Search results for: Schrödinger wave equation

Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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Authors: Hsuan-Ku Liu, Ming Long Liu

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In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Arvind Srivastav, Tarun Kanti Bhattacharyya

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The north-eastern, Himalayan, and Eastern Ghats Belt of India comprise of earthquake-prone, remote, and hilly terrains. Earthquakes have caused enormous damages in these regions in the past. A wireless sensor network based earthquake early warning system (EEWS) is being developed to mitigate the damages caused by earthquakes. It consists of sensor nodes, distributed over the region, that perform majority voting of the output of the seismic sensors in the vicinity, and relay a message to a base station to alert the residents when an earthquake is detected. At the heart of the EEWS is a low-power two-stage seismic sensor that continuously tracks seismic events from incoming three-axis accelerometer signal at the first-stage, and, in the presence of a seismic event, triggers the second-stage P-wave detector that detects the onset of P-wave in an earthquake event. The parameters of the P-wave detector have been optimized for minimizing detection time and maximizing the accuracy of detection.Working of the sensor scheme has been verified with seven earthquakes data retrieved from IRIS. In all test cases, the scheme detected the onset of P-wave accurately. Also, it has been established that the P-wave onset detection time reduces linearly with the sampling rate. It has been verified with test data; the detection time for data sampled at 10Hz was around 2 seconds which reduced to 0.3 second for the data sampled at 100Hz.

Keywords: Earthquake early warning system, EEWS, STA/LTA, polarization, wavelet, event detector, P-wave detector.

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Authors: Yanling Zhu

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In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.

Keywords: Method of moments, General theory of relativity, Electromagnetism, Metric tensor, schwarzchild metric, Wave Equation.

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Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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Authors: Ke Wang, Zhi-Qiang Zhang, Z. Chen

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A submerged horizontal plate type breakwater is pointed out as an efficient wave protection device for cage culture in marine fishery. In order to reveal the wave elimination principle of this type breakwater, boundary element method is utilized to investigate this problem. The flow field and the trajectory of water particles are studied carefully. The flow field analysis shows that: the interaction of incident wave and adverse current above the plate disturbs the water domain drastically. This can slow down the horizontal velocity and vertical velocity of the water particles.

Keywords: boundary element method, plate type breakwater, flow field analysis

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Authors: Nguyen Thu Huong, Nguyen Quang Bau

Abstract:

The Hall Coefficient (HC) and the Magnetoresistance (MR) have been studied in two-dimensional systems. The HC and the MR in Rectangular Quantum Wire (RQW) subjected to a crossed DC electric field and magnetic field in the presence of a Strong Electromagnetic Wave (EMW) characterized by electric field are studied in this work. Using the quantum kinetic equation for electrons interacting with optical phonons, we obtain the analytic expressions for the HC and the MR with a dependence on magnetic field, EMW frequency, temperatures of systems and the length characteristic parameters of RQW. These expressions are different from those obtained for bulk semiconductors and cylindrical quantum wires. The analytical results are applied to GaAs/GaAs/Al. For this material, MR depends on the ratio of the EMW frequency to the cyclotron frequency. Indeed, MR reaches a minimum at the ratio 5/4, and when this ratio increases, it tends towards a saturation value. The HC can take negative or positive values. Each curve has one maximum and one minimum. When magnetic field increases, the HC is negative, achieves a minimum value and then increases suddenly to a maximum with a positive value. This phenomenon differs from the one observed in cylindrical quantum wire, which does not have maximum and minimum values.

Keywords: Hall coefficient, rectangular quantum wires, electron-optical phonon interaction, quantum kinetic equation.

