Search results for: weak non-linear waves

Authors: Gigih Priyandoko, Mohd Fairusham Ghazali, Tan Siew Fun

Abstract:

This paper discusses about the defect detection of plastic pipe by using nonlinear acoustic wave modulation method. It is a sensitive method for damage detection and it is based on the propagation of high frequency acoustic waves in plastic pipe with low frequency excitation. The plastic pipe is excited simultaneously with a slow amplitude modulated vibration pumping wave and a constant amplitude probing wave. The frequency of both the excitation signals coincides with the resonances of the plastic pipe. A PVP pipe is used as the specimen as it is commonly used for the conveyance of liquid in many fields. The results obtained are being observed and the difference between uncracked specimen and cracked specimen can be distinguished clearly.

Keywords: plastic pipe, defect detection, nonlinear acoustic modulation, excitation

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Authors: A. A. Abid

Abstract:

The magnetospheric multiscale (MMS) satellite observations in the inner magnetosphere were used to detect the proton band of the electromagnetic ion cyclotron (EMIC) waves on December 14, 2015, which have been significantly contributing to the dynamics of the magnetosphere. It has been examined that the intensity of EMIC waves gradually increases by decreasing the L shell. The waves are triggered by hot proton thermal anisotropy. The low-energy cold protons (ions) can be activated by the EMIC waves when the EMIC wave intensity is high. As a result, these previously invisible protons are now visible. As a result, the EMC waves also excite the helium ions. The EMIC waves, whose frequency in the magnetosphere of the Earth ranges from 0.001 Hz to 5 Hz, have drawn a lot of attention for their ability to carry energy. Since these waves act as a mechanism for the loss of energetic electrons from the Van Allen radiation belt to the atmosphere, therefore, it is necessary to understand how and where they can be produced, as well as the direction of waves along the magnetic field lines. This work examines how the excitation of EMIC waves is affected by the energy of hot proton temperature anisotropy, and It has a minimum resonance energy of 6.9 keV and a range of 7 to 26 keV. On the hot protons, however, the reverse effect can be seen for energies below the minimum resonance energy. It is demonstrated that throughout the energy range of 1 eV to 100 eV, the number density and temperature anisotropy of the protons likewise rise as the intensity of the EMIC waves increases. Key Points: 1. The analysis of EMIC waves produced by hot proton temperature anisotropy using MMS data. 2. The number density and temperature anisotropy of the cold protons increases owing to high-intensity EMIC waves. 3. The cold protons with an energy range of 1-100eV are energized by EMIC waves using the Magnetospheric Multiscale (MMS) satellite not been discussed before

Keywords: EMIC waves, temperature anisotropy of hot protons, energization of the cold proton, magnetospheric multiscale (MMS) satellite observations

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Authors: Marsden Jacques, Dennis Wong

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A weak order is a way to rank n objects where ties are allowed. In this talk, we present a recursive framework to generate Gray codes for weak orders. We then describe a simple algorithm based on the framework that generates 2-Gray codes for weak orders in constant amortized time per string. This framework can easily be modified to generate other Gray codes for weak orders. We provide an example on using the framework to generate the first Shift Gray code for weak orders, also in constant amortized time, where consecutive strings differ by a shift or a symbol change.

Keywords: weak order, Cayley permutation, Gray code, shift Gray code

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

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Authors: M. A. Tayfun, M. A. Alkhalidi

Abstract:

