Mathematical Modelling and Scientific Computing with Applications

An external source of disturbance in a material, even of point size, give rise to waves propagating away from the concerned region in its interior at a specified time. Such an impulse may be best described with the aid of Dirac delta function. Green’s function is primarily utilized in solving these problems of elastodynamics. The present study focuses to investigate the propagation characteristics of Love-type wave influenced by an impulsive point source in a layered structure comprised of a heterogeneous piezoelectric layer lying over a heterogeneous isotropic half-space. Green’s function technique is adopted in order to obtain the dispersion equation, which is further reduced to the classical result of Love wave. For sake of computation, numerical data of PZT-5H ceramics for the heterogeneous piezoelectric layer is considered. Influence of heterogeneity, piezoelectricity and dielectric constant associated with the heterogeneous piezoelectric layer; and effect of heterogeneity parameter and corresponding magnification factor concerned with heterogeneity in the isotropic half-space has been reported through graphical delineation.

In this paper two interacting species in presence of adaptation (dormancy of the predators such as resting eggs) has been discussed. The dormant stage is an equipment to survive in harsh environment. We have discussed the stability analysis of system without diffusion and in presence of diffusion. Our numerical investigation reveals that above the critical value of interference among the zooplankton the system become stable. Spatiotemporal pattern shows a transient complex spatiotemporal pattern by increasing the time and space.

In this paper, we introduce the time fractional dual power Zakharov-Kuznetsov-Burgers equation in the sense of modified Riemann-Liouville derivative. We briefly describe one direct ansatz method namely $$(G'/G)$$-expansion method in adherence of fractional complex transformation and applying this method exploit miscellaneous exact traveling wave solutions including solitary wave, kink-type wave, breaking wave and periodic wave solutions of the equation. Next we investigate the dynamical behavior, bifurcations and phase portrait analysis of the exact traveling wave solutions of the system in presence and absence of damping effect. Moreover, we demonstrate the exceptional features of the traveling wave solutions and phase portraits of planar dynamical system via interesting figures.

Mathematics plays an important role in study of biological systems through mathematical models. In the present paper, we extended the work of Nirwani et al. (Nonlinear Anal Differ Equ 4:43–50, 2016) [5] by introducing the transmission rate $$ \eta $$ from the exposed class E to infectious class I and converted the model into an Susceptible-Exposed-Infectious-Quarantine-Recovered epidemic model with saturated incidence rate. Determine the equilibrium points of the model and basic reproduction number $$ R_{q} $$ is obtained. Stability analysis have been discussed of both equilibrium points by Routh-Hurwitz criteria and Lyapunov function criteria. Also, Numerical simulations are carried out for the model.

The present paper enunciates the propagation behaviour of Shear Horizontal (SH) wave in a layered structure comprised of a slightly compressible layer overlying a slightly compressible half-space with rectangular shaped irregularity and parabolic shaped irregularity at the common interface in two distinct cases. Dispersion relations have been deduced analytically in closed form for both the cases. As a particular case, the obtained dispersion equations have been found to be in agreement with the classical Love wave equation in isotropic case. The impact of various parameters, viz. wave number, rectangular shaped irregularity and parabolic shaped irregularity associated at the common interface, on the phase velocity of SH wave has been studied for the layered structure. Numerical computation and graphical illustration has been done in order to analyse the impact of irregularity parameters (rectangular and parabolic) more profoundly for slightly compressible varga material which serves as one of the major highlight of the present study.

Intracellular calcium governs the most versatile and universal signalling mechanism in living systems which includes contraction of the cardiac tissues, information processing in the brain, release of digestive enzymes by the liver etc. Various investigations have been made on study of calcium signalling in cardiac myocyte to understand its mechanisms. But most of existing investigations have mainly focused on study of calcium signalling in cardiac myocyte cell without paying attention on interdependence of calcium signalling and inositol 1; 4; 5-trisphosphate signalling. In this paper, we propose a mathematical model to understand the impact of the source geometry of calcium on these coupled signalling processes. This study suggests that the source geometry plays a vital role in these signalling processes. Also, calcium and inositol 1; 4; 5-trisphosphate shows a beautiful coordination with each other, which explains the role of inositol 1; 4; 5-trisphosphate in calcium signalling in cardiac myocyte cell. Such studies will provide the better understanding of various factors involved in calcium signalling in cardiac myocytes, which as a result will be of great use to biomedical scientists for making protocols for various heart diseases and their cure.