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Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

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In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

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Authors: S. Ayub, S.N. Danish, S.R. Qureshi

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The world's population continues to grow at a quarter of a million people per day, increasing the consumption of energy. This has made the world to face the problem of energy crisis now days. In response to the energy crisis, the principles of renewable energy gained popularity. There are much advancement made in developing the wind and solar energy farms across the world. These energy farms are not enough to meet the energy requirement of world. This has attracted investors to procure new sources of energy to be substituted. Among these sources, extraction of energy from the waves is considered as best option. The world oceans contain enough energy to meet the requirement of world. Significant advancements in design and technology are being made to make waves as a continuous source of energy. One major hurdle in launching wave energy devices in a developing country like Pakistan is the initial cost. A simple, reliable and cost effective wave energy converter (WEC) is required to meet the nation-s energy need. This paper will present a novel design proposed by team SAS for harnessing wave energy. This paper has three major sections. The first section will give a brief and concise view of ocean wave creation, propagation and the energy carried by them. The second section will explain the designing of SAS-2. A gear chain mechanism is used for transferring the energy from the buoy to a rotary generator. The third section will explain the manufacturing of scaled down model for SAS-2 .Many modifications are made in the trouble shooting stage. The design of SAS-2 is simple and very less maintenance is required. SAS-2 is producing electricity at Clifton. The initial cost of SAS-2 is very low. This has proved SAS- 2 as one of the cost effective and reliable source of harnessing wave energy for developing countries.

Keywords: Clean Energy, Wave energy

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Authors: Awadhesh Pachauri, Manabendra Bhuyan

Abstract:

Electrocardiogram (ECG) is considered to be the backbone of cardiology. ECG is composed of P, QRS & T waves and information related to cardiac diseases can be extracted from the intervals and amplitudes of these waves. The first step in extracting ECG features starts from the accurate detection of R peaks in the QRS complex. We have developed a robust R wave detector using wavelets. The wavelets used for detection are Daubechies and Symmetric. The method does not require any preprocessing therefore, only needs the ECG correct recordings while implementing the detection. The database has been collected from MIT-BIH arrhythmia database and the signals from Lead-II have been analyzed. MatLab 7.0 has been used to develop the algorithm. The ECG signal under test has been decomposed to the required level using the selected wavelet and the selection of detail coefficient d4 has been done based on energy, frequency and cross-correlation analysis of decomposition structure of ECG signal. The robustness of the method is apparent from the obtained results.

Keywords: ECG, P-QRS-T waves, Wavelet Transform, Hard Thresholding, R-wave Detection.

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Authors: Fred Lacy

Abstract:

Electrical resistivity is a fundamental parameter of metals or electrical conductors. Since resistivity is a function of temperature, in order to completely understand the behavior of metals, a temperature dependent theoretical model is needed. A model based on physics principles has recently been developed to obtain an equation that relates electrical resistivity to temperature. This equation is dependent upon a parameter associated with the electron travel time before being scattered, and a parameter that relates the energy of the atoms and their separation distance. Analysis of the energy parameter reveals that the equation is optimized if the proportionality term in the equation is not constant but varies over the temperature range. Additional analysis reveals that the theoretical equation can be used to determine the mean free path of conduction electrons, the number of defects in the atomic lattice, and the ‘equivalent’ charge associated with the metallic bonding of the atoms. All of this analysis provides validation for the theoretical model and provides insight into the behavior of metals where performance is affected by temperatures (e.g., integrated circuits and temperature sensors).

Keywords: Callendar–van Dusen, conductivity, mean free path, resistance temperature detector, temperature sensor.

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

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In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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Authors: Peter N. Khakina, Mohammed I. Ali, Enchun Zhu, Huazhang Zhou, Baydaa H. Moula

Abstract:

Rise/span ratio has been mentioned as one of the reasons which contribute to the lower buckling load as compared to the Classical theory buckling load but this ratio has not been quantified in the equation. The purpose of this study was to determine a more realistic buckling load by quantifying the effect of the rise/span ratio because experiments have shown that the Classical theory overestimates the load. The buckling load equation was derived based on the theorem of work done and strain energy. Thereafter, finite element modeling and simulation using ABAQUS was done to determine the variables that determine the constant in the derived equation. The rise/span was found to be the determining factor of the constant in the buckling load equation. The derived buckling load correlates closely to the load obtained from experiments.

