Search results for: wave boundary

Authors: Alsaidi M. Altaher, Mohd Tahir Ismail

Abstract:

Wavelet thresholding has been a power tool in curve estimation and data analysis. In the presence of outliers this non parametric estimator can not suppress the outliers involved. This study proposes a new two-stage combined method based on the use of the median filter as primary step before applying wavelet thresholding. After suppressing the outliers in a signal through the median filter, the classical wavelet thresholding is then applied for removing the remaining noise. We use automatic boundary corrections; using a low order polynomial model or local polynomial model as a more realistic rule to correct the bias at the boundary region; instead of using the classical assumptions such periodic or symmetric. A simulation experiment has been conducted to evaluate the numerical performance of the proposed method. Results show strong evidences that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating outlier’s sensitivity.

Keywords: boundary correction, median filter, simulation, wavelet thresholding

Procedia PDF Downloads 430

Authors: Subal Kar, Madhuja Ghosh, Soumik Das, Antara Saha

Abstract:

A novel technique has been developed to generate ultra-stable millimeter-wave signal by optical heterodyning of the output from two slave laser (SL) sources injection-locked to the sidebands of a frequency modulated (FM) master laser (ML). Precise thermal tuning of the SL sources is required to lock the particular slave laser frequency to the desired FM sidebands of the ML. The output signals from the injection-locked SL when coherently heterodyned in a fast response photo detector like high electron mobility transistor (HEMT), extremely stable millimeter-wave signal having very narrow line width can be generated. The scheme may also be used to generate ultra-stable sub-millimeter-wave/terahertz signal.

Keywords: FM sideband injection locking, master-slave injection locking, millimetre-wave signal generation, optical heterodyning

Procedia PDF Downloads 392

Authors: Végh Ádám, Mekler Csaba, Dezső András, Szabó Dávid, Stomp Dávid, Kaptay György

Abstract:

Grain boundary segregation transition (GBST) has been calculated by a thermodynamic model in binary alloys. The method is used on cementite (Fe3C) segregation in base-centered cubic (ferrite) iron (Fe) in the Fe-C binary system. The GBST line is shown in the Fe3C lacking part of the phase diagram with high solvent (Fe) concentration. At a lower solute content (C) or at higher temperature the grain boundary is composed mostly of the solvent atoms (Fe). On higher concentration compared to the GBST line or at lower temperature a phase transformation occurs at the grain boundary, the latter mostly composed of the associates (Fe3C). These low-segregation and high-segregation states are first order interfacial phase transitions of the grain boundary and can be transformed into each other reversibly. These occur when the GBST line is crossed by changing the bulk composition or temperature.

Keywords: GBST, cementite, segregation, Fe-C alloy

Procedia PDF Downloads 585

Authors: Armin Bodaghkhani, Bruce Colbourne, Yuri S. Muzychka

Abstract:

The process of spray-cloud formation and flow kinematics produced from breaking wave impact on vertical and slant lab-scale bow-shaped models were experimentally investigated. Bubble Image Velocimetry (BIV) and Image Processing (IP) techniques were applied to study the various types of wave-model impacts. Different wave characteristics were generated in a tow tank to investigate the effects of wave characteristics, such as wave phase velocity, wave steepness on droplet velocities, and behavior of the process of spray cloud formation. The phase ensemble-averaged vertical velocity and turbulent intensity were computed. A high-speed camera and diffused LED backlights were utilized to capture images for further post processing. Various pressure sensors and capacitive wave probes were used to measure the wave impact pressure and the free surface profile at different locations of the model and wave-tank, respectively. Droplet sizes and velocities were measured using BIV and IP techniques to trace bubbles and droplets in order to measure their velocities and sizes by correlating the texture in these images. The impact pressure and droplet size distributions were compared to several previously experimental models, and satisfactory agreements were achieved. The distribution of droplets in front of both models are demonstrated. Due to the highly transient process of spray formation, the drag coefficient for several stages of this transient displacement for various droplet size ranges and different Reynolds number were calculated based on the ensemble average method. From the experimental results, the slant model produces less spray in comparison with the vertical model, and the droplet velocities generated from the wave impact with the slant model have a lower velocity as compared with the vertical model.

