Abstract: In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.
Abstract: Fractional Fourier Transform is a generalization of the
classical Fourier Transform. The Fractional Fourier span in general
depends on the amplitude and phase functions of the signal and varies
with the transform order. However, with the development of the
Fractional Fourier filter banks, it is advantageous in some cases to
have different transform orders for different filter banks to achieve
better decorrelation of the windowed and overlapped time signal. We
present an expression that is useful for finding the perturbation in the
Fractional Fourier span due to the erroneous transform order and the
possible variation in the window shape and length. The expression is
based on the dependency of the time-Fractional Fourier span
Uncertainty on the amplitude and phase function of the signal. We
also show with the help of the developed expression that the
perturbation of span has a varying degree of sensitivity for varying
degree of transform order and the window coefficients.
Abstract: We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated.
Abstract: The analytical solutions for geodesic acoustic
eigenmodes in tokamak plasmas with circular concentric magnetic
surfaces are found. In the frame of ideal magnetohydrodynamics the
dispersion relation taking into account the toroidal coupling between
electrostatic perturbations and electromagnetic perturbations with
poloidal mode number |m| = 2 is derived. In the absence of such
a coupling the dispersion relation gives the standard continuous
spectrum of geodesic acoustic modes. The analysis of the existence
of global eigenmodes for plasma equilibria with both off-axis
and on-axis maximum of the local geodesic acoustic frequency is
performed.
Abstract: Nonlinear propagation of ion-acoustic waves in a selfgravitating
dusty plasma consisting of warm positive ions,
isothermal two-temperature electrons and negatively charged dust
particles having charge fluctuations is studied using the reductive
perturbation method. It is shown that the nonlinear propagation of
ion-acoustic waves in such plasma can be described by an uncoupled
third order partial differential equation which is a modified form of
the usual Korteweg-deVries (KdV) equation. From this nonlinear
equation, a new type of solution for the ion-acoustic wave is
obtained. The effects of two-temperature electrons, gravity and dust
charge fluctuations on the ion-acoustic solitary waves are discussed
with possible applications.
Abstract: Small signal stability causes small perturbations in the
generator that can cause instability in the power network. It is
generally known that small signal stability are directly related to the
generator and load properties. This paper examines the effects of
generator input variations on power system oscillations for a small
signal stability study. Eigenvaules and eigenvectors are used to
examine the stability of the power system. The dynamic power
system's mathematical model is constructed and thus calculated using
load flow and small signal stability toolbox on MATLAB. The power
system model is based on a 3-machine 9-bus system that was
modified to suit this study. In this paper, Participation Factors are a
means to gauge the effects of variation in generation with other
parameters on the network are also incorporated.
Abstract: The Institute of Product Development is dealing
with the development, design and dimensioning of micro components
and systems as a member of the Collaborative Research
Centre 499 “Design, Production and Quality Assurance of
Molded micro components made of Metallic and Ceramic Materials".
Because of technological restrictions in the miniaturization
of conventional manufacturing techniques, shape and
material deviations cannot be scaled down in the same proportion
as the micro parts, rendering components with relatively
wide tolerance fields. Systems that include such components
should be designed with this particularity in mind, often requiring
large clearance. On the end, the output of such systems
results variable and prone to dynamical instability. To save
production time and resources, every study of these effects
should happen early in the product development process and
base on computer simulation to avoid costly prototypes. A
suitable method is proposed here and exemplary applied to a
micro technology demonstrator developed by the CRC499. It
consists of a one stage planetary gear train in a sun-planet-ring
configuration, with input through the sun gear and output
through the carrier. The simulation procedure relies on ordinary
Multi Body Simulation methods and subsequently adds
other techniques to further investigate details of the system-s
behavior and to predict its response. The selection of the relevant
parameters and output functions followed the engineering
standards for regular sized gear trains. The first step is to
quantify the variability and to reveal the most critical points of
the system, performed through a whole-mechanism Sensitivity
Analysis. Due to the lack of previous knowledge about the system-s
behavior, different DOE methods involving small and
large amount of experiments were selected to perform the SA.
