Abstract: The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.
Abstract: In this work, we solve multipoint boundary value
problems where the boundary value conditions are equations using
the Newton-Broyden Shooting method (NBSM).The proposed
method is tested upon several problems from the literature and the
results are compared with the available exact solution. The
experiments are given to illustrate the efficiency and implementation
of the method.
Abstract: We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.
Abstract: We provide a maximum norm analysis of a finite
element Schwarz alternating method for a nonlinear elliptic boundary
value problem of the form -Δu = f(u), on two overlapping sub
domains with non matching grids. We consider a domain which is
the union of two overlapping sub domains where each sub domain
has its own independently generated grid. The two meshes being
mutually independent on the overlap region, a triangle belonging to
one triangulation does not necessarily belong to the other one. Under
a Lipschitz assumption on the nonlinearity, we establish, on each sub
domain, an optimal L∞ error estimate between the discrete Schwarz
sequence and the exact solution of the boundary value problem.
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: In this work we adopt a combination of Laplace
transform and the decomposition method to find numerical solutions
of a system of multi-pantograph equations. The procedure leads to a
rapid convergence of the series to the exact solution after computing a
few terms. The effectiveness of the method is demonstrated in some
examples by obtaining the exact solution and in others by computing
the absolute error which decreases as the number of terms of the series
increases.
Abstract: We address the balancing problem of transfer lines in
this paper to find the optimal line balancing that minimizes the nonproductive
time. We focus on the tool change time and face
orientation change time both of which influence the makespane. We
consider machine capacity limitations and technological constraints
associated with the manufacturing process of auto cylinder heads.
The problem is represented by a mixed integer programming model
that aims at distributing the design features to workstations and
sequencing the machining processes at a minimum non-productive
time. The proposed model is solved by an algorithm established using
linearization schemes and Benders- decomposition approach. The
experiments show the efficiency of the algorithm in reaching the
exact solution of small and medium problem instances at reasonable
time.
Abstract: This paper deals with the helical flow of a Newtonian
fluid in an infinite circular cylinder, due to both longitudinal and
rotational shear stress. The velocity field and the resulting shear
stress are determined by means of the Laplace and finite Hankel
transforms and satisfy all imposed initial and boundary conditions.
For large times, these solutions reduce to the well-known steady-state
solutions.
Abstract: In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.
Abstract: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Abstract: In this paper, we explore the applicability of the Sinc-
Collocation method to a three-dimensional (3D) oceanography model.
The model describes a wind-driven current with depth-dependent
eddy viscosity in the complex-velocity system. In general, the
Sinc-based methods excel over other traditional numerical methods
due to their exponentially decaying errors, rapid convergence and
handling problems in the presence of singularities in end-points.
Together with these advantages, the Sinc-Collocation approach that
we utilize exploits first derivative interpolation, whose integration
is much less sensitive to numerical errors. We bring up several
model problems to prove the accuracy, stability, and computational
efficiency of the method. The approximate solutions determined by
the Sinc-Collocation technique are compared to exact solutions and
those obtained by the Sinc-Galerkin approach in earlier studies. Our
findings indicate that the Sinc-Collocation method outperforms other
Sinc-based methods in past studies.
Abstract: We study the spatial design of experiment and we want to select a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations and possibly at different times. In spatial design, when the design region and the set of interest are discrete then the covariance matrix completely describe any objective function and our goal is to choose a feasible design that minimizes the resulting uncertainty. The problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. This problem is NP-hard. For using these designs in computer experiments, in many cases, the design space is very large and it's not possible to calculate the exact optimal solution. Heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective and exact solution not possible. We developed a GA algorithm to take advantage of the exploratory power of this algorithm. The successful application of this method is demonstrated in large design space. We consider a real case of design of experiment. In our problem, design space is very large and for solving the problem, we used proposed GA algorithm.
Abstract: Panoramic view generation has always offered
novel and distinct challenges in the field of image processing.
Panoramic view generation is nothing but construction of bigger
view mosaic image from set of partial images of the desired view.
The paper presents a solution to one of the problems of image
seascape formation where some of the partial images are color and
others are grayscale. The simplest solution could be to convert all
image parts into grayscale images and fusing them to get grayscale
image panorama. But in the multihued world, obtaining the colored
seascape will always be preferred. This could be achieved by picking
colors from the color parts and squirting them in grayscale parts of
the seascape. So firstly the grayscale image parts should be colored
with help of color image parts and then these parts should be fused to
construct the seascape image.
The problem of coloring grayscale images has no exact solution.
