Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrari...Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L0≤1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.展开更多
The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation(NLSE).The first method is to ...The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation(NLSE).The first method is to derive a Korteweg–de Vries(KdV)-type equation and then derive the NLSE from the KdV-type equation,while the second one is to directly derive the NLSE from the original equation.It is found that the envelope waves from the two methods have different dispersion relations,different group velocities.The results indicate that two envelope wave solutions from two different methods are completely different.The results also show that the application scope of the envelope wave obtained from the second method is wider than that of the first one,though both methods are valuable in the range of their corresponding application scopes.It is suggested that,for other systems,both methods to derive NLSE may be correct,but their nonlinear wave solutions are different and their application scopes are also different.展开更多
Large amplitude (1+1)-dimensional nonlinear ion acoustic waves are theoretically studied in multicomponent plasma consisting of positively charged ions and negatively charged ions, ion beam, kappa-distributed electron...Large amplitude (1+1)-dimensional nonlinear ion acoustic waves are theoretically studied in multicomponent plasma consisting of positively charged ions and negatively charged ions, ion beam, kappa-distributed electrons, and dust grains,respectively. By using the Sagdeev potential method, the dynamical system and the Sagdeev potential function are obtained.The important influences of system parameters on the phase diagram of this system are investigated. It is found that the linear waves, the nonlinear waves and the solitary waves are coexistent in the multicomponent plasma system. Meanwhile,the variations of Sagdeev potential with parameter can also be obtained. Finally, it seems that the propagating characteristics of (1+1)-dimensional nonlinear ion acoustic solitary waves and ion acoustic nonlinear shock wave can be influenced by different parameters of this system.展开更多
The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlin...The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.展开更多
Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relativ...Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device(CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.展开更多
It is recognized that standing wave effects appearing in large-area,very-high-frequency capacitively coupled plasma(CCP)reactors cause center-high plasma non-uniformity.Using a high-frequency magnetic probe,we present...It is recognized that standing wave effects appearing in large-area,very-high-frequency capacitively coupled plasma(CCP)reactors cause center-high plasma non-uniformity.Using a high-frequency magnetic probe,we present a direct experimental diagnostic of the nonlinear standing waves and bulk ohmic electron power absorption dynamics in low pressure CCP discharges for different driving frequencies of 13.56,30,and 60 MHz.The design,principle,calibration,and validation of the probe are described in detail.Spatial structures of the harmonics of the magnetic field,determined by the magnetic probe,were used to calculate the distributions of the harmonic current and the corresponding ohmic electron power deposition,providing insights into the behavior of nonlinear harmonics.At a low driving frequency,i.e.13.56 MHz,no remarkable nonlinear standing waves were identified and the bulk ohmic electron power absorption was observed to be negligible.The harmonic magnetic field/current was found to increase dramatically with the driving frequency,due to decreased sheath reactance and more remarkable nonlinear standing waves at a higher driving frequency,leading to the enhancements of the ohmic heating and the plasma density in the bulk,specifically at the electrode center.At a high driving frequency,i.e.60 MHz,the high-order harmonic current density and the corresponding ohmic electron power absorption exhibited a similar node structure,with the main peak on axis,and one or more minor peaks between the electrode center and the edge,contributing to the center-high profile of the plasma density.展开更多
This letter reports experimental observation of a direct correlation between the acoustic nonlinearity parameter (NP) measured with nonlinear Rayleigh waves and the accumulation of plasticity damage in an AZ31 magnesi...This letter reports experimental observation of a direct correlation between the acoustic nonlinearity parameter (NP) measured with nonlinear Rayleigh waves and the accumulation of plasticity damage in an AZ31 magnesium alloy plate specimen.Rayleigh waves are generated and detected with wedge transducers,and the NPs are measured at different stress levels.The results show that there is a significant increase in the NPs with monotonic tensile loads surpassing the material's yielding stress.The research suggests an effective nondestructive evaluation method to track the surface damage in metals.展开更多
The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation ...The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation of the Korteweg-de Vries equations for solitons by using the method of multiple scale expansion. The proposed problem describes the behavior of the system for free surface between air and water in a nonlinear approach. To solve this problem, we use the well-known analytical method, namely, variational iteration method (VIM). The proposed method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. The proposed method provides a sequence of functions which may converge to the exact solution of the proposed problem. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves.展开更多
