Nonlinear Wave Theory Research Articles

Development of jacket platform tsunami risk rating system in waters offshore North Borneo

This work details the simulation of tsunami waves generated by seaquakes in the Manila Trench and their effect on fixed oil and gas jacket platforms in waters offshore North Borneo. For this study, a four-leg living quarter jacket platform located in a water depth of 63m is modelled in SACS v5.3. Malaysia has traditionally been perceived to be safe from the hazards of earthquakes and tsunamis. Local design practices tend to neglect tsunami waves and include no such provisions. In 2004, a 9.3M w seaquake occurred off the northwest coast of Aceh, which generated tsunami waves that caused destruction in Malaysia totalling US$ 25 million and 68 deaths. This event prompted an awareness of the need to study the reliability of fixed offshore platforms scattered throughout Malaysian waters. In this paper, we present a review of research on the seismicity of the Manila Trench, which is perceived to be high risk for Southeast Asia. From the tsunami numerical model TUNA-M2, we extract computer-simulated tsunami waves at prescribed grid points in the vicinity of the platforms in the region. Using wave heights as input, we simulate the tsunami using SACS v5.3 structural analysis software of offshore platforms, which is widely accepted by the industry. We employ the nonlinear solitary wave theory in our tsunami loading calculations for the platforms, and formulate a platform-specific risk quantification system. We then perform an intensive structural sensitivity analysis and derive a corresponding platform-specific risk rating model.

Nonlinear Wave‐Based Measurement Location Design and Online Estimation of a High‐Purity Heat‐Integrated Distillation Column

AbstractA heat‐integrated distillation column (HIDiC) provides a great opportunity for energy conservation in distillation. The nonlinear wave theory offers an accurate and simplified description of the HIDiC. To utilize the wave model online, an estimator design is necessary since the wave model parameters cannot be measured directly. A method for selecting the location of the stage concentration measurements is proposed here to estimate the wave model parameters online. The first several measurement locations are selected based on a weighted principal component analysis (PCA) method, and the remaining measurements are decided on by a relative distribution index. Separation of a benzene‐toluene mixture is used to illustrate the performance of the selection and estimation. The simulation results show that the proposed method has a stronger adaptability than the method based on PCA.

Pseudo random interpretation of double hinged ALP under aerodynamic loading

Summary Wind produces three different types of effects on structure: static, dynamic and aerodynamic. When the structure deflects in response to wind load then the dynamic and aerodynamic effects should be analysed. The basic mode of an articulated tower is the motion characterized by rigid body sway compliant with a relatively high natural period. The higher modes of oscillation have smaller periods, and their influence is rather insignificant in the overall platform motion. Since the wind velocity spectrum of the fluctuating component has lower frequency energy content, the wind induced vibration of an articulated tower may be significant. The wind induced overturning moment increases linearly with the height of the structure, and thus, as these structures are built in deep and deeper water, the effects of wind drag then become increasingly significant in design. To approach towards the realistic environment, the dynamic analysis of double-hinged articulated tower under the action of wind, waves and current has been carried out. The wave forces with the interaction of current have been computed by the application of Stokes’ fifth order nonlinear wave theory. The sea state with respect to wind speed of 25 m/s (Hs = 18.03 m, Tz = 13.59 s) has been considered and standard wind velocity spectrum Ahsan Kareem has been used for the dynamic analysis. The Pierson Moskowitz sea surface elevation spectrum has been used to model the random wave loads. The responses have been obtained under multi-point wind field. The study shows that energy content under combined action of wave and wind forces is more than energy derived under wave alone forces. Results also show that upper hinge is more dynamically active than lower hinge due to wind forces. PSDF shows that wind forces do not practically affect the bending moment, which is predominantly governed by the second mode of frequency; however, the other response parameters like deck displacement, hinge rotation and hinge shear were affected in significant manner under the action of wind forces.

