Department of Mathematics

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Mathematics

In general, the nonlinear interconnected systems are highly interconnected with N number of sub-systems, therefore, it is difficult to a design decentralized control scheme for analyzing the stability of the system. This study is mainly concerned with fuzzy based sliding mode control design to analyze the stability and stabilization of nonlinear interconnected systems. In order to derive the stabilization condition, we proposed a fuzzy-based- sliding model controller and the sufficient condition is derived based on suitable Lyapunov function and LMI approach. The sufficient condition contains the information on the sliding motions, some tuning parameters and slack variables. The condition ensures that the asymptotic stability of the states of nonlinear interconnected systems under the fuzzy-based sliding mode controller. Finally, the numerical example and their simulation results are given to demonstrate the effectiveness of the proposed conditions. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

School of Advanced Sciences

Chennai Campus

World University root node

Studies in Systems, Decision and Control

Fuzzy-based sliding mode control design for stability analysis of nonlinear interconnected systems

To evaluate the heat transfer performance (HTP) of hybrid nanofluids, numerical simulations are carried out in an industrial length single pass shell and tube heat exchanger. In shell, ISO VG 68 oil enters with 75°C and with 30°C, the coolant passes into the tube. CNT-TiO2/water and CNT-TiO2/sodium alginate (SA) are used as Newtonian and non-Newtonian hybrid nanofluid, respectively. The influence of base fluid and nanoparticles on thermal performance of heat exchanger is studied. The chosen nanoparticles are reliable to the industrial deployment. The current numerical procedure is validated with the earlier experimental results. Volume fraction of nanoparticles is optimized for an effective HTP of the heat exchanger. About 60% increment in heat transfer coefficient is observed when hybrid nanofluid is employed. By using Newtonian hybrid nanofluid, 50% improvement in Nusselt number is marked out. Effectiveness and heat transfer rate of heat exchanger are higher with the employment of Newtonian hybrid nanofluid. Results indicated that, even though Newtonian hybrid nanofluid shows higher thermal performance, non-Newtonian hybrid nanofluid is preferable for energy consumption point of view. © 2021 World Scientific Publishing Company.

International Journal of Modern Physics C

Modeling of Newtonian and non-Newtonian-based coolants for deployment in industrial length-scale shell and tube heat exchanger

Internet connectivity is now considered to be a basic human right and in this era of information technology, more efficient ways of browsing the web are being found. The most popular search engine, Google uses its ‘Page Rank Algorithm’ for its searches. In this paper, we aim to find out a more efficient way of searching the web and better organising the search result based on the categories of the pages. The results of the proposed algorithm are compared with the existing Page Rank algorithms, which include the original PageRank Algorithm and a Weighted PageRank Algorithm. The results obtained in this paper have been experimentally compared with the data of the above-mentioned algorithms using comparison graphs. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Wireless Networks

Study and analysis of category based PageRank method

Malaria is a life-threatening mosquito-borne disease. It is transmitted through the bite of an infected Anopheles mosquito. Malaria may be fatal if not treated promptly. Malaria is a major public health problem in India. Here we propose an SIRS model to study the transmission dynamics of malaria with saturated treatment. We assume that the mosquito population is growing logistically in the environment. Here we include a saturated type treatment function which is more suitable for the regions with limited resources. We discuss the existence and stability of different equilibria of the proposed model. We also compute the basic reproduction number R which plays an important role in existence and stability of equilibria of the model. For R< 1 , backward bifurcation occurs, which suggests that lowering R below one is not enough to eliminate the disease from the population. We estimate the key parameter corresponding to transmission of malaria using real data from different states of India by least square method. We also perform sensitivity analysis using PRCC to identify the key parameters which influence the infection prevalence of the disease and the basic reproduction number. Numerical simulations are presented to illustrate the analytic findings. Our numerical results suggest that infected population should get proper treatment and increase in the death rate of mosquito can also help to eradicate the malaria disease from the population. © 2021, Korean Society for Informatics and Computational Applied Mathematics.

Journal of Applied Mathematics and Computing

Modeling the transmission dynamics of malaria with saturated treatment: a case study of India

Schistosomiasis is a snail-borne parasitic disease, which is affecting almost 240 million people worldwide. The number of humans affected by schistosomiasis is continuously increasing with the rise in the use of agrochemicals. In this paper, a mathematical model is formulated and analyzed to assess the effect of agrochemicals on the transmission of schistosomiasis. The proposed model incorporates the effects of fertilizers, herbicides and insecticides on susceptible snails and snail predators along with schistosomiasis disease transmission. The existence and stability of the equilibria in the model are discussed. Sensitivity analysis is performed to identify the key parameters of the proposed model, which contributes most in the transmission of this disease. Numerical simulations are also performed to assess the impact of fertilizers, herbicides and insecticides on schistosomiasis outbreaks. Our study reveals that the agricultural pollution can enhance the transmission intensity of schistosomiasis, and in order to prevent the outbreak of schistosomiasis, the use of pesticides should be controlled. © 2021 World Scientific Publishing Company.

