Abstract: This article is devoted to the numerical solution of
large-scale quadratic eigenvalue problems. Such problems arise in
a wide variety of applications, such as the dynamic analysis of
structural mechanical systems, acoustic systems, fluid mechanics,
and signal processing. We first introduce a generalized second-order
Krylov subspace based on a pair of square matrices and two initial
vectors and present a generalized second-order Arnoldi process for
constructing an orthonormal basis of the generalized second-order
Krylov subspace. Then, by using the projection technique and the
refined projection technique, we propose a restarted generalized
second-order Arnoldi method and a restarted refined generalized
second-order Arnoldi method for computing some eigenpairs of largescale
quadratic eigenvalue problems. Some theoretical results are also
presented. Some numerical examples are presented to illustrate the
effectiveness of the proposed methods.
Abstract: Avalanche release of snow has been modeled in the present studies. Snow is assumed to be represented by semi-solid and the governing equations have been studied from the concept of continuum approach. The dynamical equations have been solved for two different zones [starting zone and track zone] by using appropriate initial and boundary conditions. Effect of density (ρ), Eddy viscosity (η), Slope angle (θ), Slab depth (R) on the flow parameters have been observed in the present studies. Numerical methods have been employed for computing the non linear differential equations. One of the most interesting and fundamental innovation in the present studies is getting initial condition for the computation of velocity by numerical approach. This information of the velocity has obtained through the concept of fracture mechanics applicable to snow. The results on the flow parameters have found to be in qualitative agreement with the published results.
Abstract: The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.
Abstract: The Sphere Method is a flexible interior point algorithm for linear programming problems. This was developed mainly by Professor Katta G. Murty. It consists of two steps, the centering step and the descent step. The centering step is the most expensive part of the algorithm. In this centering step we proposed some improvements such as introducing two or more initial feasible solutions as we solve for the more favorable new solution by objective value while working with the rigorous updates of the feasible region along with some ideas integrated in the descent step. An illustration is given confirming the advantage of using the proposed procedure.
Abstract: The present work is motivated by the idea that the
layer deformation in anisotropic elasticity can be estimated from the
theory of interfacial dislocations. In effect, this work which is an
extension of a previous approach given by one of the authors
determines the anisotropic displacement fields and the critical
thickness due to a complex biperiodic network of MDs lying just
below the free surface in view of the arrangement of dislocations.
The elastic fields of such arrangements observed along interfaces
play a crucial part in the improvement of the physical properties of
epitaxial systems. New results are proposed in anisotropic elasticity
for hexagonal networks of MDs which contain intrinsic and extrinsic
stacking faults. We developed, using a previous approach based on
the relative interfacial displacement and a Fourier series formulation
of the displacement fields, the expressions of elastic fields when
there is a possible dissociation of MDs. The numerical investigations
in the case of the observed system Si/(111)Si with low twist angles
show clearly the effect of the anisotropy and thickness when the
misfit networks are dissociated.
Abstract: Molecular dynamics simulation of annular flow
boiling in a nanochannel with 70000 particles is numerically
investigated. In this research, an annular flow model is developed to
predict the superheated flow boiling heat transfer characteristics in a
nanochannel. To characterize the forced annular boiling flow in a
nanochannel, an external driving force F ext ranging from 1to12PN
(PN= Pico Newton) is applied along the flow direction to inlet fluid
particles during the simulation. Based on an annular flow model
analysis, it is found that saturation condition and superheat degree
have great influences on the liquid-vapor interface. Also, the results
show that due to the relatively strong influence of surface tension in
small channel, the interface between the liquid film and vapor core is
fairly smooth, and the mean velocity along the stream-wise direction
does not change anymore.
