Vol. 2 No. 5 (2024)

Open Access

Article

Article ID: 1594

The Navier-Stokes equation and a fully developed turbulence
by Marian Apostol

Journal of AppliedMath, Vol.2, No.5, 2024; 721 Views, 126 PDF Downloads

DOI: https://doi.org/10.59400/jam1594

In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an incompressible fluid and an isentropic flow, the Navier-Stokes equation has approximate vorticial (rotational) solutions, generated by viscosity. However, in general, these vortices are unstable, and a discrete distribution of vorticial solutions is not in me chanical equilibrium; it forms an unstable vorticial liquid. On the other hand, these solutions may exhibit turbulent, fluctuating instabilities for large variations of the velocity over short distances. We represent a fully developed turbulence as a homogeneous, isotropic and highly-fluctuating distribution of singular centres of turbulence. A regular mean flow can be included. In these circumstances the Navier-Stokes equation exhibits three time scales. The equations of the mean flow can be disentangled from the equations of the fluctuating part, which is reduced to a vanishing inertial term. This latter equation is not satisfied after averaging out the temporal fluctuations. For a homogeneous and isotropic distribution of non-singular turbulence centres the equation for the inertial term is satisfied trivially, i.e. both the average fluctuating velocity and the average fluctuating inertial term are zero. If the velocity is singular at the turbulence centres, we are left with a quasi-ideal classical gas of singularities, or a solution of singularities (solute) in quasi thermal equilibrium in the background fluid (solvent). This is an example of an emergent dynamics. We give three examples of vorticial liquids.

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Open Access

Article

Article ID: 1826

Elimination of oscillation causing Hopf bifurcations in engineering problems
by Lakshmi N. Sridhar

Journal of AppliedMath, Vol.2, No.5, 2024; 640 Views, 300 PDF Downloads

DOI: https://doi.org/10.59400/jam1826

Bifurcation analysis was performed on various engineering process problems that exhibit undesirable oscillation causing Hopf bifurcations. Hopf bifurcations result in oscillatory behavior which is problematic for optimization and control tasks. Additionally, the presence of oscillations causes a reduction in product quality and in some cases causes equipment damage. The hyperbolic tangent function activation factor is normally used in neural networks and optimal control problems to eliminate spikes in optimum profiles. Spikes are similar to oscillatory profiles and this is the motivation to investigate whether the hyperbolic tangent function activation factor can eliminate the oscillation causing Hopf bifurcations. The results of this paper show that the hyperbolic tangent function activation factor eliminates the Hopf bifurcations. Bifurcation analysis is performed using The MATLAB software MATCONT. Five examples involving problems that exhibit Hopf bifurcations are presented.

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Open Access

Article

Article ID: 1829

Positivity results to iterative system of higher order boundary value problems
by Kanakayya Namana, Sreedhar Namburi, Rajendra Prasad Kapula

Journal of AppliedMath, Vol.2, No.5, 2024; 709 Views, 31 PDF Downloads

DOI: https://doi.org/10.59400/jam1829

The present research explores the existence of positive solutions for the iterative system of higher-order differential equations with integral boundary conditions that include a non-homogeneous term. To address the boundary value problem, the solution is expressed as a solution of an equivalent integral equation involving kernels. Subsequently, bounds for these kernels are determined to facilitate further analysis. The primary tool employed in this study is the Guo-Krasnosel’skii fixed-point theorem, which is utilized to establish the existence of positive solutions within a cone of a Banach space. This approach enables a rigorous exploration of the existence of at least one positive solution and provides insights into the behavior of the differential equation under the given boundary conditions.

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Open Access

Article

Article ID: 1771

On the relation between perfect powers and tetration frozen digits
by Marco Ripà

Journal of AppliedMath, Vol.2, No.5, 2024; 1083 Views, 530 PDF Downloads

DOI: https://doi.org/10.59400/jam1771

This paper provides a link between integer exponentiation and integer tetration since it is devoted to introducing some peculiar sets of perfect powers characterized by any given value of their constant congruence speed, revealing a fascinating relation between the degree of every perfect power belonging to any congruence class modulo 20 and the number of digits frozen by these special tetration bases, in radix-10, for any unit increment of the hyperexponent. In particular, given any positive integer c, we constructively prove the existence of infinitely many c -th perfect powers having a constant congruence speed of c .

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Open Access

Article

Article ID: 1797

On mathematical analysis of the impact of bilinear therapeutic controls with monolytic vaccination for HBV infection model
by Bassey Echeng Bassey

Journal of AppliedMath, Vol.2, No.5, 2024; 1330 Views, 147 PDF Downloads

DOI: https://doi.org/10.59400/jam1797

While in acknowledgment of varying existing novel results on control of hepatitis B virus (HBV) dynamic infection, the methodological implementation of bilinear control functions in the presence of designated vaccination has not been explicitly considered. Therefore, the present investigation extending an existing study formulated and redeveloped a 6-dimensional HBV mathematical model that seeks and investigates the mathematical and epidemiological composition of the derived model as well as the methodological behavioral impact of applied bilinear therapeutic control functions and monolytic vaccination. The components of analytic predictions explored differential theory in conjunction with the classical Cauchy-Lipschitz condition. Numerical simulations were conducted using the in-built Runge-Kutta in a Mathcad surface. Results obtained indicated early decline of HBV viral load with intense rejuvenation of the recovered and susceptible state-space, following coherent induced bilinear control functions with designated vaccines. The study is highly recommended for HBV-related cases of co-infectivity.

