Abstract: Direct numerical simulation (DNS) is used to study the evolution of a boundary layer that was laminar initially followed by separation and then reattachment owing to generation of turbulence. This creates a closed region of recirculation, known as the laminar-separation bubble. The present simulation emulates the flow environment encountered in a modern LP turbine blade, where a laminar separation bubble may occur on the suction surface. The unsteady, incompressible three-dimensional (3-D) Navier-Stokes (NS) equations have been solved over a flat plate in the Cartesian coordinates. The adverse pressure gradient, which causes the flow to separate, is created by a boundary condition. The separated shear layer undergoes transition through appearance of ╬ø vortices, stretching of these create longitudinal streaks. Breakdown of the streaks into small and irregular structures makes the flow turbulent downstream.
Abstract: Economic Load Dispatch (ELD) is a method of determining
the most efficient, low-cost and reliable operation of a power
system by dispatching available electricity generation resources to
supply load on the system. The primary objective of economic
dispatch is to minimize total cost of generation while honoring
operational constraints of available generation resources. In this paper
an intelligent water drop (IWD) algorithm has been proposed to
solve ELD problem with an objective of minimizing the total cost of
generation. Intelligent water drop algorithm is a swarm-based natureinspired
optimization algorithm, which has been inspired from natural
rivers. A natural river often finds good paths among lots of possible
paths in its ways from source to destination and finally find almost
optimal path to their destination. These ideas are embedded into
the proposed algorithm for solving economic load dispatch problem.
The main advantage of the proposed technique is easy is implement
and capable of finding feasible near global optimal solution with
less computational effort. In order to illustrate the effectiveness of
the proposed method, it has been tested on 6-unit and 20-unit test
systems with incremental fuel cost functions taking into account the
valve point-point loading effects. Numerical results shows that the
proposed method has good convergence property and better in quality
of solution than other algorithms reported in recent literature.
Abstract: Unsteady boundary layer flow of an incompressible
micropolar fluid over a stretching sheet when the sheet is stretched in
its own plane is studied in this paper. The stretching velocity is
assumed to vary linearly with the distance along the sheet. Two equal
and opposite forces are impulsively applied along the x-axis so that the
sheet is stretched, keeping the origin fixed in a micropolar fluid. The
transformed unsteady boundary layer equations are solved
numerically using the Keller-box method for the whole transient from
the initial state to final steady-state flow. Numerical results are
obtained for the velocity and microrotation distributions as well as the
skin friction coefficient for various values of the material parameter K.
It is found that there is a smooth transition from the small-time
solution to the large-time solution.
Abstract: This paper deals with the problem of non-uniform
torsion in thin-walled elastic beams with asymmetric cross-section,
removing the basic concept of a fixed center of twist, necessary in the
Vlasov-s and Benscoter-s theories to obtain a warping stress field
equivalent to zero. In this new torsion/flexure theory, despite of the
classical ones, the warping function will punctually satisfy the first
indefinite equilibrium equation along the beam axis and it wont- be
necessary to introduce the classical congruence condition, to take into
account the effect of the beam restraints. The solution, based on the
Fourier development of the displacement field, is obtained assuming
that the applied external torque is constant along the beam axis and
on both beam ends the unit twist angle and the warping axial
displacement functions are totally restrained.
Finally, in order to verify the feasibility of the proposed method
and to compare it with the classical theories, two applications are
carried out. The first one, relative to an open profile, is necessary to
test the numerical method adopted to find the solution; the second
one, instead, is relative to a simplified containership section,
considered as full restrained in correspondence of two adjacent
transverse bulkheads.
Abstract: In wavelet regression, choosing threshold value is a crucial issue. A too large value cuts too many coefficients resulting in over smoothing. Conversely, a too small threshold value allows many coefficients to be included in reconstruction, giving a wiggly estimate which result in under smoothing. However, the proper choice of threshold can be considered as a careful balance of these principles. This paper gives a very brief introduction to some thresholding selection methods. These methods include: Universal, Sure, Ebays, Two fold cross validation and level dependent cross validation. A simulation study on a variety of sample sizes, test functions, signal-to-noise ratios is conducted to compare their numerical performances using three different noise structures. For Gaussian noise, EBayes outperforms in all cases for all used functions while Two fold cross validation provides the best results in the case of long tail noise. For large values of signal-to-noise ratios, level dependent cross validation works well under correlated noises case. As expected, increasing both sample size and level of signal to noise ratio, increases estimation efficiency.
Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper considers the indirect minimum Jerk
method for higher order differential equation in dynamics
optimization proposes a simple yet very interesting indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of indirect jerks are found using the dynamic optimization methods
together with the numerical approximation. This case considers the
linear equation of a simple system, for instance, mass, spring and
damping. The simple system uses two mass connected together by
springs. The boundary initial is defined the fix end time and end
point. The higher differential order is solved by Galerkin-s methods
weight residual. As the result, the 6th higher differential order shows
the faster solving time.
Abstract: The RK5GL3 method is a numerical method for solving
initial value problems in ordinary differential equations, and is based
on a combination of a fifth-order Runge-Kutta method and 3-point
Gauss-Legendre quadrature. In this paper we describe the propagation
of local errors in this method, and show that the global order of
RK5GL3 is expected to be six, one better than the underlying Runge-
Kutta method.
