Search results for: wave equation

Authors: Mezghiche Kamel

Abstract:

We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

Procedia PDF Downloads 745

Authors: Guesh Simretab Gebremedhin, Saumya Rajan Jena

Abstract:

In this work, a septic B-spline scheme has been used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long-wave equation (GR-RLWE) with initial boundary conditions. The resulting system of first-order ODEs has dealt with Butcher’s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time-dependent variables at each time level. Here, no transformation or any kind of linearization technique is employed to tackle the nonlinearity of the equation. Two test problems have been selected for numerical justifications and comparisons with other researchers on the basis of efficiency, accuracy, and results of the two invariants Mᵢ (mass) and Eᵢ (energy) of some motion that has been used to test the conservative properties of the proposed scheme.

Keywords: septic B-spline scheme, Butcher's fifth order Runge-Kutta approach, error norms, generalized Rosenau-RLW equation

Procedia PDF Downloads 39

Authors: Ayda Nikkar, Roghayye Ahmadiasl

Abstract:

In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

Procedia PDF Downloads 282

Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

Abstract:

Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

Procedia PDF Downloads 192

Authors: Abhinav Singhal, Sanjeev A. Sahu

Abstract:

Propagation of Rayleigh-type surface waves in an initially stressed piezomagnetic half- space with irregular boundary is investigated. The materials are assumed to be transversely isotropic crystals. The dispersion relations have been derived for electrically open and short cases. Effect of initial stress and corrugation have been shown graphically. It is also found that piezomagnetic material properties have an important effect on wave propagation. The result is relevant to the analysis and design of various acoustic surface wave devices constructed from piezomagnetic materials.

Keywords: corrugation, frequency equation, piezomagnetic, rayleigh-type wave

Procedia PDF Downloads 242

Authors: T. J. Hasanova, C. N. Imamalieva

Abstract:

The problem about the movement of the rigid cylinder keeping the vertical position under the influence of running superficial waves in a liquid is considered. The indignation of a falling wave caused by the presence of the cylinder which moves is thus considered. Special decomposition on a falling harmonious wave is used. The problem dares an operational method. For a finding of the original decision, Considering that the image denominator represents a tabular function, Voltaire's integrated equation of the first sort which dares a numerical method is used. Cylinder movement in the continuous environment under the influence of waves is considered in work. Problems are solved by an operational method, thus originals of required functions are looked for by the numerical definition of poles of combinations of transcendental functions and calculation of not own integrals. Using specificity of a task below, Decisions are under construction the numerical solution of the integrated equation of Volter of the first sort that does not create computing problems of the complex roots of transcendental functions connected with search.

Keywords: rigid cylinder, linear interpolation, fluctuations, Voltaire's integrated equation, harmonious wave

Procedia PDF Downloads 302

Authors: Tarek Sabri Duzan

Abstract:

Knowledge of the magnitude of Geo-pressures (Pore, Fracture & Over-burden pressures) is vital especially during drilling, completions, stimulations, Enhance Oil Recovery. Many times problems, like lost circulation could have been avoided if techniques for calculating Geo-pressures had been employed in the well planning, mud weight plan, and casing design. In this paper, we focused on the relationships between Geo-pressures and wave velocities (P-Wave (Vp) and S-wave (Vs)) in shallow Libyan carbonate reservoir in the western part of the Sirte Basin (Dahra F-Area). The data used in this report was collected from four new wells recently drilled. Those wells were scattered throughout the interested reservoir as shown in figure-1. The data used in this work are bulk density, Formation Mult -Tester (FMT) results and Acoustic wave velocities. Furthermore, Eaton Method is the most common equation used in the world, therefore this equation has been used to calculate Fracture pressure for all wells using dynamic Poisson ratio calculated by using acoustic wave velocities, FMT results for pore pressure, Overburden pressure estimated by using bulk density. Upon data analysis, it has been found that there is a linear relationship between Geo-pressures (Pore, Fracture & Over-Burden pressures) and wave velocities ratio (Vp/Vs). However, the relationship was not clear in the high-pressure area, as shown in figure-10. Therefore, it is recommended to use the output relationship utilizing the new seismic data for shallow carbonate reservoir to predict the Geo-pressures for future oil operations. More data can be collected from the high-pressure zone to investigate more about this area.

Keywords: bulk density, formation mult-tester (FMT) results, acoustic wave, carbonate shalow reservoir, d/jfield velocities

Procedia PDF Downloads 268

Authors: Armenuhi Ghazaryan, Qnarik Poghosyan, Tadevos Markosyan

Abstract:

We have considered the high-order harmonic generation in-plane graphene quantum dots of hexagonal shape by the independent quasiparticle approximation-tight binding model. We have investigated how such a nonlinear effect is affected by a strong optical wave field, quantum dot typical band gap and lateral size, and dephasing processes. The equation of motion for the density matrix is solved by performing the time integration with the eight-order Runge-Kutta algorithm. If the optical wave frequency is much less than the quantum dot intrinsic band gap, the main aspects of multiphoton high harmonic emission in quantum dots are revealed. In such a case, the dependence of the cutoff photon energy on the strength of the optical pump wave is almost linear. But when the wave frequency is comparable to the bandgap of the quantum dot, the cutoff photon energy shows saturation behavior with an increase in the wave field strength.

