Search results for: Schrodinger’s wave equations

Authors: Zuhier Altawallbeh

Abstract:

This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Bruno Coelho Lima, Joao F.A. Martos, Paulo G. P. Toro, Israel S. Rego

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The shock tube is a ground-facility widely used in aerospace and aeronautics science and technology for studies on gas dynamic and chemical-physical processes in gases at high-temperature, explosions and dynamic calibration of pressure sensors. A shock tube in its simplest form is comprised of two separate tubes of equal cross-section by a diaphragm. The diaphragm function is to separate the two reservoirs at different pressures. The reservoir containing high pressure is called the Driver, the low pressure reservoir is called Driven. When the diaphragm is broken by pressure difference, a normal shock wave and non-stationary (named Incident Shock Wave) will be formed in the same place of diaphragm and will get around toward the closed end of Driven. When this shock wave reaches the closer end of the Driven section will be completely reflected. Now, the shock wave will interact with the boundary layer that was created by the induced flow by incident shock wave passage. The interaction between boundary layer and shock wave force the separation of the boundary layer. The aim of this paper is to make an analysis of influences of separation of the boundary layer in the reservoir pressure in the shock tube. A comparison among CDF (Computational Fluids Dynamics), experiments test and analytical analysis were performed. For the analytical analysis, some routines in Python was created, in the numerical simulations (Computational Fluids Dynamics) was used the Ansys Fluent, and the experimental tests were used T1 shock tube located in IEAv (Institute of Advanced Studies).

Keywords: boundary layer separation, moving shock wave, shock tube, transient simulation

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Authors: Fathi Alwafie

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In this paper we present the simulation of the propagation characteristics of the picocellular propagation channel environment. The first aim has been to find a correct description of the environment for received wave. The result of the first investigations is that the environment of the indoor wave significantly changes as we change the electric parameters of material constructions. A modified 3D ray tracing image method tool has been utilized for the coverage prediction. A detailed analysis of the dependence of the indoor wave on the wide-band characteristics of the channel: Root Mean Square (RMS) delay spread characteristics and mean excess delay, is also investigated.

Keywords: propagation, ray tracing, network, mobile computing

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: R. E. Fat-Helbary, A. A. Abdel-latief, M. S. Arfa, Alaa Mostafa

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The Egyptian Government proposed a general plan, aiming at constructing new settlements for Nubian in south Aswan in different places around Nasser Lake, one of these settlements in Kurkur area. The Nubian habitations in Wadi Kurkur are located around 30 km southwest of Aswan City. This area are affecting by near distance earthquakes from Kalabsha faults system. The shallow seismic refraction technique was conducted at the study area, to evaluate the soil and rock material quality and geotechnical parameters, in addition to the detection of the subsurface ground model under the study area. The P and S-wave velocities were calculated. The surface layer has P-wave, velocity ranges from 900 m/sec to 1625 m/sec and S-wave velocity ranges from 650 m/sec to 1400 m/sec. On the other hand the bedrock has P-wave velocity ranges from 1300 m/sec to 1980 m/sec and S-wave velocity ranges from 1050 m/sec to1725 m/sec. Measuring Vp and Vs velocities together with bulk density are calculated and used to extract the mechanical properties and geotechnical parameters of the foundation material at the study area. Output of this study is very important for solving the problems, which associated with the construction of various civil engineering purposes, for land use planning and for earthquakes resistant structure design.

