Investigating Transformations in the Cartesian Plane Using Spreadsheets
The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.
A Comparative Study on Different Approaches to Evaluate Ship Equilibrium Point
The aim of this paper is to present a comparative
study on two different methods for the evaluation of the equilibrium
point of a ship, core issue for designing an On Board Stability System
(OBSS) module that, starting from geometry information of a ship
hull, described by a discrete model in a standard format, and the
distribution of all weights onboard calculates the ship floating
conditions (in draught, heel and trim).
2 – Block 3 - Point Modified Numerov Block Methods for Solving Ordinary Differential Equations
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.
Solar Radiation Studies for Dubai and Sharjah, UAE
Global Solar Radiation (H) for Dubai and Sharjah,
Latitude 25.25oN, Longitude 55oE and 25.29oN, Longitude 55oE
respectively have been studied using sunshine hour data (n) of the
areas using various methods. These calculated global solar radiation
values are then compared to the measured values presented by
NASA. Furthermore, the extraterrestrial (H0), diffuse (Hd) and beam
radiation (Hb) are also calculated. The diffuse radiation is calculated
using methods proposed by Page and Liu and Jordan (L-J). Diffuse
Radiation from the Page method is higher than the L-J method.
Moreover, the clearness index (KT) signifies a clear sky almost all
year round. Rainy days are hardly a few in a year and limited in the
months December to March. The temperature remains between 25oC
in winter to 44oC in summer and is desirable for thermal applications
of solar energy. From the estimated results, it appears that solar
radiation can be utilized very efficiently throughout the year for
photovoltaic and thermal applications.
Some Solid Transportation Models with Crisp and Rough Costs
In this paper, some practical solid transportation models are formulated considering per trip capacity of each type of conveyances with crisp and rough unit transportation costs. This is applicable for the system in which full vehicles, e.g. trucks, rail coaches are to be booked for transportation of products so that transportation cost is determined on the full of the conveyances. The models with unit transportation costs as rough variables are transformed into deterministic forms using rough chance constrained programming with the help of trust measure. Numerical examples are provided to illustrate the proposed models in crisp environment as well as with unit transportation costs as rough variables.
Computational Initial Value Method for Vibration Analysis of Symmetrically Laminated Composite Plate
In the present paper, an improved initial value
numerical technique is presented to analyze the free vibration of
symmetrically laminated rectangular plate. A combination of the
initial value method (IV) and the finite differences (FD) devices is
utilized to develop the present (IVFD) technique. The achieved
technique is applied to the equation of motion of vibrating laminated
rectangular plate under various types of boundary conditions. Three
common types of laminated symmetrically cross-ply, orthotropic and
isotropic plates are analyzed here. The convergence and accuracy of
the presented Initial Value-Finite Differences (IVFD) technique have
been examined. Also, the merits and validity of improved technique
are satisfied via comparing the obtained results with those available
in literature indicating good agreements.
Tailoring the Sharpness of Tungsten Nanotips via Laser Irradiation Enhanced Etching in KOH
Controlled modification of appropriate sharpness for
nanotips is of paramount importance to develop novel materials and
functional devices at a nanometer resolution. Herein, we present a
reliable and unique strategy of laser irradiation enhanced
physicochemical etching to manufacture super sharp tungsten tips
with reproducible shape and dimension as well as high yields
(~80%). The corresponding morphology structure evolution of
tungsten tips and laser-tip interaction mechanisms were
systematically investigated and discussed using field emission
scanning electron microscope (SEM) and physical optics statistics
method with different fluences under 532 nm laser irradiation. This
work paves the way for exploring more accessible metallic tips
applications with tunable apex diameter and aspect ratio, and,
furthermore, facilitates the potential sharpening enhancement
technique for other materials used in a variety of nanoscale devices.
Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation
The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.
