Mathematical Modeling and Computational Tools

Electrophoresis is a process by which a charged colloid is propelled in a polar media under the action of an externally imposed electric field. This has been recognized as a useful tool to characterize macromolecules such as DNA, microorganisms, biocolloids or synthetic nanoparticles. Electrophoresis is also found to be an efficient method in separating, sorting and purification process. The microfluidic technology to address problems in biology, medical technology, such as controlled drug delivery and disease diagnostic are based on the electrophoresis phenomena. Thus, a correct relation between the electrostatic parameters and the electrophoretic velocity constitutes an important research topic. In this chapter, we have elaborated some of the existing simplified models for electrophoretic velocity. The shortcomings of these linear models or models based on weak-field consideration are illustrated in this chapter. An account of improved theory on electrophoresis is provided. The electrophoresis of a hydrophobic colloid is also addressed in the present chapter.

The motivation of the present work is to form vortical flow by designing potential heterogeneity in a different manner on both walls of a microchannel. A complete mathematical model of two-dimensional is considered to control the solute transport and mixing efficiency in the combined flow for electroosmotic and pressure gradient. The characteristics equation of this model is governed by simultaneously solving the nonlinear Poisson equation, the Nernst–Planck equations and modified Navier–Stokes equations. The pressure gradient forms in flow direction due to potential heterogeneity of microchannel wall. The vortex forms on patch, increases with ionic concentration and diminishes with the favorable pressure gradient case. The average flow is always increased for pressure-assisted electroosmotic flow. The vortex formation in electroosmotic flow has very much essential for solute mixing. The potential heterogeneity in walls develops a vortex which generates the pressure gradient to promote the mixing efficiency. The mixing performance is compared with the plane channel and several other forms of surface heterogeneity such as patches with symmetric and asymmetric manners and single patch. The mixing performance increases by introducing potential heterogeneity in channel surface. The potential heterogeneity in an asymmetric manner gives maximum mixing performance of a solute. There is no such effective variation on solute mixing between symmetric and asymmetric potential heterogeneity cases. The mixing index decreases with imposed pressure gradient for all forms of surface heterogeneity.

Microfluidics has broad utilizations in the field of medical science. The architecture of microfluidic devices desires an improved compassionate of the action of flow and heat transfer attributes in micro- or nano-channel. Electroosmosis is one of the main electrokinetic effects. For the hydrophobic surfaces, a slip boundary condition is established. The present study investigates the effect of temperature-dependent electrostatic parameters on electroosmotic flow with hydrophobic patches. The present study comprises the coupled Poisson–Boltzmann equation, the modified Navier–Stokes equations, the modified Nernst–Planck equation, and the modified energy equation. Governing equations with proper boundary conditions are solved numerically through control volume approach over a staggered grid arrangement. The results are expressed in terms of velocity profiles and surface temperature. Also, we have considered average entropy generation, Savg; average Bejan number, Beavg.

In the present chapter, we have investigated an unsteady incompressible laminar electrically conducting heat and mass transfer distributions of couple stress nanofluid flow through parallel plates with porous medium having the thermal slip boundary condition. By applying the suitable similarity transformations, the governing partial differential equations are reduced to nonlinear ordinary differential equations, which are numerically solved by the shooting method along with Runge–Kutta fourth-order scheme. The influence of different non-dimensional numbers on the fluid flow, heat and mass transfer characteristics of the fluid is presented in graphs and discussed in detail. Numerical values of skin friction, Sherwood number and Nusselt number with different parameters are also computed and presented in the form of tables. The Hartmann number, chemical reaction parameter and thermophoresis parameter were having the same result on velocity, concentration and temperature distributions. The data presented are compared with the recent viscous case conditions and are concluded to be in better agreement.

There are several real-life problems exist where fluid flows over the heated solid body. In the present work, drag force and Nusselt number are studied for centrally fixed heated sphere. Computational fluid dynamics tool is used to simulate the present problem. The heated sphere is fixed radially at the centre of the cylinder. Total four cases corresponding to Reynolds numbers 100, 200, 300 and 500 are simulated to analyse the effects of blockage ratio of drag. The simulated results show that drag reduction is about 5%. The maximum value of drag coefficient is computed for the blockage ratio 0.8, and it decreases as the Reynolds numbers increases.