Keywords: strong wave field, multiphoton, bandgap, wave field strength, nanostructure

Procedia PDF Downloads 115

Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

Procedia PDF Downloads 164

Authors: A. Abdikian

Abstract:

Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.

Keywords: bifurcation theory, phase portrait, magnetized electron-positron plasma, the Zakharov-Kuznetsov equation

Procedia PDF Downloads 220

Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

Abstract:

The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

Procedia PDF Downloads 302

Authors: Jitendra Kumar Chawla, Mukesh Kumar Mishra

Abstract:

The nonlinear amplitude modulation of ion-acoustic wave is studied in the presence of two-electron temperature distribution in unmagnetized electron-positron-ion plasmas. The Krylov-Bogoliubov-Mitropolosky (KBM) perturbation method is used to derive the nonlinear Schrödinger equation. The dispersive and nonlinear coefficients are obtained which depend on the temperature and concentration of the hot and cold electron species as well as the positron density and temperature. The modulationally unstable regions are studied numerically for a wide range of wave number. The effects of the temperature and concentration of the hot and cold electron on the modulational stability are investigated in detail.

Keywords: modulational instability, ion acoustic wave, KBM method

Procedia PDF Downloads 630

Authors: S. S. Abas, Y. M. Yatim

Abstract:

In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

Procedia PDF Downloads 285

Authors: A. Zerarka, W. Djoudi

Abstract:

The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

Procedia PDF Downloads 633

Authors: Tokuei Sako

Abstract:

Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied.

Keywords: pulsed laser field, nanowire, electron wave packet, quantum dots, time-dependent Schrödinger equation

Procedia PDF Downloads 332

Authors: Sergio Pérez-López, Daniel Tarrazó-Serrano, José M. Fuster, Pilar Candelas, Constanza Rubio

Abstract:

Fresnel Zone Plates (FZPs) are widely used in many areas, such as optics, microwaves or acoustics. On the design of FZPs, plane wave incidence is typically considered, but that is not usually the case in ultrasounds, especially in applications where a piston emitter is placed at a certain distance from the lens. In these cases, having control of the focal distance is very important, and with the usual Fresnel equation a focal displacement from the theoretical distance is observed due to the plane wave supposition. In this work, a comparison between FZP with plane wave incidence design and FZP with point source design in the case of piston emitter is presented. Influence of the main parameters of the piston in the final focalization profile has been studied. Numerical models and experimental results are shown, and they prove that when spherical wave incidence is considered for the piston case, it is possible to have a fine control of the focal distance in comparison with the classical design method.

Keywords: focusing, Fresnel zone plates, FZP, ultrasound

Procedia PDF Downloads 224

Authors: Mohammad Ahmad, Dayalan Kasilingam

Abstract:

In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

Procedia PDF Downloads 382

Authors: Sumit Kumar Vishwakarma

Abstract:

The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

Procedia PDF Downloads 106

Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

Abstract:

As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

Procedia PDF Downloads 518

Authors: A. A. Soliman

Abstract:

The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

Procedia PDF Downloads 280

Authors: Jyoti Wadhwa, Arvinder Singh

Abstract:

This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.

Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.

Procedia PDF Downloads 148

Authors: Mishu Gupta, Rama Gupta

Abstract:

It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

Procedia PDF Downloads 127

Authors: Zakiul Fuady, Michaela Spiske

Abstract:

Inundation events, such as storms and tsunamis can leave onshore sedimentary evidence like sand deposits or large boulders. These deposits store indirect information on the related inundation parameters (e.g., flow velocity, flow depth, wave height). One tool to reveal these parameters are inverse models that use the physical characteristics of the deposits to refer to the magnitude of inundation. This study used boulders of the 2004 Indian Ocean Tsunami from Thailand (Pakarang Cape) and form a historical tsunami event that inundated the outer British Virgin Islands (Anegada). For the largest boulder found in Pakarang Cape with a volume of 26.48 m³ the required tsunami wave height is 0.44 m and storm wave height are 1.75 m (for a bulk density of 1.74 g/cm³. In Pakarang Cape the highest tsunami wave height is 0.45 m and storm wave height are 1.8 m for transporting a 20.07 m³ boulder. On Anegada, the largest boulder with a diameter of 2.7 m is the asingle coral head (species Diploria sp.) with a bulk density of 1.61 g/cm³, and requires a minimum tsunami wave height of 0.31 m and storm wave height of 1.25 m. The highest required tsunami wave height on Anegada is 2.12 m for a boulder with a bulk density of 2.46 g/cm³ (volume 0.0819 m³) and the highest storm wave height is 5.48 m (volume 0.216 m³) from the same bulk density and the coral type is limestone. Generally, the higher the bulk density, volume, and weight of the boulders, the higher the minimum tsunami and storm wave heights required to initiate transport. It requires 4.05 m/s flow velocity by Nott’s equation (2003) and 3.57 m/s by Nandasena et al. (2011) to transport the largest boulder in Pakarang Cape, whereas on Anegada, it requires 3.41 m/s to transport a boulder with diameter 2.7 m for both equations. Thus, boulder equations need to be handled with caution because they make many assumptions and simplifications. Second, the physical boulder parameters, such as density and volume need to be determined carefully to minimize any errors.

