Search results for: singularly perturbed problem

Authors: Y. N. Reddy

Abstract:

The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Nana Adjoah Mbroh, Suares Clovis Oukouomi Noutchie

Abstract:

Singularly perturbed problems are parameter dependent problems, and they play major roles in the modelling of real-life situational problems in applied sciences. Thus, designing efficient numerical schemes to solve these problems is of much interest since the exact solutions of such problems may not even exist. Generally, singularly perturbed problems are identified by a small parameter multiplying at least the highest derivative in the equation. The presence of this parameter causes the solution of these problems to be characterized by rapid oscillations. This unique feature renders classical numerical schemes inefficient since they are unable to capture the behaviour of the exact solution in the part of the domain where the rapid oscillations are present. In this paper, a numerical scheme is proposed to solve a singularly perturbed Volterra Integro-differential equation. The scheme is based on the midpoint rule and employs the non-standard finite difference scheme to solve the differential part whilst the composite trapezoidal rule is used for the integral part. A fully fledged error estimate is performed, and Richardson extrapolation is applied to accelerate the convergence of the scheme. Numerical simulations are conducted to confirm the theoretical findings before and after extrapolation.

Keywords: midpoint rule, non-standard finite difference schemes, Richardson extrapolation, singularly perturbed problems, trapezoidal rule, uniform convergence

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

Abstract:

In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Ophir Nave

Abstract:

In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system.

Keywords: polydisperse spray, model reduction, asymptotic analysis, multi-scale systems

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Authors: Wieslaw Marszalek, Zdzislaw Trzaska

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Interesting properties of various one-period loops of singularly perturbed memristive circuits with mixed-mode oscillations (MMOs) are analyzed in this paper. The analysis is mixed, both analytical and numerical and focused on the properties of pinched hysteresis of the memristive element and other one-period loops formed by pairs of time-series solutions for various circuits' variables. The memristive element is the only nonlinear element in the two circuits. A theorem on periods of mixed-mode oscillations of the circuits is formulated and proved. Replacements of memristors by parallel G-C or series R-L circuits for a MMO response with equivalent RMS values is also discussed.

Keywords: mixed-mode oscillations, memristive circuits, pinched hysteresis, one-period loops, singularly perturbed circuits

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Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

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In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

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Authors: H. S. Kang

Abstract:

Coupled electrical and optical model for conversion of electrical energy into coherent optical energy for transmitter-receiver link by solid state device is presented. Probability distribution for travelling laser beam switching time intervals and the number of switchings in the time interval is obtained. Selector function mapping is employed to regulate optical data transmission speed. It is established that regulated laser transmission from PhotoActive Laser transmitter follows principal of invariance. This considerably simplifies design of PhotoActive Laser Transmission networks.

Keywords: computational mathematics, finite difference Markov chain methods, sequence spaces, singularly perturbed differential equations

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Authors: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov

Abstract:

Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done.

Keywords: dynamics of polymeric liquid, heat dissipation, singularly perturbed problem, pseudospectral method, Chebyshev polynomials, stabilization technique

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Authors: Arcady Ponosov

Abstract:

Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

Abstract:

Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Sadaoui Djaouida

Abstract:

In this paper, the predictive control method is proposed to control the synchronization of two perturbed satellites attitude motion. Based on delayed feedback control of continuous-time systems combines with the prediction-based method of discrete-time systems, this approach only needs a single controller to realize synchronization, which has considerable significance in reducing the cost and complexity for controller implementation.

Keywords: predictive control, synchronization, satellite attitude, control engineering

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Authors: Y. Sefir, Z. Aziz, S. Cherid, Z. F. Meghoufel, F. Bendahama, S. Terkhi, B. Bouadjemi. A. Zitouni S. Bentata

Abstract:

This work is to study the effect of the variation of structural parameters on the band structure in the quasiperiodic Fibonacci superlattices AlxGa1-xAs/GaAs using the formalism of the transfer matrix and Airy function. Our results show that increasing the width of Fibonacci’s wells of allows to the confinement of subminibands with a widening of minigaps, this causes a consistent and coherent fragmentation. The barrier thickness of Fibonacci bf acts on the width of subminibands by controlling the interaction force between neighboring eigenstates. Its increase gives rise to singularly extended states. The barrier height Fibonacci Vf permit to control the degree of structural disorder in these structures. The variation of these parameters permits the design of laser with modulated wavelength.

Keywords: transmission coefficient – Quasiperiodic superlattices- singularly localized and extended states- structural parameters- Laser with modulated wavelength

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Authors: Zhanar Imanova

Abstract:

Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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Authors: D. Srinivasacharya, Nidhi Humnekar

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The goal of this research is to numerically investigate the convection of nanofluid flow in an inclined porous channel. Brownian motion and thermophoresis effects are accounted for by nanofluid. In addition, the flow in the porous region governs Brinkman’s equation. The perturbed state of the generalized eigenvalue problem is obtained using normal mode analysis, and Chebyshev spectral collocation was used to solve this problem. For various values of the governing parameters, the critical wavenumber and critical Rayleigh number are calculated, and preferred modes are identified.