Wave interaction with a circular elastic porous plate, floating in a two-layer fluid is investigated under the linearized theory of water waves. The eigenfunction expansion method—along with the Darcy’s law for wave past porous structure under the assumption that the flexible structure is having fine pores and is of homogeneous structural rigidity—is exploited to obtain an analytic solution of the problem. The plate deflection and flow distribution around the plate are further computed to study the effects of various wave and structural parameters. The study reveals that the porosity of the plate renders major part of the wave energy to dissipate.

The present article manifests the transference of horizontally polarised shear (SH) wave in an aluminium (Al) plate overlying by a Functionally Graded Piezoelectric Material (FGPM) layer. The separation of variables method is adopted to find the solution. The phase velocity of the wave is calculated for both electrically open and short cases. The significant influence of various affecting parameters on the phase velocity curve is demonstrated through graphs. Findings may be applicable in the structural health monitoring, surface acoustic wave (SAW) devices and ultrasonic inspection techniques.

This paper is concerned with a predator-prey system with a prey group defense and non-linear harvesting of the predator incorporating deterrence hypothesis for predators. Inclusion of predator deterrence rate makes the modelling approach more practicable and exhibits significant impact on the net predation. Taking all possible interactions into account, model equations are formulated. In brief qualitative analysis, existence of interior equilibrium and stabilities of all equilibrium points of the system are discussed to investigate the dynamical behavior of the ecosystem. Hopf, transcritical and saddle-node bifurcations are illustrated for various parameters. Numerical simulations are ecologically justified and supportive of theoretical results.

Within the framework of a heterogeneous anisotropic layer laid over a pre-stressed half-space, propagation of torsional surface wave is investigated. We have considered two different cases of heterogeneity function in the anisotropic layer, namely exponential and trigonometric hyperbolic functions. We have also obtained two different dispersion equations for both cases of heterogeneities on the torsional wave propagation in the said model. The effects of heterogeneities and pre-stress on the torsional wave of phase velocity have been shown graphically for their different numerical values.

This paper irradiates the influence of initial stress, heterogeneity and viscoelasticity on the propagation behavior of shear wave in a heterogeneous orthotropic layer under initial stress overlying a heterogeneous viscoelastic half-space. A separation of variables method has been adopted to obtain the analytical solutions for both the layer and half-space separately. A complex frequency equation has been derived by using suitable boundary conditions. Thereafter, the complex frequency equation has been separated into dispersion and absorption equations. The effects of heterogeneities, initial stress and attenuation coefficient on the phase velocity and dissipation function of shear wave have been shown graphically.

In this paper, we have given a brief history of the Haar wavelet. Later the operational matrix which is obtained from Haar wavelet is used to find the numerical solutions of some differential equations. The solutions thus obtained from operational matrix method are compared with exact solution as well as solution from Runge-Kutta method and Modified Euler’s method is presented.

The design of active control for large and complex engineering structures requires accurate modeling and prediction of their dynamic response and instabilities. The performance of traditional model based control may be limited due to the errors in model approximation, size of the problem and/or availability of limited data for realizing active control. To overcome some of these challenges the method of receptances is developed. This method allows design and computation of controller gains based on a modest size of receptance matrices which can be extracted from transfer functions associated with available sensors and actuators. The area of active aeroelastic control deals with developing wing technology for the next generation aircrafts to achieve increased performance by controlling and manipulating the aeroelastic response by active means. In these applications, receptance based controller design is found to be promising as it eliminates the modeling of complex aeroelastic interaction between elastic structure and surrounding aerodynamics. In this paper, fundamental of the receptance based control is introduced and recent progress in this area is summarized. The effectiveness of the controller designed with on-board sensors (embedded) and actuators (control surfaces) for suppressing the flutter instabilities and flutter boundary extension is demonstrated with numerical examples. The performance of the controller such as its ability to control prescribed modes of interest without influencing the other is also presented. Ongoing research in this area is briefly summarized in this paper.