A comparative study between the IGN-2 equations and the fully nonlinear, weakly dispersive Boussinesq equations

This work focuses on the comparison between the fully nonlinear, and weakly dispersive Boussinesq equations and the irrotational Green–Naghdi Level 2 (IGN-2) equations for incompressible and inviscid fluid and irrotational flow resulting from waves in finite water depth. We provide in this paper for the first time a comprehensive comparison of the GN/IGN and Boussinesq wave theories for strongly nonlinear and weakly dispersive waves. The Boussinesq approach results in many different theories depending on the different orders of approximation of nonlinearity and dispersion used in the corresponding perturbation series. The fully nonlinear, weakly dispersive Boussinesq equations have been widely used in problems involving coastal regions and harbors because it is more efficient than fully nonlinear, strongly dispersive Boussinesq equations. A competing theory is the strongly nonlinear IGN-2 wave theory. Since both sets of equations have comparable complexity, it is appropriate to compare the results of these equations with known numerically exact solutions to determine the advantages of each approach. In this study, we use the same iterative algorithm to obtain the steady solutions of the IGN-2 and Boussinesq equations for periodic waves. The steady solutions of the IGN-2 and Boussinesq equations are studied for four different wavelengths that cover a range of applicability of the theories. We show in this study that the Boussinesq equations give more accurate results for the velocity distribution at the wave-crest transection. The IGN-2 equations give more accurate results for the velocity distribution at the wave-trough transection. Moreover, it is shown that the IGN-2 equations give more accurate results on the wave speed and wave profile, and that they can treat accurately waves higher than the ones that the Boussinesq equations can treat. The calculations show that both of these sets of equations are very good for strongly nonlinear wave simulations and the limitations of each are different.

On the two - dimensional nonlinear Korteweg - de Vries equation with cubic stream function

In the theory of nonlinear oscillations and waves with dissipation and dispersion of the medium, it is applied the two-dimensional Korteweg - de Vries equation. In this paper a generalized nonlinear partial differential equation of third order with a cubic stream function is considered. The exact analytical solutions of two-dimensional Korteweg - de Vries equation and Kadomtsev - Petviashvili equation are obtained. The graphs effect of non-linear parameters of medium to the maximum amplitude of the waves is presented.

Numerical simulation analysis of high efficient SFG and color separation in far field in high power laser facility based on noncollinear phase matching by KDP crystal

Asymmetric property of wedge lens in 3 optical path which is used as frequency separation, and focusing element is considered to be an unfavourable factor for target alignment in inertial confinement fusion (ICF). Furthermore, the thickness of wedge lens in 3 optical path will lead to laser induced damage inevitably. For the purpose of scheme improvement of final optical assembly, types I and II noncollinear sum frequency generation in KDP crystal at room temperature are discussed based on nonlinear coupled wave theory. As illustrated by simulated result, in addition to type II collinear SFG used in ICF recently, 351 nm (3) waves can be generated by type I or II noncollinear SFG process. This method can realize color separations of , 2, 3 in far field without asymmetric element such as wedge lens and posses adequate tolerance of matching angle corresponding to the high efficiency conversion. As calculated, for type I SFG, when the noncollinear angle is in the interval from 0 to 19.99, phase matching condition can be satisfied in KDP crystal. The noncritical phase matching angle 3 is 90 and the corresponding noncollinear angle is about 19.99. The tolerance of mismatching angle is about 20 mrad. For type II SFG, the noncollinear angle interval that can satisfy phase matching process is about 0-13.55. Like type I SFG, there is also an noncritical solution in type II process whose matching angle is about (3) = 86.53. Because of the smaller effective nonlinear coefficient in this case, high efficiency conversion needs about 5 cm thick SFG crystal under 1 GW/cm2. Correspondingly, tolerance of mismatching angle is about 20 mrad. Because of the harsh tolerance of noncollinear angle between and 2 and for the purpose of compactness of final optical assembly, another method of noncollinear SFG is proposed: a piece of silica wedge with 12 wedged angle is mounted behind the SHG crystal in order to produce a 3.5 mrad intersection angle between and 2, and after type II noncollinear SFG process, , 2, 3 will be frequency separated in far field automatically by using thin lens. The tolerance of incident angle corresponding to high efficient conversion is about 1.0 mrad. This scheme can improve the the final optical assembly used recently.