Keywords: tsunami wave height, storm wave height, flow velocity, boulders, Anegada, Pakarang Cape

Procedia PDF Downloads 214

Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

Abstract:

Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

Procedia PDF Downloads 494

Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

Procedia PDF Downloads 469

Authors: Yingchen Yang

Abstract:

Ocean waves are a rich renewable energy source that is nearly untapped to date, even though many wave energy conversion (WEC) technologies are currently under development. The present work discusses a vertical-axis WEC rotor for power generation. The rotor was specially designed to allow easy rearrangement of the same blades to achieve different rotor configurations and result in different wave-rotor interaction behaviors. These rotor configurations were tested in a wave tank under various wave conditions. The testing results indicate that all the rotor configurations perform unidirectional rotation about the vertical axis in waves, but the response characteristics are somewhat different. The rotor's unidirectional rotation about its vertical axis is essential in wave energy harvesting since it makes the rotor respond well in a wide range of the wave frequency and in any wave propagation directions. Result comparison among different configurations leads to a preferred rotor design for further hydrodynamic optimization.

Keywords: unidirectional rotation, vertical axis rotor, wave energy conversion, wave-rotor interaction

Procedia PDF Downloads 148

Authors: Ross Calvert, Colin Whittaker, Alison Raby, Alistair G. L. Borthwick, Ton S. van den Bremer

Abstract:

Large concentrations of plastic have polluted the seas in the last half century, with harmful effects on marine wildlife and potentially to human health. Plastic pollution will have lasting effects because it is expected to take hundreds or thousands of years for plastic to decay in the ocean. The question arises how waves transport plastic in the ocean. The predominant motion induced by waves creates ellipsoid orbits. However, these orbits do not close, resulting in a drift. This is defined as Stokes drift. If a particle is infinitesimally small and the same density as water, it will behave exactly as the water does, i.e., as a purely Lagrangian tracer. However, as the particle grows in size or changes density, it will behave differently. The particle will then have its own inertia, the fluid will exert drag on the particle, because there is relative velocity, and it will rise or sink depending on the density and whether it is on the free surface. Previously, plastic pollution has all been considered to be purely Lagrangian. However, the steepness of waves in the ocean is small, normally about α = k₀a = 0.1 (where k₀ is the wavenumber and a is the wave amplitude), this means that the mean drift flows are of the order of ten times smaller than the oscillatory velocities (Stokes drift is proportional to steepness squared, whilst the oscillatory velocities are proportional to the steepness). Thus, the particle motion must have the forces of the full motion, oscillatory and mean flow, as well as a dynamic buoyancy term to account for the free surface, to determine whether inertia is important. To track the motion of a floating inertial particle under wave action requires the fluid velocities, which form the forcing, and the full equations of motion of a particle to be solved. Starting with the equation of motion of a sphere in unsteady flow with viscous drag. Terms can added then be added to the equation of motion to better model floating plastic: a dynamic buoyancy to model a particle floating on the free surface, quadratic drag for larger particles and a slope sliding term. Using perturbation methods to order the equation of motion into sequentially solvable parts allows a parametric equation for the transport of inertial finite-sized floating particles to be derived. This parametric equation can then be validated using numerical simulations of the equation of motion and flume experiments. This paper presents a parametric equation for the transport of inertial floating finite-size particles by ocean waves. The equation shows an increase in Stokes drift for larger, less dense particles. The equation has been validated using numerical solutions of the equation of motion and laboratory flume experiments. The difference in the particle transport equation and a purely Lagrangian tracer is illustrated using worlds maps of the induced transport. This parametric transport equation would allow ocean-scale numerical models to include inertial effects of floating plastic when predicting or tracing the transport of pollutants.

Keywords: perturbation methods, plastic pollution transport, Stokes drift, wave flume experiments, wave-induced mean flow

Procedia PDF Downloads 97

Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, 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 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 bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. 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 92

Authors: Iwan Setiawan, Bobby Eka Gunara, Katshuhiro Nakamura

Abstract:

The theory to accelerate system on quantum dynamics has been constructed to get the desired wave function on shorter time. This theory is developed on adiabatic quantum dynamics which any regulation is done on wave function that satisfies Schrödinger equation. We show accelerated manipulation of WFs with the use of a parameter-dependent in asymmetric double-well potential and also when it’s influenced by electromagnetic fields.

Keywords: driving potential, Adiabatic Quantum Dynamics, regulation, electromagnetic field

Procedia PDF Downloads 312

Authors: R. K. Apalowo, D. Chronopoulos

Abstract:

A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

Procedia PDF Downloads 132