Keywords: spray charachteristics, droplet size and velocity, wave-body interactions, bubble image velocimetry, image processing

Procedia PDF Downloads 300

Authors: Kbab H, Hamitouche T

Abstract:

In recent years, significant progress has been accomplished in the field of aerospace propulsion and propulsion systems. These developments are associated with efforts to enhance the accuracy of the analysis of aerothermodynamic phenomena in the engine. This applies in particular to the flow in the nozzles used. One of the most remarkable processes in this field is thrust vectoring by means of devices able to orientate the thrust vector and control the deflection of the exit jet in the engine nozzle. In the study proposed, we are interested in the fluid thrust vectoring using a second injection in the nozzle divergence. This fluid injection causes complex phenomena, such as boundary layer separation, which generates a shock wave in the primary jet upstream of the fluid interacting zone (primary jet - secondary jet). This will cause the deviation of the main flow, and therefore of the thrust vector with reference to the axis nozzle. In the modeling of the fluidic thrust vector, various parameters can be used. The Mach number of the primary jet and the injected fluid, the total pressures ratio, the injection rate, the thickness of the upstream boundary layer, the injector position in the divergent part, and the nozzle geometry are decisive factors in this type of phenomenon. The complexity of the latter challenges researchers to understand the physical phenomena of the turbulent boundary layer encountered in supersonic nozzles, as well as the calculation of its thickness and the friction forces induced on the walls. The present study aims to numerically simulate the thrust vectoring by secondary injection using the ANSYS-FLUENT, then to analyze and validate the results and the performances obtained (angle of deflection, efficiency...), which will then be compared with those obtained by other authors.

Keywords: CD Nozzle, TVC, SVC, NPR, CFD, NPR, SPR

Procedia PDF Downloads 134

Authors: Zhenjie Liu

Abstract:

This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

Keywords: mixed monotone operator, boundary value problem, time scale, green's function, positive solution, singularity

Procedia PDF Downloads 257

Authors: M. Berrehail, F. Benamira

Abstract:

We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

Procedia PDF Downloads 493

Authors: Rafael Muñoz, Juan Melchor, Alicia Valera, Laura Peralta, Guillermo Rus

Abstract:

A torsional piezoelectric ultrasonic transducer design is proposed to measure shear moduli in soft tissue with direct access availability, using shear wave elastography technique. The measurement of shear moduli of tissues is a challenging problem, mainly derived from a) the difficulty of isolating a pure shear wave, given the interference of multiple waves of different types (P, S, even guided) emitted by the transducers and reflected in geometric boundaries, and b) the highly attenuating nature of soft tissular materials. An immediate application, overcoming these drawbacks, is the measurement of changes in cervix stiffness to estimate the gestational age at delivery. The design has been optimized using a finite element model (FEM) and a semi-analytical estimator of the probability of detection (POD) to determine a suitable geometry, materials and generated waves. The technique is based on the time of flight measurement between emitter and receiver, to infer shear wave velocity. Current research is centered in prototype testing and validation. The geometric optimization of the transducer was able to annihilate the compressional wave emission, generating a quite pure shear torsional wave. Currently, mechanical and electromagnetic coupling between emitter and receiver signals are being the research focus. Conclusions: the design overcomes the main described problems. The almost pure shear torsional wave along with the short time of flight avoids the possibility of multiple wave interference. This short propagation distance reduce the effect of attenuation, and allow the emission of very low energies assuring a good biological security for human use.

Keywords: cervix ripening, preterm birth, shear modulus, shear wave elastography, soft tissue, torsional wave

Procedia PDF Downloads 346

Authors: Naila Nasreen, Dianchen Lu

Abstract:

This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

Procedia PDF Downloads 101

Authors: Manoj Reghu, Prabhu Rajagopal, C. V. Krishnamurthy, Krishnan Balasubramaniam

Abstract:

A thorough understanding of guided ultrasonic wave behavior in structures is essential for the application of existing Non Destructive Evaluation (NDE) technologies, as well as for the development of new methods. However, the analysis of guided wave phenomena is challenging because of their complex dispersive and multimodal nature. Although numerical solution procedures have proven to be very useful in this regard, the increasing complexity of features and defects to be considered, as well as the desire to improve the accuracy of inspection often imposes a large computational cost. Hybrid models that combine numerical solutions for wave scattering with faster alternative methods for wave propagation have long been considered as a solution to this problem. However usually such models require modification of the base code of the solution procedure. Here we aim to develop Generic Hybrid models that can be directly applied to any two different solution procedures. With this goal in mind, a Numerical Hybrid model and an Analytical-Numerical Hybrid model has been developed. The concept and implementation of these Hybrid models are discussed in this paper.