The nonlinear propagation of positron acoustic periodic(PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ...The nonlinear propagation of positron acoustic periodic(PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov-Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis,and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. The present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.展开更多
Propagation of coupled electrostatic drift and ion-acoustic waves(DIAWs) is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves ...Propagation of coupled electrostatic drift and ion-acoustic waves(DIAWs) is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct(small, intermediate and large) scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa–Mima equation for the electrostatic potential(involving both vector and scalar nonlinearities) and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.展开更多
Major differences in beach erosion between two neighboring artificial beaches Xiangluwan Beach(XL beach)and Meiliwan Beach(ML beach)in Zhuhai,China,were studied after Super Typhoon Hato.In this study,a fully nonlinear...Major differences in beach erosion between two neighboring artificial beaches Xiangluwan Beach(XL beach)and Meiliwan Beach(ML beach)in Zhuhai,China,were studied after Super Typhoon Hato.In this study,a fully nonlinear Boussinesq wave model(FUNWAVE)-Total Variation Diminishing(TVD)was used to distinguish the main impact factors,their relative contributions,and the hydrodynamic mechanisms underlying the different beach responses.Results show that compared to the ML beach,the main reason for the relatively weak erosion on Xiangluwan(XL)beach was the smaller beach berm height(accounting for approximately 75.9%of the erosion response).Regarding the beach with a higher berm,the stronger wave-induced undertow flow,along with the higher sediment concentration,led to a higher offshore sediment transport flux,resulting in more severe erosion relative to the beach with a smaller berm height.The second most important reason explaining the weak erosion on XL beach was the absence of seawalls(accounting for approximately 17.9%of the erosion response).Wave reflection induced by the seawall could cause higher suspended sediment concentration,resulting in a toe scouring near the seawall.The offshore submerged breakwater protected XL beach slightly(accounting for approximately 6.1%of the erosion response).Due to the higher water level induced by storm surge,most of the wave energy could penetrate through the submerged breakwater.The effect of the larger berm width of XL beach was negligible.Compared to the beach with a larger berm width,the erosion/deposition regions in the beach with a narrower berm width showed shoreward migration,without significant changes in the erosion/deposition extent.Despite of this,the larger berm width could reduce the wave energy reaching the shoreline.This study of the storm stability of artificial beaches may be applied to beach restoration design.展开更多
Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the(G′/G)method to exhibit the effects of dust cha...Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the(G′/G)method to exhibit the effects of dust charge fluctuations on the evolution of nonlinear waves. The coherent features of the shock and solitary waves along with the generation of high-energy waves have been amplified through the solution of the Korteweg–de Vries–Burgers equation,and the different natures of the waves were found successfully. Results are discussed graphically with the thoughtful choice of typical plasma parameters from different space plasma environments, exactly those found in cosmic dusty plasmas laden in ionospheric auroral region,radial spokes of Saturn's rings, planetary nebulae and solar F-corona region. All conclusions are in good accordance with the actual occurrences and could be of interest to further investigations of space. Moreover, the applicability of the present method is hoped to be a great enhancement by its use as ingenious mechanism used to evaluate the soliton dynamics and Burgers shock waves.展开更多
The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of el...The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of electron clouds used in chemistry. The relativistic wave equation is associated with a Lagrangian density, thus also with an energy-momentum tensorial density. The wave of an electron cloud adds these energy-momentum densities, while photons in light are precisely those differences between such energy-momentum densities.展开更多
We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures.Simulation models of three-dimensional(3D)aluminum plates a...We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures.Simulation models of three-dimensional(3D)aluminum plates and composite laminates are established by ABAQUS software,where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage.The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated.Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes.There is a positive correlation among crack length,height,and sum and difference frequency amplitudes for an aluminum plate,with both amplitudes decreasing as crack thickness increased,i.e.,nonlinear effect weakens as the micro-crack becomes thicker.The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates.Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.展开更多
