Abstract: We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).
Abstract: This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.
Abstract: In this paper, according to the classical algorithm
LSQR for solving the least-squares problem, an iterative method is
proposed for least-squares solution of constrained matrix equation. By
using the Kronecker product, the matrix-form LSQR is presented to
obtain the like-minimum norm and minimum norm solutions in a
constrained matrix set for the symmetric arrowhead matrices. Finally,
numerical examples are also given to investigate the performance.
Abstract: Annihilations, phase shifts, scattering lengths and
elastic cross sections of low energy positrons scattering from
magnesium atoms were studied using the least-squares variational
method (LSVM). The possibility of positron binding to the
magnesium atoms is investigated. A trial wave function is suggested
to represent e+-Mg elastic scattering and scattering parameters were
derived to estimate the binding energy and annihilation rates. The
trial function is taken to depend on several adjustable parameters, and
is improved iteratively by increasing the number of terms. The
present results have the same behavior as reported semi-empirical,
theoretical and experimental results. Especially, the estimated
positive scattering length supports the possibility of positronmagnesium
bound state system that was confirmed in previous
experimental and theoretical work.
Abstract: In this article, we used the residual correction method
to deal with transient thermoelastic problems with a hollow spherical
region when the continuum medium possesses spherically isotropic
thermoelastic properties. Based on linear thermoelastic theory, the
equations of hyperbolic heat conduction and thermoelastic motion
were combined to establish the thermoelastic dynamic model with
consideration of the deformation acceleration effect and non-Fourier
effect under the condition of transient thermal shock. The approximate
solutions of temperature and displacement distributions are obtained
using the residual correction method based on the maximum principle
in combination with the finite difference method, making it easier and
faster to obtain upper and lower approximations of exact solutions.
The proposed method is found to be an effective numerical method
with satisfactory accuracy. Moreover, the result shows that the effect
of transient thermal shock induced by deformation acceleration is
enhanced by non-Fourier heat conduction with increased peak stress.
The influence on the stress increases with the thermal relaxation time.
Abstract: Si-Ge solid solutions (bulk poly- and mono-crystalline
samples, thin films) are characterized by high perspectives for
application in semiconductor devices, in particular, optoelectronics
and microelectronics. From this point of view, complex studying of
structural state of the defects and structural-sensitive physical
properties of Si-Ge solid solutions depending on the contents of Si
and Ge components is very important. Present work deals with the
investigations of microstructure, microhardness, internal friction and
shear modulus of Si1-xGex(x≤0,02) bulk monocrystals conducted at
room temperature. Si-Ge bulk crystals were obtained by Czochralski
method in [111] crystallographic direction. Investigated
monocrystalline Si-Ge samples are characterized by p-type
conductivity and carriers’ concentration 5.1014-1.1015cm-3.
Microhardness was studied on Dynamic Ultra Micro hardness Tester
DUH-201S with Berkovich indenter. Investigate samples are characterized with 0,5x0,5x(10-15)mm3
sizes, oriented along [111] direction at torsion oscillations ≈1Hz,
multistage changing of internal friction and shear modulus has been
revealed in an interval of strain amplitude of 10-5-5.10-3. Critical
values of strain amplitude have been determined at which hysteretic
changes of inelastic characteristics and microplasticity are observed. The critical strain amplitude and elasticity limit values are also
determined. Dynamic mechanical characteristics decreasing trend is
shown with increasing Ge content in Si-Ge solid solutions. Observed
changes are discussed from the point of view of interaction of various
dislocations with point defects and their complexes in a real structure
of Si-Ge solid solutions.
Abstract: We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study.
Abstract: In this study, we demonstrate a high-resolution
refractive index sensor based on a Magnetic Photonic Crystal (MPC)
composed of a triangular lattice array of air holes embedded in Si
matrix. A microcavity is created by changing the radius of an air hole
in the middle of the photonic crystal. The cavity filled with gyrotropic
materials can serve as a refractive index sensor. The shift of the
resonant frequency of the sensor is obtained numerically using finite
difference time domain method under different ambient conditions
having refractive index from n = 1.0 to n = 1.1. The numerical results
show that a tiny change in refractive index of Δn = 0.0001 is
distinguishable. In addition, the spectral response of the MPC sensor is
studied while an external magnetic field is present. The results show
that the MPC sensor exhibits a dramatic improvement in resolution.