Keywords: guided ultrasonic waves, Finite Element Method (FEM), Hybrid model

Procedia PDF Downloads 466

Authors: Mohamed Razi Nalim, Shahrzad Ghadiri

Abstract:

With current concerns regarding global warming, demand for a society with greater environmental awareness significantly increases. With gradual development in hybrid and electric vehicles and the availability of renewable energy resources, increasing efficiency in fossil fuel and combustion engines seems a faster solution toward sustainability and reducing greenhouse gas emissions. This paper aims to provide a comprehensive review of recent progress in wave rotor combustor, one of the combustion concepts with considerable potential to improve power output and emission standards. A wave rotor is an oscillatory flow device that uses the unsteady gas dynamic concept to transfer energy by generating pressure waves. From a thermodynamic point of view, unlike conventional positive-displacement piston engines which follow the Brayton cycle, wave rotors offer higher cycle efficiency due to pressure gain during the combustion process based on the Humphrey cycle. First, the paper covers all recent and ongoing computational and experimental studies around the world with a quick look at the milestones in the history of wave rotor development. Second, the main similarity and differences in the ignition system of the wave rotor with piston engines are considered. Also, the comparison is made with another pressure gain device, rotating detonation engines. Next, the main challenges and research needs for wave rotor combustor commercialization are discussed.

Keywords: wave rotor combustor, unsteady gas dynamic, pre-chamber jet ignition, pressure gain combustion, constant-volume combustion

Procedia PDF Downloads 85

Authors: Victoria Bessonova, Robert Dorrell, Nina Dethlefs, Evdokia Tapoglou, Katharine York

Abstract:

As the global pursuit of renewable energy intensifies, offshore wind farms have emerged as a promising solution to combat climate change. The global offshore wind installed capacity is projected to increase 56-fold by 2055. However, the impacts of climate change, particularly changes in wave climate, are not widely understood. Offshore wind installation and maintenance activities often require specific weather windows, characterized by calm seas and low wave heights, to ensure safe and efficient operations. However, climate change-induced alterations in wave characteristics can reduce the availability of suitable weather windows, leading to delays and disruptions in project timelines. it applied the operational limits of installation and maintenance vessels to past and future climate wave projections. This revealed changes in the annual and monthly accessibility of offshore wind farms at key global development locations. When accessibility is only defined by significant wave height, spatial patterns in the annual accessibility roughly follow changes in significant wave height, with increased availability where significant wave height is decreasing. This resulted in a 1-6% increase in Europe and North America and a similar decrease in South America, Australia and Asia. Monthly changes suggest unchanged or slightly decreased (1-2%) accessibility in summer months and increased (2-6%) in winter. Further assessment includes assessing the sensitivity of accessibility to operational limits defined by wave height combined with wave period and wave height combined with wind speed. Results of this assessment will be included in the presentation. These findings will help stakeholders inform climate change adaptations in installation and maintenance planning practices.

Keywords: climate change, offshore wind, offshore wind installation, operations and maintenance, wave climate, wind farm accessibility

Procedia PDF Downloads 86

Authors: Liu Bijin

Abstract:

Floating breakwaters have several advantages, including being environmentally friendly, easy to construct, and cost-effective regardless of water depth. They have a broad range of applications in coastal engineering. However, they face significant challenges due to the unstable effect of wave dissipation, structural vulnerability, and high mooring system requirements. This paper investigates the wave dissipation performance of a floating breakwater structure. The structure consists of double cylinders, double vertical plates, and horizontal connecting plates. The investigation is carried out using physical model tests and numerical simulation methods based on STAR-CCM+. This paper discusses the impact of wave elements, relative vertical plate heights, and relative horizontal connecting plate widths on the wave dissipation performance of the double-cylinder, double-plate floating breakwater (DCDPFB). The study also analyses the changes in local vorticity and velocity fields around the DCDPFB to determine the optimal structural dimensions. The study found that the relative width of the horizontal connecting plate, the relative height of the vertical plate, and the size of the semi-cylinder are the key factors affecting the wave dissipation performance of the DCDPFB. The transmittance coefficient is minimally affected by the wave height and the depth of water entry. The local vortex and velocity field formed around the DCDPFB are important factors for dissipating wave energy. The test section of the DCDPFB, constructed according to the relative optimal structural dimensions, showed good wave dissipation performance during offshore prototype tests. The test section of DCDPFB, constructed with optimal structural dimensions, exhibits excellent wave dissipation performance in offshore prototype tests.