An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper.Starting from the basic model equations of oceanic motions,a Korteweg de Vries equation is deriv...An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper.Starting from the basic model equations of oceanic motions,a Korteweg de Vries equation is derived to simulate the evolution of equatorial nonlinear near-inertial waves by using methods of scaling analysis and perturbation expansions under the equatorial beta plane approximation.Theoretical dynamic analysis is finished based on the obtained Korteweg de Vries equation,and the results show that the horizontal component of Coriolis parameters is of great importance to the propagation of equatorial nonlinear near-inertial solitary waves by modifying its dispersion relation and by interacting with the basic background flow.展开更多
This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of plana...This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefcients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form.展开更多
A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic non...A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.展开更多
A distant-neighbor quantum-mechanical method is used to study the nonlinear optical wave mixing in graphene nanoflakes(GNFs),including sum-and difference-frequency generation,as well as four-wave mixing.Our analysis s...A distant-neighbor quantum-mechanical method is used to study the nonlinear optical wave mixing in graphene nanoflakes(GNFs),including sum-and difference-frequency generation,as well as four-wave mixing.Our analysis shows that molecular-scale GNFs support quantum plasmons in the visible spectrum region,and significant enhancement of nonlinear optical wave mixing is achieved.Specifically,the second-and third-order wave-mixing polarizabilities of GNFs are dramatically enhanced,provided that one(or more) of the input or output frequencies coincide with a quantum plasmon resonance.Moreover,by embedding a cavity into hexagonal GNFs,we show that one can break the structural inversion symmetry and enable otherwise forbidden second-order wave mixing,which is found to be enhanced by the quantum plasmon resonance too.This study reveals that the molecular-sized graphene could be used in the quantum regime for nanoscale nonlinear optical devices and ultrasensitive molecular sensors.展开更多
In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and ...In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.展开更多
基金This research was financially supported by China National Key Basic Research Project "Circulation Principal and Mathematic Model" (Grant No. 1999043810) Guangdong Science and Technology Innovation Project: "Disaster Diagnoses of Sea Walls" (99B07102G)
文摘Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L0≤1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11965019 and 42004131)the Foundation of Gansu Educational Committee(Grant No.2022QB-178).
文摘The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation(NLSE).The first method is to derive a Korteweg–de Vries(KdV)-type equation and then derive the NLSE from the KdV-type equation,while the second one is to directly derive the NLSE from the original equation.It is found that the envelope waves from the two methods have different dispersion relations,different group velocities.The results indicate that two envelope wave solutions from two different methods are completely different.The results also show that the application scope of the envelope wave obtained from the second method is wider than that of the first one,though both methods are valuable in the range of their corresponding application scopes.It is suggested that,for other systems,both methods to derive NLSE may be correct,but their nonlinear wave solutions are different and their application scopes are also different.
文摘Large amplitude (1+1)-dimensional nonlinear ion acoustic waves are theoretically studied in multicomponent plasma consisting of positively charged ions and negatively charged ions, ion beam, kappa-distributed electrons, and dust grains,respectively. By using the Sagdeev potential method, the dynamical system and the Sagdeev potential function are obtained.The important influences of system parameters on the phase diagram of this system are investigated. It is found that the linear waves, the nonlinear waves and the solitary waves are coexistent in the multicomponent plasma system. Meanwhile,the variations of Sagdeev potential with parameter can also be obtained. Finally, it seems that the propagating characteristics of (1+1)-dimensional nonlinear ion acoustic solitary waves and ion acoustic nonlinear shock wave can be influenced by different parameters of this system.
基金financially supported by the National Key Research and Development Program of China(Grant Nos.2021YFB2600700 and 2022YFC3102302)the Central Public-Interest Scientific Institution Basal Research Fund(Grant No.Y221007)+2 种基金the National Natural Science Foundation of China(Grant No.52271274)the Key Laboratory of Ministry of Education for Coastal Disaster and Protection,Hohai University(Grant No.202205)the Key Project of NSFC-Shandong Joint Research Funding POW3C(Grant No.U1906230).
文摘The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.
基金financially supported by the National Natural Science Foundation of China(Grant No.11272079)the National Basic Research Program of China(973 Program,Grant No.2011CB013702)
文摘Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device(CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.