In this particular case the parameter space can be divided into
two well defined groups, one of them containing the gear-s profile
information and the other the components- spatial location.
This has been exploited to explore the different DOE techniques
more promptly. A reduced set of parameters is derived for
further investigation and to feed the final optimization process,
whether as optimization parameters or as external perturbation
collective. The 10 most relevant perturbation factors and 4 to 6
prospective variable parameters are considered in a new, simplified
model. All of the parameters are affected by the mentioned
production variability. The objective functions of interest
are based on scalar output-s variability measures, so the
problem becomes an optimization under robustness and reliability constrains. The study shows an initial step on the development
path of a method to design and optimize complex micro
mechanisms composed of wide tolerated elements accounting
for the robustness and reliability of the systems- output.
Abstract: In this study Homotopy Perturbation Method (HPM) is employed to investigate free vibration of an Euler beam with variable stiffness resting on an elastic foundation. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear problems. HPM produces analytical approximate expression which is continuous in the solution domain. This work shows that HPM is a promising method for free vibration analysis of nonuniform Euler beams on elastic foundation. Several case problems have been solved by using the technique and solutions have been compared with those available in the literature.
Abstract: This paper presents a numerical approach for the static
and dynamic analysis of hydrodynamic radial journal bearings. In the
first part, the effect of shaft and housing deformability on pressure
distribution within oil film is investigated. An iterative algorithm that
couples Reynolds equation with a plane finite elements (FE)
structural model is solved. Viscosity-to-pressure dependency (Vogel-
Barus equation) is also included. The deformed lubrication gap and
the overall stress state are obtained. Numerical results are presented
with reference to a typical journal bearing configuration at two
different inlet oil temperatures. Obtained results show the great
influence of bearing components structural deformation on oil
pressure distribution, compared with results for ideally rigid
components. In the second part, a numerical approach based on
perturbation method is used to compute stiffness and damping
matrices, which characterize the journal bearing dynamic behavior.
Abstract: In this paper, a frequency-variation based method has
been proposed for transistor parameter estimation in a commonemitter
transistor amplifier circuit. We design an algorithm to estimate
the transistor parameters, based on noisy measurements of the output
voltage when the input voltage is a sine wave of variable frequency
and constant amplitude. The common emitter amplifier circuit has
been modelled using the transistor Ebers-Moll equations and the
perturbation technique has been used for separating the linear and
nonlinear parts of the Ebers-Moll equations. This model of the amplifier
has been used to determine the amplitude of the output sinusoid as
a function of the frequency and the parameter vector. Then, applying
the proposed method to the frequency components, the transistor
parameters have been estimated. As compared to the conventional
time-domain least squares method, the proposed method requires
much less data storage and it results in more accurate parameter
estimation, as it exploits the information in the time and frequency
domain, simultaneously. The proposed method can be utilized for
parameter estimation of an analog device in its operating range of
frequencies, as it uses data collected from different frequencies output
signals for parameter estimation.
Abstract: A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.
Abstract: The wide increase and diffusion on telecommunication
technologies have caused a huge spread of electromagnetic sources
in most European Countries. Since the public is continuously being
exposed to electromagnetic radiation the possible health effects have
become the focus of population concerns. As a result, electromagnetic
field monitoring stations which control field strength in commercial
frequency bands are being placed on the flat roof of many buildings.
However there is no guidance on where to place them. This paper
presents an analysis of frequency, polarization and angles of incidence
of a plane wave which impinges on a flat roof security wall and its
dependence on electromagnetic field strength meters placement.
Abstract: In this paper, we apply the PQ theory with shunt active power filter in an unbalanced and distorted power system voltage to compensate the perturbations generated by non linear load. The power factor is also improved in the current source. The PLL system is used to extract the fundamental component of the even sequence under conditions mentioned of the power system voltage.