Keywords: Brinkman model, inclined channel, nanofluid, linear stability, porous media

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Authors: J. Y. Heo, H. G. Sung

Abstract:

Numerical simulations have been performed for assessment of compressibility correction of two-equation turbulence models suitable for large scale separation flows perturbed by pintle strokes. In order to take into account pintle movement, a sliding mesh method was applied. The chamber pressure, mass flow rate, and thrust have been analyzed, and the response lag and sensitivity at the chamber and nozzle were estimated for a movable pintle. The nozzle performance for pintle reciprocating as its insertion and extraction processes, were analyzed to better understand the dynamic performance of the pintle nozzle.

Keywords: pintle, sliding mesh, turbulent model, compressibility correction

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Authors: G. Judakova, M. Bause

Abstract:

The ability to model and simulate numerically natural gas flow in pipelines has become of high importance for the design of pipeline systems. The understanding of the formation of hydrate particles and their dynamical behavior is of particular interest, since these processes govern the operation properties of the systems and are responsible for system failures by clogging of the pipelines under certain conditions. Mathematically, natural gas flow can be described by multiphase flow models. Using the two-fluid modeling approach, the gas phase is modeled by the compressible Euler equations and the particle phase is modeled by the pressureless Euler equations. The numerical simulation of compressible multiphase flows is an important research topic. It is well known that for nonlinear fluxes, even for smooth initial data, discontinuities in the solution are likely to occur in finite time. They are called shock waves or contact discontinuities. For hyperbolic and singularly perturbed parabolic equations the standard application of the Galerkin finite element method (FEM) leads to spurious oscillations (e.g. Gibb's phenomenon). In our approach, we use stabilized FEM, the streamline upwind Petrov-Galerkin (SUPG) method, where artificial diffusion acting only in the direction of the streamlines and using a special treatment of the boundary conditions in inviscid convective terms, is added. Numerical experiments show that the numerical solution obtained and stabilized by SUPG captures discontinuities or steep gradients of the exact solution in layers. However, within this layer the approximate solution may still exhibit overshoots or undershoots. To suitably reduce these artifacts we add a discontinuity capturing or shock capturing term. The performance properties of our numerical scheme are illustrated for two-phase flow problem.

Keywords: two-phase flow, gas-particle mixture, inviscid two-fluid model, euler equation, finite element method, streamline upwind petrov-galerkin, shock capturing

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Authors: Mezghiche Kamel

Abstract:

We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Djaouida Sadaoui

Abstract:

In this paper, the design procedure of the active sliding mode controller which is a combination of the active controller and the sliding mode controller is given first and then the problem of synchronization of two satellites systems is discussed for the proposed method. Finally, numerical results are presented to evaluate the robustness and effectiveness of the proposed control strategy.

Keywords: active control, sliding mode control, synchronization, satellite attitude

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Authors: A. B. Disu, M. S. Dada

Abstract:

This study was conducted to investigate two dimensional heat transfer of a free convective-radiative MHD (Magneto-hydrodynamics) flow with temperature dependent viscosity and heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls. The fluid viscosity is assumed to vary as an exponential function of temperature. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities were expressed in terms of complex exponential series of plane wave equation. The resultant differential equations were solved by Differential Transform Method (DTM). The numerical computations were presented graphically to show the salient features of the fluid flow and heat transfer characteristics. The skin friction and Nusselt number were also analyzed for various governing parameters.

Keywords: differential transform method, MHD free convection, porous medium, two dimensional radiation, two wavy walls

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Authors: Walid Moudani

Abstract:

The Crew Reserve Assignment Problem (CRAP) considers the assignment of the crew members to a set of reserve activities covering all the scheduled flights in order to ensure a continuous plan so that operations costs are minimized while its solution must meet hard constraints resulting from the safety regulations of Civil Aviation as well as from the airlines internal agreements. The problem considered in this study is of highest interest for airlines and may have important consequences on the service quality and on the economic return of the operations. In this communication, a new mathematical formulation for the CRAP is proposed which takes into account the regulations and the internal agreements. While current solutions make use of Artificial Intelligence techniques run on main frame computers, a low cost approach is proposed to provide on-line efficient solutions to face perturbed operating conditions. The proposed solution method uses a dynamic programming approach for the duties scheduling problem and when applied to the case of a medium airline while providing efficient solutions, shows good potential acceptability by the operations staff. This optimization scheme can then be considered as the core of an on-line Decision Support System for crew reserve assignment operations management.