An unsteady two-dimensional transport equation is considered to investigate the distribution of suspended sediment in an open channel turbulent flow, where the mechanism of hindered settling is also taken into account. Due to the consideration of concentration-dependent settling velocity on sediment transportation, the transport equation is a partial differential equation with a highly nonlinear term, which has been solved numerically by using the alternating direction implicit (ADI) finite-difference method. It is found that the sediment concentration increases along the vertical direction due to the inclusion of hindered settling effect.

The present study focuses on vertical distribution of concentration in a turbulent flow where the swapping of fluid parcels and suspended sediment parcels takes place over a vertical distance lm, the mixing length and generates a net vertical flux of momentum and sediment. The Fickian diffusivity of sediment has been considered not to be equal to the Fickian diffusivity of momentum, i.e., the eddy viscosity. Also, the study assumes that in the stream-wise direction the velocity of fluid and solid particles is identical, and in the transverse direction, they differ by the particle settling velocity $$w_{\text{s}}$$. Apart from these, the study considers the reduction of mixing length due to the presence of suspended solid particles which damp the characteristic oscillation of turbulent flow. The model is solved numerically and is validated by comparing the solution with relevant set of laboratory experimental data.

In this paper, a study has been carried out to understand the effect of the fluid, flow and the mechanical parameters on a pulsatile flow of a Newtonian fluid in an expanding and contracting pipe. The fluid parameters considered are the viscosity and the density, flow parameters are the amplitude of the pressure gradient and the frequency of oscillations, and the mechanical parameter considered is the radius of the pipe. A mathematical model is constructed in the cylindrical polar coordinate system with the fluid flow assumed to be axisymmetric. Further, the fluid is taken to be incompressible, and the radius of the pipe to vary with time. Navier–Stokes equations are used to describe this fluid flow problem. The resulting nonlinear coupled system of equations together with an appropriate boundary and initial conditions is solved using the homotopy perturbation method. The model is then applied to the human circulatory system, and the effect of the three sets of parameters on wall shear stress and volumetric flux is studied. Data for the model parameters are taken from literature on human blood, and human circulatory system and graphs have been plotted to understand their effect on the flow.

This research work is done to investigate the magnetohydrodynamic unsteady stagnation point nanofluid flow and the heat transfer influenced by the thermal radiation. The suitable transformations give rise to ordinary differential equations. A similar form of differential equations is solved numerically by successive linearization method (SLM). The influence of various active flow parameters, such as thermal radiation parameter, and stagnation parameter on the flow field, concentration field, and temperature field are plotted graphically and described in detail. Various critical outcomes are uncovered in this investigation. The outcome indicates that increment in stretching parameter increases the fluid velocity but it decreases fluid temperature and nanoparticle concentration.

New classification of fluid flow components which includes ligaments describing fine filaments or interfaces, together with waves and products of their nonlinear interactions is proposed. The classification is based on total solutions of the linearized system of the fundamental equations taking into account the compatibility condition. General analysis of periodic motion structures is illustrated by numerical calculations and schlieren visualizations of flow fields generated by uniform motion of a vertical plate in a stratified medium. Both the numerical and laboratory visualization results show that the flow patterns, which contain complex systems of internal waves, including upstream and attached waves, as well as thin interfaces, such as ligaments, formed due to the combined influence of the stratification and dissipation effects. The observation and calculation results are in good qualitative and quantitative agreement. Visualization of ligaments in a flow induced by a drop impact in targeted fluid presents to support the universality of classification.

We study the causal relation in a fluid dynamical system, for the impulse and frequency response approaches as instability theories and corresponding experiments. The zero-pressure-gradient (ZPG) boundary layer is analyzed to find complementary aspects of these approaches. The drawbacks of instability study are in formulating it as a homogeneous system. Another difficulty for the instability is in classifying it for either temporal or spatial growth. When viscous effects were included in the spatial theory, it predicted wave solution (known as Tollmien–Schlichting (TS) waves), which left many scientists unconvinced. Experimental verification remained difficult as instability does not require explicit excitation, and dependence on background noise makes experiment non-repeatable. The classic experiment of Schubauer and Skramstad for the boundary layer (J Aero Sci 14(2), 69–78, [24]) excited a monochromatic source inside to obtain spatially growing TS waves—considered as the frequency response of the boundary layer. In contrast, Gaster and Grant (Proc R Soc A 347(1649), 253–269, [13]) tried to create TS waves by a localized impulse excitation and ended up creating a wave-packet by the impulse response of the dynamical system. Here, we focus mainly on the impulse response of the ZPG boundary layer using Bromwich contour integral method (BCIM) developed by the authors for spatio-temporal growth of disturbance field in creating spatio-temporal wave-front (STWF). The main achievement of BCIM is in identifying the cause for the creation of STWF by both the approaches.