Keywords: Buckling, Finite element, Rise/span ratio, Sphericalcap

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Authors: Nguyen Quang Bau, Nguyen Thu Huong, Dang Thi Thanh Thuy

Abstract:

The analytic expression for the Hall Coefficient (HC) caused by the confined electrons in the presence of a strong electromagnetic wave (EMW) including the effect of phonon confinement in rectangular quantum wires (RQWs) is calculated by using the quantum kinetic equation for electrons in the case of electron - optical phonon scattering. It is because the expression of the HC for the confined phonon case contains indexes m, m’ which are specific to the phonon confinement. The expression in a RQW is different from that for the case of unconfined phonons in a RQW or in 2D. The results are numerically calculated and discussed for a GaAs/GaAsAl RQW. The numerical results show that HC in a RQW can have both negative and positive values. This is different from the case of the absence of EMW and the case presence of EMW including the effect of phonon unconfinement in a RQW. These results are also compared with those in the case of unconfined phonons in a RQW and confined phonons in a quantum well. The conductivity in the case of confined phonon has more resonance peaks compared with that in case of unconfined phonons in a RQW. This new property is the same in quantum well. All results are compared with the case of unconfined phonons to see differences.

Keywords: Hall coefficient, rectangular quantum wires, electron-optical phonon interaction, quantum kinetic equation, confined phonons.

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Authors: G. Toker, V. Bulatov, T. Kovalchuk, I. Schechter

Abstract:

Dynamics of laser radiation – metal target interaction in water at 1064 nm by applying Mach-Zehnder interference technique was studied. The mechanism of generating the well developed regime of evaporation of a metal surface and a spherical shock wave in water is proposed. Critical intensities of the NIR for the well developed evaporation of silver and gold targets were determined. Dynamics of shock waves was investigated for earlier (dozens) and later (hundreds) nanoseconds of time. Transparent expanding plasma-vapor-compressed water object was visualized and measured. The thickness of compressed layer of water and pressures behind the front of a shock wave for later time delays were obtained from the optical treatment of interferograms.

Keywords: laser, shock wave, metal target, underwater

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Authors: Xiguang Li

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.

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Authors: Srinivasan Chandrasekaran, Shihas A. Khader

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Motion response of floating structures is of great concern in marine engineering. Nonlinearity is an inherent property of any floating bodies subjected to irregular waves. These floating structures are continuously subjected to environmental loadings from wave, current, wind etc. This can result in undesirable motions of the vessel which may challenge the operability. For a floating body to remain in its position, it should be able to induce a restoring force when displaced. Mooring is provided to enable this restoring force. This paper discusses the hydrodynamic performance and motion characteristics of an 8 point spread mooring system applied to a pipe laying barge operating in the West African sea. The modelling of the barge is done using a computer aided-design (CAD) software RHINOCEROS. Irregular waves are generated using a suitable wave spectrum. Both frequency domain and time domain analysis is done. Numerical simulations based on potential theory are carried out to find the responses and hydrodynamic performance of the barge in both free floating as well as moored conditions. Initially, potential flow frequency domain analysis is done to obtain the Response Amplitude Operator (RAO) which gives an idea about the structural motion in free floating state. RAOs for different wave headings are analyzed. In the following step, a time domain analysis is carried out to obtain the responses of the structure in the moored condition. In this study, wave induced motions are only taken into consideration. Wind and current loads are ruled out and shall be included in further studies. For the current study, 2000 seconds simulation is taken. The results represent wave induced motion responses, mooring line tensions and identify critical mooring lines.

Keywords: Irregular wave, moored barge, time domain analysis, numerical simulation.

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: Analytical method, mechanical responses, spherical wave propagation, traumatic brain injury.

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Authors: Ning Dong, Bo Yu

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We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algorithm.