Abstract: A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.
Abstract: Experiments have been carried out at sub-critical
Reynolds number to investigate free-to-roll motions induced by
forebody and/or wings complex flow on a 30° swept back nonslender
wings-slender body-model for static and dynamic (pitch-up)
cases. For the dynamic (pitch-up) case it has been observed that roll
amplitude decreases and lag increases with increase in pitching
speed. Decrease in roll amplitude with increase in pitch rate is
attributed to low disturbing rolling moment due to weaker interaction
between forebody and wing flow components. Asymmetric forebody
vortices dominate and control the roll motion of the model in
dynamic case when non-dimensional pitch rate ≥ 1x10-2.
Effectiveness of the active control scheme utilizing rotating nose with
artificial tip perturbation is observed to be low in the angle of attack
region where the complex flow over the wings has contributions from
both forebody and wings.
Abstract: The three-time-scale plant model of a wind power
generator, including a wind turbine, a flexible vertical shaft, a Variable
Inertia Flywheel (VIF) module, an Active Magnetic Bearing (AMB)
unit and the applied wind sequence, is constructed. In order to make
the wind power generator be still able to operate as the spindle speed
exceeds its rated speed, the VIF is equipped so that the spindle speed
can be appropriately slowed down once any stronger wind field is
exerted. To prevent any potential damage due to collision by shaft
against conventional bearings, the AMB unit is proposed to regulate
the shaft position deviation. By singular perturbation order-reduction
technique, a lower-order plant model can be established for the
synthesis of feedback controller. Two major system parameter
uncertainties, an additive uncertainty and a multiplicative uncertainty,
are constituted by the wind turbine and the VIF respectively.
Frequency Shaping Sliding Mode Control (FSSMC) loop is proposed
to account for these uncertainties and suppress the unmodeled
higher-order plant dynamics. At last, the efficacy of the FSSMC is
verified by intensive computer and experimental simulations for
regulation on position deviation of the shaft and counter-balance of
unpredictable wind disturbance.
Abstract: In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).
Abstract: Identifying the nature of protein-nanoparticle
interactions and favored binding sites is an important issue in
functional characterization of biomolecules and their physiological
responses. Herein, interaction of silver nanoparticles with lysozyme
as a model protein has been monitored via fluorescence spectroscopy.
Formation of complex between the biomolecule and silver
nanoparticles (AgNPs) induced a steady state reduction in the
fluorescence intensity of protein at different concentrations of
nanoparticles. Tryptophan fluorescence quenching spectra suggested
that silver nanoparticles act as a foreign quencher, approaching the
protein via this residue. Analysis of the Stern-Volmer plot showed
quenching constant of 3.73 μM−1. Moreover, a single binding site in
lysozyme is suggested to play role during interaction with AgNPs,
having low affinity of binding compared to gold nanoparticles.
Unfolding studies of lysozyme showed that complex of lysozyme-
AgNPs has not undergone structural perturbations compared to the
bare protein. Results of this effort will pave the way for utilization of
sensitive spectroscopic techniques for rational design of
nanobiomaterials in biomedical applications.
Abstract: In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.
Abstract: Iterative learning control aims to achieve zero tracking
error of a specific command. This is accomplished by iteratively
adjusting the command given to a feedback control system, based on
the tracking error observed in the previous iteration. One would like
the iterations to converge to zero tracking error in spite of any error
present in the model used to design the learning law. First, this need
for stability robustness is discussed, and then the need for robustness
of the property that the transients are well behaved. Methods of
producing the needed robustness to parameter variations and to
singular perturbations are presented. Then a method involving
reverse time runs is given that lets the world behavior produce the
ILC gains in such a way as to eliminate the need for a mathematical
model. Since the real world is producing the gains, there is no issue
of model error. Provided the world behaves linearly, the approach
gives an ILC law with both stability robustness and good transient
robustness, without the need to generate a model.