Abstract: Linear stability analysis of double diffusive convection
in a horizontal porous layer saturated with fluid is examined by
considering the effects of viscous dissipation, concentration based
internal heat source and vertical throughflow. The basic steady
state solution for Governing equations is derived. Linear stability
analysis has been implemented numerically by using shooting
and Runge-kutta methods. Critical thermal Rayleigh number Rac
is obtained for various values of solutal Rayleigh number Sa,
vertical Peclet number Pe, Gebhart number Ge, Lewis number
Le and measure of concentration based internal heat source
γ. It is observed that Ge has destabilizing effect for upward
throughflow and stabilizing effect for downward throughflow. And
γ has considerable destabilizing effect for upward throughflow and
insignificant destabilizing effect for downward throughflow.
Abstract: This paper presents a fully Lagrangian coupled
Fluid-Structure Interaction (FSI) solver for simulations of
fluid-structure interactions, which is based on the Moving Particle
Semi-implicit (MPS) method to solve the governing equations
corresponding to incompressible flows as well as elastic structures.
The developed solver is verified by reproducing the high velocity
impact loads of deformable thin wedges with three different materials
such as mild steel, aluminium and tin during water entry. The present
simulation results for aluminium are compared with analytical solution
derived from the hydrodynamic Wagner model and linear Wan’s
theory. And also, the impact pressure and strain on the water entry
wedge with three different materials, such as mild steel, aluminium
and tin, are simulated and the effects of hydro-elasticity are discussed.
Abstract: Batch production plants provide a wide range of
scheduling problems. In pharmaceutical industries a batch process
is usually described by a recipe, consisting of an ordering of tasks
to produce the desired product. In this research work we focused
on pharmaceutical production processes requiring the culture of
a microorganism population (i.e. bacteria, yeasts or antibiotics).
Several sources of uncertainty may influence the yield of the culture
processes, including (i) low performance and quality of the cultured
microorganism population or (ii) microbial contamination. For
these reasons, robustness is a valuable property for the considered
application context. In particular, a robust schedule will not collapse
immediately when a cell of microorganisms has to be thrown away
due to a microbial contamination. Indeed, a robust schedule should
change locally in small proportions and the overall performance
measure (i.e. makespan, lateness) should change a little if at all.
In this research work we formulated a constraint programming
optimization (COP) model for the robust planning of antibiotics
production. We developed a discrete-time model with a multi-criteria
objective, ordering the different criteria and performing a
lexicographic optimization. A feasible solution of the proposed
COP model is a schedule of a given set of tasks onto available
resources. The schedule has to satisfy tasks precedence constraints,
resource capacity constraints and time constraints. In particular
time constraints model tasks duedates and resource availability
time windows constraints. To improve the schedule robustness, we
modeled the concept of (a, b) super-solutions, where (a, b) are input
parameters of the COP model. An (a, b) super-solution is one in
which if a variables (i.e. the completion times of a culture tasks)
lose their values (i.e. cultures are contaminated), the solution can be
repaired by assigning these variables values with a new values (i.e.
the completion times of a backup culture tasks) and at most b other
variables (i.e. delaying the completion of at most b other tasks).
The efficiency and applicability of the proposed model is
demonstrated by solving instances taken from a real-life
pharmaceutical company. Computational results showed that
the determined super-solutions are near-optimal.
Abstract: An investigation has been presented to analyze the
effect of internal heat source on the onset of Hadley-Prats flow in
a horizontal fluid saturated porous medium. We examine a better
understanding of the combined influence of the heat source and mass
flow effect by using linear stability analysis. The resultant eigenvalue
problem is solved by using shooting and Runga-Kutta methods for
evaluate critical thermal Rayleigh number with respect to various
flow governing parameters. It is identified that the flow is switch from
stabilizing to destabilizing as the horizontal thermal Rayleigh number
is enhanced. The heat source and mass flow increases resulting a
stronger destabilizing effect.
Abstract: Propagation of arbitrary amplitude nonlinear Alfven
waves has been investigated in low but finite β electron-positron-ion
plasma including full ion dynamics. Using Sagdeev pseudopotential
method an energy integral equation has been derived. The Sagdeev
potential has been calculated for different plasma parameters and it
has been shown that inclusion of ion parallel motion along the
magnetic field changes the nature of slow shear Alfven wave solitons
from dip type to hump type. The effects of positron concentration,
plasma-β and obliqueness of the wave propagation on the solitary
wave structure have also been examined.