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Prabal Singh Verma

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Electrostatic Waves in plasma have emerged as a new source for the acceleration of charged particles. The accelerated particles have a wide range of applications, for example in cancer therapy to cutting and melting of hard materials. The maximum acceleration can only be achieved when the amplitude of the plasma wave stays below a critical limit known as wave-breaking amplitude. Beyond this limit amplitude of the wave diminishes dramatically as the coherent energy of the wave starts to convert into random kinetic energy. In this work, spatiotemporal evolution of non-relativistic electrostatic waves in a cold plasma has been studied in the wave-breaking regime using a 1D particle-in-cell simulation (PIC). It is found that plasma gets heated after the wave-breaking but a fraction of initial energy always remains with the remnant wave in the form of Bernstein-Greene-Kruskal (BGK) mode in warm plasma. Another interesting finding of this work is that the frequency of the resultant BGK wave is found be below electron plasma frequency which decreases with increasing initial amplitude and the acceleration mechanism after the wave-breaking is also found to be different from the previous work. In order to explain the results observed in the numerical experiments, a simplified theoretical model is constructed which exhibits a good agreement with the simulation. In conclusion, it is shown in this work that electrostatic waves get shower after the wave-breaking and a fraction of initial coherent energy always remains with remnant wave. These investigations have direct relevance in wakefield acceleration experiments.

Keywords: nonlinear plasma waves, longitudinal, wave-breaking, wake-field acceleration

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Authors: Manoj Kumar Patel

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In this paper, we introduce and give various properties of weak* Rad-plus-supplemented and cofinitely weak* Rad-plus-supplemented modules over some special kinds of rings, in particular, artinian serial ring and semiperfect ring. Also prove that ring R is artinian serial if and only if every right and left R-module is weak* Rad-plus-supplemented. We provide the counter example which proves that weak* Rad-plus-supplemented module is the generalization of plus-supplemented and Rad-plus-supplemented modules. Furthermore, as an application of above finding results of this research article, our main focus is to characterized the semisimple ring, artinian principal ideal ring, semilocal ring, semiperfect ring, perfect ring, commutative noetherian ring and Dedekind domain in terms of weak* Rad-plus-supplemented module.

Keywords: cofinitely weak* Rad-plus-supplemented module , Dedekind domain, Rad-plus-supplemented module, semiperfect ring

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Authors: Hua Cao, Laurent Peyrodie, Olivier Agnani, Cecile Donze

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Multiple sclerosis (MS) is a disease, which affects the central nervous system, and causes balance problem. In clinical, this disorder is usually evaluated using static posturography. Some linear or nonlinear measures, extracted from the posturographic data (i.e. center of pressure, COP) recorded during a balance test, has been used to analyze postural control of MS patients. In this study, the trend (TREND) and the sample entropy (SampEn), two nonlinear parameters were chosen to investigate their relationships with the expanded disability status scale (EDSS) score. Forty volunteers with different EDSS scores participated in our experiments with eyes open (EO) and closed (EC). TREND and two types of SampEn (SampEn1 and SampEn2) were calculated for each combined COP’s position signal. The results have shown that TREND had a weak negative correlation to EDSS while SampEn2 had a strong positive correlation to EDSS. Compared to TREND and SampEn1, SampEn2 showed a better significant correlation to EDSS and an ability to discriminate the MS patients in the EC case. In addition, the outcome of the study suggests that the multi-dimensional nonlinear analysis could provide some information about the impact of disability progression in MS on dynamics of the COP data.

Keywords: balance, multiple sclerosis, nonlinear analysis, postural sway

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Authors: Hassan Al Salman

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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Ying Zhang

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Surface waves provide critical constraints about the earth's structure in the crust and upper mantle. However, different modes of Love waves with close group velocities often arrive at a similar time and interfere with each other. This problem is typical for Love waves at intermediate periods that travel through the oceanic lithosphere. Therefore, we developed a two-step inversion approach to separate the waveforms of the fundamental and first higher mode of Love waves. We first solve the phase velocities of the two modes and their amplitude ratios. The misfit function is based on the sum of phase differences among the station pairs. We then solve the absolute amplitudes of the two modes and their initial phases using obtained phase velocities and amplitude ratio. The separated waveforms of each mode from the two-step inversion method can be further used in surface wave tomography to improve model resolution.

