International Journal of Mathematical Modelling and Numerical Optimisation (7 papers in press)

Regular Issues

• Bio-inspired mix design optimization of self-compacting concrete using machine learning algorithms  
  by Sriman Pankaj B, Vasan A, Jabez Christopher J 
  Abstract: This study focuses on optimising concrete mix design using a hybrid bio-inspired optimisation algorithm that combines differential evolution (DE) and cuckoo search (CS). The study also evaluates the performance of two strength prediction models, artificial neural networks (ANNs) and support vector machine regression (SVR), in determining optimal mix proportions. The hybrid algorithm is tested using 11 benchmark test functions and the best approach is chosen to solve a mix design optimisation problem with the objectives of maximising compressive strength, minimising carbon emissions, and minimising cost. Results show that ANN outperforms SVR in terms of compressive strength, with a 30% increase observed. Both prediction models produce optimal mix proportions with minimal variation for cost and embodied carbon minimisation scenarios. The study demonstrates the efficacy of the hybrid optimisation algorithm in conjunction with a prediction model in determining optimal concrete mix proportions.
  Keywords: bio-inspired optimisation; swarm intelligence algorithms; machine learning; compressive strength prediction model; concrete mix design optimisation; cuckoo search; differential evolution.
  DOI: 10.1504/IJMMNO.2024.10058653
   
  
• Startup of oscillating heat pipes via Hopf bifurcation  
  by Carmen Chicone, Z.C. Feng, Stephen Lombardo, David G. Retzloff 
  Abstract: Phase changes occur in oscillating heat pipes (OHPs) inside a tube partially filled with liquid that loops through the hot and cold zones of the device. Evaporation occurs in the hot zone, condensation in the cold zone. Their net effect would intuitively lead to accumulation of liquid slugs in the cold zone and flow stagnation. In recent work, however, self-oscillations observed in a single-branch heat pipe are explained as self-excited mechanical resonator motion. We extend their analysis to typical OHP geometry. Based on a model that combines slug dynamics with a phenomenological model of evaporation, linear stability of the equilibrium corresponding to liquid slugs filling up the cold zone of the heat exchanger is analysed. Our results reveal relations among the system parameters that determine stability and oscillatory behaviour via Hopf bifurcations. Thus, an explanation is proposed for successful start-up - one of the grand challenges for OHP design.
  Keywords: oscillating heat pipe; mathematical model; linearisation; Hopf bifurcation; start-up; model validation.
  DOI: 10.1504/IJMMNO.2024.10059141
   
  
• Adaptive finite element method for wick stochastic partial differential equations  
  by Boujemâa Achchab, Khalid Bouihat, Abderrezzak El-Bouayadi 
  Abstract: In this paper we approximate the solution of the wick stochastic partial differential equation by the affine conforming finite element method. Then we provide a priori and a posteriori error estimations and prove the convergence of the numerical method. In particular, we construct a Galerkin approximation scheme and we derive the local residual based on posteriori error indicator, all the while proving its efficiency and reliability. Finally, two numerical examples are presented and analysed to illustrate the derived theoretical results, the effectiveness of the proposed adaptive algorithm and the good behaviour of the numerical solution and the mesh adaptation strategy used.
  Keywords: wick stochastic equation; finite element method; a posteriori error estimation; error indicators; adaptive meshes.
  DOI: 10.1504/IJMMNO.2023.10056693
   
  
• Optimising reactive power using a hybrid improved shuffled bat algorithm  
  by J. Gowrishankar, G. Balasundaram, J. Manikandan, D. Chandrakala, P. Munisekhar 
  Abstract: One well-known example of a challenging mixed-integer nonlinear optimisation problem is the problem of optimum reactive power dispatch. The bats analyse the echo to determine the position of their prey as well as its size before continuing on their hunt. We compare the outcomes of our technique to those of other bio-inspired algorithms, like the biogeography-based optimisation (BBO) algorithm, to determine its effectiveness. The suggested strategy has the potential to be more successful than almost all of existing methods in terms of having lower minimum values and lower maximum values for the control parameters, according to comparisons of the findings. Bus no. 29 now has a solar power generation system, resulting in an additional 0.3 kW loss reduction. The simulation findings suggest that the bat optimisation algorithm (BOA) is more effective than the other algorithms tested from the research.
  Keywords: optimisation optimal power system dispatch; solar grids; the bat algorithm; whale optimisation; microgrids; ORPD.
  DOI: 10.1504/IJMMNO.2023.10058301
   
  
• A robust semi-analytical approach to study fractional coupled Sokolov Wilson system in shallow water waves  
  by Yogeshwari F. Patel, Jayesh M. Dhodiya 
  Abstract: In this paper, a semi-analytical approach namely, modified differential transform method is suggested to investigate coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations (CFDSWE) that arise in shallow water flow models. The Caputo sense is used to characterise the fractional derivative. The solution of coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations is obtained for two different cases. The obtained solution shows an excellent agreement with the exact solution for classical order which shows the effectiveness and reliability of the method. The results show that the fractional modified differential transform method is a promising tool to find the analytical solution of highly nonlinear fractional PDEs. The computational work is done in the MATLAB software package.
  Keywords: shallow water waves; modified differential transform method; fractional coupled partial differential equation; coupled Sokolov Wilson system.
  DOI: 10.1504/IJMMNO.2023.10058044
   
  
• Post COVID-19 dynamics through fractional-order  
  by Nita H. Shah, Nisha Sheoran 
  Abstract: In this article, a fractional-order model for the COVID-19 scenario in India is formulated using nine different compartments in the Caputo sense. The fractional-order model mainly focuses on memory giving a better understanding of results. The formulated model has three equilibrium points namely disease-free, asymptomatic-free, and endemic equilibria. The basic reproduction number is computed for the model. The local stability conditions are derived for all three equilibrium points. Also, after four lockdowns in India, in this study, the unlocked COVID-19 data is considered for the best fit using the least curve fit method shown in numerical simulation. The figures and graphs are plotted to show the effectiveness of fractional-order and other various dynamics of the system.
  Keywords: COVID-19; basic reproduction number; equilibrium points; local stability; Caputo derivative; sensitivity analysis; least curve fit.
  DOI: 10.1504/IJMMNO.2023.10057423
   
  
• Computational models to study the infectious disease COVID-19: a review  
  by Amit Sharma, Gaurang Sharma, Fateh Singh 
  Abstract: The current COVID-19 pandemic that is still waging in the world is a threat to humanity, and the cure for it is a big challenge for researchers, scientists, and the bio-medical community. However, the vaccine is available nowadays, but the infection is still increasing globally. In this paper, the different types of existing mathematical models related to the COVID-19 outbreak, namely, SI, SIS, SEIS, SIR, SIRS, SEIR, AI, logistic growth model, Poisson model and the expanded models are discussed. The basic reproduction number is one of the most important parameters for predicting the future of COVID-19, and existing models use it to forecast coronavirus disease around the globe. The motive of present study is to elaborate the key factors related to control of pandemic and to introduce the different type of existing mathematical models and applications to the readers under one platform. The initial description of the existing mathematical models gives us better insight of the disease and based on existing literature, future prediction of the spread of COVID-19 can be done more accurately and efficiently.
  Keywords: mathematical model; logistic growth model; Poisson model; COVID-19.
  DOI: 10.1504/IJMMNO.2023.10058159