Keywords: shallow seismic refraction technique, Kurkur area, p and s-wave velocities, geotechnical parameters, bulk density, Kalabsha faults

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Fatemeh Sadat Sharifi

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In the present study, the capabilities of WAVEWATCH-III and MIKE21-SW for predicting the characteristics of wind waves in Hormuz Strait are evaluated. The GFS wind data (Global Forecast System) were derived. The bathymetry of gride with 2 arc-minute resolution, also were extracted from the ETOPO1. WAVEWATCH-III findings illustrate more valid prediction of wave features comparing to the MIKE-21 SW in deep water. Apparently, in shallow area, the MIKE-21 provides more uniformities with altimetry measurements. This may be due to the merits of the unstructured grid which are used in MIKE-21, leading to better representations of the coastal area. The findings on the direction of waves generated by wind in the modeling area indicate that in some regions, despite the increase in wind speed, significant wave height stays nearly unchanged. This is fundamental because of swift changes in wind track over the Strait of Hormuz. After discussing wind-induced waves in the region, the impact of instability of the surface layer on wave growth has been considered. For this purpose, the average monthly mean air temperature has been used. The results in cold months, when the surface layer is unstable, indicates an acceptable increase in the accuracy of prediction of the indicator wave height.

Keywords: numerical modeling, WAVEWATCH-III, Strait of Hormuz, MIKE21-SW

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Haode Huo, Jingjing He, Rui Kang, Xuefei Guan

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This paper presents a study of Lamb wave damage diagnosis of composite delamination using instantaneous phase data. Numerical experiments are performed using the finite element method. Different sizes of delamination damages are modeled using finite element package ABAQUS. Lamb wave excitation and responses data are obtained using a pitch-catch configuration. Empirical mode decomposition is employed to extract the intrinsic mode functions (IMF). Hilbert–Huang Transform is applied to each of the resulting IMFs to obtain the instantaneous phase information. The baseline data for healthy plates are also generated using the same procedure. The size of delamination is correlated with the instantaneous phase change for damage diagnosis. It is observed that the unwrapped instantaneous phase of shows a consistent behavior with the increasing delamination size.

Keywords: delamination, lamb wave, finite element method, EMD, instantaneous phase

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Chuan-Wen Liu, Min-Hsien Liu, Chung-Chieh Tai, Bing-Cheng Kuo, Cheng-Lung Chen, Huazhen Shen

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A recent surge in research on magnetic radar absorbing materials (RAMs) has presented researchers with new opportunities and challenges. This study was performed to gain a better understanding of the wave-absorbing phenomenon of magnetic RAMs. First, we hypothesized that the absorbing phenomenon is dependent on the particle shape. Using the Material Studio program and the micro-dot magnetic dipoles (MDMD) method, we obtained results from magnetic RAMs to support this hypothesis. The total MDMD energy of disk-like iron particles was greater than that of spherical iron particles. In addition, the particulate aggregation phenomenon decreases the wave-absorbance, according to both experiments and computational data. To conclude, this study may be of importance in terms of explaining the wave- absorbing characteristic of magnetic RAMs. Combining molecular dynamics simulation results and the theory of magnetization of magnetic dots, we investigated the magnetic properties of iron materials with different particle shapes and degrees of aggregation under external magnetic fields. The MDMD of the materials under magnetic fields of various strengths were simulated. Our results suggested that disk-like iron particles had a better magnetization than spherical iron particles. This result could be correlated with the magnetic wave- absorbing property of iron material.

Keywords: wave-absorbing property, magnetic material, micro-dot magnetic dipole, particulate aggregation

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Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

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The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

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Authors: Richard Mitchell, Robert Mitchell, Thai Duong, Kyungbin Bae, Daegon Kim, Youngsub Lee, Inho Kim, Inho Park, Hyungseok Lee

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Although X-band radar is commonly used to measure the properties of ocean waves, the use of a higher frequency has several advantages, such as increased backscatter coefficient, better Doppler sensitivity, lower power, and a smaller package. A low-power Ku-band radar system was developed to demonstrate these advantages. It is fully coherent, and it interleaves short and long pulses to achieve a transmit duty ratio of 25%, which makes the best use of solid-state amplifiers. The range scales are 2 km, 4 km, and 8 km. The minimum range is 100 m, 200 m, and 400 m for the three range scales, and the range resolution is 4 m, 8 m, and 16 m for the three range scales. Measurements of the significant wave height, wavelength, wave period, and wave direction have been made using traditional 3D-FFT methods. Radar and ultrasonic sensor results collected over an extended period of time at a coastal site in South Korea are presented.

