Band 23, Heft 7-8

This paper addresses the problem of coordinated target tracking in sensor networks. For a typical target tracking scene with nonlinear bearing-only measurements, we first investigate the mutual information between multiple sensors and the target state. To improve the performance of target tracking, we analyzed the relative positions between sensor agents and the target to be tracked and derived the optimal positions for sensors in the network by mutual information maximization. Simulation results are presented and discussed to demonstrate that the performance of estimated target states could be improved by the proposed method.

The main aim of the current article is to describe an uni-dimensional moving boundary problem with conduction and convection effect when thermal conductivity and specific heat varying linearly with temperature and time. The Mathematical model has nonlinearity due to presence of variable thermal conductivity and specific heat. A Legendre wavelet residual approach is introduced to get the solution of the problem with high accuracy. The surface heat flux is taken as an exponent function of time while latent heat is presented as an exponent function of position. Galerkin technique is used to obtain the numerical solution in case of constant physical properties while collocation technique is used for variable thermal physical properties. When it is considered that thermal physical properties are constant then obtained numerical solution was compared with exact solution and found in good acceptance. The effect of convection and variable thermal conductivity with time and temperature on the location of the moving layer thickness is analyzed. Further the effect of Peclet number and other physical parameters on the location of moving layer thickness are discussed in detail.

Magnetic carriers for guiding, delivery, and capturing of drugs to desired place attract interest in the field of smart treatment of various pathological conditions. Presented paper, therefore, deals with one such application with the theoretical model of magnetic fluid flow through vessel bifurcation with one arm treated with ferromagnetic vascular stent placed in an external originally homogeneous magnetic field. This flow was described as laminar Newtonian incompressible continuum of the magnetic many-bead system, with Reynolds number ≈ 1 $\approx 1$ , using magnetic force variant of the Nernst–Planck equation coupled with the Navier–Stokes equations, solved numerically by the finite element method (FEM). This approach allowed us to quantify capturing efficiency of magnetic beads in each arm of bifurcation vessels. Results show reduction of the number of magnetic beads entering as well as leaving the arm treated with stent in comparison with the untreated one. For stented bifurcation arm, the significant amount of beads are captured to its luminal surface, which may be used for drug delivery using magnetic carriers.

A novel extended logistic map has been proposed and tested mathematically for security-based applications. Because the designed extended logistic map behaves chaotically across a wide range of logistic control parameters, it is extremely difficult to predict using even the most exhaustive search methods. The map overcomes a significant drawback of simple logistic mapping, which is commonly used in encryption algorithms. The chaotic map designed was also used as a key to shuffle the pixel position of the image for the image shuffling algorithm developed. The algorithm developed produced excellent results and is adequate for providing an encrypted image in resource-constrained systems. Performance results show that this map is highly chaotic and provides high security when applied in image encryption systems.

Valuation of the American options encountered commonly in finance is quite difficult due to the possibility of early exercise alternatives. Since an exact solution for the American options does not exist, effective numerical methods are needed to understand the behavior of option pricing models. Therefore, in this paper, a new approach based on a high-order difference scheme is proposed to discuss the valuation of an American put option as a free boundary problem. Using a front-fixing approach that transforms the unknown free boundary (optimal stopping) into a fixed one, a sixth-order finite difference scheme (FD6) in space and a third-order strong-stability preserving Runge–Kutta (SSPRK3) in time are applied to the model converted to a nonlinear partial differential equation. The computed results revealed that the combined method is seen to attempt to pull up the capacity of the algorithm to achieve higher accuracy. It is seen that the quantitative and qualitative results produced by the method proposed with minimal computational effort are sufficiently accurate and meaningful. Therefore, this article provides some new insights about the physical characteristics of financial problems and such realistic phenomena.