Development of Extended Generic Model Control for High-Purity Heat Integrated Distillation Column Using Online Concentration Estimation

A hybrid control scheme consisting of an online concentration estimator and an extended generic model controller (EGMC) is proposed for the high-purity control of the heat integrated distillation column (HIDiC). The estimator is designed based on a principal component analysis (PCA) based method and the nonlinear wave theory of HIDiC. The PCA-based method is introduced to determine the locations of a limited number of measurements, while the nonlinear wave theory is presented to estimate the stage concentration according to the wave profile parameters estimated from the selected measurements. Then the EGMC controller coupling with the online estimation is established. A benzene–toluene system is taken as an illustration, and a comparative simulation study is carried out among the proposed EGMC, a nonlinear-wave-based classical generic model controller (WGMC), proportional–integral–derivative control (PID), and a model predictive control scheme (MPC). Finally, EGMC shows a superior performance over the oth...

Polarization modulation instability in a Manakov fiber system

The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formation. Here, we report experiments in optical fiber that provide evidence of passband and baseband polarization modulation instabilities in a defocusing Manakov system. In the spontaneous regime, we also reveal a unique saturation effect as the pump power increases. We anticipate that such observations may impact the application of this minimal model to describe and understand more complicated phenomena in nature, such as the formation of extreme waves in multicomponent systems.

THE STRUCTURE OF SPIRAL SHOCKS EXCITED BY PLANETARY-MASS COMPANIONS

Direct imaging observations have revealed spiral structures in protoplanetary disks. Previous studies have suggested that planet-induced spiral arms cannot explain some of these spiral patterns, due to the large pitch angle and high contrast of the spiral arms in observations. We have carried out three dimensional (3-D) hydrodynamical simulations to study spiral wakes/shocks excited by young planets. We find that, in contrast with linear theory, the pitch angle of spiral arms does depend on the planet mass, which can be explained by the non-linear density wave theory. A secondary (or even a tertiary) spiral arm, especially for inner arms, is also excited by a massive planet. With a more massive planet in the disk, the excited spiral arms have larger pitch angle and the separation between the primary and secondary arms in the azimuthal direction is also larger. We also find that although the arms in the outer disk do not exhibit much vertical motion, the inner arms have significant vertical motion, which boosts the density perturbation at the disk atmosphere. Combining hydrodynamical models with Monte-Carlo radiative transfer calculations, we find that the inner spiral arms are considerably more prominent in synthetic near-IR images using full 3-D hydrodynamical models than images based on 2-D models assuming vertical hydrostatic equilibrium, indicating the need to model observations with full 3-D hydrodynamics. Overall, companion-induced spiral arms not only pinpoint the companion's position but also provide three independent ways (pitch angle, separation between two arms, and contrast of arms) to constrain the companion's mass.

Aspects regarding at 13C isotope separation column control using Petri nets system

This paper is intended to show that Petri nets can be also applicable in the chemical industry. It used linear programming, modeling underlying Petri nets, especially discrete event systems for isotopic separation, the purpose of considering and control events in real-time through graphical representations. In this paper it is simulate the control of 13C Isotope Separation column using Petri nets. The major problem with 13C comes from the difficulty of obtaining it and raising its natural fraction. Carbon isotopes can be obtained using many methods, one of them being the cryogenic distillation of carbon monoxide. Some few aspects regarding operating conditions and the construction of such cryogenic plants are known today, and even less information are available as far as the separation process modeling and control are concerned. In fact, the efficient control of the carbon monoxide distillation process represents a necessity for large-scale 13C production. Referring to a classic distillation process, some models for carbon isotope separation have been proposed, some based on mass, component and energy balance equations, some on the nonlinear wave theory or the Cohen equations. For modeling the system it was used Petri nets because in this case it is deal with discrete event systems. In use of the non-timed and with auxiliary times Petri model, the transport stream was divided into sections and these sections will be analyzed successively. Because of the complexity of the system and the large amount of calculations required it was not possible to analyze the system as a unitary whole. A first attempt to model the system as a unitary whole led to the blocking of the model during simulation, because of the large processing times.