Higher-Dimensional Quantum Cryptography
We report on a high-speed quantum cryptography
system that utilizes simultaneous entanglement in polarization and in
“time-bins". With multiple degrees of freedom contributing to the
secret key, we can achieve over ten bits of random entropy per detected coincidence. In addition, we collect from multiple spots o
the downconversion cone to further amplify the data rate, allowing usto achieve over 10 Mbits of secure key per second.
Investigation of Short Time Scale Variation of Solar Radiation Spectrum in UV, PAR, and NIR Bands due to Atmospheric Aerosol and Water Vapor
Long terms variation of solar insolation had been
widely studied. However, its parallel observations in short time scale
is rather lacking. This paper aims to investigate the short time scale
evolution of solar radiation spectrum (UV, PAR, and NIR bands) due
to atmospheric aerosols and water vapors. A total of 25 days of
global and diffused solar spectrum ranges from air mass 2 to 6 were
collected using ground-based spectrometer with shadowband
technique. The result shows that variation of solar radiation is the
least in UV fraction, followed by PAR and the most in NIR. Broader
variations in PAR and NIR are associated with the short time scale
fluctuations of aerosol and water vapors. The corresponding daily
evolution of UV, PAR, and NIR fractions implies that aerosol and
water vapors variation could also be responsible for the deviation
pattern in the Langley-plot analysis.
Probability of Globality
The objective of global optimization is to find the
globally best solution of a model. Nonlinear models are ubiquitous
in many applications and their solution often requires a global
search approach; i.e. for a function f from a set A ⊂ Rn to
the real numbers, an element x0 ∈ A is sought-after, such that
∀ x ∈ A : f(x0) ≤ f(x). Depending on the field of application,
the question whether a found solution x0 is not only a local minimum
but a global one is very important.
This article presents a probabilistic approach to determine the
probability of a solution being a global minimum. The approach is
independent of the used global search method and only requires a
limited, convex parameter domain A as well as a Lipschitz continuous
function f whose Lipschitz constant is not needed to be known.
Wave Vortex Parameters as an Indicator of Breaking Intensity
The study of the geometric shape of the plunging wave enclosed vortices as a possible indicator for the breaking intensity of ocean waves has been ongoing for almost 50 years with limited success. This paper investigates the validity of using the vortex ratio and vortex angle as methods of predicting breaking intensity. Previously published works on vortex parameters, based on regular wave flume results or solitary wave theory, present contradictory results and conclusions. Through the first complete analysis of field collected irregular wave breaking vortex parameters it is illustrated that the vortex ratio and vortex angle cannot be accurately predicted using standard breaking wave characteristics and hence are not suggested as a possible indicator for breaking intensity.
Optimization of a Hybrid Wind-Pv-Diesel Standalone System: Case Chlef, Algeria
In this work, an attempt is made to design an optimal
wind/pv/diesel hybrid power system for a village of Ain Merane,
Chlef, Algeria, where the wind speed and solar radiation
measurements were made. The aim of this paper is the optimization
of a hybrid wind/solar/diesel system applied in term of technical and
economic feasibility by simulation using HOMER. A comparison
was made between the performance of wind/pv/diesel system and the
classic connecting system.
Main Variables Competition in DFB Lasers under Dual Optical Injection
We theoretically investigate the effects of frequency
detuning and injection power on the nonlinear dynamics of DFB
lasers under dual external optical injection.
Photonic Crystal Waveguide 1x3 Flexible Power Splitter for Optical Network
A compact 1x3 power splitter based on Photonic
Crystal Waveguides (PCW) with flexible power splitting ratio is
presented in this paper. Multimode interference coupler (MMI) is
integrated with PCW. The device size reduction compared with the
conventional MMI power splitter is attributed to the large dispersion
of the PCW. Band Solve tool is used to calculate the band structure of
PCW. Finite Difference Time Domain (FDTD) method is adopted to
simulate the relevant structure at 1550nm wavelength. The device is
polarization insensitive and allows the control of output (o/p) powers
within certain percentage points for both polarizations.