In gas transmission networks, the pressure drop caused by friction is one of the main operation costs that is compensated through consuming energy in the compressors. In the competitive market of energy, considering the demand variation is inevitable. Hence, the power minimization should be carried out in transient state. Since the minimization problem is severely nonlinear and nonconvex subjected to nonlinear constraints, utilizing a powerful minimization tool with a straightforward procedure is very helpful. In this paper, a novel approach is proposed based on metaheuristic algorithms for power minimization of a gas transmission network in fully transient conditions. The metaheuristic algorithms, unlike the gradient dependent method, can solve the complicated minimization problem without simplification. In the proposed strategy, the cost function is not expressed explicitly as a function of minimization variables; therefore, the transient minimization can be as precise as possible. The minimization is carried out by a straightforward methodology in each time sample, which leads to more precise solutions as compared to the quasi transient minimization. The metaheuristic minimizer, called the particle swarm optimization gravitational search algorithm (PSOGSA), is utilized to find the optimum operating set points. The numerical results also confirm the accuracy and well efficiency of the proposed method.

In this work, a priori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived. These equations are time dependent strongly coupled system of five semilinear convection-diffusion-reaction equations. The a priori error estimates for all the five variables are obtained for the error measured in L ∞ ( L 2 ) and L 2 ( E ) ${L}^{2}\left(\mathcal{E}\right)$ , E $\mathcal{E}$ is the energy norm.

Based on the Hirota bilinear form for the (3 + 1)-dimensional Jimbo–Miwa equation, we constructed the first-order, second-order, third-order and fourth-order rogue waves for this equation using the symbolic computation approach. Also some properties of the higher-order rogue waves and their interaction are explained by some figures via some special choices of the parameters.

The effects of nozzle structures and working pressure on the dynamic characteristics of supersonic turbulent free jets have been investigated numerically. Four types of nozzles (namely Laval, pipe, contraction I, and contraction II, respectively) and four pressure conditions (namely K = 0.8, 1, 1.5, and 2, respectively) were considered. A Standard k - ε model was utilized for the calculation of the supersonic turbulent free jets. Validation of the model was performed on the Laval jet by comparing it with the experiment and large-eddy simulation (LES). A perfect agreement was achieved in terms of the centerline and radial axial velocity profiles. The jets issuing from the Laval and the pipe had a longer potential core and a larger centerline axial velocity with the same outlet momentum. The length of the potential core was proportional to the working pressure, but variations of the centerline axial velocity decay rate were inverse for all nozzles. The effects of nozzle structures and work pressure on the spreading rates of the jets were insignificant. No obvious change trend could be observed on the kinematic and geometric virtual origins. The study can provide references for the nozzle and working pressure selection in practical application.

In this work, we emphasize the use of singularity analysis in obtaining analytic solutions for equations for which standard Lie point symmetry analysis fails to make any lucid decision. We study the higher-dimensional Kadomtsev–Petviashvili, Boussinesq, and Kaup–Kupershmidt equations in a more general sense. With higher-order equations, there can be a commensurate number of resonances and when consistency for the full equation is examined at each resonance the constant of integration is supposed to vanish from the expression so that it remains arbitrary, but if there is an instance of this not happening, the consistency can be partially established by giving the offending constant the value from the defining equation. If consistency is otherwise not compromised, the equation can be said to be partially integrable, i.e., integrable on a surface of the complex space. Furthermore, we propose an approach that is meant to magnify the scope of singularity analysis for equations admitting higher values for resonances or positive leading-order exponent.

The nonlinear dynamics of a discretized form of quasi-periodic plasma perturbations model (Q-PPP) with nonlocal fractional differential operator possessing singular kernel are investigated. For example, the conditions for the stability and occurrence of Neimark–Sacker (NS) and flip bifurcations in the proposed discretized equations are provided. Moreover, analysis of nonlinearities such as the existence of chaos in this map is proved numerically via bifurcation diagrams, Lyapunov exponents and analytically via Marotto’s Theorem. Also, some simulation results are utilized to confirm the theoretical results and to show that the obtained map exhibits double routes to chaos: one is via flip bifurcation and the other is via NS bifurcation. Furthermore, more complex dynamical phenomena such as existence of closed invariant curves, homoclinic orbits, homoclinic connections, period 3 and period 4 attractors are shown. This kind of research is useful for physicists who work with tokamak models.