Keywords: airlines operations management, combinatorial optimization, dynamic programming, crew scheduling

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Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

Abstract:

In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

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Authors: Mmbulaheni Ramulondi, Sandy Van Vuuren, Helene De Wet

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The use of plant combinations to treat various medical conditions is not a new concept, and it is known that traditional people do not only rely on a single plant extract for efficacy but often combine various plant species for treatment. The knowledge of plant combinations is transferred from one generation to the other in the belief that combination therapy may enhance efficacy, reduce toxicity, decreases adverse effects, increase bioavailability and result in lower dosages. However, combination therapy may also be harmful when the interaction is antagonistic, since it may result in increasing toxicity. Although a fair amount of research has been done on the toxicity of medicinal plants, there is very little done on the toxicity of medicinal plants in combination. The aim of the study was to assess the toxicity potential of 19 plant combinations which have been documented as treatments of hypertension in northern KwaZulu-Natal by lay people. The aqueous extracts were assessed using two assays; the Brine shrimp assay (Artemia franciscana) and the Ames test (Mutagenicity). Only one plant combination (Aloe marlothii with Hypoxis hemerocallidea) in the current study has been previously assessed for toxicity. With the Brine shrimp assay, the plant combinations were tested in two concentrations (2 and 4 mg/ml), while for mutagenicity tests, they were tested at 5 mg/ml. The results showed that in the Brine shrimp assay, six combinations were toxic at 4 mg/ml. The combinations were Albertisia delagoensis with Senecio serratuloides (57%), Aloe marlothii with Catharanthus roseus (98%), Catharanthus roseus with Hypoxis hemerocallidea (66%), Catharanthus roseus with Musa acuminata (89%), Catharanthus roseus with Momordica balsamina (99%) and Aloe marlothii with Trichilia emetica and Hyphaene coriacea (50%). However when the concentration was reduced to 2 mg/ml, only three combinations were toxic which were Aloe marlothii with Catharanthus roseus (76%), Catharanthus roseus with Musa acuminata (66%) and Catharanthus roseus with Momordica balsamina (73%). For the mutagenicity assay, only the combinations between Catharanthus roseus with Hypoxis hemerocallidea and Catharanthus roseus with Momordica balsamina were mutagenic towards the Salmonella typhimurium strains TA98 and TA100. Most of the combinations which were toxic involve C. roseus which was also toxic when tested singularly. It is worth noting that C. roseus was one of the most frequently used plant species both to treat hypertension singularly and in combination and some of the individuals have been using this for the last 20 years. The mortality percentage of the Brine shrimp showed a significant correlation between dosage and toxicity thus toxicity was dosage dependant. A combination which is worth noting is the combination between A. delagoensis and S. serratuloides. Singularly these plants were non-toxic towards Brine shrimp, however their combination resulted in antagonism with the mortality rate of 57% at the total concentration of 4 mg/ml. Low toxicity was mostly observed, giving some validity to combined use, however the few combinations showing increased toxicity demonstrate the importance of analysing plant combinations.

Keywords: dosage, hypertension, plant combinations, toxicity

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Authors: Makito Sakai, Takahiro Kiwata, Takumi Awa, Hiroshi Teramoto, Takaaki Kono, Kuniaki Toyoda

Abstract:

Using experimental and numerical results, this paper describes the effects of tabs on the flow characteristics of a plane jet at comparatively low Reynolds numbers while focusing on the velocity field and the vortical structure. The flow visualization and velocity measurements were respectively carried out using laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). In addition, three-dimensional (3D) plane jet numerical simulations were performed using ANSYS Fluent, a commercially available computational fluid dynamics (CFD) software application. We found that the spreads of jets perturbed by large delta tabs and round tabs were larger than those produced by the other tabs tested. Additionally, it was determined that a plane jet with square tabs had the smallest jet spread downstream, and the jet’s centerline velocity was larger than those of jets perturbed by the other tabs tested. It was also observed that the spanwise vortical structure of a plane jet with tabs disappeared completely. Good agreement was found between the experimental and numerical simulation velocity profiles in the area near the nozzle exit when the laminar flow model was used. However, we also found that large eddy simulation (LES) is better at predicting the developing flow field of a plane jet than the laminar and the standard k-ε turbulent models.

Keywords: plane jet, flow control, tab, flow measurement, numerical simulation

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

Abstract:

The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: S. Aditya, K. T. Nideesh, N. Guruprasad

Abstract:

Being a subclass of linear programing problem, the Transportation Problem is a classic Operations Research problem where the objective is to determine the schedule for transporting goods from source to destination in a way that minimizes the shipping cost while satisfying supply and demand constraints. In this paper, we are representing the transportation problem for various warehouses along with various dealers situated in Bangalore city to reduce the transportation cost incurred by them as of now. The problem is solved by obtaining the Initial Basic feasible Solution through various methods and further proceeding to obtain optimal cost.

Keywords: NW method, optimum utilization, transportation problem, Vogel’s approximation method

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

Abstract:

This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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