Abstract: We report the electronic structure and optical
properties of NdF3 compound. Our calculations are based on density
functional theory (DFT) using the full potential linearized augmented
plane wave (FPLAPW) method with the inclusion of spin orbit
coupling. We employed the local spin density approximation (LSDA)
and Coulomb-corrected local spin density approximation, known for
treating the highly correlated 4f electrons properly, is able to
reproduce the correct insulating ground state. We find that the
standard LSDA approach is incapable of correctly describing the
electronic properties of such materials since it positions the f-bands
incorrectly resulting in an incorrect metallic ground state. On the
other hand, LSDA + U approximation, known for treating the highly
correlated 4f electrons properly, is able to reproduce the correct
insulating ground state. Interestingly, however, we do not find any
significant differences in the optical properties calculated using
LSDA, and LSDA + U suggesting that the 4f electrons do not play a
decisive role in the optical properties of these compounds. The
reflectivity for NdF3 compound stays low till 7 eV which is
consistent with their large energy gaps. The calculated energy gaps
are in good agreement with experiments. Our calculated reflectivity
compares well with the experimental data and the results are analyzed
in the light of band to band transitions.
Abstract: The boundary layer flow and heat transfer on a
stretched surface moving with prescribed skin friction is studied for
permeable surface. The surface temperature is assumed to vary
inversely with the vertical direction x for n = -1. The skin friction at
the surface scales as (x-1/2) at m = 0. The constants m and n are the
indices of the power law velocity and temperature exponent
respectively. Similarity solutions are obtained for the boundary layer
equations subject to power law temperature and velocity variation.
The effect of various governing parameters, such as the buoyancy
parameter λ and the suction/injection parameter fw for air (Pr = 0.72)
are studied. The choice of n and m ensures that the used similarity
solutions are x independent. The results show that, assisting flow (λ >
0) enhancing the heat transfer coefficient along the surface for any
constant value of fw. Furthermore, injection increases the heat
transfer coefficient but suction reduces it at constant λ.
Abstract: The paper presents an analytical solution for dispersion
of a solute in the peristaltic motion of a micropolar fluid in the
presence of magnetic field and both homogeneous and heterogeneous
chemical reactions. The average effective dispersion coefficient has
been found using Taylor-s limiting condition under long wavelength
approximation. The effects of various relevant parameters on the average
coefficient of dispersion have been studied. The average effective
dispersion coefficient increases with amplitude ratio, cross viscosity
coefficient and heterogeneous chemical reaction rate parameter. But it
decreases with magnetic field parameter and homogeneous chemical
reaction rate parameter. It can be noted that the presence of peristalsis
enhances dispersion of a solute.
Abstract: Traffic congestion has become a major problem in
many countries. One of the main causes of traffic congestion is due
to road merges. Vehicles tend to move slower when they reach the
merging point. In this paper, an enhanced algorithm for traffic
simulation based on the fluid-dynamic algorithm and kinematic wave
theory is proposed. The enhanced algorithm is used to study traffic
congestion at a road merge. This paper also describes the
development of a dynamic traffic simulation tool which is used as a
scenario planning and to forecast traffic congestion level in a certain
time based on defined parameter values. The tool incorporates the
enhanced algorithm as well as the two original algorithms. Output
from the three above mentioned algorithms are measured in terms of
traffic queue length, travel time and the total number of vehicles
passing through the merging point. This paper also suggests an
efficient way of reducing traffic congestion at a road merge by
analyzing the traffic queue length and travel time.
Abstract: In this work, we propose a hybrid heuristic in order to
solve the Team Orienteering Problem (TOP). Given a set of points (or
customers), each with associated score (profit or benefit), and a team
that has a fixed number of members, the problem to solve is to visit a
subset of points in order to maximize the total collected score. Each
member performs a tour starting at the start point, visiting distinct
customers and the tour terminates at the arrival point. In addition,
each point is visited at most once, and the total time in each tour
cannot be greater than a given value. The proposed heuristic combines
beam search and a local optimization strategy. The algorithm was
tested on several sets of instances and encouraging results were
obtained.
Abstract: In this paper, the criteria of Ψ-eventual stability have been established for generalized impulsive differential systems of multiple dependent variables. The sufficient conditions have been obtained using piecewise continuous Lyapunov function. An example is given to support our theoretical result.
Abstract: In this paper a new embedded Singly Diagonally
Implicit Runge-Kutta Nystrom fourth order in fifth order method for
solving special second order initial value problems is derived. A
standard set of test problems are tested upon and comparisons on the
numerical results are made when the same set of test problems are
reduced to first order systems and solved using the existing
embedded diagonally implicit Runge-Kutta method. The results
suggests the superiority of the new method.