Beyond the KdV: Post-explosion development.

Several threads of the last 25 years' developments in nonlinear wave theory that stem from the classical Korteweg-de Vries (KdV) equation are surveyed. The focus is on various generalizations of the KdV equation which include higher-order nonlinearity, large-scale dispersion, and a non-local integral dispersion. We also discuss how relatively simple models can capture strongly nonlinear dynamics and how various modifications of the KdV equation lead to qualitatively new, non-trivial solutions and regimes of evolution observable in the laboratory and in nature. As the main physical example, we choose internal gravity waves in the ocean for which all these models are applicable and have genuine importance. We also briefly outline the authors' view of the future development of the chosen lines of nonlinear wave theory.

Vorticity effects on nonlinear wave–current interactions in deep water

The effects of uniform vorticity on a train of ‘gentle’ and ‘steep’ deep-water waves interacting with underlying flows are investigated through a fully nonlinear boundary integral method. It is shown that wave blocking and breaking can be more prominent depending on the magnitude and direction of the shear flow. Reflection continues to occur when sufficiently strong adverse currents are imposed on ‘gentle’ deep-water waves, though now affected by vorticity. For increasingly positive values of vorticity, the induced shear flow reduces the speed of right-going progressive waves, introducing significant changes to the free-surface profile until waves are completely blocked by the underlying current. A plunging breaker is formed at the blocking point when ‘steep’ deep-water waves interact with strong adverse currents. Conversely negative vorticities augment the speed of right-going progressive waves, with wave breaking being detected for strong opposing currents. The time of breaking is sensitive to the vorticity’s sign and magnitude, with wave breaking occurring later for negative values of vorticity. Stopping velocities according to nonlinear wave theory proved to be sufficient to cause wave blocking and breaking.

Nonlinear s-polarized quasi-surface waves in the symmetric structure with a metamaterial core

The theory of nonlinear s-polarized surface waves, which propagate in a symmetric planar threelayered structure with a metamaterial core and nonlinear coverings, has been constructed. It has been shown that the occurrence of only nonlinear quasi-surface waves is possible in such a structure. Dispersion laws and energy fluxes of symmetric, even, and odd modes at different parameters have been found and investigated. The qualitative behavior of dispersion laws substantially depends on the core thickness.

A reaction-diffusion model of cholinergic retinal waves.

Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.

A model for internal bores in continuous stratification

AbstractWe describe a model for the speed of an internal bore as a function of amplitude in continuous stratification of arbitrary form. The model is developed from the Dubreil-Jacotin–Long theory for nonlinear solitary waves in the conjugate flow limit, which represents an internal hydraulic jump, by allowing dissipation across the jump. The bore speeds predicted by the model are consistent in both the small- and large-amplitude limits with the waveguide intrinsic to the ambient stratification. The model therefore represents a significant advancement over previous theories limited to sharp two-layer stratification. The model shows good agreement with Navier–Stokes simulations of both undular and turbulent internal bores generated by dam break into a continuously stratified ambient with a finite pycnocline, predicting both the front speed as well as the velocity and density structure through the bore. A model is required for the structure of the energy dissipation, and we introduce a one-parameter closure that produces excellent agreement with numerical results, particularly in the parameter limit that maximizes the overall dissipation. By varying the dissipation parameter, the model reproduces previous two-layer theories in the thin-pycnocline limit, and suggests an improved two-layer front speed relationship. It is demonstrated that, even for the sharp two-layer limit, continuous stratification, and particularly the nonlinear waveguide, must be accounted for in order to accurately predict the bore speed and structure.