Magnetic Nanoparticles (MNPs) have been proposed as therapeutic agents for treatment of medical conditions like cancer by using them either as drug carriers to specific locations in the body or as agents for localized heating. For these treatments to be effective, a substantial quantity of MNPs need to reach the target site from the site of injection. However, this may not be the case if blood flow alone is relied on to transport the MNPs as losses to branching blood vessels that lead to transport in directions away from the target site can occur. We have carried out numerical simulations on the flow of a dilute concentration of magnetic particles (MPs), where inter particle interactions can be ignored, in channels that mimic human vasculature like conditions. This has been done using Open Field Operation And Manipulation (OpenFOAM). Blood has been treated as a Newtonian fluid and only laminar flows are considered. The size of channels and direction of flow, which is always towards the target site, mimics the situation in arteries and arterioles. We have only taken into consideration situations where the main channel gives rise to a single daughter channel at different branching angles to the direction of flow. We find that a substantial number of MPs are lost to the daughter channel when the branching angle is less than 45° while a moderate loss is seen for branching angles greater than 45°. Application of an optimum external magnetic field gradient significantly improves the fraction of particles moving towards the target site in the case of branching angles less than 90° and ensures practically no loss for branching angles greater than 90°.

The fluid flow in collapsible channels or tubes is an interesting problem with several physiological applications; for example, blood flow in veins, air flow in lungs and wheezing. In this paper, we present a fluid-structure interaction based model for single-phase fluid flow through a microchannel containing two elastic walls. A two-dimensional model is developed and simulations have been performed using a commercial software. The deforming geometry is analyzed using moving mesh. The flow field and deformation of the elastic walls for different boundary loads and inlet flow conditions are presented and discussed.

The present work focus on water boundary layer flow over an exponential permeable stretching sheet in the presence of suction/injection with variable viscosity and prandtl number. The nonlinear partial differential equations governing flow and thermal fields are presented in non-dimensional form using suitable non-similar transformation. Finally non dimensional partial differential the equations are solved by the implicit finite difference method in combination with the Quasi-linearization technique. The numerical results for skin-friction and local Nusselt number are shown graphically to display effects of physical parameters.

The numerical study presents a two dimensional mathematical modelling and computational simulation of blood flow in a stenosed coronary artery in the presence of magnetic field. Blood flow model is considered based on second grade fluid flow and heat transfer with the suspension of nanoparticles. Vogel’s model is employed for viscosity of blood as a function of temperature. In order to complete our model, the variability in design and size of stenosis is considered. The finite element method is used to solve the transformed conservation equations numerically in conjunction of variational approach and FreeFEM++. The results show that an increase in the thermophoresis parameter ($$ N_{t} $$) decreases the velocity while the increment in the Brownian motion parameter ($$ N_{b} $$) increases the velocity in the whole domain. An increase in $$ N_{t} $$ and Brownian motion parameter ($$ N_{b} $$), there is an increase in temperature values and nanoparticles concentration at the throat of the stenosis and as well as in the remaining domain. These properties changes in the domain by changing the shapes and designs of the stenosis in the domain.

In this paper, we conduct a comparative study amongst different boundary conditions with two dimensional single-relaxation time lattice Boltzmann method (SRT-LBM), for incompressible laminar flow. Three types of boundary condition are considered for the simulation: including full-way bounce-back, half-way bounce-back, and modified bounce-back for the implementation of no-slip boundary condition on the wall with, pressure (density) boundary condition proposed by Zuo and He (Phys Fluids 9(6):1591–1598, 1997 [1]) for inlet/oulet. The benchmark fluid flow problem of steady plane Poiseuille’s flow with Reynolds number, Re = 75 is choosen. The numerical simulations are validated with the analytical solution, and grid convergence test are performed to compare accuracy of different boundary conditions.