The current paper analyzes the generation of entropy in a sloped channel with a Cu–H2O nanofluid-saturated porous media for the mixed convection of nanofluids under the influence of thermal radiation. The entropy characteristics and their dependence on flow parameters are studied and analyzed thoroughly, namely Darcy numbers, Brinkman numbers, Peclet numbers, radiation parameters, channel angle inclination, mixed convection parameters and volume fractions of nanoparticles. The results achieved are compared with the existing literature for limiting values and found to be excellent.

The analysis of fluid flow and heat transfer enhancement in a lid-driven square enclosure inclined at an angle ψ and partially heated from below is developed numerically. A heater is placed at the middle of the bottom wall whereas the upper wall, moving horizontally at a constant speed, is maintained at a lessened temperature. Governing discretized equations are solved by applying the finite volume method with a pressure correction-based SIMPLE algorithm. Results are obtained for various parameters such as Richardson number (0.1 ≤ Ri ≤ 3), solid volume fraction (0 ≤ ϕ ≤ 0.1) with the inclination angle varying from −60° to 60°. The change in the rate of heat transfer due to inclusion of the nanoparticles is investigated. Flow field as well as the heat transfer has dependency on the inclination angle of the enclosure. The augmentation in heat transfer is obtained at a comparatively higher rate than that of the entropy generation in our proposed model.

This paper presents a discrete-time prey–predator model in which the prey exhibits herd behavior, and hence, the predator interacts along the outer corridor of the herd of the prey. Due to the unavailability of numerical information of the biological parameters, we consider the model with interval parameters in the parametric functional form. The existence and stability of the proposed model are analyzed. We give a flip bifurcation analysis and chaos control procedure. The bifurcation diagrams, phase portraits and time graphs are presented for different model parameters. Here, we introduce a new concept in bifurcation analysis. The codimension of a bifurcation is the number of parameters which must be varied for the bifurcation to occur. When we consider p as bifurcation parameter, ultimately, we consider here 4 bifurcation parameter in a certain range, but interesting fact is that using our technic, we convert this 4 codim bifurcation in 1 codim. Numerical simulations exhibit that the present model is a chaotic with rich dynamics.

In physics and mathematics, heat equation is a special case of diffusion equation and is a partial differential equation (PDE). Partial differential equations are useful tools for mathematical modeling. A few problems can be solved analytically, whereas difficult boundary value problem can be solved by numerical methods easily. A very popular numerical method known as finite difference methods (explicit and implicit schemes) is applied expansively for solving heat equations successfully. Explicit schemes are Forward Time and Centre Space (FTCS), Dufort and Frankel methods, whereas implicit schemes are Laasonen and Crank-Nicolson methods. In this study, explicit and implicit finite difference schemes are applied for simple one-dimensional transient heat conduction equation with Dirichlet’s initial-boundary conditions. MATLAB code is used to solve the problem for each scheme in fine mesh grids. Comparing results with analytical results, Crank-Nicolson method gives the best approximate solution. FTCS scheme is conditionally stable, whereas other schemes are unconditionally stable. Convergence, stability and truncation error analysis are investigated. Transient temperature distribution plot and surface temperature plots for different time are presented. Also, unstable plot for FTCS method is represented.

In this paper, fractional version of advection–diffusion equation (FADE) has been considered for the numerical solution. It is acquired from the classical advection–diffusion equation (ADE) by substituting the space and time derivatives with a generalized Caputo fractional derivative. Moreover, we have proposed novel discretization for space and time using radial basis functions and Chebyshev polynomials, respectively. The proposed scheme is truly meshless thereby able to manage both space and time fractional derivatives simultaneously with appropriate boundary conditions. Lastly, we have discussed numerical example to affirm this proposed scheme whilst revealing the accuracy and performance of the same.