In this paper, we proposed wavelet based collocation methods for solving neutral delay differential equations. We use Legendre wavelet, Hermite wavelet, Chebyshev wavelet and Laguerre wavelet to solve the neutral delay differential equations numerically. We solved five linear and one nonlinear problem to demonstrate the accuracy of wavelet series solution. Wavelet series solution converges fast and gives more accurate results in comparison to other methods present in literature. We compare our results with Runge–Kutta-type methods by Wang et al. (Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equations,” Appl . Math . Model , vol. 33, no. 8, pp. 3319–3329, 2009) and one-leg θ methods by Wang et al. (Stability of one-leg θ method for nonlinear neutral differential equations with proportional delay,” Appl . Math . Comput ., vol. 213, no. 1, pp. 177–183, 2009) and observe that our results are more accurate.

In this article, the approximate solution of the fractional-order reaction advection-diffusion equation with the prescribed initial and boundary conditions is found with the help of a cubic B-spline collocation method, which is unconditionally stable and convergent. The accuracy of the scheme is validated by applying the method on four existing problems having analytical solutions and through the evaluation of the absolute errors between numerical results and the exact solutions for different particular cases. Applying the proposed method on the last two numerical problems, it is shown that the method performs better than the existing methods even for very less number of spatial and temporal discretizations. The main contribution of the article is to develop an efficient method to solve the proposed fractional order nonlinear problem and to find the effect on solute concentration graphically due to increase in the non-linearity in the diffusion term for different particular values of parameters.

For a third-order nonlinear boundary value problem (BVP), we develop two novel methods to find the solutions, satisfying boundary conditions automatically. A boundary shape function (BSF) is created to automatically satisfy the boundary conditions, which is then employed to develop new numerical algorithms by adopting two different roles of the free function in the BSF. In the first type algorithm, we let the BSF be the solution of the BVP and the free function be a new variable. In doing so, the nonlinear BVP is certainly and exactly transformed to an initial value problem for the new variable with its terminal values as unknown parameters, whereas the initial conditions are given. In the second type algorithm, let the free functions be a set of complete basis functions and the corresponding boundary shape functions be the new bases. Since the solution already satisfies the boundary conditions automatically, we can apply a simple collocation technique inside the domain to determine the expansion coefficients and then the solution is obtained. For the general higher-order boundary conditions, the BSF method (BSFM) can easily and quickly find a very accurate solution. Resorting on the BSFM, the existence of solution is proved, under the Lipschitz condition for the ordinary differential equation system of the new variable. Numerical examples, including the singularly perturbed ones, confirm the high performance of the BSF-based numerical algorithms.

In this paper, we study the number of classical positive radial solutions for Dirichlet problems of type ( P ) − d i v ∇ u 1 − | ∇ u | 2 = λ f ( u )   in B 1 , u = 0                     on ∂ B 1 , $$\left\{\begin{aligned}\hfill & -\mathrm{d}\mathrm{i}\mathrm{v}\left(\frac{\nabla u}{\sqrt{1-\vert \nabla u{\vert }^{2}}}\right)=\lambda f\left(u\right)\quad \text{in} {B}_{1},\hfill \\ \hfill & u=0\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text{on} \partial {B}_{1}, \hfill \end{aligned}\right.$$ where λ is a positive parameter, B 1 = { x ∈ R N : | x | < 1 } ${B}_{1}=\left\{x\in {\mathbb{R}}^{N}:\vert x\vert {< }1\right\}$ , f : [0, ∞) → [0, ∞) is a continuous function. Using the fixed point index in a cone, we prove the results on both uniqueness and multiplicity of positive radial solutions of ( P ).