The present study deals with the effects of floating flexible membrane on the instability of a gravity-driven flow down an incline. Linear stability of the flow system is explored using normal-mode analysis. Free surface gravity-driven flow is unstable at much lower Reynolds numbers. Instability of such a flow can be controlled either by changing behavioral of the lower wall or by altering the surface waves at the free surface which is done here by including a floating flexible membrane at the top of the liquid layer. Influence of membrane tension is taken into account in terms of stress jump at the free surface. The Orr-Sommerfeld system of the flow is solved numerically using spectral collocation method. The results displays a destabilizing role of membrane tension for a wide range of parameters. The growth rate of the perturbation waves increases with an increase of membrane tension and the critical Reynolds number becomes smaller. Therefore, it is possible to enhance the instability of the flow system with help of membrane properties, which may be useful in Ocean engineering and coating industries.

This work delineates the investigation of static and dynamical behavior of transverse domain walls in ferromagnetic heterostructure in which the thin ferromagnetic layer is sandwiched between a heavy metal and a metal oxide layers. We consider the metallic ferromagnet with high perpendicular magnetic anisotropy and exhibits structural inversion asymmetry. The presence of a strong inversion asymmetry in the ferromagnetic material leads to additional spin-orbit coupling torque terms into the dynamics qualitatively different from the standard spin-transfer torques. The evolution of magnetization inside the ferromagnetic layer is governed by the one-dimensional model of generalized Landau-Lifshitz-Gilbert-Slonczewski equation consisting of the standard spin transfer and spin-orbit coupling torque terms along with the nonlinear dissipation factors viz. viscous and dry-friction. Under this framework, first, we establish the static magnetization profile in the two faraway domains in the presence of transverse magnetic field once the electric and longitudinal magnetic fields are switched off. Then, by means of regular perturbation expansion method, we derive the zero order traveling wave solutions under the influence of small applied magnetic field and spin-polarized electric currents.

In this research study, an investigation of three-dimensional (3D) CNT based nanofluid flow through a horizontal rotating channel under the influence of viscous dissipation, is carried out. We have considered that the upper sheet of the channel is permeable and fixed while the lower sheet is impermeable and the sole reason for fluid flow initiation is the stretching of the lower sheet. The mathematical model of the problem is developed and is presented in the form of a system of nonlinear partial differential equations. Suitable similarity technique is employed to transform these governing partial differential equations into the set of ordinary differential equations which are nonlinear. The transformed equations are then solved numerically by the bvp4c routine of MATLAB. Computations for the nanofluid velocity and nanofluid temperature along with skin friction coefficient and Nusselt number are, carried out for relevant flow parameters. A comparative analysis of single-wall carbon nanotubes as well as multiwall carbon nanotubes on temperature and velocity distribution is carried out. Three dimensional flow of CNT-based nanofluid inside a horizontal channel whose one wall is permeable and the other is not, has not been considered before. Although up to some extent, such an analysis has practical bearings in the industries related with lubrication under the influence of magnetic field. The temperature of the fluid is getting increased with growing values of Eckert number and rotation parameter while a completely opposite trend is found for suction/injection and Reynolds number.

The intention behind carrying out this research problem is to understand the nature of two-dimensional hydromagnetic flow of an electro-conductive and thermally radiating viscoelastic fluid past a non-linear stretching surface, considering viscous and Joule dissipation. With a perspective of converting the governing PDEs into a system of ODEs, appropriate similarity transformation has been incorporated. Optimal Homotopy Analysis Method (OHAM) is used for solving the converted non-linear and coupled equations. Impact of several regulatory flow parameters on temperature, velocity and species concentration are explained via graphs while the variation of some engineering quantities such as Nusselt number, skin friction coefficient and Sherwood number are shown by tables. One of the major outcomes of this investigation is that velocity is getting decreased by viscoelastic parameter whereas the convective heat transfer condition enhances the fluid temperature.

IFS can handle non-stochastic non-determinism that arises due to single membership function for both membership and non-membership grade. PIFS may handle non-determinacy because of both stochastic and non-stochastic reasons. In this study, we propose PIFS based FTS forecasting model to control the both kind of non-determinism along with non-stochastic uncertainty in TS forecasting. The developed model describes issue of non-determinism which rises due to both randomness as well as linguistic representation of TS data. An aggregation operator to aggregate the PIFS into IFS is also used in this study. The presented method has been simulated using financial TS data of TAIEX to confirm it’s outperformance using RMSE.