基金financially supported by National Natural Science Foundation of China(NSFC)(Nos.12005035 and 11935005)China Postdoctoral Science Foundation(Nos.2020M670741 and 2021T140085)+2 种基金Fundamental Research Funds for the Central Universities(No.DUT20LAB201)National Science Foundation(No.PHY-1500518)Department of Energy Office of Fusion Energy Science(No.DE-SC0001939)for financial support。
文摘It is recognized that standing wave effects appearing in large-area,very-high-frequency capacitively coupled plasma(CCP)reactors cause center-high plasma non-uniformity.Using a high-frequency magnetic probe,we present a direct experimental diagnostic of the nonlinear standing waves and bulk ohmic electron power absorption dynamics in low pressure CCP discharges for different driving frequencies of 13.56,30,and 60 MHz.The design,principle,calibration,and validation of the probe are described in detail.Spatial structures of the harmonics of the magnetic field,determined by the magnetic probe,were used to calculate the distributions of the harmonic current and the corresponding ohmic electron power deposition,providing insights into the behavior of nonlinear harmonics.At a low driving frequency,i.e.13.56 MHz,no remarkable nonlinear standing waves were identified and the bulk ohmic electron power absorption was observed to be negligible.The harmonic magnetic field/current was found to increase dramatically with the driving frequency,due to decreased sheath reactance and more remarkable nonlinear standing waves at a higher driving frequency,leading to the enhancements of the ohmic heating and the plasma density in the bulk,specifically at the electrode center.At a high driving frequency,i.e.60 MHz,the high-order harmonic current density and the corresponding ohmic electron power absorption exhibited a similar node structure,with the main peak on axis,and one or more minor peaks between the electrode center and the edge,contributing to the center-high profile of the plasma density.
基金supported by the Beijing Natural Science Foundation (KZ200810005001)the National Basic Research Program of China (973 Program) (2010CB732104)
文摘This letter reports experimental observation of a direct correlation between the acoustic nonlinearity parameter (NP) measured with nonlinear Rayleigh waves and the accumulation of plasticity damage in an AZ31 magnesium alloy plate specimen.Rayleigh waves are generated and detected with wedge transducers,and the NPs are measured at different stress levels.The results show that there is a significant increase in the NPs with monotonic tensile loads surpassing the material's yielding stress.The research suggests an effective nondestructive evaluation method to track the surface damage in metals.
文摘The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation of the Korteweg-de Vries equations for solitons by using the method of multiple scale expansion. The proposed problem describes the behavior of the system for free surface between air and water in a nonlinear approach. To solve this problem, we use the well-known analytical method, namely, variational iteration method (VIM). The proposed method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. The proposed method provides a sequence of functions which may converge to the exact solution of the proposed problem. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves.
文摘The nonlinear propagation of positron acoustic periodic(PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov-Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis,and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. The present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.
文摘Propagation of coupled electrostatic drift and ion-acoustic waves(DIAWs) is presented. It is shown that nonlinear solitary vortical structures can be formed by low-frequency coupled electrostatic DIAWs. Primary waves of distinct(small, intermediate and large) scales are considered. Appropriate set of 3 D equations consisting of the generalized Hasegawa–Mima equation for the electrostatic potential(involving both vector and scalar nonlinearities) and the equation of motion of ions parallel to magnetic field are obtained. According to experiments of laboratory plasma mainly focused to large scale DIAWs, the possibility of self-organization of DIAWs into the nonlinear solitary vortical structures is shown analytically. Peculiarities of scalar nonlinearities in the formation of solitary vortical structures are widely discussed.
基金Supported by the National Natural Science Foundation of China(Nos.42006176,42330406,U1706220,41901006)the Basic Research Project of the Science and Technology Innovation Development Program of in Yantai(No.2022JCYJ028)。
文摘Major differences in beach erosion between two neighboring artificial beaches Xiangluwan Beach(XL beach)and Meiliwan Beach(ML beach)in Zhuhai,China,were studied after Super Typhoon Hato.In this study,a fully nonlinear Boussinesq wave model(FUNWAVE)-Total Variation Diminishing(TVD)was used to distinguish the main impact factors,their relative contributions,and the hydrodynamic mechanisms underlying the different beach responses.Results show that compared to the ML beach,the main reason for the relatively weak erosion on Xiangluwan(XL)beach was the smaller beach berm height(accounting for approximately 75.9%of the erosion response).Regarding the beach with a higher berm,the stronger wave-induced undertow flow,along with the higher sediment concentration,led to a higher offshore sediment transport flux,resulting in more severe erosion relative to the beach with a smaller berm height.The second most important reason explaining the weak erosion on XL beach was the absence of seawalls(accounting for approximately 17.9%of the erosion response).Wave reflection induced by the seawall could cause higher suspended sediment concentration,resulting in a toe scouring near the seawall.The offshore submerged breakwater protected XL beach slightly(accounting for approximately 6.1%of the erosion response).Due to the higher water level induced by storm surge,most of the wave energy could penetrate through the submerged breakwater.The effect of the larger berm width of XL beach was negligible.Compared to the beach with a larger berm width,the erosion/deposition regions in the beach with a narrower berm width showed shoreward migration,without significant changes in the erosion/deposition extent.Despite of this,the larger berm width could reduce the wave energy reaching the shoreline.This study of the storm stability of artificial beaches may be applied to beach restoration design.