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Open Access

Article

Article ID: 1807

Mathematical modelling of dengue fever transmission dynamics in Kenya
by Brian Nyanaro, George Kimathi, Mary Wainaina

Journal of AppliedMath, Vol.2, No.5, 2024; 47 Views, 21 PDF Downloads

DOI: https://doi.org/10.59400/jam1807

Dengue fever is one of the diseases emerging in Kenya due to effects of climate change and urbanization. The disease is caused by a family of four flavivirus serotypes DENV 1 to DENV4. A deterministic compartmental model for the dengue fever spread dynamics was developed and utilized to examine dengue fever spread dynamics in Kenya. The model was established to be well-stated mathematically and epidemiologically well-posed through positivity and boundedness analysis. The dengue-free equilibrium state was determined as part of the solution to the system of differential equations defining the spread dynamics. The basic reproduction number was determined through the next-generation matrix and used to confirm the stability of the steady state determined before. The study found that when the basic reproduction number was greater than one, the dengue endemic state dominated the solution of the spread dynamics, while when the basic reproduction number was less than one, the dengue free state dominated the solution, implying the disease died down progressively. Sensitivity analysis of the basic reproduction number was carried out to determine the candidate parameters for an optimal control solution. The study found that the infection rate of susceptible mosquitoes, the survival rate of pre-adult mosquitoes, the natural death rate of mosquitoes, the rate at which mosquito survived the extrinsic incubation stage, and the egg-laying of mosquitoes were the most sensitive parameters of the model.

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Editor-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

eISSN

2972-4805

Publication Frequency

Bi-monthly

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

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Volume Arrangement

2024

2023

Featured Articles

Octagonal-square tessellation model for masting GSM network: A case study of MTN Kumasi-East, Ghana

Masting in GSM network design is one of the most challenging problems in cell planning. The effect of uniform design pattern has been proven geographically to be hexagonal using uniform cell range. In this paper, we present a new uniform greedy semi-regular tessellation model called the octagonal square tessellation model (OSTM) to address the problem of global minimum overlap difference and area. Data from MTN Kumasi-East Ghana was collected and analyzed using the developed model. The original layout for the 0.6 km cell range accounted for an overlap difference of 937.66 m and a total area of 21.41 km² for 50 GSM mosts whereas the OSTM model accounted for an overlap difference of 1316.95 m with an area of 34.23 km². This is a 59.87% reduction of the original total area. Our solution is shown to be optimal in overlap difference and area for non-uniform cell range.

Computation of topological indices of linear chains of perylene and coronene using M-polynomial

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

H∞ hybrid control and MRD in a steel frame building subjected to excessivevibrations caused by the dynamic action of wind and earthquake

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

Topological analysis of multiple tables

The paper proposes a topological approach in order to explore several data tables simultaneously. These data tables of quantitative and/or qualitative variables measured on different homogeneous themes, collected from the same individuals. This approach, called topological analysis of multiple tables (TAMT), is based on the notion of neighborhood graphs in the context of a joint analysis of several data tables. It allows the simultaneous study of possible links between several thematic tables. The structure of the correlations or associations of the variables in each thematic table is analyzed according to quantitative, qualitative or mixed variables considered. Like the multiple factorial analysis (MFA), the TAMT allows several tables of variables to be analyzed simultaneously, and to obtain results, in particular graphical representations, which make it possible to study the relationship between individuals, variables and tables of data. These can also be tables of temporal data, collected at different times on the same individuals. The proposed TAMT approach is illustrated using real data associated with several and different homogeneous themes. Its results are compared to those from the MFA method.

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset

Intrusion detection in information technology as well as operational technology networks is highly required in modern day systems due to the increased spate of cyber-attacks in both number and complexity. Anomaly-based intrusion detection systems which have the capacity to detect novel or zero-day attacks are highly employed in this regard. One important component of anomaly-based intrusion detection systems which ensures their behaviour is artificial intelligence in general and machine learning in particular. The burden in modern day cybersecurity research is to investigate and develop models that can outperform existing ones. This paper is aimed at developing a hybrid decision tree model using the stacking ensemble approach. Performances were measured on the basis of recall, precision, accuracy, F1-score, receiver operating characteristics and confusion matrices. The hybrid model presented a precision of 97%, accuracy of 81%, F1-score of 80% and AUC score of 0.96, respectively.