Keywords: surface wave inversion, waveform separation, love waves, higher-mode interference

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: S. Belgherras Bekkouche, T. Benouaz, S. M. A. Bekkouche

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Tokamak plasma is far from having a stable background. The study of turbulent transport is an important part of the current research and advanced scenarios were devised to minimize it. To do this, we used a three-wave interaction model which allows to investigate the occurrence drift-wave turbulence driven by pressure gradients in the edge plasma of a tokamak. In order to simulate the energy redistribution among different modes, the growth/decay rates for the three waves was added. After a numerical simulation, we can determine certain aspects of the temporal dynamics exhibited by the model. Indeed for a wide range of the wave decay rate, an intermittent transition from periodic behavior to chaos is observed. Then, a control strategy of chaos was introduced with the aim of reducing or eliminating the weak turbulence.

Keywords: wave interaction, plasma drift waves, wave turbulence, tokamak, edge plasma, chaos

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Authors: Mohammed Daher Albalwi

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The transcritical flow of a stratified fluid over an obstacle for negative forcing amplitude (hole) that generation upstream and downstream, connected by an unsteady solution, is examined. In the weakly nonlinear, weakly dispersive regime, the problem is formulated in the forced Korteweg-de Vries–Burgers framework. This is done by including the influence of the viscosity of the fluid beyond the Korteweg–de Vries approximation. The results show that the influence of viscosity is crucial in determining various wave properties, including the amplitudes of solitary waves in the upstream and downstream directions, as well as the widths of the bores. We focused here on weak damping, and the results are presented for transcritical, supercritical, and subcritical flows. In general, the outcomes are not qualitatively similar to those from the forced Korteweg-de–Vries equation when the value of the viscous is small, interesting differences emerge as the magnitude of the value of viscous increases.

Keywords: Korteweg–de Vries–Burgers equation, soliton, transcritical flow, viscous flow

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Authors: Sanjit Kumar Paul, A. A. Mamun, M. R. Amin

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The Linear propagation of the dust-acoustic wave in a dusty plasma consisting of Boltzmann distributed electrons and ions and mobile charge fluctuating positive dust grains has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and its responsible for the formation of the dust-acoustic waves in such a dusty plasma. The basic features of such dust-acoustic waves have been identified. It has been proposed to design a new laboratory experiment which will be able to identify the basic features of the dust-acoustic waves predicted in this theoretical investigation.

Keywords: dust acoustic waves, dusty plasma, Boltzmann distributed electrons, charge fluctuation

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Ehsan Pegah, Huabei Liu

Abstract:

Characterizing the deformation properties of fill materials in a wide stress range always has been an important issue in geotechnical engineering. The hyperbolic Duncan-Chang model is a very popular model of stress-strain relationship that captures the nonlinear deformation of granular geomaterials in a very tractable manner. It consists of a particular set of the model parameters, which are generally measured from an extensive series of laboratory triaxial tests. This practice is both time-consuming and costly, especially in large projects. In addition, undesired effects caused by soil disturbance during the sampling procedure also may yield a large degree of uncertainty in the results. Accordingly, non-invasive geophysical seismic approaches may be utilized as the appropriate alternative surveys for measuring the model parameters based on the seismic wave velocities. To this end, the conventional seismic refraction profiles were carried out in the test sites with the granular fill materials to collect the seismic waves information. The acquired shot gathers are processed, from which the P- and S-wave velocities can be derived. The P-wave velocities are extracted from the Seismic Refraction Tomography (SRT) technique while S-wave velocities are obtained by the Multichannel Analysis of Surface Waves (MASW) method. The velocity values were then utilized with the equations resulting from the rigorous theories of elasticity and soil mechanics to evaluate the Duncan-Chang model parameters. The derived parameters were finally compared with those from laboratory tests to validate the reliability of the results. The findings of this study may confidently serve as the useful references for determination of nonlinear deformation parameters of granular fill geomaterials. Those are environmentally friendly and quite economic, which can yield accurate results under the actual in-situ conditions using the surface seismic methods.