International Journal of Biomathematics

Assessing the impact of agrochemicals on schistosomiasis transmission: A mathematical study

The current study focused on forced convection water boundary layer flow on permeable diverging channel for variable physical properties of fluid. The formation of coupled nonlinear partial differential equations is expressed in terms of non-dimensional quantity using similarity transformation. The solution of non-dimensional differential equation obtained by numerical finite difference scheme with combination of quasi-linearization technique. It is found that the Eckert number is significant in the boundary layer region in laminar flow, and also, the effects of physical parameters are investigated numerically and shown graphically. © 2021, Springer Nature Singapore Pte Ltd.

Lecture Notes in Mechanical Engineering

Effect of Viscous Dissipation of Laminar Flow over a Flat Plate with Variable Properties

An interesting attempt is taken to form a hybrid model by integrating Fuzzy Cognitive Map (FCM), the Delphi Method, and the DEMATEL method through the Haar ranking of Hexagonal Fuzzy Number. To examine this model, the problem of solid waste management is taken. Solid waste arises from human and animal activities can generate major health problems and horrible living environment when they are not dumped of safely and appropriately. The proper disposal of solid waste helps to reduce the terrible impacts on both human health and environment to sustain economic growth and better quality of life. Therefore, this present study analyzes the solid waste management through the Haar FCM with DEMATEL technique. © 2021, Springer Nature Singapore Pte Ltd.

Lecture Notes in Electrical Engineering

Haar FCM with DEMATEL Technique to Analyze the Solid Waste Management

Coronavirus disease 2019 (COVID-19) is a viral disease which is declared as a pandemic by WHO. This disease is posing a global threat, and almost every country in the world is now affected by this disease. Currently, there is no vaccine for this disease, and because of this, containing COVID-19 is not an easy task. It is noticed that elderly people got severely affected by this disease specially in Europe. In the present paper, we propose and analyze a mathematical model for COVID-19 virus transmission by dividing whole population in old and young groups. We find disease-free equilibrium and the basic reproduction number (R0). We estimate the parameter corresponding to rate of transmission and rate of detection of COVID-19 using real data from Italy and Spain by least square method. We also perform sensitivity analysis to identify the key parameters which influence the basic reproduction number and hence regulate the transmission dynamics of COVID-19. Finally, we extend our proposed model to optimal control problem to explore the best cost-effective and time-dependent control strategies that can reduce the number of infectives in a specified interval of time. © 2021 John Wiley & Sons, Ltd.

Mathematical Methods in the Applied Sciences

Modeling and optimal control analysis of COVID-19: Case studies from Italy and Spain

The purpose of this study report is to examine the unsteady force convection flow on irregular boundary over a diverging channel with effect of viscous dissipation. The fundamental equations of fluid, continuity, momentum, and energy equations are converted into dimensionless form. The resulting coupled partial differential equations are linearized by quasilinearization technique, the backward, and central difference scheme for nonuniform mesh used to solve the system of linear equations. We found that finite difference scheme for nonuniform mesh gives smoothness of solution compared to finite difference scheme for uniform mesh on irregular boundary, this is evident from Figure 2. Near the wall region, as viscous dissipation (Ec) increases from 0.2 to 0.5, the temperature profiles overshoots 20% to 112%. Also the effects of Reynolds number (Re) on heat transfer coefficient is comparatively less than skin-friction coefficient. © 2020 Wiley Periodicals LLC

Heat Transfer

Analysis of unsteady force convection flows on irregular boundary over a diverging channel

Consider an information diffusion process on a graph G that starts with k&amp;gt; 0 burnt vertices, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as k other unburnt vertices. The k-burning number of G is the minimum number of steps bk(G) such that all the vertices can be burned within bk(G) steps. Note that the last step may have smaller than k unburnt vertices available, where all of them are burned. The 1-burning number coincides with the well-known burning number problem, which was proposed to model the spread of social contagion. The generalization to k-burning number allows us to examine different worst-case contagion scenarios by varying the spread factor k. In this paper we prove that computing k-burning number is APX-hard, for any fixed constant k. We then give an O((n+ m) log n) -time 3-approximation algorithm for computing k-burning number, for any k≥ 1, where n and m are the number of vertices and edges, respectively. Finally, we show that even if the burning sources are given as an input, computing a burning sequence itself is an NP-hard problem. © 2021, Springer Nature Switzerland AG.