Keywords: floating breakwater, wave dissipation performance, transmittance coefficient, model test

Procedia PDF Downloads 57

Authors: Liliana Rusu

Abstract:

The goal of the proposed work is to provide a more comprehensive picture of the wind and wave climate in the Romanian nearshore, using the results provided by numerical models. The Romanian coastal environment is located in the western side of the Black Sea, the more energetic part of the sea, an area with heavy maritime traffic and various offshore operations. Information about the wind and wave climate in the Romanian waters is mainly based on observations at Gloria drilling platform (70 km from the coast). As regards the waves, the measurements of the wave characteristics are not so accurate due to the method used, being also available for a limited period. For this reason, the wave simulations that cover large temporal and spatial scales represent an option to describe better the wave climate. To assess the wind climate in the target area spanning 1992–2016, data provided by the NCEP-CFSR (U.S. National Centers for Environmental Prediction - Climate Forecast System Reanalysis) and consisting in wind fields at 10m above the sea level are used. The high spatial and temporal resolution of the wind fields is good enough to represent the wind variability over the area. For the same 25-year period, as considered for the wind climate, this study characterizes the wave climate from a wave hindcast data set that uses NCEP-CFSR winds as input for a model system SWAN (Simulating WAves Nearshore) based. The wave simulation results with a two-level modelling scale have been validated against both in situ measurements and remotely sensed data. The second level of the system, with a higher resolution in the geographical space (0.02°×0.02°), is focused on the Romanian coastal environment. The main wave parameters simulated at this level are used to analyse the wave climate. The spatial distributions of the wind speed, wind direction and the mean significant wave height have been computed as the average of the total data. As resulted from the amount of data, the target area presents a generally moderate wave climate that is affected by the storm events developed in the Black Sea basin. Both wind and wave climate presents high seasonal variability. All the results are computed as maps that help to find the more dangerous areas. A local analysis has been also employed in some key locations corresponding to highly sensitive areas, as for example the main Romanian harbors.

Keywords: numerical simulations, Romanian nearshore, waves, wind

Procedia PDF Downloads 345

Authors: Ayaz Ahmad

Abstract:

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

Procedia PDF Downloads 215

Authors: Po-Chun Wang, Yan-Ru Lai, Sophia I. C. Lin, Alvin W. Y. Su

Abstract:

The Generative Theory of Tonal Music (GTTM) provides systematic approaches to recognizing local boundaries of music. The rules have been implemented in some automated melody segmentation algorithms. Besides, there are also deep learning methods with GTTM features applied to boundary detection tasks. However, these studies might face constraints such as a lack of or inconsistent label data. The GTTM database is currently the most widely used GTTM database, which includes manually labeled GTTM rules and local boundaries. Even so, we found some problems with these labels. They are sometimes discrepancies with GTTM rules. In addition, since it is labeled at different times by multiple musicians, they are not within the same scope in some cases. Therefore, in this paper, we examine this database with musicians from the aspect of classical music and relabel the scores. The relabeled database - GTTM Database v2.0 - will be released for academic research usage. Despite the experimental and statistical results showing that the relabeled database is more consistent, the improvement in boundary detection is not substantial. It seems that we need more clues than GTTM rules for boundary detection in the future.

Keywords: dataset, GTTM, local boundary, neural network

Procedia PDF Downloads 147

Authors: Mohammad Ranjbaran Madiseh

Abstract:

In this research, an experimental apparatus has been developed for observing interfacial stability and deformation of multilayer pressure-driven channel flows. The interface instability of the co-extrusion flow of polyethylene and polypropylene is studied experimentally in a slit geometry. By investigating the growing interfacial wave (IW) and tensile stress of extrudate samples, a relationship between interfacial instability (II) and mechanical properties of polypropylene (PP) and high-density polyethylene (HDPE) has been established. It is shown that the mechanism of interfacial strength is related to interfacial instabilities as well as interfacial strength. It is shown that there is an ability to forecast the quality of final products in the co-extrusion process. In this study, it is found that the instability is controlled by its dominant wave number, which is associated with maximum tensile stress at the interface.