Keywords: measurement of ocean wave parameters, Ku-band radar, coherent radar, compact radar

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Ruichong Zhang, Fadi Sawaged, Lotfi Gargab

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This paper introduces a wave-based approach for system identification of high-rise building structures with a pair of seismic recordings, which can be used to evaluate structural integrity and detect damage in post-earthquake structural condition assessment. The fundamental of the approach is based on wave features of generalized impulse and frequency response functions (GIRF and GFRF), i.e., wave responses at one structural location to an impulsive motion at another reference location in time and frequency domains respectively. With a pair of seismic recordings at the two locations, GFRF is obtainable as Fourier spectral ratio of the two recordings, and GIRF is then found with the inverse Fourier transformation of GFRF. With an appropriate continuous model for the structure, a closed-form solution of GFRF, and subsequent GIRF, can also be found in terms of wave transmission and reflection coefficients, which are related to structural physical properties above the impulse location. Matching the two sets of GFRF and/or GIRF from recordings and the model helps identify structural parameters such as wave velocity or shear modulus. For illustration, this study examines ten-story Millikan Library in Pasadena, California with recordings of Yorba Linda earthquake of September 3, 2002. The building is modelled as piecewise continuous layers, with which GFRF is derived as function of such building parameters as impedance, cross-sectional area, and damping. GIRF can then be found in closed form for some special cases and numerically in general. Not only does this study reveal the influential factors of building parameters in wave features of GIRF and GRFR, it also shows some system-identification results, which are consistent with other vibration- and wave-based results. Finally, this paper discusses the effectiveness of the proposed model in system identification.

Keywords: wave-based approach, seismic responses of buildings, wave propagation in structures, construction

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Deborah Eric, Abbas Ahmad Khan

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Lead halide perovskites quantum dots have attracted immense scientific and technological interest for successful photovoltaic applications because of their remarkable optoelectronic properties. In this paper, we have simulated CsMAPbI3-xBrx based quantum dots to implement their use in intermediate band solar cells (IBSC). These types of materials exhibit optical and electrical properties distinct from their bulk counterparts due to quantum confinement. The conceptual framework provides a route to analyze the electronic properties of quantum dots. This layer of quantum dots optimizes the position and bandwidth of IB that lies in the forbidden region of the conventional bandgap. A three-dimensional MAPbI3 quantum dot (QD) with geometries including spherical, cubic, and conical has been embedded in the CsPbBr3 matrix. Bound energy wavefunction gives rise to miniband, which results in the formation of IB. If there is more than one miniband, then there is a possibility of having more than one IB. The optimization of QD size results in more IBs in the forbidden region. One band time-independent Schrödinger equation using the effective mass approximation with step potential barrier is solved to compute the electronic states. Envelope function approximation with BenDaniel-Duke boundary condition is used in combination with the Schrödinger equation for the calculation of eigen energies and Eigen energies are solved for the quasi-bound states using an eigenvalue study. The transfer matrix method is used to study the quantum tunneling of MAPbI3 QD through neighbor barriers of CsPbI3. Electronic states are computed using Schrödinger equation with effective mass approximation by considering quantum dot and wetting layer assembly. Results have shown the varying the quantum dot size affects the energy pinning of QD. Changes in the ground, first, second state energies have been observed. The QD is non-zero at the center and decays exponentially to zero at boundaries. Quasi-bound states are characterized by envelope functions. It has been observed that conical quantum dots have maximum ground state energy at a small radius. Increasing the wetting layer thickness exhibits energy signatures similar to bulk material for each QD size.

