Search results for: visco acoustic wave equation

Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Patcharin Saechan, Isares Dhuchakallaya

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Thermoacoustic refrigerator is a cooling device which uses the acoustic waves to produce the cooling effect. The aim of this paper is to explore the experimental and numerical feasibility of a standing-wave thermoacoustic refrigerator. The effects of the stack length, position of stack and operating frequency on the cooling performance are carried out. The circular pore stacks are tested under the atmospheric pressure. A low-cost loudspeaker is used as an acoustic driver. The results show that the location of stack installed in resonator tube has a greater effect on the cooling performance than the stack length and operating frequency, respectively. The temperature difference across the ends of the stack can be generated up to 13.7°C, and the temperature of cold-end is dropped down by 5.3°C from the ambient temperature.

Keywords: cooling performance, refrigerator, standing-wave, thermoacoustics

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: S. M. Giripunje, Mohit Kumar

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Acoustic energy that exists in our everyday life and environment have been overlooked as a green energy that can be extracted, generated, and consumed without any significant negative impact to the environment. The harvested energy can be used to enable new technology like wireless sensor networks. Technological developments in the realization of truly autonomous MEMS devices and energy storage systems have made acoustic energy harvesting (AEH) an increasingly viable technology. AEH is the process of converting high and continuous acoustic waves from the environment into electrical energy by using an acoustic transducer or resonator. AEH is not popular as other types of energy harvesting methods since sound waves have lower energy density and such energy can only be harvested in very noisy environment. However, the energy requirements for certain applications are also correspondingly low and also there is a necessity to observe the noise to reduce noise pollution. So the ability to reclaim acoustic energy and store it in a usable electrical form enables a novel means of supplying power to relatively low power devices. A quarter-wavelength straight-tube acoustic resonator as an acoustic energy harvester is introduced with polyvinylidene fluoride (PVDF) and PVDF doped with ZnO nanoparticles, piezoelectric cantilever beams placed inside the resonator. When the resonator is excited by an incident acoustic wave at its first acoustic eigen frequency, an amplified acoustic resonant standing wave is developed inside the resonator. The acoustic pressure gradient of the amplified standing wave then drives the vibration motion of the PVDF piezoelectric beams, generating electricity due to the direct piezoelectric effect. In order to maximize the amount of the harvested energy, each PVDF and PVDF-ZnO piezoelectric beam has been designed to have the same structural eigen frequency as the acoustic eigen frequency of the resonator. With a single PVDF beam placed inside the resonator, the harvested voltage and power become the maximum near the resonator tube open inlet where the largest acoustic pressure gradient vibrates the PVDF beam. As the beam is moved to the resonator tube closed end, the voltage and power gradually decrease due to the decreased acoustic pressure gradient. Multiple piezoelectric beams PVDF and PVDF-ZnO have been placed inside the resonator with two different configurations: the aligned and zigzag configurations. With the zigzag configuration which has the more open path for acoustic air particle motions, the significant increases in the harvested voltage and power have been observed. Due to the interruption of acoustic air particle motion caused by the beams, it is found that placing PVDF beams near the closed tube end is not beneficial. The total output voltage of the piezoelectric beams increases linearly as the incident sound pressure increases. This study therefore reveals that the proposed technique used to harvest sound wave energy has great potential of converting free energy into useful energy.

Keywords: acoustic energy, acoustic resonator, energy harvester, eigenfrequency, polyvinylidene fluoride (PVDF)

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Authors: Faisal AlShammari, Abdulmajid Addali

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Monitoring the conditions of rotating machinery as bearing is important in order to improve its stability of works. Acoustic emission (AE) and vibration analysis are some of the most accomplished techniques used for this purpose. Acoustic emission has the ability to detect the initial phase of component degradation. Moreover, it has been observed that the success of vibration analysis does not take place below 100 rpm rotational speed. This because the energy generated below 100 rpm rotational speed is not detectable using conventional vibration. From this pint, this paper has presented a focused review of using acoustic emission techniques for monitoring bearings condition.