Keywords: Fast algorithm, Cyclic reduction, Overdampedquadratic matrix equation, Structure-preserving doubling algorithm

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Authors: Sikder Mohammad Faruk, Mir Mofajjal Hossain, Muhibul Haque Bhuyan

Abstract:

In this investigative research paper, we have presented the simulation results of a three-phase rectifier circuit to improve the input side current using the passive filters, such as capacitors and inductors at the output and input terminals of the rectifier circuit respectively. All simulation works were performed in a personal computer using the PSPICE simulator software, which is a virtual circuit design and simulation software package. The output voltages and currents were measured across a resistive load of 1 k. We observed that the output voltage levels, input current wave shapes, harmonic contents through the harmonic spectrum, and total harmonic distortion improved due to the use of such filters.

Keywords: input current wave, three-phase rectifier, passive filter, PSPICE Simulation

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

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Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: Standard finite difference schemes, non–standard schemes, Laplace equation, Dirichlet boundary conditions.

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Authors: A. Bekbaev, M. Dzhamanbaev, R. Abitaeva, A. Karbozova, G. Nabyeva

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In this paper, the regression dependence of dancing intensity from wind speed and length of span was established due to the statistic data obtained from multi-year observations on line wires dancing accumulated by power systems of Kazakhstan and the Russian Federation. The lower and upper limitations of the equations parameters were estimated, as well as the adequacy of the regression model. The constructed model will be used in research of dancing phenomena for the development of methods and means of protection against dancing and for zoning plan of the territories of line wire dancing.

Keywords: Power lines, line wire dancing, dancing intensity, regression equation, dancing area intensity.

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Authors: Noha M. Rashad, W. Swelam, M. H. Abd ElAzeem

Abstract:

A simple design of array antenna is presented in this paper, supporting millimeter wave applications which can be used in short range wireless communications such as 5G applications. This design enhances the use of V-band, according to IEEE standards, as the antenna works in the 70 GHz band with bandwidth more than 11 GHz and peak gain more than 13 dBi. The design is simulated using different numerical techniques achieving a very good agreement.

Keywords: 5G Technology, array antenna, microstrip, millimeter wave.

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

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We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: Run-up waves, Shallow water equations, finite volume method, wet/dry interface, dam-break problem.

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Authors: M. M. Selim

Abstract:

The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflection coefficients of P and SV waves- incident at the free surface of an initially stressed dissipative medium are obtained. Numerical computations, using these expressions, are carried out for a particular model. Computations made with the results predicted in presence and absence of the initial stresses and the results have been shown graphically. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). Also the numerical results presented indicate that initial stresses and dissipation might affect the reflection coefficients significantly.

Keywords: Dissipation medium, initial stress, longitudinal waves, reflection coefficients, reflection of plane waves, transverse waves.

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Authors: Surender Singh Jadav, Venkatesan Jayaprakash, Arijit Basu, Barij Nayan Sinha

Abstract:

Chikungunya virus (CHICKV) is an arboviruses belonging to family Tagoviridae and is transmitted to human through by mosquito (Aedes aegypti and Aedes albopictus) bite. A large outbreak of chikungunya has been reported in India between 2006 and 2007, along with several other countries from South-East Asia and for the first time in Europe. It was for the first time that the CHICKV outbreak has been reported with mortality from Reunion Island and increased mortality from Asian countries. CHICKV affects all age groups, and currently there are no specific drugs or vaccine to cure the disease. The need of antiviral agents for the treatment of CHICKV infection and the success of virtual screening against many therapeutically valuable targets led us to carry out the structure based drug design against Chikungunya nSP2 protease (PDB: 3TRK). Highthroughput virtual screening of publicly available databases, ZINC12 and BindingDB, has been carried out using the Openeye tools and Schrodinger LLC software packages. Openeye Filter program has been used to filter the database and the filtered outputs were docked using HTVS protocol implemented in GLIDE package of Schrodinger LLC. The top HITS were further used for enriching the similar molecules from the database through vROCS; a shape based screening protocol implemented in Openeye. The approach adopted has provided different scaffolds as HITS against CHICKV protease. Three scaffolds: Indole, Pyrazole and Sulphone derivatives were selected based on the docking score and synthetic feasibility. Derivatives of Pyrazole were synthesized and submitted for antiviral screening against CHICKV.

Keywords: Chikungunya, nsP2 protease, ADME filter, HTVS, Docking, Active site.

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