In the present paper, computational fluid dynamics (CFD) simulation of blood flow in the human heart is performed using angiography images. The angiography was taken from CT scan images of a healthy person. The two-dimensional model is created using the Ansys Workbench software. Three inlet velocities (blood flow) of 0.15, 0.3, and 0.65 m/s corresponding to normal, moderately, and exercise (running) conditions are considered in this study. The CFD prediction of blood flow in the coronary artery is useful for diagnosis, prognosis, and prevention from coronary diseases.

Subdual of heat transfer rate across a porous medium is an important aspect of many engineering applications like thermal insulations, energy storage and contemporary building walls. One effective way is to employ diathermal partitions within the porous enclosure. Yet, the literature is scarce with the knowledge on the effect of partition orientation and configuration on free convection in porous enclosures. The objective of current paper is to suppress the rate of heat transfer across a differentially heated porous enclosure with the help of horizontally and vertically orientated partition clustering and to assess the best combination of cluster that yields the least value of the Nusselt number. The Darcy model is solved using successive accelerated replacement (SAR) scheme with second-order finite difference method. Streamlines and isotherms are observed for qualitative analysis while the Nusselt number is evaluated for quantitative analysis. The computational code is validated against the benchmark solutions available in the literature. The novelty of present work is the approach of obstructing the fluid flow, which is targeted at only those regions where temperature gradient is high.

In this era of miniaturization, micro-EDM process plays a significant role. Micro-EDM due to its characteristic non-contact nature and ability to machine any material irrespective of its mechanical properties is ideal for the high precise micro-machining operations. The model describes the transient machining process using the two-dimensional heat conduction equation in cylindrical coordinates with flux boundary conditions. It also incorporates the different process elements like Gaussian distribution of heat flux and temperature-independent specific heat and thermal conductivity. A novel numerical scheme for the simulation of the crater shape formed on the workpiece during the micro-EDM process is introduced. This numerical scheme based on the finite volume method in cylindrical coordinates is developed for the real-time simulation of the process dynamics. The existing numerical schemes describe the material removal phenomenon without taking into effect the actual material removal mechanism. The proposed scheme is designed to replicate the anode erosion mechanism, where the phase change in the material, once the temperature exceeds the threshold value, is included. Single-spark micro-EDM experiments are conducted for the same simulation process parameter. The predicted crater shapes obtained from the real-time numerical scheme agree well with the experimental results with a relative error of less than 3%.

We study positive solutions to the $$n\times n$$ system: $$\begin{aligned} \left\{ \begin{aligned} -\Delta _{p_1} u_{1}&= \lambda \left( u_{1}^{(p_1-1-\alpha _{1})}+f_{1}(u_{2})\right) ~~~~~~~~~&\mathrm {in}~~ \Omega ;\\ -\Delta _{p_2} u_{2}&= \lambda \left( u_{2}^{(p_2-1-\alpha _{2})}+f_{2}(u_{3})\right) ~~~~~~~~~&\mathrm {in}~~ \Omega ;\\ ~~~~\vdots&=~~~~~\vdots&\\ -\Delta _{p_{n-1}} u_{n-1}&= \lambda \left( u_{n-1}^{(p_{n-1}-1-\alpha _{n-1})}+f_{n-1}(u_{n})\right) ~&\mathrm {in}~~ \Omega ;\\ -\Delta _{p_n} u_{n}&= \lambda \left( u_{n}^{(p_n-1-\alpha _{n})}+f_{n}(u_{1})\right) ~~~~~~~~~&\mathrm {in}~~ \Omega ;\\ u_{1}=&u_{2}=\cdots =u_{n}=0 ~~~~~~~~~~~~~~~~~~~~~~&\mathrm {on}~~ \partial \Omega . \end{aligned} \right. \end{aligned}$$where $$\Omega $$ is a bounded domain in $$\mathbb {R}^N$$; $$N\ge 1$$ with smooth boundary $$\partial \Omega $$, $$\lambda >0$$, $$p_i>1$$, $$\alpha _i\in (0,p_i-1)$$ for $$i=1,2,\ldots ,n$$ and $$\Delta _{m}w:=\text{ div }(|\nabla w|^{m-2}\nabla w)$$; $$m>1$$ is the m-Laplacian operator of w. Here, $$f_i:[0,\infty )\rightarrow [0,\infty )$$ are non-decreasing continuous functions such that $$f_i(0)=0$$ for $$i=1,2,\ldots ,n$$ and satisfy a combined sublinear condition at infinity. We will discuss bifurcation, existence, and multiplicity results. We establish our results via the method of sub-super solutions.