Keywords: perovskite, intermediate bandgap, quantum dots, miniband formation

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Authors: Ganesh Nandakumaran, Mehmet Karaata

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A wave is a distributed execution, often made up of a broadcast phase followed by a feedback phase, requiring the participation of all the system processes before a particular event called decision is taken. Wave algorithms with one initiator such as the 1-wave algorithm have been shown to be very efficient for broadcasting messages in tree networks. Extensions of this algorithm broadcasting a sequence of waves using a single initiator have been implemented in algorithms such as the m-wave algorithm. However as the network size increases, having a single initiator adversely affects the message delivery times to nodes further away from the initiator. As a remedy, broadcast waves can be allowed to be initiated by multiple initiator nodes distributed across the network to reduce the completion time of broadcasts. These waves initiated by one or more initiator processes form a collection of waves covering the entire network. Solutions to global-snapshots, distributed broadcast and various synchronization problems can be solved efficiently using waves with multiple concurrent initiators. In this paper, we propose the first stabilizing multi-wave sequence algorithm implementing waves started by multiple initiator processes such that every process in the network receives at least one sequence of broadcasts. Due to being stabilizing, the proposed algorithm can withstand transient faults and do not require initialization. We view a fault as a transient fault if it perturbs the configuration of the system but not its program.

Keywords: distributed computing, multi-node broadcast, propagation of information with feedback and cleaning (PFC), stabilization, wave algorithms

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Authors: Shamsul Chowdhury

Abstract:

The objective of this paper is to present the detailed analysis of the turbulent wave boundary layer produced by progressive finite-amplitude waves theory. Most of the works have done for the mass transport in the turbulent boundary layer assuming the eddy viscosity is not time varying, where the sediment movement is induced by the mean velocity. Near the ocean bottom, the waves produce a thin turbulent boundary layer, where the flow is highly rotational, and shear stress associated with the fluid motion cannot be neglected. The magnitude and the predominant direction of the sediment transport near the bottom are known to be closely related to the flow in the wave induced boundary layer. The magnitude of water particle velocity at the Crest phase differs from the one of the Trough phases due to the non-linearity of the waves, which plays an important role to determine the sediment movement. The non-linearity of the waves become predominant in the surf zone area, where the sediment movement occurs vigorously. Therefore, in order to describe the flow near the bottom and relationship between the flow and the movement of the sediment, the analysis was done using the non-linear boundary layer equation and the finite amplitude wave theory was applied to represent the velocity fields in the turbulent wave boundary layer. At first, the calculation was done for turbulent wave boundary layer by two-dimensional model where throughout the calculation is non-linear. But Stokes second order wave profile is adopted at the upper boundary. The calculated profile was compared with the experimental data. Finally, the calculation is done based on various modes of the velocity and turbulent energy. The mean velocity is found to differ from condition of the relative depth and the roughness. It is also found that due to non-linearity, the absolute value for velocity and turbulent energy as well as Reynolds stress are asymmetric. The mean velocity of the laminar boundary layer is always positive but in the turbulent boundary layer plays a very complicated role.

Keywords: wave boundary, mass transport, mean velocity, shear stress

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Authors: Alireza Abbasi Moshaii, Shaghayegh Nasiri, Mehdi Tale Masouleh

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The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3-RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. Mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, their CAD model has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: robotic, static analysis, 3-RCC, 3-RRS

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Authors: Alireza Abdikian

Abstract:

By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: O. Rahli, N. Mimouni, R. Bennacer, K. Bouhadef

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This numerical study investigates the travelling wave’s appearance and the behavior of Poiseuille-Rayleigh-Benard (PRB) flow induced in 3D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The governing equations are discretized by using a control volume method with third order Quick scheme in approximating the advection terms. Simpler algorithm is used to handle coupling between the momentum and continuity equations. To avoid the excessively high computer time, full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For a broad range of dimensionless controlling parameters, the contribution of this work is to analyzing the flow regimes of the steady longitudinal thermoconvective rolls (noted R//) for both thermal and mass transfer (TSMC). The transition from the opposed volume forces to cooperating ones, considerably affects the birth and the development of the longitudinal rolls. The heat and mass transfers distribution are also examined.