Keywords: Duncan-Chang deformation parameters, granular fill materials, seismic waves velocity, multichannel analysis of surface waves, seismic refraction tomography

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Authors: Alexander Kelíšek, Denisa Janasová, Veronika Mitašová

Abstract:

Weak signals using is often associated with early warning. It is possible to find a link between early warning, respectively early problems detection and risk management. The idea of early warning is very important in the context of crisis management because of the risk prevention possibility. Weak signals are likened to risk symptoms. Nowadays, their usefulness as a tool of proactive problems solving is emphasized. Based on it, it is possible to use weak signals not only in strategic planning, project management, or early warning system, but also as a subsidiary element in risk management. The main question is how to effectively integrate weak signals into risk management. The main aim of the paper is to point out the possibilities of weak signals using in small and medium enterprises risk management.

Keywords: early warning system, weak signals, risk management, small and medium enterprises (SMEs)

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Authors: Jalil Qoulizadeh, Hasan Sadeghi

Abstract:

Brain waves are electrical wave patterns that are produced in the human brain. Knowing these waves and activating them can have a positive effect on brain function and ultimately create an ideal life. The brain has the ability to produce waves from 0.1 to above 65 Hz. (The Beta One device produces exactly these waves) This is because it is said that the waves produced by the Beta One device exactly match the waves produced by the brain. The function and method of this device is based on the magnetic stimulation of the brain. The technology used in the design and producƟon of this device works in a way to strengthen and improve the frequencies of brain waves with a pre-defined algorithm according to the type of requested function, so that the person can access the expected functions in life activities. to perform better. The effect of this field on neurons and their stimulation: In order to evaluate the effect of this field created by the device, on the neurons, the main tests are by conducting electroencephalography before and after stimulation and comparing these two baselines by qEEG or quantitative electroencephalography method using paired t-test in 39 subjects. It confirms the significant effect of this field on the change of electrical activity recorded after 30 minutes of stimulation in all subjects. The Beta One device is able to induce the appropriate pattern of the expected functions in a soft and effective way to the brain in a healthy and effective way (exactly in accordance with the harmony of brain waves), the process of brain activities first to a normal state and then to a powerful one. Production of inexpensive neuroscience equipment (compared to existing rTMS equipment) Magnetic brain stimulation for clinics - homes - factories and companies - professional sports clubs.

Keywords: stimulation, brain, waves, betaOne

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Authors: Swapan Maiti, Dipanwita Roy Chowdhury

Abstract:

Nonlinear functions are essential in different cryptoprimitives as they play an important role on the security of the cipher designs. Rule 30 was identified as a powerful nonlinear function for cryptographic applications. However, an attack (MS attack) was mounted against Rule 30 Cellular Automata (CA). Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide maximum length cycle as well as better cryptographic primitives and they are also secure against MS attack.

Keywords: cellular automata, maximum period nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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Authors: Swati Sharma, R. P. Sharma

Abstract:

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: Joseph Zernik

Abstract:

The mechanics of rip currents are complex, involving interactions between waves, currents, water levels and the bathymetry, that present particular challenges for numerical models. Here, the effects of a grid-spacing dependent horizontal mixing on the wave-current interactions are studied. Near the shore, wave rays diverge from channels towards bar crests because of refraction by topography and currents, in a way that depends on the rip current intensity which is itself modulated by the horizontal mixing. At low resolution with the grid-spacing dependent horizontal mixing, the wave motion is the same for both coupling modes because the wave deviation by the currents is weak. In high-resolution case, however, classical results are found with the stabilizing effect of the flow by feedback of waves on currents. Lastly, wave-current interactions and the horizontal mixing strongly affect the intensity of the three-dimensional rip velocity.