In this paper, we demonstrate the uniqueness and asymptotic property of the solutions of a coagulation–fragmentation equation. We take into account coagulation kernels with singularities and fragmentation kernels of the kind which influences breaking of a particle into multiple ones. A numerical example of stability behavior of the time-dependent solution for coagulation–fragmentation equation is given.

Creation of electronic equipment, heat exchangers, and thermal insulation of buildings is related to the development of effective cooling systems or heat storage systems. One of the solutions to the considered problem is the usage of phase change materials (PCMs) that can essentially enhance the characteristics of the developed system. Phase change materials are characterized by high phase transition heat at a fixed temperature, and these materials have a thermal capacity higher than the typical heat storage media. The aim of this study is a numerical simulation of free convection melting of PCM within a chamber with a heat-generating element of time-dependent volumetric thermal production and finned radiator system. The presented new numerical results for the effective cooling system for the heat-generating unit including the copper heat sink, n-octadecane as PCM have been analyzed.

In this paper, obliquely incident surface ocean waves interaction with a horizontal submerged thin floating elastic plate is investigated in ocean water of finite depth. Firstly, a proper Green’s function associated with the physical problem is developed. Applying Green’s second identity on the upper plate and lower plate regions and using the plate conditions, the BVP is converted into a hypersingular integral equation. Most of the time, these kinds of hypersingular integral equations are solved by using some standard numerical solution techniques. But in the present case, this hypersingular integral equation is directly solved using the plate deflection in terms of summations of horizontal components of eigenfunctions related to the flexural gravity waves. In this way, a system of linear algebraic equations is obtained from the hypersingular integral equation. Further, using the plate edge conditions, some more equations involving the unknowns are obtained and solved to get the required unknowns. Variations of reflection and transmission coefficients for a wide range of physical parameters are evaluated, plotted, and analyzed.

The Bleustein–Gulyaev (BG) waves propagation in bedded composite structure is studied to calculate the dispersion relation by Liouville–Green (LG) method. The composite structure is made of functionally graded piezoelectric material (FGPM) layer over a dielectric substrate immersed in viscous liquid. The variation of material variables are taken quadratic in nature for FGPM layer. The method of separation of variables is employed in viscous liquid as well as dielectric medium. Dispersion relations are obtained for electrically open and short circuit cases. To portray the dependencies of different material variables on the phase velocity of the considered wave, numerical examples have been taken into account. The proposed work bestows a theoretical model for the purpose of designing of surface acoustic wave (SAW) devices and sensors.

The inverse sum indeg (ISI) index of a graph $$G = \left( {V,E} \right)$$ is defined as$${\text{ISI}}\left( G \right) = \sum\limits_{pq \in E} {\frac{{d_{p} d_{q} }}{{d_{p} + d_{q} }}} ,$$where $$d_{p}$$ and $$d_{q}$$ are the degrees of the vertices p and q in G, respectively. This index is found to be useful in predicting total surface area (TSA) of octane isomers. In this paper, we investigate ISI index of R-sum of graphs. We also discuss the extremal cases.

Multi-objective optimisation handles the optimisation of multiple objectives on a multi-dimensional space (Lootsma in Fuzzy Multi-Objective Optimization. Springer, Boston, 1997 [1]). There are various classical methods and a wide variety of genetic algorithms for determining the Pareto-optimal front in MOOP. Most of the MOOP algorithms dealing with fuzzy systems treat fuzzy parameters (Young-Jou and Ching-Lai in Fuzzy multiple objective decision making: Methods and applications, Springer, Berlin, 1994 [2]), fuzzy inequalities (Chuntian in Hydrological Sciences Journal 44(4): 573–582, 1999 [3]) and fuzzy objective function (Young Jou and Ching-Lai in Fuzzy Sets and Systems 54(2): 135–146, 1993 [4]). In this article, an algorithm for multi-objective optimisation using neural network is presented where the variables are fuzzy. The paper deals with the core of the issue that is the fuzzy variables in multi-objective optimisation. Here, the variables are treated as triangular fuzzy variables. The arithmetic on these fuzzy variables is defined, according to the existing available work. As a numerical illustration, the new algorithm has been tested on two fractional functions. The results obtained after implementing the new algorithm using MATLAB code is presented. The algorithm uses neural network to approximate the Pareto front. This proposed algorithm is an illustration of possible optimisation technique in the fuzzy domain using Neural Network.