文摘Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main aim is to use a new method known as the(G′/G)method to exhibit the effects of dust charge fluctuations on the evolution of nonlinear waves. The coherent features of the shock and solitary waves along with the generation of high-energy waves have been amplified through the solution of the Korteweg–de Vries–Burgers equation,and the different natures of the waves were found successfully. Results are discussed graphically with the thoughtful choice of typical plasma parameters from different space plasma environments, exactly those found in cosmic dusty plasmas laden in ionospheric auroral region,radial spokes of Saturn's rings, planetary nebulae and solar F-corona region. All conclusions are in good accordance with the actual occurrences and could be of interest to further investigations of space. Moreover, the applicability of the present method is hoped to be a great enhancement by its use as ingenious mechanism used to evaluate the soliton dynamics and Burgers shock waves.
文摘The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of electron clouds used in chemistry. The relativistic wave equation is associated with a Lagrangian density, thus also with an energy-momentum tensorial density. The wave of an electron cloud adds these energy-momentum densities, while photons in light are precisely those differences between such energy-momentum densities.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61571222,61602235,and 11474160)the Six Talent Peaks Project of Jiangsu Province,China
文摘We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures.Simulation models of three-dimensional(3D)aluminum plates and composite laminates are established by ABAQUS software,where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage.The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated.Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes.There is a positive correlation among crack length,height,and sum and difference frequency amplitudes for an aluminum plate,with both amplitudes decreasing as crack thickness increased,i.e.,nonlinear effect weakens as the micro-crack becomes thicker.The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates.Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.
基金The National Natural Science Foundation of China under contract No.11762011the Natural Science Foundation of Inner Mongolia Autonomous Region under contract No.2020BS01002+1 种基金the Research Program of Science at Universities of Inner Mongolia Autonomous Region under contract No.NJZY20003the Scientific Starting Foundation of Inner Mongolia University under contract No.21100-5185105
文摘An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper.Starting from the basic model equations of oceanic motions,a Korteweg de Vries equation is derived to simulate the evolution of equatorial nonlinear near-inertial waves by using methods of scaling analysis and perturbation expansions under the equatorial beta plane approximation.Theoretical dynamic analysis is finished based on the obtained Korteweg de Vries equation,and the results show that the horizontal component of Coriolis parameters is of great importance to the propagation of equatorial nonlinear near-inertial solitary waves by modifying its dispersion relation and by interacting with the basic background flow.
基金Project supported by the National Natural Science Foundation of China(No.11071164)the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ118)+1 种基金the Shanghai Leading Academic Discipline Project(No.XTKX2012)the Innovation Fund Project for Graduate Stu-dent of Shanghai(No.JWCXSL1201)
文摘This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefcients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
基金supported by the National Natural Science Foundation of China under Grant No.11772341the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB22040203。
文摘A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.
基金Project supported by the National Natural Science Foundation of China(Grant No.11947007)the Natural Science Foundation of Guangdong Province,China(Grant No.2019A1515011499)the Department of Education of Guangdong Province,China(Grant No.2019KTSCX087)。
文摘A distant-neighbor quantum-mechanical method is used to study the nonlinear optical wave mixing in graphene nanoflakes(GNFs),including sum-and difference-frequency generation,as well as four-wave mixing.Our analysis shows that molecular-scale GNFs support quantum plasmons in the visible spectrum region,and significant enhancement of nonlinear optical wave mixing is achieved.Specifically,the second-and third-order wave-mixing polarizabilities of GNFs are dramatically enhanced,provided that one(or more) of the input or output frequencies coincide with a quantum plasmon resonance.Moreover,by embedding a cavity into hexagonal GNFs,we show that one can break the structural inversion symmetry and enable otherwise forbidden second-order wave mixing,which is found to be enhanced by the quantum plasmon resonance too.This study reveals that the molecular-sized graphene could be used in the quantum regime for nanoscale nonlinear optical devices and ultrasensitive molecular sensors.
基金Project supported by the National Natural Science Foundation of China(Nos.11922209,11991031 and 12021002)。
文摘In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.