Keywords: condition monitoring, stress wave analysis, low-speed bearings, bearing defect diagnosis

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Authors: Jesus Ruano, Asensi Oliva

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The hydrodynamic field generated by a jet expansion is computed via three dimensional compressible Large Eddy Simulation (LES). Finite Volume Method (FVM) will be the discretization used during this simulation as well as hybrid schemes based on Kinetic Energy Preserving (KEP) schemes and up-winding Godunov based schemes with instabilities detectors. Velocity and pressure fields will be stored at different surfaces near the jet, but far enough to enclose all the fluctuations, in order to use them as input for the acoustic solver. The acoustic field is obtained in the far-field region at several locations by means of a hybrid method based on Ffowcs-Williams and Hawkings (FWH) equation. This equation will be formulated in the spectral domain, via Fourier Transform of the acoustic sources, which are modeled from the results of the initial simulation. The obtained results will allow the study of the broadband noise generated as well as sound directivities.

Keywords: far-field noise, Ffowcs-Williams and Hawkings, finite volume method, large eddy simulation, jet noise

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Authors: Amit Sharma, J. N. Sharma

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This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor halfspace and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

Keywords: quasilongitudinal, reflection and transmission, semiconductors, acoustics

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Authors: Yuanda Ma, Zhiyong Zhang, Zailin Yang, Guanxixi Jiang

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Anisotropy is very common in underground media, such as rock, sand, and soil. Hence, the dynamic response of anisotropy medium under elastic waves is significantly different from the isotropic one. Moreover, underground heterogeneities and structures, such as pipelines, cylinders, or tunnels, are usually made by composite materials, leading to the anisotropy of these heterogeneities and structures. Both the anisotropy of the underground medium and the heterogeneities have an effect on the surface motion of the ground. Aiming at providing theoretical references for earthquake engineering and seismology, the surface motion of anisotropic half-space with a cylindrical anisotropic inclusion embedded under the SH wave is investigated in this work. Considering the anisotropy of the underground medium, the governing equation with three elastic parameters of SH wave propagation is introduced. Then, based on the complex function method and multipolar coordinates system, the governing equation in the complex plane is obtained. With the help of a pair of transformation, the governing equation is transformed into a standard form. By means of the same methods, the governing equation of SH wave propagation in the cylindrical inclusion with another three elastic parameters is normalized as well. Subsequently, the scattering wave in the half-space and the standing wave in the inclusion is deduced. Different incident wave angle and anisotropy are considered to obtain the reflected wave. Then the unknown coefficients in scattering wave and standing wave are solved by utilizing the continuous condition at the boundary of the inclusion. Through truncating finite terms of the scattering wave and standing wave, the equation of boundary conditions can be calculated by programs. After verifying the convergence and the precision of the calculation, the validity of the calculation is verified by degrading the model of the problem as well. Some parameters which influence the surface displacement of the half-space is considered: dimensionless wave number, dimensionless depth of the inclusion, anisotropic parameters, wave number ratio, shear modulus ratio. Finally, surface displacement amplitude of the half space with different parameters is calculated and discussed.

Keywords: anisotropy, complex function method, sh wave, surface displacement amplitude

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Authors: Hyunjoo Choi, Jeonghun Nam, Chae Seung Lim

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Acoustomicrofluidics has gained much attention due to the advantages, such as noninvasiveness and easy integration with other miniaturized systems, for clinical and biological applications. However, a limitation of acoustomicrofluidics is the complicated and costly fabrication process of electrodes. In this study, we propose a low-cost and lithography-free device using Lamb wave for blood analysis. Using a Lamb wave, calcium ion-removed blood plasma and coagulation reagents can be rapidly mixed for blood coagulation test. Due to the coagulation process, the viscosity of the sample increases and the viscosity change can be monitored by internal acoustic streaming of microparticles suspended in the sample droplet. When the acoustic streaming of particles stops by the viscosity increase is defined as the coagulation time. With the addition of calcium ion at 0-25 mM, the coagulation time was measured and compared with the conventional index for blood coagulation analysis, prothrombin time, which showed highly correlated with the correlation coefficient as 0.94. Therefore, our simple and cost-effective Lamb wave-based blood analysis device has the powerful potential to be utilized in clinical settings.