Abstract: Particle size distribution, the most important
characteristics of aerosols, is obtained through electrical
characterization techniques. The dynamics of charged nanoparticles
under the influence of electric field in Electrical Mobility
Spectrometer (EMS) reveals the size distribution of these particles.
The accuracy of this measurement is influenced by flow conditions,
geometry, electric field and particle charging process, therefore by
the transfer function (transfer matrix) of the instrument. In this work,
a wire-cylinder corona charger was designed and the combined fielddiffusion
charging process of injected poly-disperse aerosol particles
was numerically simulated as a prerequisite for the study of a
multichannel EMS. The result, a cloud of particles with no uniform
charge distribution, was introduced to the EMS. The flow pattern and
electric field in the EMS were simulated using Computational Fluid
Dynamics (CFD) to obtain particle trajectories in the device and
therefore to calculate the reported signal by each electrometer.
According to the output signals (resulted from bombardment of
particles and transferring their charges as currents), we proposed a
modification to the size of detecting rings (which are connected to
electrometers) in order to evaluate particle size distributions more
accurately. Based on the capability of the system to transfer
information contents about size distribution of the injected particles,
we proposed a benchmark for the assessment of optimality of the
design. This method applies the concept of Von Neumann entropy
and borrows the definition of entropy from information theory
(Shannon entropy) to measure optimality. Entropy, according to the
Shannon entropy, is the ''average amount of information contained in
an event, sample or character extracted from a data stream''.
Evaluating the responses (signals) which were obtained via various
configurations of detecting rings, the best configuration which gave
the best predictions about the size distributions of injected particles,
was the modified configuration. It was also the one that had the
maximum amount of entropy. A reasonable consistency was also
observed between the accuracy of the predictions and the entropy
content of each configuration. In this method, entropy is extracted
from the transfer matrix of the instrument for each configuration.
Ultimately, various clouds of particles were introduced to the
simulations and predicted size distributions were compared to the
exact size distributions.
Abstract: Steepest descent method is a simple gradient method
for optimization. This method has a slow convergence in heading to
the optimal solution, which occurs because of the zigzag form of the
steps. Barzilai and Borwein modified this algorithm so that it
performs well for problems with large dimensions. Barzilai and
Borwein method results have sparked a lot of research on the method
of steepest descent, including alternate minimization gradient method
and Yuan method. Inspired by previous works, we modified the step
size of the steepest descent method. We then compare the
modification results against the Barzilai and Borwein method,
alternate minimization gradient method and Yuan method for
quadratic function cases in terms of the iterations number and the
running time. The average results indicate that the steepest descent
method with the new step sizes provide good results for small
dimensions and able to compete with the results of Barzilai and
Borwein method and the alternate minimization gradient method for
large dimensions. The new step sizes have faster convergence
compared to the other methods, especially for cases with large
dimensions.
Abstract: In this study, one dimensional phase change problem
(a Stefan problem) is considered and a numerical solution of this
problem is discussed. First, we use similarity transformation to
convert the governing equations into ordinary differential equations
with its boundary conditions. The solutions of ordinary differential
equation with the associated boundary conditions and interface
condition (Stefan condition) are obtained by using a numerical
approach based on operational matrix of differentiation of shifted
second kind Chebyshev wavelets. The obtained results are compared
with existing exact solution which is sufficiently accurate.
Abstract: We propose new multiple-channel piezoelectric (PZT)
actuated tunable optical filter based on racetrack multi-ring
resonators for wavelength de-multiplexing network applications. We
design tunable eight-channel wavelength de-multiplexer consisting of
eight cascaded PZT actuated tunable multi-ring resonator filter with a
channel spacing of 1.6nm. The filter for each channel is basically
structured on a suspended beam, sandwiched with piezoelectric
material and built in integrated ring resonators which are placed on
the middle of the beam to gain uniform stress and linearly varying
longitudinal strain. A reference single mode serially coupled multi
stage racetrack ring resonator with the same radii and coupling length
is designed with a line width of 0.8974nm with a flat top pass band at
1dB of 0.5205nm and free spectral range of about 14.9nm. In each
channel, a small change in the perimeter of the rings is introduced to
establish the shift in resonance wavelength as per the defined channel
spacing. As a result, when a DC voltage is applied, the beams will
elongate, which involves mechanical deformation of the ring
resonators that induces a stress and a strain, which brings a change in
refractive index and perimeter of the rings leading to change in the
output spectrum shift providing the tunability of central wavelength
in each channel. Simultaneous wave length shift as high as
45.54pm/