International Journal of Mathematical Modelling and Numerical Optimisation (12 papers in press)
Numerical analysis on thermal performance of a trapezoidal micro-channel heat sink using an improved version of the augmented -constraint method
by Lagouge Tartibu
Abstract: This work proposes the use of an improved version of the augmented ɛ-constraint method (AUGMENCON2) for the analysis of the thermal performance of a micro-channel heat sink. In order to highlight the strength and the effectiveness of this new approach, a trapezoidal micro-channel heat sink has been considered. The geometrical configuration namely the micro-channel widths and depth are the main variables considered in this study. Surrogate models based on the Response Surface methodology have been adopted to approximate the thermal resistance and the pumping power which provide an indication of the thermal performance of the micro-channel heat sink. A two-objective Non-Linear Problem have been formulated and implemented within the General Algebraic Modelling System. Global Pareto optimal solutions has been computed using the proposed method. Despite being a relatively straightforward method, the AUGMENCON2 provides a reasonable level of accuracy and shortens the required computational time in comparison to two existing approaches.
Keywords: Multi-objective optimization; ε-constraint method; heat sink; AUGMENCON.
Frequency regulation of a power system integrated with renewables using a novel DE-DA optimized controller.
by Sayantan Sinha, Ranjan Kumar Mallick, Srikanta Patnaik
Abstract: The proposed research paper mainly focuses on the automatic generation control of an interconnected power system integrated with solar power. The work has taken into consideration a two area power system consisting of a conventional thermal power source and a solar power plant in one area. The penetration of renewable sources give rise to deviations of frequency from their scheduled values. The AGC plays a very important role in minimizing the frequency deviations of the system by reducing the Area Control error to zero with the help of suitable controllers. A maiden attempt has been made to incorporate two degree of freedom proportional integral and derivative controller for AGC purposed. A novel attempt has been made to design a hybrid optimized Dragonfly algorithm- Differential Evolution technique for tuning the controller gains. The performance of the controller is also compared with the conventional PID controller under a system disturbance of 0.01 p.u when applied to area 1. The system performances are further analyzed with varying system parameters and different loading conditions. Comparisons with traditional PID controllers have also been done in terms of dynamic system parameters like settling time, maximum overshoot and minimum undershoot
Keywords: AGC; Deregulated; benchmark; hybrid; PID; 2 DOF PID; renewables; two area.
Numerical Analysis of the European and American Options with the SPH method.
by Abdelmjid Qadi El Idrissi, Boujemaa Achchab, Abdellahi Cheikh Maloum
Abstract: In this paper, we propose a numerical method to solve the European and the American
options by using the SPH method. Because its robustness and efficacy, this numerical method has been widely applied in the computation of partial differential equations particularly in fluid dynamic. To model these financial options, we use the Black Scholes equation. It is a mathematical model consisting of a set of partial differential equation supplemented by some boundary
conditions. We evaluate the accuracy of our numerical method by giving some comparisons between the analytic solution and the numerical simulation.
Keywords: Black Scholes equation; European option; American option; SPH Method.
A Higher-Order Hybrid Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with Boundary and Weak Interior Layers
by Anirban Majumdar, Srinivasan Natesan
Abstract: In this paper, we study the numerical solutions of singularly perturbed convection-diffusion two-point BVP as well as one-dimensional parabolic convection-diffusion IBVP with discontinuous convection coefficient and source term. Because of the positivity of the convection coefficient throughout the domain and the discontinuity of the convection coefficient and the source term at $x=xi$, the analytical solutions of these kind of problems exhibit a boundary layer near $x=0$ and a weak interior layer near $x=xi$. We discretize the spatial domain by the piecewise-uniform Shishkin mesh and the temporal domain by a uniform mesh. To approximate the spatial derivatives, we apply the hybrid finite difference scheme, which is a combination of the central difference scheme in layer regions and the midpoint upwind scheme in outer regions. The implicit-Euler scheme is used for discretizing the temporal derivative. For the time independent problem, we derive that the proposed hybrid scheme is $varepsilon$-uniformly convergent of almost second-order and for the time dependent problem, we also prove that the proposed scheme is $varepsilon$-uniformly convergent of almost second-order in space and first-order in time. To validate the theoretical estimates, some numerical results are presented.