Abstract: The dynamics of a predator-prey model with continuous
threshold policy harvesting functions on the prey is studied. Theoretical
and numerical methods are used to investigate boundedness
of solutions, existence of bionomic equilibria, and the stability properties
of coexistence equilibrium points and periodic orbits. Several
bifurcations as well as some heteroclinic orbits are computed.
Abstract: An inverse geometry problem is solved to predict an
unknown irregular boundary profile. The aim is to minimize the
objective function, which is the difference between real and
computed temperatures, using three different versions of Conjugate
Gradient Method. The gradient of the objective function, considered
necessary in this method, obtained as a result of solving the adjoint
equation. The abilities of three versions of Conjugate Gradient
Method in predicting the boundary profile are compared using a
numerical algorithm based on the method. The predicted shapes show
that due to its convergence rate and accuracy of predicted values, the
Powell-Beale version of the method is more effective than the
Fletcher-Reeves and Polak –Ribiere versions.
Abstract: The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease.
Abstract: This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.
Abstract: The most influential programming paradigm today
is object oriented (OO) programming and it is widely used in
education and industry. Recognizing the importance of equipping
students with OO knowledge and skills, it is not surprising that most
Computer Science degree programs offer OO-related courses. How
do we assess whether the students have acquired the right objectoriented
skills after they have completed their OO courses? What are
object oriented skills? Currently none of the current assessment
techniques would be able to provide this answer. Traditional forms of
OO programming assessment provide a ways for assigning numerical
scores to determine letter grades. But this rarely reveals information
about how students actually understand OO concept. It appears
reasonable that a better understanding of how to define and assess
OO skills is needed by developing a criterion referenced model. It is
even critical in the context of Malaysia where there is currently a
growing concern over the level of competency of Malaysian IT
graduates in object oriented programming. This paper discussed the
approach used to develop the criterion-referenced assessment model.
The model can serve as a guideline when conducting OO
programming assessment as mentioned. The proposed model is
derived by using Goal Questions Metrics methodology, which helps
formulate the metrics of interest. It concluded with a few suggestions
for further study.
Abstract: Beginning from the creator of integro-differential
equations Volterra, many scientists have investigated these
equations. Classic method for solving integro-differential
equations is the quadratures method that is successfully applied up
today. Unlike these methods, Makroglou applied hybrid methods
that are modified and generalized in this paper and applied to the
numerical solution of Volterra integro-differential equations. The
way for defining the coefficients of the suggested method is also
given.
Abstract: In the present work, we propose a new method for
solving the matrix equation AXB=F . The new method can
be considered as a generalized form of the well-known global full
orthogonalization method (Gl-FOM) for solving multiple linear
systems. Hence, the method will be called extended Gl-FOM (EGl-
FOM). For implementing EGl-FOM, generalized forms of block
Krylov subspace and global Arnoldi process are presented. Finally,
some numerical experiments are given to illustrate the efficiency of
our new method.
Abstract: This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5·106 and 5·107) and six different Prandtl numbers (3 · 105 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (N u) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.
Abstract: In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.
Abstract: We present a theory for optimal filtering of infinite sets of random signals. There are several new distinctive features of the proposed approach. First, we provide a single optimal filter for processing any signal from a given infinite signal set. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.
Abstract: We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.
Abstract: Different techniques for estimating seasonal water
use from soil profile water depletion frequently do not account for
flux below the root zone. Shallow water table contribution to supply
crop water use may be important in arid and semi-arid regions.
Development of predictive root uptake models, under influence of
shallow water table makes it possible for planners to incorporate
interaction between water table and root zone into design of irrigation
projects. A model for obtaining soil moisture depletion from root
zone and water movement below it is discussed with the objective to
determine impact of shallow water table on seasonal moisture
depletion patterns under water table depth variation, up to the bottom
of root zone. The role of different boundary conditions has also been
considered. Three crops: Wheat (Triticum aestivum), Corn (Zea
mays) and Potato (Solanum tuberosum), common in arid & semi-arid
regions, are chosen for the study. Using experimentally obtained soil
moisture depletion values for potential soil moisture conditions,
moisture depletion patterns using a non linear root uptake model have
been obtained for different water table depths. Comparative analysis
of the moisture depletion patterns under these conditions show a wide
difference in percent depletion from different layers of root zone
particularly top and bottom layers with middle layers showing
insignificant variation in moisture depletion values. Moisture
depletion in top layer, when the water table rises to root zone
increases by 19.7%, 22.9% & 28.2%, whereas decrease in bottom
layer is 68.8%, 61.6% & 64.9% in case of wheat, corn & potato
respectively. The paper also discusses the causes and consequences
of increase in moisture depletion from top layers and exceptionally
high reduction in bottom layer, and the possible remedies for the
same. The numerical model developed for the study can be used to
help formulating irrigation strategies for areas where shallow
groundwater of questionable quality is an option for crop production.
Abstract: Solution of some practical problems is reduced to the
solution of the integro-differential equations. But for the numerical
solution of such equations basically quadrature methods or its
combination with multistep or one-step methods are used. The
quadrature methods basically is applied to calculation of the integral
participating in right hand side of integro-differential equations. As
this integral is of Volterra type, it is obvious that at replacement with
its integrated sum the upper limit of the sum depends on a current
point in which values of the integral are defined. Thus we receive the
integrated sum with variable boundary, to work with is hardly.
Therefore multistep method with the constant coefficients, which is
free from noted lack and gives the way for finding it-s coefficients is
present.