Multi-choice programming (MCP) problem is a type of combinatorial optimization problem where the decision maker has to choose a value for a parameter from many alternative values. Genetic algorithm (GA) is a very popular approach used for solving combinatorial optimization problems. If some or all parameters present in the MCP problem are random, then it is known as multi-choice stochastic programming or multi-choice probabilistic programming (MCPP) problem. Chance-constrained programming (CCP) and two-stage stochastic programming (TSSP) are widely used to solve problems involving randomness. In this paper, we have considered an MCPP problem where some parameters are multi-choice types, and some are random variables. First, we apply the CCP technique to convert it to a deterministic MCP problem. While solving MCP problems, generally, some transformation techniques are used to transform the MCP problem into a mixed-integer programming (MIP) problem. After that, a standard mathematical programming approach is followed to solve the transformed MIP problem. These transformation techniques generate some extra variables and extra constraints which complicates the problem. But here we have proposed a GA to solve the MCP problem directly (without using any transformation technique). At last, a numerical example is provided to demonstrate the proposed algorithm and the solution approach.

We have many associated graphs when it comes to the domain of a connected graph. Vertex-semitotal graph $$R\left( G \right)$$, total graph $$T\left( G \right)$$, edge-semitotal graph $$Q\left( G \right)$$ and line graph $$L\left( G \right)$$ are some examples of such graphs. In this paper, we study the ISI index of $$Q\left( G \right)$$, $$T\left( G \right)$$, Q-sums and T-sums and obtain explicit expressions for the same. Also, the extremal cases of the index for these graphs have been investigated.

The intermolecular forces of a chemical compound exist not only in between the atoms but also between the atoms and the molecular bonds. The F-sums of graphs, namely subdivision graph, vertex-semi-total graph, edge-semi-total graph, and total graph of a graph which are popularly denoted by S, Q, R, and T, respectively, can capture this property of chemical compound. In this paper, we present four operations of graphs based on tensor product of graphs and establish explicit expressions of Zagreb indices of the newly defined graph operations.

This manuscript provides some oscillatory results of a dynamic equation with variable coefficients, in which a Riccati transformation technique is used. Besides, we obtain the Kamenev-type and Philos-type oscillation criteria for our dynamic equation. Finally, we present an example in the last section.

An investment is the current commitment of money or other resources with the expectation of reaping future benefits [1]. Also, investment is a long-term planning at least one year, with low or moderate risks having low or moderate of return. In case planning is short term (few days or months), risk is high with high rates of return. Investment decisions are influenced by hearsay, market psychology and resort to borrowed funds. Market psychology depends on investment analytic descriptions or abstract terms such as purpose, time risks, tools, financial data monitor and adjustment. Each financial product or investment program has rules restrictions, time commitment and cost associate with it. Establishing a time frame for each purpose or goal allows us to make better choices about the tools we use to achieve the purpose. In this paper, the introduction describes a brief literature defining investment decision support technical terms such as expected return or risks, portfolio and steps in decision process of investment analysis. In the second section, we discuss types of investment and investment calculation attributes. The third section contains the formulation of a constrained linear programming modeled investment problem and calculates the optimal decision variable values using simplex algorithm solver MATLAB [2] and TORA [3] tools. In the fourth section, we discuss the application of binary integer program to decide optimum profitable investment projects from a set of listed investment project outcome values.