Keywords: Singularly Perturbed Convection-Diffusion Problem; Interior Layer; Piecewise-Uniform Shishkin Mesh; Finite Difference Scheme; Uniform Convergence.
Reconstruction of an orthotropic thermal conductivity from nonlocal heat flux measurements
by Mousa Huntul, Mohammed Hussein, Daniel Lesnic, M.I. Ivanchov, N. Kinash
Abstract: Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fiber composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.
Keywords: Inverse problem; Orthotropic thermal conductivity; Two-dimensional heat equation; Nonlinear optimization.
Stability and Numerical Study of Theoretical Model of Zika Virus Transmission
by Maghnia Hamou Maamar, Leila Bouzid, Omar Belhamiti, Fethi Bin Muhammad Belgacem
Abstract: In this paper, we examine the Zika virus transmission for human and mosquito populations. At the first time, a compartment model based on two populations, humans and mosquitoes, are proposed and analyzed quantitatively using the stability theory of the differential equations. In the second time, a nonhuman primate (monkey) is considered, we prove the influence of this second reservoir host on the spread of the disease. Numerical simulation of the models is implemented to investigate the effect of certain key parameters on the transmission of Zika virus.
Keywords: Zika Virus Disease; Equilibrium Stability; Reproduction Number; Jacobi Multi-Wavelets Method.
Community Detection in Complex Networks Using Multi-objective Bat Algorithm
by Iyad Abu-Doush
Abstract: Community detection is the problem of identifying communities in which we aim to discover groups of nodes with high connectivity within the same group and with low connectivity outside the group. Community detection is considered to be a non-deterministic polynomial-time hard problem. Heuristic algorithms can be used to solve such a complex optimization problem. Bat Algorithm (BA) is a meta-heuristic optimization algorithm. The BA can be used to model a multi-objective optimization problem. In this paper, the Multi-objective Bat algorithm (MOBA) is adapted to model and solve the community detection problem. In order to evaluate the algorithm, four real-world datasets are used. The performance of the algorithm is compared with seven other methods from the literature. The comparison was in terms of two metrics to check the quality of the obtained community namely Modularity (Q) and Normalized Mutual Information (NMI). The results show that the proposed algorithm outperforms all algorithms in one dataset and that it is competitive in other cases.
Keywords: Bat algorithm; Community detection; Multi-objective optimization; Multi-objective Bat algorithm.
Temperature and rainfall dependent mathematical modelling for progression of Zika virus infection
by Narender Kumar, Md Imam Faizan, Shama Parveen, Ravins Dohare
Abstract: We formulated a susceptible-exposed-infected-recovered (SEIR) mathematical model for transmission of ZIKV. The model was used to estimate different parameters using the outbreak data obtained from Puerto Rico during 2015-2016 in this region. The inclusion of climatic factors in the model assisted in more realistic predictions of the transmission dynamics of ZIKV. The value basic reproduction number R0= 3.2869 calculated at estimated parameters suggested outbreak of infection in this region. The sensitivity analysis revealed that R0 was highly influenced by death rate, mosquito biting rate and maturation rate of immature mosquitoes. The R0 further implied that around 70% of the individuals should be immunised to develop herd immunity to prevent propagation of the disease. The simulation of controlled reproduction number revealed the values of different isolation coefficients (ε1 > 0.4, ε2 > 0.14, τ1 < 0.1). These coefficients might be utilised by policy makers in the control strategies against the infection.
Keywords: Zika virus infection; basic reproduction number; disease free equilibrium; DFE; simulation.
