Scholarly

A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation

Year: 2015 Volume: 9 Issue: 8 498 - 501 Pages

Abstract: By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.

Two-Photon Ionization of Silver Clusters

Year: 2015 Volume: 9 Issue: 8 494 - 497 Pages

Abstract: In this paper, we calculate the two-photon ionization (TPI) cross-section for pump-probe scheme in Ag neutral cluster. The pump photon energy is assumed to be close to the surface plasmon (SP) energy of cluster in dielectric media. Due to this choice, the pump wave excites collective oscillations of electrons-SP and the probe wave causes ionization of the cluster. Since the interband transition energy in Ag exceeds the SP resonance energy, the main contribution into the TPI comes from the latter. The advantage of Ag clusters as compared to the other noble metals is that the SP resonance in silver cluster is much sharper because of peculiarities of its dielectric function. The calculations are performed by separating the coordinates of electrons corresponding to the collective oscillations and the individual motion that allows taking into account the resonance contribution of excited SP oscillations. It is shown that the ionization cross section increases by two orders of magnitude if the energy of the pump photon matches the surface plasmon energy in the cluster.

A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation

Year: 2015 Volume: 9 Issue: 8 488 - 493 Pages

Authors:
Aziz Sezgin

Abstract: We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Uncontrollable Inaccuracy in Inverse Problems

Year: 2015 Volume: 9 Issue: 8 483 - 487 Pages

Authors:
Yu. Menshikov

Abstract: In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influence of uncontrollable inaccuracy have been suggested.

Some Results on the Generalized Higher Rank Numerical Ranges

Year: 2015 Volume: 9 Issue: 8 478 - 482 Pages

Authors:
Mohsen Zahraei

Abstract: In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for Є > 0, the notion of Birkhoff-James approximate orthogonality sets for Є−higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Studies on Pre-Ignition Chamber Dynamics of Solid Rockets with Different Port Geometries

Year: 2015 Volume: 9 Issue: 8 471 - 477 Pages

Abstract: In this paper numerical studies have been carried out to examine the pre-ignition flow features of high-performance solid propellant rocket motors with two different port geometries but with same propellant loading density. Numerical computations have been carried out using a validated 3D, unsteady, 2nd-order implicit, SST k- ω turbulence model. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-Averaged, Navier- Stokes equations is employed. We have observed from the numerical results that in solid rocket motors with highly loaded propellants having divergent port geometry the hot igniter gases can create preignition pressure oscillations leading to thrust oscillations due to the flow unsteadiness and recirculation. We have also observed that the igniter temperature fluctuations are diminished rapidly thereby reaching the steady state value faster in the case of solid propellant rocket motors with convergent port than the divergent port irrespective of the igniter total pressure. We have concluded that the prudent selection of the port geometry, without altering the propellant loading density, for damping the total temperature fluctuations within the motor is a meaningful objective for the suppression and control of instability and/or thrust oscillations often observed in solid propellant rocket motors with non-uniform port geometry.

Starting Torque Study of Darrieus Wind Turbine

Year: 2015 Volume: 9 Issue: 8 465 - 470 Pages

Abstract: The aim of our study is to project an optimized wind turbine of Darrieus type. This type of wind turbine is characterized by a low starting torque in comparison with the Savonius rotor allowing them to operate for a period greater than wind speed. This led us to reconsider the Darrieus rotor to optimize a design which will increase its starting torque. The study of a system of monitoring and control of the angle of attack of blade profile, which allows an auto start to wind speeds as low as possible is presented for the straight blade of Darrieus turbine. The study continues to extend to other configurations namely those of parabolic type.

Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials

Year: 2015 Volume: 9 Issue: 8 461 - 464 Pages

Abstract: In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr¨odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Luminescent Si Nanocrystals Synthesized by Si Ion Implantation and Reactive Pulsed Laser Deposition: The Effects of RTA, Excimer-UV and E-Beam Irradiation

Year: 2015 Volume: 9 Issue: 8 457 - 460 Pages

Abstract: Si ion implantation was widely used to synthesize specimens of SiO2 containing supersaturated Si and subsequent high temperature annealing induces the formation of embedded luminescent Si nanocrystals. In this work, the potentialities of excimer UV-light (172 nm, 7.2 eV) irradiation and rapid thermal annealing (RTA) to enhance the photoluminescence and to achieve low temperature formation of Si nanocrystals have been investigated. The Si ions were introduced at acceleration energy of 180 keV to fluence of 7.5 x 1016 ions/cm2. The implanted samples were subsequently irradiated with an excimer-UV lamp. After the process, the samples were rapidly thermal annealed before furnace annealing (FA). Photoluminescence spectra were measured at various stages at the process. We found that the luminescence intensity is strongly enhanced with excimer-UV irradiation and RTA. Moreover, effective visible photoluminescence is found to be observed even after FA at 900 oC, only for specimens treated with excimer-UV lamp and RTA. We also prepared specimens of Si nanocrystals embedded in a SiO2 by reactive pulsed laser deposition (PLD) in an oxygen atmosphere. We will make clear the similarities and differences with the way of preparation.

Coexistence of Two Different Types of Intermittency near the Boundary of Phase Synchronization in the Presence of Noise

Year: 2015 Volume: 9 Issue: 8 453 - 456 Pages

Abstract: Intermittent behavior near the boundary of phase synchronization in the presence of noise is studied. In certain range of the coupling parameter and noise intensity the intermittency of eyelet and ring intermittencies is shown to take place. Main results are illustrated using the example of two unidirectional coupled Rössler systems. Similar behavior is shown to take place in two hydrodynamical models of Pierce diode coupled unidirectional.

Nonlinear Model Predictive Control of Water Quality in Drinking Water Distribution Systems with DBPs Objectives

Year: 2015 Volume: 9 Issue: 8 446 - 452 Pages

Abstract: The paper develops a Non-Linear Model Predictive Control (NMPC) of water quality in Drinking Water Distribution Systems (DWDS) based on the advanced non-linear quality dynamics model including disinfections by-products (DBPs). A special attention is paid to the analysis of an impact of the flow trajectories prescribed by an upper control level of the recently developed two-time scale architecture of an integrated quality and quantity control in DWDS. The new quality controller is to operate within this architecture in the fast time scale as the lower level quality controller. The controller performance is validated by a comprehensive simulation study based on an example case study DWDS.

International Journal of Engineering, Mathematical and Physical Sciences

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