Structural and Optical Characterizations of CIGST Solar Cell Materials
Structural and UV/Visible optical properties can be
useful to describe a material for the CIGS solar cell active layer,
therefore, this work demonstrates the properties like surface
morphology, X-ray Photoelectron Spectroscopy (XPS) bonding
energy (EB) core level spectra, UV/Visible absorption spectra,
refractive index (n), optical energy band (Eg), reflection spectra for
the Cu25 (In16Ga9) Se40Te10 (CIGST-1) and Cu20 (In14Ga9) Se45Te12
(CIGST-2) chalcogenide compositions. Materials have been
exhibited homogenous surface morphologies, broading /-or diffusion
of bonding energy peaks relative elemental values and a high
UV/Visible absorption tendency in the wave length range 400 nm-
850 nm range with the optical energy band gaps 1.37 and 1.42
respectively. Subsequently, UV/Visible reflectivity property in the
wave length range 250 nm to 320 nm for these materials has also
Effect of Gravity Modulation on Weakly Non-Linear Stability of Stationary Convection in a Dielectric Liquid
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.
Computational and Experimental Investigation of Supersonic Flow and their Controls
Supersonic open and closed cavity flows are investigated experimentally and computationally. Free stream Mach number of two is set. Schlieren imaging is used to visualise the flow behaviour showing stark differences between open and closed. Computational Fluid Dynamics (CFD) is used to simulate open cavity of flow with aspect ratio of 4. A rear wall treatment is implemented in order to pursue a simple passive control approach. Good qualitative agreement is achieved between the experimental flow visualisation and the CFD in terms of the expansion-shock waves system. The cavity oscillations are shown to be dominated by the first and third Rossister modes combining to high fluctuations of non-linear nature above the cavity rear edge. A simple rear wall treatment in terms of a hole shows mixed effect on the flow oscillations, RMS contours, and time history density fluctuations are given and analysed.
Numerical Method Based On Initial Value-Finite Differences for Free Vibration of Stepped Thickness Plates
The main objective of the present paper is to derive an easy numerical technique for the analysis of the free vibration through the stepped regions of plates. Based on the utilities of the step by step integration initial values IV and Finite differences FD methods, the present improved Initial Value Finite Differences (IVFD) technique is achieved. The first initial conditions are formulated in convenient forms for the step by step integrations while the upper and lower edge conditions are expressed in finite difference modes. Also compatibility conditions are created due to the sudden variation of plate thickness. The present method (IVFD) is applied to solve the fourth order partial differential equation of motion for stepped plate across two different panels under the sudden step compatibility in addition to different types of end conditions. The obtained results are examined and the validity of the present method is proved showing excellent efficiency and rapid convergence.
Variational Iteration Method for the Solution of Boundary Value Problems
In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.
Gravitino Dark Matter in (nearly) SLagy D3/D7 m-Split SUSY
In the context of large volume Big Divisor (nearly)
SLagy D3/D7 μ-Split SUSY , after an explicit identification
of first generation of SM leptons and quarks with fermionic superpartners
of four Wilson line moduli, we discuss the identification of
gravitino as a potential dark matter candidate by explicitly calculating
the decay life times of gravitino (LSP) to be greater than age of
universe and lifetimes of decays of the co-NLSPs (the first generation
squark/slepton and a neutralino) to the LSP (the gravitino) to be
very small to respect BBN constraints. Interested in non-thermal
production mechanism of gravitino, we evaluate the relic abundance
of gravitino LSP in terms of that of the co-NLSP-s by evaluating
their (co-)annihilation cross sections and hence show that the former
satisfies the requirement for a potential Dark Matter candidate. We
also show that it is possible to obtain a 125 GeV light Higgs in our
Spurious Crests in Second-Order Waves
Occurrences of spurious crests on the troughs of large,
relatively steep second-order Stokes waves are anomalous and not an
inherent characteristic of real waves. Here, the effects of such
occurrences on the statistics described by the standard second-order
stochastic model are examined theoretically and by way of
simulations. Theoretical results and simulations indicate that when
spurious occurrences are sufficiently large, the standard model leads
to physically unrealistic surface features and inaccuracies in the
statistics of various surface features, in particular, the troughs and
thus zero-crossing heights of large waves. Whereas inaccuracies can
be fairly noticeable for long-crested waves in both deep and
shallower depths, they tend to become relatively insignificant in
Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method
The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.