Keywords: interfacial instability, interfacial strength, wave number, interfacial wave

Procedia PDF Downloads 92

Authors: Amares Chattopadhyay, Akanksha Srivastava

Abstract:

A unified approach to study the reflection of a plane wave in three-dimensional model comprised of the triclinic viscoelastic medium. The phase velocities of reflected qP, qSV and qSH wave have been calculated for the concerned medium by using the eigenvalue approach. The generalized method has been implemented to compute the complex form of amplitude ratios. Further, we discussed the nature of reflection coefficients of qP, qSV and qSH wave. The viscoelastic parameter, polar angle and azimuthal angle are found to be strongly influenced by amplitude ratios. The research article is particularly focused to study the effect of viscoelasticity associated with highly anisotropic media which exhibits the notable information about the reflection coefficients of qP, qSV, and qSH wave. The outcomes may further useful to the better exploration of all types of hydrocarbon reservoir and advancement in the field of reflection seismology.

Keywords: amplitude ratios, three dimensional, triclinic, viscoelastic

Procedia PDF Downloads 232

Authors: Stephen Kirkup

Abstract:

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

Procedia PDF Downloads 163

Authors: Tory Erickson

Abstract:

The "Bidirectional Spacetime with Spatial Covariance and Wave-Particle Duality in Spacetime Flow" (BST-SCWPDF) Model introduces a framework aimed at unifying general relativity (GR) and quantum mechanics (QM). By proposing a concept of bidirectional spacetime, this model suggests that time can flow in more than one direction, thus offering a perspective on temporal dynamics. Integrated with spatial covariance and wave-particle duality in spacetime flow, the BST-SCWPDF Model resolves long-standing discrepancies between GR and QM. This unified theory has profound implications for quantum gravity, potentially offering insights into quantum entanglement, the collapse of the wave function, and the fabric of spacetime itself. The Bidirectional Spacetime with Spatial Covariance and Wave-Particle Duality in Spacetime Flow" (BST-SCWPDF) Model offers researchers a framework for a better understanding of theoretical physics.

Keywords: astrophysics, quantum mechanics, general relativity, unification theory, theoretical physics

Procedia PDF Downloads 88

Authors: Neeraj Kumar, J. P. Narayan

Abstract:

The effects of multiple Structure-Soil-Structure Interactions (SSSI) on the seismic wave-field is generally disregarded by earthquake engineers, particularly the surface waves which cause more damage to buildings. Closely built high rise buildings exchange substantial seismic energy with each other and act as a full-coupled dynamic system. In this paper, SSI effects on the building responses and the free field motion due to a small city consisting 25- homogenous buildings blocks of 10-storey are quantified. The rocking and translational behavior of building under Rayleigh wave loading is studied for different dimensions of the building. The obtained dynamic parameters of buildings revealed a reduction in building roof drift with an increase in number of buildings ahead of the considered building. The strain developed by vertical component of Rayleigh may cause tension in structural components of building. A matching of fundamental frequency of building for the horizontal component of Rayleigh wave with that for vertically incident SV-wave is obtained. Further, the fundamental frequency of building for the vertical vibration is approximately twice to that for horizontal vibration. The city insulation has caused a reduction of amplitude of Rayleigh wave up to 19.3% and 21.6% in the horizontal and vertical components, respectively just outside the city. Further, the insulating effect of city was very large at fundamental frequency of buildings for both the horizontal and vertical components. Therefore, it is recommended to consider the insulating effects of city falling in the path of Rayleigh wave propagation in seismic hazard assessment for an area.

Keywords: structure-soil-structure interactions, Rayleigh wave propagation, finite difference simulation, dynamic response of buildings

Procedia PDF Downloads 215

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

Procedia PDF Downloads 543

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

Abstract:

In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

Procedia PDF Downloads 538

Authors: Shivani Saini

Abstract:

The effect of vertical throughflow on the onset of convection in Rivlin-Ericksen Elastico-Viscous nanofluid with convective boundary condition is investigated. The flow is stimulated with modified Darcy model under the assumption that the nanoparticle volume fraction is not actively managed on the boundaries. The heat conservation equation is formulated by introducing the convective term of nanoparticle flux. A linear stability analysis based upon normal mode is performed, and an approximate solution of eigenvalue problems is obtained using the Galerkin weighted residual method. Investigation of the dependence of the Rayleigh number on various viscous and nanofluid parameter is performed. It is found that through flow and nanofluid parameters hasten the convection while capacity ratio, kinematics viscoelasticity, and Vadasz number do not govern the stationary convection. Using the convective component of nanoparticle flux, critical wave number is the function of nanofluid parameters as well as the throughflow parameter. The obtained solution provides important physical insight into the behavior of this model.