Abstract: Stresses for the elastic-plastic transition and fully
plastic state have been derived for a thin rotating disc with inclusion
and results have been discussed numerically and depicted graphically.
It has been observed that the rotating disc with inclusion and made of
compressible material requires lesser angular speed to yield at the
internal surface whereas it requires higher percentage increase in
angular speed to become fully plastic as compare to disc made of
incompressible material.
Abstract: In this paper, estimation of the linear regression
model is made by ordinary least squares method and the
partially linear regression model is estimated by penalized
least squares method using smoothing spline. Then, it is
investigated that differences and similarity in the sum of
squares related for linear regression and partial linear
regression models (semi-parametric regression models). It is
denoted that the sum of squares in linear regression is reduced
to sum of squares in partial linear regression models.
Furthermore, we indicated that various sums of squares in the
linear regression are similar to different deviance statements in
partial linear regression. In addition to, coefficient of the
determination derived in linear regression model is easily
generalized to coefficient of the determination of the partial
linear regression model. For this aim, it is made two different
applications. A simulated and a real data set are considered to
prove the claim mentioned here. In this way, this study is
supported with a simulation and a real data example.
Abstract: This paper develops an unscented grid-based filter
and a smoother for accurate nonlinear modeling and analysis
of time series. The filter uses unscented deterministic sampling
during both the time and measurement updating phases, to approximate
directly the distributions of the latent state variable. A
complementary grid smoother is also made to enable computing
of the likelihood. This helps us to formulate an expectation
maximisation algorithm for maximum likelihood estimation of
the state noise and the observation noise. Empirical investigations
show that the proposed unscented grid filter/smoother compares
favourably to other similar filters on nonlinear estimation tasks.
Abstract: In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.
Abstract: The aeration process via injectors is used to combat
the lack of oxygen in lakes due to eutrophication. A 3D numerical
simulation of the resulting flow using a simplified model is presented.
In order to generate the best dynamic in the fluid with respect to
the aeration purpose, the optimization of the injectors location is
considered. We propose to adapt to this problem the topological
sensitivity analysis method which gives the variation of a criterion
with respect to the creation of a small hole in the domain. The main
idea is to derive the topological sensitivity analysis of the physical
model with respect to the insertion of an injector in the fluid flow
domain. We propose in this work a topological optimization algorithm
based on the studied asymptotic expansion. Finally we present some
numerical results, showing the efficiency of our approach
Abstract: The Goursat partial differential equation arises in
linear and non linear partial differential equations with mixed
derivatives. This equation is a second order hyperbolic partial
differential equation which occurs in various fields of study such as
in engineering, physics, and applied mathematics. There are many
approaches that have been suggested to approximate the solution of
the Goursat partial differential equation. However, all of the
suggested methods traditionally focused on numerical differentiation
approaches including forward and central differences in deriving the
scheme. An innovation has been done in deriving the Goursat partial
differential equation scheme which involves numerical integration
techniques. In this paper we have developed a new scheme to solve
the Goursat partial differential equation based on the Adomian
decomposition (ADM) and associated with Boole-s integration rule to
approximate the integration terms. The new scheme can easily be
applied to many linear and non linear Goursat partial differential
equations and is capable to reduce the size of computational work.
The accuracy of the results reveals the advantage of this new scheme
over existing numerical method.
Abstract: We propose a decoy-pulse protocol for frequency-coded implementation of B92 quantum key distribution protocol. A direct extension of decoy-pulse method to frequency-coding scheme results in security loss as an eavesdropper can distinguish between signal and decoy pulses by measuring the carrier photon number without affecting other statistics. We overcome this problem by optimizing the ratio of carrier photon number of decoy-to-signal pulse to be as close to unity as possible. In our method the switching between signal and decoy pulses is achieved by changing the amplitude of RF signal as opposed to modulating the intensity of optical signal thus reducing system cost. We find an improvement by a factor of 100 approximately in the key generation rate using decoy-state protocol. We also study the effect of source fluctuation on key rate. Our simulation results show a key generation rate of 1.5×10-4/pulse for link lengths up to 70km. Finally, we discuss the optimum value of average photon number of signal pulse for a given key rate while also optimizing the carrier ratio.