In the proposed technique of panoramic view generation, the job of
transferring color traits from reference color image to grayscale
image is done by palette based method. In this technique, the color
palette is prepared using pixel windows of some degrees taken from
color image parts. Then the grayscale image part is divided into pixel
windows with same degrees. For every window of grayscale image
part the palette is searched and equivalent color values are found,
which could be used to color grayscale window. For palette
preparation we have used RGB color space and Kekre-s LUV color
space. Kekre-s LUV color space gives better quality of coloring. The
searching time through color palette is improved over the exhaustive
search using Kekre-s fast search technique.
After coloring the grayscale image pieces the next job is fusion of
all these pieces to obtain panoramic view. For similarity estimation
between partial images correlation coefficient is used.
Abstract: In this paper, linear multistep technique using power
series as the basis function is used to develop the block methods
which are suitable for generating direct solution of the special second
order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some
grids and off – grid points to obtain two different three discrete
schemes, each of order (4,4,4)T, which were used in block form for
parallel or sequential solutions of the problems. The computational
burden and computer time wastage involved in the usual reduction of
second order problem into system of first order equations are avoided
by this approach. Furthermore, a stability analysis and efficiency of
the block method are tested on linear and non-linear ordinary
differential equations whose solutions are oscillatory or nearly
periodic in nature, and the results obtained compared favourably with
the exact solution.
Abstract: This study presents an exact general solution for
steady-state conductive heat transfer in cylindrical composite
laminates. Appropriate Fourier transformation has been obtained
using Sturm-Liouville theorem. Series coefficients are achieved by
solving a set of equations that related to thermal boundary conditions
at inner and outer of the cylinder, also related to temperature
continuity and heat flux continuity between each layer. The solution
of this set of equations are obtained using Thomas algorithm. In this
paper, the effect of fibers- angle on temperature distribution of
composite laminate is investigated under general boundary
conditions. Here, we show that the temperature distribution for any
composite laminates is between temperature distribution for
laminates with θ = 0° and θ = 90° .
Abstract: In this paper the complete rotor system including
elastic shaft with distributed mass, allowing for the effects of oil film
in bearings. Also, flexibility of foundation is modeled. As a whole
this article is a relatively complete research in modeling and
vibration analysis of rotor considering gyroscopic effect, damping,
dependency of stiffness and damping coefficients on frequency and
solving the vibration equations including these parameters. On the
basis of finite element method and utilizing four element types
including element of shaft, disk, bearing and foundation and using
MATLAB, a computer program is written. So the responses in
several cases and considering different effects are obtained. Then the
results are compared with each other, with exact solutions and results
of other papers.
Abstract: In the traditional theory of non-uniform torsion the
axial displacement field is expressed as the product of the unit twist
angle and the warping function. The first one, variable along the
beam axis, is obtained by a global congruence condition; the second
one, instead, defined over the cross-section, is determined by solving
a Neumann problem associated to the Laplace equation, as well as for
the uniform torsion problem.
So, as in the classical theory the warping function doesn-t punctually
satisfy the first indefinite equilibrium equation, the principal aim of
this work is to develop a new theory for non-uniform torsion of
beams with axial symmetric cross-section, fully restrained on both
ends and loaded by a constant torque, that permits to punctually
satisfy the previous equation, by means of a trigonometric expansion
of the axial displacement and unit twist angle functions.
Furthermore, as the classical theory is generally applied with good
results to the global and local analysis of ship structures, two beams
having the first one an open profile, the second one a closed section,
have been analyzed, in order to compare the two theories.
Abstract: Based on the homotopy perturbation method (HPM)
and Padé approximants (PA), approximate and exact solutions are
obtained for cubic Boussinesq and modified Boussinesq equations.
The obtained solutions contain solitary waves, rational solutions.
HPM is used for analytic treatment to those equations and PA for
increasing the convergence region of the HPM analytical solution.
The results reveal that the HPM with the enhancement of PA is a
very effective, convenient and quite accurate to such types of partial
differential equations.
Abstract: The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating
that the flow equations possess an infinite set of solutions.
Abstract: The square-lattice Ising model is the simplest system
showing phase transitions (the transition between the paramagnetic
phase and the ferromagnetic phase and the transition between the
paramagnetic phase and the antiferromagnetic phase) and critical
phenomena at finite temperatures. The exact solution of the squarelattice
Ising model with free boundary conditions is not known for
systems of arbitrary size. For the first time, the exact solution of
the Ising model on the square lattice with free boundary
conditions is obtained after classifying all )
spin configurations with the microcanonical transfer matrix. Also, the
phase transitions and critical phenomena of the square-lattice Ising
model are discussed using the exact solution on the square
lattice with free boundary conditions.