With the day-by-day increase in power consumption, the transmission and distribution networks are operating on the verge of stability. The transient stability studies is one of the important study that helps to maintain the more reliable power supply with increasing demand in complex network configuration. This paper helps to understand the problem of transient stability, its effect on the power system. In this paper IEEE 9-bus system is considered to analyze a list of contingencies and its effect on the system. The contingency analysis is done using a powerful simulation tool for different generator bus.

This paper is concerned with the types of stochastic disturbances affecting the potential of the aerial system. The satellite system for continuous and discrete time domain is discussed. A phase lead compensator completes the orientation successfully. Astrom’s single-input single-output (SISO) model is implemented with using the minimum variance control strategy. The separation principle then provides the optimal control law which curtails the cost function to a value as small as possible. The satellite system is positioned for one quarter revolution with the co-ordination of generalized minimum variance controller (GMVC) and standard generalized dual controller (GDC) based on certainty equivalence assumption. The revolutions in radians are tracked as output of the system for the input specified in degrees to the system. The controller proved useful in reducing the overshoot and atmospheric disturbances which allows a stable motion even for larger time delays.

This project is a prototype of data glove which has ability to convert the movement of figure into visual display and audible sound of predefined language. I have seen many people who find it difficult to communicate with other due to language problem or due to problem in vocal chord. In a diverse country like INDIA where various types of mother tongues is spoken. People form one region of country when travelled to other region find it difficult to convey their message, which make it tedious to survive them in other region. So this data glove can convert the speaker language into the listener language which make it possible to easy communication between different language speaker. There is approximately 70 million people in world who are deaf and dumb. These people use sign language to communicate with each other. But the person with no disability in vocal chord does not learn sign language, this means that not everyone can understand sign language. So it will be a tedious task for deaf or dumb person to communicate with other person having no knowledge of sign language. This data glove can be used to replace code language which is used during war. A particular command can be converted into a gesture and the commanding officer have to make particular gesture using his hand and the command is displayed on the command receiving personnel. Data glove consists of flex sensor. In this prototype I have used 3 flex sensor which produce 8 output result. You can increase no of flex sensor up to 5 on one glove which can produce 32 output. The output produce by combination of flex sensor on data glove is in analog form which is feeded to ADC channel of Arduino microcontroller. Analog to digital converter of microcontroller convert the analog input into digital form. This digital pattern is compared with stored data and then according to comparing result a particular sentence or word is displayed on a 16 * 2 LCD and same word or sentence is played on an 8 O speaker. Speaker and LCD output is for dumb people communication while only LCD is only sufficient for deaf person. This model consists of SD card which make it possible for storing as much audio as required means there will be no limitation of memory.

Over last few decades, mathematics has played a crucial role in developing efficient algorithms for Face Recognition (FR) used in biometric systems. FR using Machine Learning (ML) techniques has impacted FR systems tremendously, towards efficient and accurate models for FR. Existing FR systems used in biometrics use ML techniques to learn patterns in the images by extracting various features from them and often require pre-processed face image data for the learning process. In this paper, we have used various pre-processing techniques and compared them in the deployed FR framework. It was observed that the Steerable Pyramid (SP) filter was the most efficient pre-processing technique among all techniques used for pre-processing in this work. Though existing feature extraction methods such as SIFT (Scale-Invariant Feature Transform), SURF (Speeded-Up Robust Features), ORB (Oriented FAST and Rotated BRIEF) have been used in the past, they have not been accurate enough in various vision based biometric systems. Hence, a novel PSI (Pose Scale and Illumination) invariant SURF-RootSIFT technique is proposed by extending the well known SIFT-RootSIFT feature extraction technique which is achieved by calculating the Bhattacharya Coefficient between the feature vectors. A framework which uses the proposed novel feature extraction technique is deployed in this work. This paper demonstrates that the novel SURF-RootSIFT based framework is proven to perform more accurately and efficiently than the other techniques, with 99.65, 99.74 and 97.93% accuracy on the Grimace, Faces95 and Faces96 databases respectively.

