Abstract: An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.
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: We present an explicit expression to estimate driving voltage attenuation through RC networks representation of an ultrahigh- speed image sensor. Elmore delay metric for a fundamental RC chain is employed as the first-order approximation. By application of dimensional analysis to SPICE simulation data, we found a simple expression that significantly improves the accuracy of the approximation. Estimation error of the resultant expression for uniform RC networks is less than 2%. Similarly, another simple closed-form model to estimate 50 % delay through fundamental RC networks is also derived with sufficient accuracy. The framework of this analysis can be extended to address delay or attenuation issues of other VLSI structures.
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: Cavitation in pumps is known as the formation of
vapor bubbles due to pressure drop and collapsing these bubbles. In
some conditions, it has been observed that the formation of bubbles
occurs at the pressure side of centrifugal pump blades. In this study,
the formation of bubbles at the pressure side of blades has been
investigated. Water is used in this study as the fluid and performance
curves were depicted for different flow rates in an approximately
constant speed. The results show that when a centrifugal pump works
in low flow rates, a secondary flow namely recirculation starts to
begin. In this condition, separation of flow increases which causes
vortex formation and local pressure drop and eventually the
formation of vapor bubbles starts.
Abstract: A thin layer on the component surface can be found
with high tensile residual stresses, due to turning operations, which
can dangerously affect the fatigue performance of the component. In
this paper an analytical approach is presented to reconstruct the
residual stress field from a limited incomplete set of measurements.
Airy stress function is used as the primary unknown to directly solve
the equilibrium equations and satisfying the boundary conditions. In
this new method there exists the flexibility to impose the physical
conditions that govern the behavior of residual stress to achieve a
meaningful complete stress field. The analysis is also coupled to a
least squares approximation and a regularization method to provide
stability of the inverse problem. The power of this new method is
then demonstrated by analyzing some experimental measurements
and achieving a good agreement between the model prediction and
the results obtained from residual stress measurement.
Abstract: This paper presents the application of a signal intensity independent registration criterion for non-rigid body registration of medical images. The criterion is defined as the weighted ratio image of two images. The ratio is computed on a voxel per voxel basis and weighting is performed by setting the ratios between signal and background voxels to a standard high value. The mean squared value of the weighted ratio is computed over the union of the signal areas of the two images and it is minimized using the Chebyshev polynomial approximation. The geometric transformation model adopted is a local cubic B-splines based model.
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 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.
Abstract: The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.
Abstract: A mathematical model for the hydrodynamics of a
surface water treatment pilot plant was developed and validated by
the determination of the residence time distribution (RTD) for the
main equipments of the unit. The well known models of ideal/real
mixing, ideal displacement (plug flow) and (one-dimensional axial)
dispersion model were combined in order to identify the structure
that gives the best fitting of the experimental data for each equipment
of the pilot plant. RTD experimental results have shown that pilot
plant hydrodynamics can be quite well approximated by a
combination of simple mathematical models, structure which is
suitable for engineering applications. Validated hydrodynamic
models will be further used in the evaluation and selection of the
most suitable coagulation-flocculation reagents, optimum operating
conditions (injection point, reaction times, etc.), in order to improve
the quality of the drinking water.
Abstract: A biophysically based multilayer continuum model of the facial soft tissue composite has been developed for simulating wrinkle formation. The deformed state of the soft tissue block was determined by solving large deformation mechanics equations using the Galerkin finite element method. The proposed soft tissue model is composed of four layers with distinct mechanical properties. These include stratum corneum, epidermal-dermal layer (living epidermis and dermis), subcutaneous tissue and the underlying muscle. All the layers were treated as non-linear, isotropic Mooney Rivlin materials. Contraction of muscle fibres was approximated using a steady-state relationship between the fibre extension ratio, intracellular calcium concentration and active stress in the fibre direction. Several variations of the model parameters (stiffness and thickness of epidermal-dermal layer, thickness of subcutaneous tissue layer) have been considered.
