smooth with no recirculation at the design point except at the last part of the suction surface where strong vortices were noticed. Despite the strong vortices, the mathematical model proved to be an effective and fast tool for the generation of the 3D shapes of turbine blades and vanes. The deviations between the 1D mean-line and 3D CFD in turbine efficiency and power output were 2.28% and 5.10%, respectively. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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16 pages, 867 KiB  
Article
Cryptocurrencies as a Financial Tool: Acceptance Factors
by Eloy Gil-Cordero, Juan Pedro Cabrera-Sánchez and Manuel Jesús Arrás-Cortés
Mathematics 2020, 8(11), 1974; https://doi.org/10.3390/math8111974 - 6 Nov 2020
Cited by 48 | Viewed by 9917
Abstract
Cryptocurrencies are a new form of digital asset that operate through blockchain technology and whose purpose is to be used as a means of exchange. Some, such as bitcoin, have become globally recognized in recent years, but the uncertainty surrounding cryptocurrencies raises questions [...] Read more.
Cryptocurrencies are a new form of digital asset that operate through blockchain technology and whose purpose is to be used as a means of exchange. Some, such as bitcoin, have become globally recognized in recent years, but the uncertainty surrounding cryptocurrencies raises questions about their intended use. This study has the task of investigating the different factors that affect the intention behind the use of cryptocurrencies by developing a new research model and using Partial Least Squares (PLS) to assess it. The results show that all the constructs proposed have significative influence, either directly or indirectly, on the intention behind the use of cryptocurrencies. The findings provide value and utility for companies’ and cryptocurrencies’ intermediaries to formulate their business strategies. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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15 pages, 17116 KiB  
Article
A Unifying Numerical Framework for the “Small-Slope” Based Core-Annular Flow Instability Models
by Antonio Quevedo, Carlos Fuentes, Carlos Chávez, Enrique González-Sosa and Carlos Mota
Mathematics 2020, 8(11), 1941; https://doi.org/10.3390/math8111941 - 3 Nov 2020
Viewed by 1647
Abstract
The snap-off is an instability phenomenon that takes place during the immiscible two-phase flow in porous media due to competing forces acting on the fluid phases and at the interface between them. Different theoretical approaches have been proposed for the development of mathematical [...] Read more.
The snap-off is an instability phenomenon that takes place during the immiscible two-phase flow in porous media due to competing forces acting on the fluid phases and at the interface between them. Different theoretical approaches have been proposed for the development of mathematical models that describe the dynamics of a fluid/fluid interface in order to analyze the snap-off mechanism. The models studied here are based on the “small-slope” approach and were derived from the mass conservation and other governing equations of two-phase flow at pore scale in circular capillaries for pure and complex interfaces. The models consist of evolution equations; highly nonlinear partial differential equations of fourth order in space and first order in time. Although the structure of the models for each type of interface is similar, different numerical techniques have been employed to solve them. Here, we propose a unifying numerical framework to solve the group of such models. Such a framework is based on the Fourier pseudo-spectral differentiation method which uses the Fast Fourier Transform (FFT) and the inverse FFT (IFFT) algorithms. We compared the solutions obtained with this method to the results reported in the literature in order to validate our framework. In general, acceptable agreements were obtained in the dynamics of the snap-off. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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17 pages, 1297 KiB  
Article
Optimization of Ordering and Allocation Scheme for Distributed Material Warehouse Based on IGA-SA Algorithm
by Han Jiang, Yunlong Wu and Qing Zhang
Mathematics 2020, 8(10), 1746; https://doi.org/10.3390/math8101746 - 11 Oct 2020
Cited by 3 | Viewed by 2113
Abstract
The distributed material warehouse is the crucial link in the process of modern enterprise construction, and the goal of the enterprise is to save the cost of material distribution and reduce the time of distribution. In order to obtain the optimal ordering and [...] Read more.
The distributed material warehouse is the crucial link in the process of modern enterprise construction, and the goal of the enterprise is to save the cost of material distribution and reduce the time of distribution. In order to obtain the optimal ordering and allocation scheme, firstly, a distributed inventory system consisting of an ordering centre, a material coordination centre and n material warehouses are considered, and the cost model of ordering and allocation of the distributed material warehouse is established. Next, the safety stock and the ordering point of the distributed material warehouse are solved. Then the improved genetic algorithm-simulated annealing algorithm (IGA-SA) is used to solve the optimization of the distributed material warehouse. Finally, the application example is given. The results show that the IGA-SA algorithm can effectively reduce inventory cost and improve inventory utilization. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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16 pages, 4103 KiB  
Article
Estimating Age-Specific Natural Mortality for Sandfish in the Eastern Coastal Waters of Korea
by Giphil Cho, Daewook Kim, Sukgeun Jung, Il Hyo Jung and Sangil Kim
Mathematics 2020, 8(9), 1612; https://doi.org/10.3390/math8091612 - 18 Sep 2020
Cited by 2 | Viewed by 2856
Abstract
To estimate age-specific natural mortality, we proposed an age-structured biomass model with an impulsive dynamical system. In the estimation of natural mortality, we considered growth rate and also reproduction rate, growth, and catch of sandfish, Arctoscopus japonicus. Assuming a linear relationship between [...] Read more.
To estimate age-specific natural mortality, we proposed an age-structured biomass model with an impulsive dynamical system. In the estimation of natural mortality, we considered growth rate and also reproduction rate, growth, and catch of sandfish, Arctoscopus japonicus. Assuming a linear relationship between observed values of the catch per unit effort (CPUE) and total biomass estimated by the age-structured biomass model, we estimated the age-specific natural mortality using the CPUE and catch data, from 1994 to 2009, for varying values of the assumed initial total biomass in 1994, by selecting the largest coefficient of determination (R2). We suggested the following empirical formula: Mi=qKL∞ln(eK(i+1−t0) − 1eK(i−t0) − 1), which estimated natural mortality of sandfish, and the derived age-specific natural mortality was significantly related to fecundity and growth. The parameters of von Bertalanffy growth equation and a logistic equation of maturity with total length were derived from the data of otolith and gonad analysis of female sandfish collected from 2005 to 2008 and from 2005 to 2006, respectively. We also conducted sensitivity analysis by varying the exponent in the inverse function of total length. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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13 pages, 2192 KiB  
Article
Modeling Soil Water Redistribution under Gravity Irrigation with the Richards Equation
by Sebastián Fuentes, Josué Trejo-Alonso, Antonio Quevedo, Carlos Fuentes and Carlos Chávez
Mathematics 2020, 8(9), 1581; https://doi.org/10.3390/math8091581 - 13 Sep 2020
Cited by 12 | Viewed by 4254
Abstract
Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a [...] Read more.
Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a numerical solution (1D, 2D, or 3D) depending on the complexity of the studied problem. In this paper, numerical solution of the equation describing water infiltration into soil using the finite difference method is studied. The finite difference solution is made via iterative schemes of local balance, including explicit, implicit, and intermediate methods; as a special case, the Laasonen method is shown. The found solution is applied to water transfer problems during and after gravity irrigation to observe phenomena of infiltration, evaporation, transpiration, and percolation. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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