Keywords: Darcy model, nanofluid, porous layer, throughflow

Procedia PDF Downloads 137

Authors: S. Kida

Abstract:

We consider the flow of an incompressible viscous fluid in a precessing sphere whose spin and precession axes are orthogonal to each other. The flow is characterized by two non-dimensional parameters, the Reynolds number Re and the Poincare number Po. For which values of (Re, Po) will the flow approach a steady state from an arbitrary initial condition? To answer it we are searching the instability boundary of the steady states in the whole (Re, Po) plane. Here, we focus the rapidly rotating and weakly precessing limit, i.e., Re >> 1 and Po << 1. The steady flow was obtained by the asymptotic expansion for small ε=Po Re¹/² << 1. The flow exhibits nearly a solid-body rotation in the whole sphere except for a thin boundary layer which develops over the sphere surface. The thickness of this boundary layer is of O(δ), where δ=Re⁻¹/², except where two circular critical bands of thickness of O(δ⁴/⁵) and of width of O(δ²/⁵) which are located away from the spin axis by about 60°. We perform the linear stability analysis of the steady flow. We assume that the disturbances are localized in the critical bands and make an expansion analysis in terms of ε to derive the eigenvalue problem for the growth rate of the disturbance, which is solved numerically. As the solution, we obtain an asymptote of the stability boundary as Po=28.36Re⁻⁰.⁸. This agrees excellently with the corresponding laboratory experiments and numerical simulations. One of the most popular instability mechanisms so far is the parametric instability, which turns out, however, not to give the correct stability boundary. The present instability is different from the parametric instability.

Keywords: boundary layer, critical band, instability, precessing sphere

Procedia PDF Downloads 154

Authors: Manana Chumburidze, David Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: the couple-stress thermoelasticity, boundary value problems, dynamic problems, approximate solution

Procedia PDF Downloads 507

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

Abstract:

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

Procedia PDF Downloads 458

Authors: Soumia Merat, Lynda Djerbal, Ramdane Bahar, Mohammed Amin Benbouras

Abstract:

Along with shear wave, many soil parameters are associated with the standard penetration test (SPT) as a dynamic in situ experiment. Both SPT-N data and geophysical data do not often exist in the same area. Statistical analysis of correlation between these parameters is an alternate method to estimate Vₛ conveniently and without additional investigations or data acquisition. Shear wave velocity is a basic engineering tool required to define dynamic properties of soils. In many instances, engineers opt for empirical correlations between shear wave velocity (Vₛ) and reliable static field test data like standard penetration test (SPT) N value, CPT (Cone Penetration Test) values, etc., to estimate shear wave velocity or dynamic soil parameters. The relation between Vs and SPT- N values of Algiers area is predicted using the collected data, and it is also compared with the previously suggested formulas of Vₛ determination by measuring Root Mean Square Error (RMSE) of each model. Algiers area is situated in high seismic zone (Zone III [RPA 2003: réglement parasismique algerien]), therefore the study is important for this region. The principal aim of this paper is to compare the field measurements of Down-hole test and the empirical models to show which one of these proposed formulas are applicable to predict and deduce shear wave velocity values.

Keywords: empirical models, RMSE, shear wave velocity, standard penetration test

Procedia PDF Downloads 339

Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

Abstract:

In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

Procedia PDF Downloads 113

Authors: Ergun Guntekin

Abstract:

This study investigated elastic constants of scots pine (Pinus sylvestris L.) grown in Turkey by means of ultrasonic waves. Three Young’s modulus, three shear modulus and six Poisson ratios were determined at constant moisture content (12 %). Three longitudinal and six shear wave velocities propagating along the principal axes of anisotropy, and additionally, three quasi-shear wave velocities at 45° with respect to the principal axes of anisotropy were measured using EPOCH 650 ultrasonic flaw detector. The measured average longitudinal wave velocities for the sapwood in L, R, T directions were 4795, 1713 and 1117 m/s, respectively. The measured average shear wave velocities ranged from 682 to 1382 m/s. The measured quasi-shear wave velocities varied between 642 and 1280 m/s. The calculated average modulus of elasticity values for the sapwood in L, R, T directions were 11913, 1565 and 663 N/mm2, respectively. The calculated shear modulus in LR, LT and RT planes were 1031, 541, 415 N/mm2. Comparing with available literature, the predicted elastic constants are acceptable.

Keywords: elastic constants, prediction, Scots pine, ultrasound

Procedia PDF Downloads 280