Keywords: heat and mass transfer, mixed convection, poiseuille-rayleigh-benard flow, rectangular duct

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Authors: Lizhou Chen, Abdelhamid Belgaid, Assem Elsayed, Xiaoming Yang

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Compression index is essential in foundation settlement calculation. The traditional method for determining compression index is consolidation test which is expensive and time consuming. Many researchers have used regression methods to develop empirical equations for predicting compression index from soil properties. Based on a large number of compression index data collected from consolidation tests, the accuracy of some popularly empirical equations were assessed. It was found that primary compression index is significantly overestimated in some equations while it is underestimated in others. The sensitivity analyses of soil parameters including water content, liquid limit and void ratio were performed. The results indicate that the compression index obtained from void ratio is most accurate. The ANOVA (analysis of variance) demonstrates that the equations with multiple soil parameters cannot provide better predictions than the equations with single soil parameter. In other words, it is not necessary to develop the relationships between compression index and multiple soil parameters. Meanwhile, it was noted that secondary compression index is approximately 0.7-5.0% of primary compression index with an average of 2.0%. In the end, the proposed prediction equations using power regression technique were provided that can provide more accurate predictions than those from existing equations.

Keywords: compression index, clay, settlement, consolidation, secondary compression index, soil parameter

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Authors: Magdy G. Asaad

Abstract:

Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted.

Keywords: Pfaffian solutions, N-soliton solutions, soliton equations, Jimbo-Miwa

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Authors: Shiuh-Kuang Yang, Sheam-Chyun Lin, Jyin-Wen Cheng, Deng-Guei Hsu

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The torsional mode of guided wave, T(0,1), has been applied to detect characteristics and defects in pipelines, especially in the cases of coated, elevated and buried pipes. The signals of minor corrosions would be covered by the noise, unfortunately, because the coated material and buried medium always induce a strong attenuation of the guided wave. Furthermore, the guided wave would be attenuated more seriously and make the signals hard to be identified when setting the array ring of the transducers on a general corrosion area of the pipe. The objective of this study is then to discuss the effects of the above-mentioned general corrosion on guided wave tests by experiments and signal processing techniques, based on the use of the finite element method, the two-dimensional Fourier transform and the continuous wavelet transform. Results show that the excitation energy would be reduced when the array ring set on the pipe surface having general corrosion. The non-uniformed contact surface also produces the unwanted asymmetric modes of the propagating guided wave. Some of them are even mixing together with T(0,1) mode and increase the difficulty of measurements, especially when a defect or local corrosion merged in the general corrosion area. It is also showed that the guided waves attenuation are increasing with the increasing corrosion depth or the rising inspection frequency. However, the coherent signals caused by the general corrosion would be decayed with increasing frequency. The results obtained from this research should be able to provide detectors to understand the impact when the array ring set on the area of general corrosion and the way to distinguish the localized corrosion which is inside the area of general corrosion.

Keywords: guided wave, finite element method, two-dimensional fourier transform, wavelet transform, general corrosion, localized corrosion

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Authors: Adewoyin O. Olusegun, Akinwumi I. Isaac

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In some part of the world where legislations related to site investigations before constructions are not strictly enforced, the expenses and time required for carrying out a comprehensive geotechnical investigation to characterize a site can discourage prospective private residential building developers. Another factor that can discourage a developer is the fact that most of the geotechnical tests procedures utilized during site investigations, to a certain extent, alter the existing environment of the site. This study suggests a quick, non-destructive and non-intrusive method of obtaining key subsoil geotechnical properties necessary for foundation design for proposed engineering facilities. Seismic wave velocities generated from near surface refraction method was used to determine the bulk density of soil, Young’s modulus, bulk modulus, shear modulus and allowable bearing capacity of a competent layer that can bear structural load at the particular study site. Also, regression equations were developed in order to directly obtain the bulk density of soil, Young’s modulus, bulk modulus, shear modulus and allowable bearing capacity from the compressional wave velocities. The results obtained correlated with the results of standard geotechnical investigations carried out.

Keywords: characterize, environment, geophysical, geotechnical, regression

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