Keywords: e-justice, federal courts, human rights, banking regulation, United States

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Authors: Andrey Cherdantsev, Mikhail Cherdantsev, Sergey Isaenkov, Dmitriy Markovich

Abstract:

In annular gas-liquid flow, liquid flows as a film along pipe walls sheared by high-velocity gas stream. Film surface is covered by large-scale disturbance waves which affect pressure drop and heat transfer in the system and are necessary for entrainment of liquid droplets from film surface into the core of gas stream. Disturbance waves are a highly complex and their properties are affected by numerous parameters. One of such aspects is flow development, i.e., change of flow properties with the distance from the inlet. In the present work, this question is studied using brightness-based laser-induced fluorescence (BBLIF) technique. This method enables one to perform simultaneous measurements of local film thickness in large number of points with high sampling frequency. In the present experiments first 50 cm of upward and downward annular flow in a vertical pipe of 11.7 mm i.d. is studied with temporal resolution of 10 kHz and spatial resolution of 0.5 mm. Thus, spatiotemporal evolution of film surface can be investigated, including scenarios of formation, acceleration and coalescence of disturbance waves. The behaviour of disturbance waves' velocity depending on phases flow rates and downstream distance was investigated. Besides measuring the waves properties, the goal of the work was to investigate the interrelation between disturbance waves properties and integral characteristics of the flow such as interfacial shear stress and flow rate of dispersed phase. In particular, it was shown that the initial acceleration of disturbance waves, defined by the value of shear stress, linearly decays with downstream distance. This lack of acceleration which may even lead to deceleration is related to liquid entrainment. Flow rate of disperse phase linearly grows with downstream distance. During entrainment events, liquid is extracted directly from disturbance waves, reducing their mass, area of interaction to the gas shear and, hence, velocity. Passing frequency of disturbance waves at each downstream position was measured automatically with a new algorithm of identification of characteristic lines of individual disturbance waves. Scenarios of coalescence of individual disturbance waves were identified. Transition from initial high-frequency Kelvin-Helmholtz waves appearing at the inlet to highly nonlinear disturbance waves with lower frequency was studied near the inlet using 3D realisation of BBLIF method in the same cylindrical channel and in a rectangular duct with cross-section of 5 mm by 50 mm. It was shown that the initial waves are generally two-dimensional but are promptly broken into localised three-dimensional wavelets. Coalescence of these wavelets leads to formation of quasi two-dimensional disturbance waves. Using cross-correlation analysis, loss and restoration of two-dimensionality of film surface with downstream distance were studied quantitatively. It was shown that all the processes occur closer to the inlet at higher gas velocities.

Keywords: annular flow, disturbance waves, entrainment, flow development

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Authors: Jade Martínez-Llinàs, Pere Colet

Abstract:

By exploring the possible dynamical regimes in a prototypical model for mutually delay-coupled OEOs, here it is shown that two mutually coupled non-identical OEOs, besides in- and out-of-phase square-waves, can generate stable square-wave pulses synchronized at a quarter of the period (T/4) in a broad parameter region. The key point to obtain T/4 solutions is that the two OEO operate with mixed feedback, namely with negative feedback in one and positive in the other. Furthermore, the coexistence of multiple solutions provides a large degree of flexibility for tuning the frequency in the GHz range without changing any parameter. As a result the two coupled OEOs system is good candidate to be implemented for information encoding as a high-capacity memory device.

Keywords: nonlinear optics, optoelectronic oscillators, square waves, synchronization

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Authors: A. C. Bennis, F. Dumas, F. Ardhuin, B. Blanke

Abstract:

The mechanics of rip currents are complex, involving interactions between waves, currents, water levels and the bathymetry, that present particular challenges for numerical models. Here, the effects of a grid-spacing dependent horizontal mixing on the wave-current interactions are studied. Near the shore, wave rays diverge from channels towards bar crests because of refraction by topography and currents, in a way that depends on the rip current intensity which is itself modulated by the horizontal mixing. At low resolution with the grid-spacing dependent horizontal mixing, the wave motion is the same for both coupling modes because the wave deviation by the currents is weak. In high-resolution case, however, classical results are found with the stabilizing effect of the flow by feedback of waves on currents. Lastly, wave-current interactions and the horizontal mixing strongly affect the intensity of the three-dimensional rip velocity.