In this current study, the transient numerical calculations using CFD code are carried out under different outlet impeller diameters for the flow field within a centrifugal pump under single-phase and cavitation conditions. Both qualitative and quantitative analyses are carried out on all of these results in order to better understand the flow structure within a centrifugal pump. Also, the investigations using different outlet impeller diameters configurations relating to the static pressure, velocity magnitude, vapour volume fraction variations, as well as pressure fluctuations in both time and frequency domain at the impeller and volute of the pump are analysed. Velocity and static pressure variations of the pump under different outlet impeller diameters range (200, 210 and 220 mm) are investigated. Reliable model is developed and validated, at various pump operating conditions, to analyse the characteristics of pressure fluctuations in both time and frequency domain. Cavitation occurrence, under different outlet impeller diameters and flow rates, are detected and correlated, using a CFD model (volume fraction distributions). Based on the developed model’s findings, at the set operating conditions ranges, the distribution and impact (cavitation and head-wises) of both the pressure and velocity are analysed. The average pressure fluctuation in the volute for do = 210 mm is higher than for do = 200 mm by about 6.74%, also the maximum pressure fluctuation for do = 220 mm is higher than for do = 210 mm by around 7.4%. Furthermore, the maximum pressure fluctuation in the impeller for do = 210 mm is higher than for do = 200 mm by 12.48%, also for do = 220 mm is higher than for do = 210 mm by 10.8%. The developed CFD models are proved valuable tools in identifying and optimizing the pump performance and characterization. The head for when do = 220 mm is higher than for when do = 200 mm under both single-phase and cavitation conditions by around 14.13% and 14.69%. The maximum pressure fluctuation for do = 200 mm is lower than for do = 210 mm by 41.58%. Furthermore, the maximum pressure fluctuation at the impeller for do = 220 mm is higher than the two models. There is a small clearance between the impeller and the volute for this model, leading to the pressure fluctuation amplitudes being higher than the other above models.

In this research, the ship power system is studied with a fractional-order approach. A 2-D model of a two-generator parallel-connected is considered. A chaotic attractor is observed for particular parameter values. The fractional-order form is calculated with the Adam–Bashforth–Moulton method. The chaotic response is identified even for the order 0.99. Phase portrait is generated using the Caputo derivative approach. Wolf’s algorithm is used to calculate Lyapunov exponents. For the considered values of parameters, one positive Lyapunov exponent confirms the existence of chaos. Bifurcation diagrams are presented to analyze the various dynamical behaviors and bifurcation points. Interestingly, the considered system is multistable. Also, antimonotonicity, period-doubling, and period halving are observed in the bifurcation diagram. As the last step, a fractional-order controller is designed to remove chaotic dynamics. Time plots are simulated to show the effectiveness of the controller.

The purpose of this article is to present the notion of graphical extended b -metric spaces, blending the concepts of graph theory and metric fixed point theory. We discuss the structure of an open ball of the new proposed space and elaborate on the newly introduced ideas in a novel way by portraying suitably directed graphs. We also provide some examples in graph structure to show that our results are sharp as compared to the results in the existing state-of-art. Furthermore, an application to the transverse oscillations of a homogeneous bar is entrusted to affirm the applicability of the established results. Additionally, we evoke some open problems for enthusiastic readers for the future aspects of the study.

This paper presents an explicit formula that approximates the fractional derivatives of Chebyshev polynomials of the first-kind in the Caputo sense. The new expression is given in terms of a terminating hypergeometric function of the type 4 F 3 (1). The integer derivatives of Chebyshev polynomials of the first-kind are deduced as a special case of the fractional ones. The formula will be applied for obtaining a spectral solution of a certain type of fractional delay differential equations with the aid of an explicit Chebyshev tau method. The shifted Chebyshev polynomials of the first-kind are selected as basis functions and the spectral tau method is employed for obtaining the desired approximate solutions. The convergence and error analysis are discussed. Numerical results are presented illustrating the efficiency and accuracy of the proposed algorithm.

Numerical solution of nonlinear chaotic fractional in space reaction–diffusion system is considered in this paper on a large but finite spatial domain size x ∈ [0, L ] for L ≫ 0, x = x ( x , y ) and t ∈ [0, T ]. The classical order chaotic ordinary differential equation is formulated by introducing the second-order spatial fractional derivative with order β ∈ (1, 2]. This second order spatial derivative is modelled by using the definition of the Riesz fractional derivative. The method of approximation combines the Fourier spectral method with the novel exponential time difference schemes. The proposed technique is known to have gained spectral accuracy over finite difference schemes. Applicability and suitability of the suggested methods are tested on Rössler chaotic system of recurring interests in one and two dimensions.