Dynamic indicator of intimate partner violence: self-regulatory perpetrator
by E. Leal-Enríquez, Aime Renata Gutiérrez-Antúnez
Abstract: A dynamic indicator to measure the level of violence between a perpetrator and victim of intimate partner violence is developed in this paper. Herein it is considered that violence can be measured through the rates of change over time of the violent interactions, considering the weight of severity of the violence committed. These rates of change are modelled by a logistic differential equation with a probabilistic parameter, the principle being the self-regulation of a perpetrator. This parameter of self-regulation is modelled by two changes of states: one of self-control and the other being a loss thereof. The transition of each state is modelled by a discrete Markov chain. With the proposed dynamic indicator, computational simulations are created to generate probable scenarios of partner violence with varying levels of severity. This dynamic indicator is then applied to a specific study of physical violence, using the prevalence of violence to approximate a state of loss of control. With the results obtained from the simulation, a qualitative analysis is made of the probable behaviours, controllable (semi-stable) and uncontrollable (potentially deadly), that can occur in a time interval of 3 and 12 months.
Keywords: dynamic indicator; mathematical model; violent scenarios; self-regulation; intimate partner violence.
A novel particle swarm optimisation with search space tuning parameter to avoid premature convergence
by Raja Chandrasekaran, R. Agilesh Saravanan, D. Ashok Kumar, N. Gangatharan
Abstract: Particle swarm optimisation is a trendy optimisation technique that is inhaled from the space navigational intelligence of birds. The optimisation technique is popular among the researchers for several decades because of the fact that it is inspired by the zonal and universal best members in all the generations. The optimisation by PSO is found better than few other optimisation techniques, in several trials with the optimisation of the mathematical benchmarks and real-time applications. But the more-than-modest orientation style of the algorithm often leads the population to premature convergence. Inertia weight parameter is used to tune the explorability of the population. In this paper, a zonal monitor (based on success in the recent iterations)-based inertia weight tuning is redressed by including universal monitors (based on the success with a universal fitness perspective). The proposed algorithm excels the conventional PSO, the PSO with zonal monitors alone. The inertia weight of the PSO with zonal monitor is also not dynamic whereas the proposed PSO's inertia weight are found to be more dynamic with tuning the explore ability with regard to zonal and universal context of fitness.
Keywords: particle swarm optimisation; PSO; adaptive inertia weight; search space tuning.
Optimisation of EOQ model with Weibull deterioration under crisp and fuzzy environment
by Anu Sayal, A.P. Singh, Deepak Aggarwal
Abstract: Deterioration is an unavoidable condition prevalent in all spheres of the inventory system involving perishable goods. Though other factors are also responsible for the depletion of the level of the inventory but the effect of deterioration in this regards is quite high. In the present paper, we have considered the deterioration rate of the form of Weibull distribution and the demand rate is taken as a ramp type function of time, when the inventory system starts without any kind of shortage. We have developed a mechanism for the optimisation of the total cost of the EOQ inventory system in both crisp and fuzzy environment. An appropriate numerical example has been proposed in order to validate the model in both crisp and fuzzy system.
Keywords: optimisation; deterioration; ramp type demand; EOQ model; fuzzy inventory system; Weibull distribution.
Natural convection analysis of water near its density extremum between finite vertical plates: a differential transform approach
by Ryoichi Chiba
Abstract: Using a two-dimensional differential transform method, we solve the steady natural convection problem of cold water between vertical isothermal plates of finite length. The cold water exhibits a density variation approximated as a quadratic function of temperature. Given the temperature-dependent viscosity, we present approximate analytical solutions in the form of power series for temperature, vertical flow velocity, and pressure defect. Numerical calculations are carried out for two cases of water temperature in which the following occur with respect to increases in temperature: 1) the density decreases monotonously; 2) the density increases and subsequently decreases. The numerical results reveal how the temperature-dependent properties affect the developing temperature and velocity profiles and pressure defect distribution along the streamwise direction.
Keywords: cold water; DTM; differential transform method; semi-analytical method; natural convection; temperature-dependent property; vertical channel; series solution; mathematical modelling; heat transfer; convective flow; density extremum.