Extraction of hydrokinetic energy from in stream flow can be an effective, sustain able and environmental friendly replacement of the conventional energy resources. Savonius hydrokinetic turbine is a vertical axis turbine, which has a poor efficiency and its operating range under various loading conditions is very short. The coefficient of performance value curves reported under different investigations on Savonius hydrokinetic turbine are highly fluctuated in respect of tip speed ratios (TSR). In order to enhance the efficiency of the turbine and to get less fluctuations in coefficient of power output curve for smooth operation under higher range of tip speed ratios, this paper aims to model a modified design of Savonius turbine with twisted blades and analyze its performance on various operating conditions. For CFD analysis commercial unsteady Reynolds-Averaged Navier-Stokes (URANS) solver in conjunction with SST k-ω turbulence model have used. Due to symmetrical cross sections on different geometrical positions 3D transient simulations are conducted to find out the average torque. Coefficient of torque and coefficient of power are analyzed and discussed. The result of this study concluded as very less deviation in power coefficient curve up to tip speed ratio 1.4, which indicates the increment of operating range and beyond that TSR value it falls down rapidly. The maximum power coefficient obtained 0.30 corresponding to a TSR value 1.4 for input water velocity of 2 m/s.

Security and identity have become one of the primary concerns of the people in this digital world. Person authentication and identification is transforming the way these services are provided. Earlier it was mainly achieved through passwords and patterns but with significant advancements in face recognition technologies, it has been exploited in providing authentication in smart phones and computers. Face Recognition (FR) extends its use in applications like face tagging in social media, surveillance system at theaters, airports and so on. The proposed mathematical model employs linear algebra and mathematical simulations for the task of person identification. Kernel singular value decomposition is used to denoise the facial image which is then passed to a feature detector and descriptor based on nonlinear diffusion filtering. The obtained descriptors are quantized into a vector using an encoding model called VLAD which uses k-means++ for clustering. Further, classification is done using Gradient boosting decision trees. The pipeline proposed aims at reducing the average computational power and also enhancing the efficiency of the system. The proposed system has been tested on the three benchmark datasets namely Face 95, Face 96 and Grimace.

Face Recognition is immensely proliferating as a research area in the paradigm of Computer Vision as it provides an extensive choice of applications in surveillance and commercial domains. This paper throws light upon the comparison of various dense feature descriptors (Dense SURF, Dense SIFT, Dense ORB) with each other and also with their classical counterparts (SURF, SIFT, ORB) using a novel technique for recognition. This proposed technique uses Laplacian of Gaussian filter for enhancement of the image. It applies various dense and classical feature descriptors on the enhanced image and outputs a feature vector. In order to achieve high performance, this feature vector is given to Fisher vector since Fisher Vector is a feature patch-aggregation method. Finally, extended nearest neighbor Classifier is used for classification over the orthodox k-nearest classifier. Experiments were carried out on three diverse datasets—ORL, Faces94, and Grimace. On scrutinizing the results, Dense SIFT and Dense ORB were found to be preeminent as measured by various performance metrics. 98.44 on Grimace, 98.15 on Faces94.

Face recognition is prevailing to be a key aspect wherever there is a need for interaction between humans and machines. This can be achieved by containing a set of sketches for all the possible individuals and then cross-validating at necessary circumstances. We propose a mechanism to fulfil this task which is centred on locally adaptive regression kernels. A comparative study has been presented at encoding stages as well as at the classification stages of the pipeline. The results are cautiously examined and analyzed to deduce the best mechanism out of the proposed methodologies. All the ideologies have been tested for multiple iterations on benchmark datasets like ORL, grimace and faces 95. The vectorized descriptors have been subjected to encoding using slightly refined methods of feature aggregation and clustering to assist classifiers in imputing the test subjects to their respective classes. The encoded vectors are classified using Gaussian Naive Bayes, Stochastic Gradient Descent classifier, linear discriminant analysis and K Nearest Neighbour to accomplish face recognition. An inference on sparse nature of locally adaptive regression kernels was made from the experimentation. A rigorous study regarding the discrepancies of the performance of LARK descriptors is reported.