Abstract: Existing image-based virtual reality applications
allow users to view image-based 3D virtual environment in a more
interactive manner. User could “walkthrough"; looks left, right, up
and down and even zoom into objects in these virtual worlds of
images. However what the user sees during a “zoom in" is just a
close-up view of the same image which was taken from a distant.
Thus, this does not give the user an accurate view of the object from
the actual distance. In this paper, a simple technique for zooming in
an object in a virtual scene is presented. The technique is based on
the 'hotspot' concept in existing application. Instead of navigation
between two different locations, the hotspots are used to focus into
an object in the scene. For each object, several hotspots are created.
A different picture is taken for each hotspot. Each consecutive
hotspot created will take the user closer to the object. This will
provide the user with a correct of view of the object based on his
proximity to the object. Implementation issues and the relevance of
this technique in potential application areas are highlighted.
Abstract: This paper proposes, for the first time, how the
challenges facing the guard-band designs including the margin
assist-circuits scheme for the screening-test in the coming process
generations should be addressed. The increased screening error
impacts are discussed based on the proposed statistical analysis
models. It has been shown that the yield-loss caused by the
misjudgment on the screening test would become 5-orders of
magnitude larger than that for the conventional one when the
amplitude of random telegraph noise (RTN) caused variations
approaches to that of random dopant fluctuation. Three fitting methods
to approximate the RTN caused complex Gamma mixtures
distributions by the simple Gaussian mixtures model (GMM) are
proposed and compared. It has been verified that the proposed
methods can reduce the error of the fail-bit predictions by 4-orders of
magnitude.
Abstract: This research uses computational linguistics, an area of study that employs a computer to process natural language, and aims at discerning the patterns that exist in declarative sentences used in technical texts. The approach is mathematical, and the focus is on instructional texts found on web pages. The technique developed by the author and named the MAYA Semantic Technique is used here and organized into four stages. In the first stage, the parts of speech in each sentence are identified. In the second stage, the subject of the sentence is determined. In the third stage, MAYA performs a frequency analysis on the remaining words to determine the verb and its object. In the fourth stage, MAYA does statistical analysis to determine the content of the web page. The advantage of the MAYA Semantic Technique lies in its use of mathematical principles to represent grammatical operations which assist processing and accuracy if performed on unambiguous text. The MAYA Semantic Technique is part of a proposed architecture for an entire web-based intelligent tutoring system. On a sample set of sentences, partial semantics derived using the MAYA Semantic Technique were approximately 80% accurate. The system currently processes technical text in one domain, namely Cµ programming. In this domain all the keywords and programming concepts are known and understood.
Abstract: Composite nanostructures of metal
core/semiconductor shell (Au/CdS) configuration were prepared
using organometalic method. UV-Vis spectra for the Au/CdS colloids
show initially two well separated bands, corresponding to surface
plasmon of the Au core, and the exciton of CdS shell. The absorption
of CdS shell is enhanced, while the Au plasmon band is suppressed
as the shell thickness increases. The shell sizes were estimated from
the optical spectra using the effective mass approximation model
(EMA), and compared to the sizes of the Au core and CdS shell
measured by high resolution transmission electron microscope
(HRTEM). The changes in the absorption features are discussed in
terms of gradual increase in the coupling strength of the Au core
surface plasmon and the exciton in the CdS. leading to charge
transfer and modification of electron oscillation in Au core.
Abstract: We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.
Abstract: Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal
non-equilibrium model is studied in this paper. The left vertical wall is
maintained at a constant hot temperature Th and the right vertical wall
is maintained at a constant cold temperature Tc, while the horizontal
walls are adiabatic. The governing equations are obtained by applying
the Darcy model and Boussinesq approximation. COMSOL’s finite
element method is used to solve the non-dimensional governing
equations together with specified boundary conditions. The governing
parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3),
the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the
time dependent (0.001 ≤ τ ≤ 0.2). The results presented for
values of the governing parameters in terms of streamlines in both
fluid/porous-layer, isotherms of fluid in fluid/porous-layer, isotherms
of solid in porous layer, and average Nusselt number.