Keywords: acoustomicrofluidics, blood analysis, coagulation, lamb wave

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Authors: Cristian Viespe, Dana Miu

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Surface acoustic wave (SAW) sensors with nanoparticles (NPs) of various dimensions and concentrations embedded in different types of polymer sensing films for detecting volatile organic compounds (VOCs) were studied. The sensors were ‘delay line’ type with a center frequency of 69.4 MHz on ST-X quartz substrates. NPs with different diameters of 7 nm or 13 nm were obtained by laser ablation with lasers having 5 ns or 10 ps pulse durations, respectively. The influence of NPs dimensions and concentrations on sensor properties such as frequency shift, sensitivity, noise and response time were investigated. To the best of our knowledge, the influence of NP dimensions on SAW sensor properties with has not been investigated. The frequency shift and sensitivity increased with increasing NP concentration in the polymer for a given NP dimension and with decreasing NP diameter for a given concentration. The best performances were obtained for the smallest NPs used. The SAW sensor with NPs of 7 nm had a limit of detection (LOD) of 65 ppm (almost five times better than the sensor with polymer alone), and a response time of about 9 s for ethanol.

Keywords: surface acoustic wave sensor, nanoparticles, volatile organic compounds, laser ablation

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Hiroyuki Aoki

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Molecular imaging has attracted much attention to visualize a tumor site in a living body on the basis of biological functions. A fluorescence in vivo imaging technique has been widely employed as a useful modality for small animals in pre-clinical researches. However, it is difficult to observe a site deep inside a body because of a short penetration depth of light. A photo-acoustic effect is a generation of a sound wave following light absorption. Because the sound wave is less susceptible to the absorption of tissues, an in vivo imaging method based on the photoacoustic effect can observe deep inside a living body. The current study developed an in vivo imaging agent for a photoacoustic imaging method. Nano-particles of poly(lactic acid) including indocyanine dye were developed as bio-compatible imaging agent with strong light absorption. A tumor site inside a mouse body was successfully observed in a photo-acoustic image. A photo-acoustic imaging with polymer nano-particle agent would be a powerful method to visualize a tumor.

Keywords: nano-particle, photo-acoustic effect, polymer, dye, in vivo imaging

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

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The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Hafiza Rizwana Kausar

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In this paper, we formulate the wave equation in modified theories, particularly in f(R) theory, scalar-tensor theory, and metric palatine f(X) theory. We solve the wave equation in each case and try to find maximum possible solutions in the form polarization modes. It is found that modified theories present at most six modes however the mentioned metric theories allow four polarization modes, two of which are tensor in nature and other two are scalars.

Keywords: gravitational waves, modified theories, polariozation modes, scalar tensor theories

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Authors: Ehsan Pegah, Huabei Liu

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Determination of the internal friction angle (φ) in natural soil deposits is an important issue in geotechnical engineering. The main objective of this study was to examine the evaluation of this parameter in overconsolidated granular soil deposits by using the P-wave velocity and the anisotropic components of S-wave velocity (i.e., both the vertical component (SV) and the horizontal component (SH) of S-wave). To this end, seventeen pairs of P-wave and S-wave seismic refraction profiles were carried out at three different granular sites in Iran using non-invasive seismic wave methods. The acquired shot gathers were processed, from which the P-wave, SV-wave and SH-wave velocities were derived. The reference values of φ and overconsolidation ratio (OCR) in the soil deposits were measured through laboratory tests. By assuming cross-anisotropy of the soils, the P-wave and S-wave velocities were utilized to develop an equation for calculating the coefficient of lateral earth pressure at-rest (K₀) based on the theory of elasticity for a cross-anisotropic medium. In addition, to develop an equation for OCR estimation in granular geomaterials in terms of SH/SV velocity ratios, a general regression analysis was performed on the resulting information from this research incorporated with the respective data published in the literature. The calculated K₀ values coupled with the estimated OCR values were finally employed in the Mayne and Kulhawy formula to evaluate φ in granular soil deposits. The results showed that reliable values of φ could be estimated based on the seismic wave velocities. The findings of this study may be used as the appropriate approaches for economic and non-invasive determination of in-situ φ in granular soil deposits using the surface seismic surveys.

Keywords: angle of internal friction, overconsolidation ratio, granular soils, P-wave velocity, SV-wave velocity, SH-wave velocity

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Authors: Kyle Saltmarsh

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Acoustic testing possesses many benefits due to its non-destructive nature and practicality. There hence exists many scenarios in which using acoustic testing for condition testing shows powerful feasibility. A wealth of information is contained within the acoustic and vibration characteristics of structures, allowing the development meaningful features for the classification of their respective condition. In this paper, methods, results, and discussions are presented on the use of non-destructive acoustic testing coupled with acoustic feature extraction and machine learning techniques for the condition testing of manufactured circular steel plates subjected to varied levels of damage.