Keywords: numerical modeling, wave-current interactions, turbulence modeling, rip currents

Procedia PDF Downloads 433

Authors: Francisco Velez, Juan David Gomez

Abstract:

Dispersion effects on the Scattering for a semicircular canyon in a micropolar continuum are analyzed, by using a computational finite element scheme. The presence of microrotational waves and the dispersive SV waves affects the propagation of elastic waves. Here, a contrast with the classic model is presented, and the dependence with the micropolar parameters is studied.

Keywords: scattering, semicircular canyon, wave dispersion, micropolar medium, FEM modeling

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Authors: Jayahar Sivasubramanian

Abstract:

Understanding laminar-turbulent transition process in hyper-sonic boundary layers is crucial for designing viable high speed flight vehicles. The study of transition becomes particularly important in the high speed regime due to the effect of transition on aerodynamic performance and heat transfer. However, even after many years of research, the transition process in hyper-sonic boundary layers is still not understood. This lack of understanding of the physics of the transition process is a major impediment to the development of reliable transition prediction methods. Towards this end, spatial Direct Numerical Simulations are conducted to investigate the instability waves generated by a localized disturbance in a hyper-sonic flat plate boundary layer. In order to model a natural transition scenario, the boundary layer was forced by a short duration (localized) pulse through a hole on the surface of the flat plate. The pulse disturbance developed into a three-dimensional instability wave packet which consisted of a wide range of disturbance frequencies and wave numbers. First, the linear development of the wave packet was studied by forcing the flow with low amplitude (0.001% of the free-stream velocity). The dominant waves within the resulting wave packet were identified as two-dimensional second mode disturbance waves. Hence the wall-pressure disturbance spectrum exhibited a maximum at the span wise mode number k = 0. The spectrum broadened in downstream direction and the lower frequency first mode oblique waves were also identified in the spectrum. However, the peak amplitude remained at k = 0 which shifted to lower frequencies in the downstream direction. In order to investigate the nonlinear transition regime, the flow was forced with a higher amplitude disturbance (5% of the free-stream velocity). The developing wave packet grows linearly at first before reaching the nonlinear regime. The wall pressure disturbance spectrum confirmed that the wave packet developed linearly at first. The response of the flow to the high amplitude pulse disturbance indicated the presence of a fundamental resonance mechanism. Lower amplitude secondary peaks were also identified in the disturbance wave spectrum at approximately half the frequency of the high amplitude frequency band, which would be an indication of a sub-harmonic resonance mechanism. The disturbance spectrum indicates, however, that fundamental resonance is much stronger than sub-harmonic resonance.

Keywords: boundary layer, DNS, hyper sonic flow, instability waves, wave packet

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Authors: Jaime E. Munoz, Jose C. Arcos, Oscar E. Bautista, Ivan E. Campos

Abstract:

The influence of slippage phenomenon over the destabilization and atomization mechanisms induced via surface acoustic waves on a Newtonian, millimeter-sized, drop deposited on a hydrophilic substrate is studied theoretically. By implementing the Navier-slip model and a lubrication-type approach into the equations which govern the dynamic response of a drop exposed to acoustic stress, a highly nonlinear evolution equation for the air-liquid interface is derived in terms of the acoustic capillary number and the slip coefficient. By numerically solving such an evolution equation, the Spatio-temporal deformation of the drop's free surface is obtained; in this context, atomization of the initial drop into micron-sized droplets is predicted at our numerical model once the acoustically-driven capillary waves reach a critical value: the instability length. Our results show slippage phenomenon at systems with partial and complete wetting favors the formation of capillary waves at the free surface, which traduces in a major volume of liquid being atomized in comparison to the no-slip case for a given time interval. In consequence, slippage at the wall possesses the capability to affect and improve the atomization rate for a drop exposed to a high-frequency acoustic field.

Keywords: capillary instability, lubrication theory, navier-slip condition, SAW atomization

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

Abstract:

On the basis of the finite deformation theory, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: acoustoelasticity, dispersion, finite deformation, lamb waves

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Authors: Rafat Alshorman, Fadi Awawdeh

Abstract:

By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Bououden Soraya

Abstract:

This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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