New evidence for generation mechanisms of discrete and hiss‐like whistler mode waves

AbstractLinear theory suggests that whistler mode wave growth rates are proportional to the ratio of hot electron (~1 to 30 keV) density to total electron density (Nh/Nt), whereas nonlinear wave theory suggests that an optimum linear growth rate is required to generate rising tone chorus from hiss‐like emissions. Using the Time History of Events and Macroscale Interactions during Substorms waveform data collected by three probes over the past ~5 years, we investigate the correlation between Nh/Nt and wave amplitude/wave occurrence rate for rising tone, falling tone, and hiss‐like emissions separately. Statistical results show that the rising and falling tones preferentially occur in the region with a limited Nh/Nt range, whereas both the occurrence rate and wave amplitudes of hiss‐like emissions become larger for higher values of Nh/Nt. Our statistical results not only provide an important clue on the generation mechanism of hiss‐like emissions, but also provide supporting experimental evidence for the nonlinear theory of generating rising tone chorus.

Experimental characterization of granite damage using nonlinear ultrasonic techniques

In this paper, a nondestructive evaluation (NDE) technique based on the nonlinear second harmonic wave theory is developed and used to characterize damage of granite samples subjected to compressive loadings. The nonlinear parameter defined in the new NDE technique is measured and compared with two traditional parameters including ultrasonic pulse velocity and dynamic modulus. The nonlinear parameter is found to be much more sensitive to the damage development in granites than traditional parameters. It is shown that the increase of nonlinear parameter is close to an exponential trend with respect to the increased loading level, which also indicates a faster increase rate of the nonlinear parameter corresponding to the internal damage of granite samples. A practical damage index is thus defined based on the exponential increasing trend of the nonlinear parameter. The new damage index based on nonlinear parameter is found to have a positive correlation with the loading level. This observation suggests that the new damage index may become a valuable indicator of loading level (or correspondingly material degradation) of granites in the in situ NDE tests.

Ion acoustic traveling waves

AbstractModels for traveling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron–proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the traveling waves can be reduced to a single first-order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron–proton or an electron–positron plasma). Besides its intrinsic interest, the integral equation solution provides a useful analytical test for numerical codes that include a proton–electron mass ratio as a fundamental constant, such as for particle in cell (PIC) codes. The integral equation is used to delineate the physical characteristics of ion acoustic traveling waves consisting of hot electron and cold proton fluids.

Graphical Krein Signature Theory and Evans--Krein Functions

Two concepts, evidently very different in nature, have proved to be useful in analytical and numerical studies of spectral stability in nonlinear wave theory: (i) the Krein signature of an eigenvalue, a quantity usually defined in terms of the relative orientation of certain subspaces that is capable of detecting the structural instability of imaginary eigenvalues and, hence, their potential for moving into the right half-plane leading to dynamical instability under perturbation of the system; and (ii) the Evans function, an analytic function detecting the location of eigenvalues. One might expect these two concepts to be related, but unfortunately examples demonstrate that there is no way in general to deduce the Krein signature of an eigenvalue from the Evans function, for example, by studying derivatives of the latter. The purpose of this paper is to recall and popularize a simple graphical interpretation of the Krein signature well known in the spectral theory of polynomial operator pencils. Once esta...

陸前高田地区気仙大橋の津波被害分析

Many bridges in the coast of Rikuzentakata Area were destructed by the tsunami due to Great East Japan Earthquake. From field surveys, it was confirmed that many bridge girders were swept away and a variety of videos recording tsunami were obtained. In this research, the video analysis and two-dimensional numerical analysis based on the non-linear long wave theory were conducted. Moreover, it was observed that the Kesen Bridge was not affected by bore wave at surge front, but was washed away by the steady flow with the velocity of about 6.0m/s.