Research on asymptotic model selection in the context of stochastic differential equations (SDEs) is almost nonexistent in the literature. In particular, when a collection of SDEs is considered, the problem of asymptotic model selection has not been hitherto investigated. Indeed, even though the diffusion coefficients may be considered known, questions on appropriate choice of the drift functions constitute a non-trivial model selection problem. In this article, we develop the asymptotic theory for comparisons between collections of SDEs with respect to the choice of drift functions using Bayes factors when the number of equations (individuals) in the collection of SDEs tends to infinity while the time domains remain bounded for each equation. Our asymptotic theory covers situations when the observed processes associated with the SDEs are independently and identically distributed (iid), as well as when they are independently but not identically distributed (non-iid). In particular, we allow incorporation of available time-dependent covariate information into each SDE through a multiplicative factor of the drift function; we also permit different initial values and domains of observations for the SDEs. Our model selection problem thus encompasses selection of a set of appropriate time-dependent covariates from a set of available time-dependent covariates, besides selection of the part of the drift function free of covariates. For both iid and non-iid set-ups, we establish almost sure exponential convergence of the Bayes factor. Furthermore, we demonstrate with simulation studies that even in non-asymptotic scenarios Bayes factor successfully captures the right set of covariates.

Developing an assistive system for visually impaired people using computer vision is an active area of research. The proposed assistive system is developed in an aim to be implemented in Braille e-book reader which facilitates visually impaired persons to recognize the text through tactile or speech output. Examples for such facilities include recognizing text in medicine pills, traffic sign detection, automatic mobile robot navigation, etc. This paper presents an automated system to recognize text in an image based on structural features like size, orientation, and distance between the successive region of interest (ROI). The system is based on two stages, the first performs text localization and the second performs the text detection. In the first stage, the localizing of text area is done by intelligent grouping algorithm. In the second stage, text detection is done based on text shape structural features. Our proposed system achieved an average of 76.26% precision rate, 75.8% of recall/sensitivity rate, and 76.03% of F-measure rate. The advantage of such a simple and lightweight model is that it can be deployed rapidly in any single-board microprocessors like Raspberry Pi and can be made to run effortlessly to produce quality results in real time.

Optimization nowadays is not a choice. We need a system of check and balance in any dynamic system. For this, we must have a general system of equations, some mathematical model, some much generalized yet fundamentally strong algorithm having large domain of applications. We need to understand all the visible constraints which presently cannot be ignored. Simultaneously, we must realize the demand of the situation and the limitations of the present algorithms. By algorithms, we mean those who definitely reach out to global optima in finite time. Such techniques are lagging in situations where the goal is to achieve states which are, in general, functions bounded by variable constraints (Krumke in Wireless networks 7(6):575–584, [1]). Hence, this is the time when we look for an algorithm which is multidimensional, recursive and is expected to reason fastest to the solution when several variable boundaries are on the line.

In the driven nonlinear complex dynamical earthquake system in which the event occurrences are distributed along a frequency-magnitude spectrum, “natural time” statistics can be utilized to evaluate the contemporary state of earthquake hazards in a region. The natural times, in contrary to the clock/calendar times, are nothing but the interspersed number of small magnitude counts between successive large earthquake events in a fixed area. Natural times are positive and often random in nature. In this paper, our aim is to investigate the best-fit probability distribution in order to develop natural time statistics in the seismogenic northwest Himalayan orogen including some part of north-central India, east-northeast Pakistan and its contiguous regions. We consider eight continuous probability distributions to fit the observed natural time data. We use maximum likelihood strategy for model parameter estimation and several goodness-of-fit measures for model prioritization. Results based on the natural times corresponding to $$M \ge 3$$ events between $$M \ge 6$$ events reveal that the exponential, exponentiated exponential, Weibull and exponentiated Weibull distributions provide the best fit to the observed natural times in the study area. In addition, assuming that the seismicity statistics of larger northwest Himalaya region is indifferent from the “local” regions (e.g., cities) embedded in the larger area, we calculate “nowcast” values for a number of cities, namely Jammu, Ludhiana, Chandigarh, Shimla, Dehradun and New Delhi, to assess the current state of earthquake hazards in these cities. It is found that their earthquake potential scores (%) are 99, 89, 86, 87, 83 and 58, respectively. From these results, we argue that the concept of natural times and thereby nowcasting technique provide a rapid, alternative and effective way to analyze earthquake hazards in a seismic region.

Air transportation network is one of the most important transport networks in recent time. In the air transportation network, the study of robustness of airlines network plays a key role. Robustness is the ability of a network to continue to perform properly when it is subject to failures or attacks. We adopt a complex network approach to analyze the robustness of three major airlines of India viz. Indigo, Air India, Jet Airways by simulating random attack and targeted attack on the separate airlines networks. Random attack is based on the removal of random airports from the network and targeted attack is based on the removal of important airports based on the node attributes like degree, betweenness.