Keywords: plates, deformation, acoustic features, machine learning

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Authors: Pham Ngoc Thang, Le Thai Hung, Nguyen Quang Bau

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The influence of confined acoustic phonons on the Shubnikov – de Haas magnetoresistance oscillations in a doped semiconductor superlattice (DSSL), subjected in a magnetic field, DC electric field, and a laser radiation, has been theoretically studied based on quantum kinetic equation method. The analytical expression for the magnetoresistance in a DSSL has been obtained as a function of external fields, DSSL parameters, and especially the quantum number m characterizing the effect of confined acoustic phonons. When m goes to zero, the results for bulk phonons in a DSSL could be achieved. Numerical calculations are also achieved for the GaAs:Si/GaAs:Be DSSL and compared with other studies. Results show that the Shubnikov – de Haas magnetoresistance oscillations amplitude decrease as the increasing of phonon confinement effect.

Keywords: Shubnikov–de Haas magnetoresistance oscillations, quantum kinetic equation, confined acoustic phonons, laser radiation, doped semiconductor superlattices

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Authors: Arshad Alfoqaha, Seth Bard, Dustin Demetriou

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A new multi-physics acoustic modeling approach using ANSYS Mechanical FEA and FLUENT CFD methods is developed for modeling servers mounted to racks, such as IBM Z and IBM Power Systems, in data centers. This new approach allows users to determine the thermal and acoustic conditions that people are exposed to within the data center. The sound pressure level (SPL) exposure for a human working inside a hot aisle containment system inside the data center is studied. The SPL is analyzed at the noise source, at the human body, on the rack walls, on the containment walls, and on the ceiling and flooring plenum walls. In the acoustic CFD simulation, it is assumed that a four-inch diameter sphere with monopole acoustic radiation, placed in the middle of each rack, provides a single-source representation of all noise sources within the rack. Ffowcs Williams & Hawkings (FWH) acoustic model is employed. The target frequency is 1000 Hz, and the total simulation time for the transient analysis is 1.4 seconds, with a very small time step of 3e-5 seconds and 10 iterations to ensure convergence and accuracy. A User Defined Function (UDF) is developed to accurately simulate the acoustic noise source, and a Dynamic Mesh is applied to ensure acoustic wave propagation. Initial validation of the acoustic CFD simulation using a closed-form solution for the spherical propagation of an acoustic point source is performed.

Keywords: data centers, FLUENT, acoustics, sound pressure level, SPL, hot aisle containment, IBM

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Authors: Abbas Ali Husseini, Ali Mohammad Yazdani, Fatemeh Ghadiri, Alper Şişman

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We developed a microchip device that uses surface acoustic waves for rapid lysis of low level of cell samples. The device incorporates sharp-edge glass microparticles for improved performance. We optimized the lysis conditions for high efficiency and evaluated the device's feasibility for point-of-care applications. The microchip contains a 13-finger pair interdigital transducer with a 30-degree focused angle. It generates high-intensity acoustic beams that converge 6 mm away. The microchip operates at a frequency of 16 MHz, exciting Rayleigh waves with a 250 µm wavelength on the LiNbO3 substrate. Cell lysis occurs when Candida albicans cells and glass particles are placed within the focal area. The high-intensity surface acoustic waves induce centrifugal forces on the cells and glass particles, resulting in cell lysis through lateral forces from the sharp-edge glass particles. We conducted 42 pilot cell lysis experiments to optimize the surface acoustic wave-induced streaming. We varied electrical power, droplet volume, glass particle size, concentration, and lysis time. A regression machine-learning model determined the impact of each parameter on lysis efficiency. Based on these findings, we predicted optimal conditions: electrical signal of 2.5 W, sample volume of 20 µl, glass particle size below 10 µm, concentration of 0.2 µg, and a 5-minute lysis period. Downstream analysis successfully amplified a DNA target fragment directly from the lysate. The study presents an efficient microchip-based cell lysis method employing acoustic streaming and microparticle collisions within microdroplets. Integration of a surface acoustic wave-based lysis chip with an isothermal amplification method enables swift point-of-care applications.