The Bipartite Ramsey Numbers b(C2m; C2n)
Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b such that any subgraph G of the complete bipartite graph Kb,b, either G contains a copy of H1 or its complement relative to Kb,b contains a copy of H2. It is known that b(K2,2;K2,2) = 5, b(K2,3;K2,3) = 9, b(K2,4;K2,4) = 14 and b(K3,3;K3,3) = 17. In this paper we study the case that both H1 and H2 are even cycles, prove that b(C2m;C2n) ≥ m + n - 1 for m = n, and b(C2m;C6) = m + 2 for m ≥ 4.
The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation
In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
An Analytical Method to Analysis of Foam Drainage Problem
In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.
Periodic Orbits in a Delayed Nicholson's Blowflies Model
In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.
Bifurcations for a FitzHugh-Nagumo Model with Time Delays
In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.
Characterization of Solutions of Nonsmooth Variational Problems and Duality
In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established.
A Computational Fluid Dynamic Model of Human Sniffing
The objective of this paper is to develop a computational model of human nasal cavity from computed tomography (CT) scans using MIMICS software. Computational fluid dynamic techniques were employed to understand nasal airflow. Gambit and Fluent software was used to perform CFD simulation. Velocity profiles, iteration plots, pressure distribution, streamline and pathline patterns for steady, laminar airflow inside the human nasal cavity of healthy and also infected persons are presented in detail. The implications for olfaction are visualized. Results are validated with the available numerical and experimental data. The graphs reveal that airflow varies with different anatomical nasal structures and only fraction of the inspired air reaches the olfactory region. The Deviations in the results suggest that the treatment of infected volunteers will improve the olfactory function.
Anomalous Thermal Behavior of CuxMg1-xNb2O6 (x=0,0.4,0.6,1) for LTCC Substrate
LTCC (Low Temperature Co-fired Ceramics) being the most advantageous technology towards the multilayer substrates for various applications, demands an extensive study of its raw materials. In the present work, a series of CuxMg1-xNb2O6 (x=0,0.4,0.6,1) has been prepared using sol-gel synthesis route and sintered at a temperature of 900°C to study its applicability for LTCC technology as the firing temperature is 900°C in this technology. The phase formation has been confirmed using X-ray Diffraction. Thermal properties like thermal conductivity and thermal expansion being very important aspect as the former defines the heat flow to avoid thermal instability in layers and the later provides the dimensional congruency of the dielectric material and the conductors, are studied here over high temperature up to the firing temperature. Although the values are quite satisfactory from substrate requirement point view, results have shown anomaly over temperature. The anomalous thermal behavior has been further analyzed using TG-DTA.
A Simplified Higher-Order Markov Chain Model
In this paper, we present a simplified higher-order Markov chain model for multiple categorical data sequences also called as simplified higher-order multivariate Markov chain model.
Two Different Computing Methods of the Smith Arithmetic Determinant
The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.
On the Hierarchical Ergodicity Coefficient
In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.
Effect of Time-Periodic Boundary Temperature on the Onset of Nanofluid Convection in a Layer of a Saturated Porous Medium
The linear stability of nanofluid convection in a horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. The model used for the nanofluid incorporates the effects of Brownian motion and thermopherosis, while the Darcy model is used for the porous medium. The analysis revels that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles. The contribution of nanoparticles to the thermal energy equation being a second-order effect. It is found that the critical thermal Rayleigh number can be found reduced or decreased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution, phase angle and frequency of modulation.