Keywords: cell lysis, surface acoustic wave, micro-glass particle, droplet

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Authors: M. S. Gaafar, S. Y. Marzouk, I. S. Mahmoud, S. Al-Zobaidi

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Makishima and Mackenzie model was used to simulation of acoustic properties (longitudinal and shear ultrasonic wave velocities, elastic moduli theoretically for many tellurite and borate glasses. The model was proposed mainly depending on the values of the experimentally measured density, which are obtained before. In this search work, we are trying to obtain the values of densities of amorphous glasses (as the density depends on the geometry of the network structure of these glasses). In addition, the problem of simulating the slope of linear regression between the experimentally determined bulk modulus and the product of packing density and experimental Young's modulus, were solved in this search work. The results showed good agreement between the experimentally measured values of densities and both ultrasonic wave velocities, and those theoretically determined.

Keywords: glasses, ultrasonic wave velocities, elastic modulus, Makishima & Mackenzie Model

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Authors: Nirav J. Patel, Kalpesh K. Dudani

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Partial discharge (PD) is the dissipation of energy caused by localized breakdown of insulation. Power transformers are one of the most important components in the electrical energy network. Insulation degradation of transformer is frequently linked to PD. This is why PD detection is used in power system to monitor the health of high voltage transformer. If such problem are not detected and repaired, the strength and frequency of PD may increase and eventually lead to the catastrophic failure of the transformer. This can further cause external equipment damage, fires and loss of revenue due to an unscheduled outage. Hence, reliable online PD detection is a critical need for power companies to improve personnel safety and decrease the probability of loss of service. The PD phenomenon is manifested in a variety of physically observable signals including Ultra High Frequency (UHF) radiation and Acoustic Disturbances, Electrical pulses. Acoustic method is based on sensing the radiated acoustic emission from discharge sites in the insulation. Propagated wave from the PD fault site are captured sensor are consequently pre-amplified, filtered, recorded and analyze.

Keywords: acoustic, partial discharge, perfectly matched layer, sensor

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Authors: Hamid Reza Pakzad

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In this paper, the properties of dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma, whose constituents are inertial ions, superthermal electrons, and stationary dust particles, are investigated by employing the reductive perturbation method. The dissipation is taken into account the kinematic viscosity among the plasma constituents. It is shown that the basic features of DIA shock waves are significantly modified by the effects of electron superthermality and ion kinematic viscosity.

Keywords: reductive perturbation method, dust ion acoustic shock wave, superthermal electron, dissipative plasmas

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Authors: Swati Sharma, R. P. Sharma

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We intend to study the nonlinear evolution of the parallel propagating finite frequency Alfvén wave (also called Dispersive Alfvén wave/Hall MHD wave) propagating in the solar wind regime of the solar region when a perpendicularly propagating magnetosonic wave is present in the background. The finite frequency Alfvén wave behaves differently from the usual non-dispersive behavior of the Alfvén wave. To study the nonlinear processes (such as filamentation) taking place in the solar regions such as solar wind, the dynamical equation of both the waves are derived. Numerical simulation involving finite difference method for the time domain and pseudo spectral method for the spatial domain is then performed to analyze the transient evolution of these waves. The power spectra of the Dispersive Alfvén wave is also investigated. The power spectra shows the distribution of the magnetic field intensity of the Dispersive Alfvén wave over different wave numbers. For DAW the spectra shows a steepening for scales larger than the proton inertial length. This means that the wave energy gets transferred to the solar wind particles as the wave reaches higher wave numbers. This steepening of the power spectra can be explained on account of the finite frequency of the Alfvén wave. The obtained results are consistent with the observations made by CLUSTER spacecraft.

Keywords: solar wind, turbulence, dispersive alfven wave

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Emmanuel Ifeanyi Ugwu

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Calcium Sulphide which is one of Chalcogenide group of thin films has been analyzed in this work using a theoretical approach in which a scalar wave was propagated through the material thin film medium deposited on a glass substrate with the assumption that the dielectric medium has homogenous reference dielectric constant term, and a perturbed dielectric function, representing the deposited thin film medium on the surface of the glass substrate as represented in this work. These were substituted into a defined scalar wave equation that was solved first of all by transforming it into Volterra equation of second type and solved using the method of separation of variable on scalar wave and subsequently, Green’s function technique was introduced to obtain a model equation of wave propagating through the thin film that was invariably used in computing the propagated field, for different input wavelengths representing UV, Visible and Near-infrared regions of field considering the influence of the dielectric constants of the thin film on the propagating field. The results obtained were used in turn to compute the band gaps, solid state and optical properties of the thin film.

Keywords: scalar wave, dielectric constant, calcium sulphide, solid state, optical properties

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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