In this study we theoretically demonstrate ultrahigh-resolution two-dimensional atomic localization within a three-levelλ-type atomic medium via superposition of asymmetric and symmetric standing wave fields.Our anal...In this study we theoretically demonstrate ultrahigh-resolution two-dimensional atomic localization within a three-levelλ-type atomic medium via superposition of asymmetric and symmetric standing wave fields.Our analysis provides an understanding of the precise spatial localization of atomic positions at the atomic level,utilizing advanced theoretical approaches and principles of quantum mechanics.The dynamical behavior of a three-level atomic system is thoroughly analyzed using the density matrix formalism within the realm of quantum mechanics.A theoretical approach is constructed to describe the interaction between the system and external fields,specifically a control field and a probe field.The absorption spectrum of the probe field is thoroughly examined to clarify the spatial localization of the atom within the proposed configuration.A theoretical investigation found that symmetric and asymmetric superposition phenomena significantly influence the localized peaks within a two-dimensional spatial domain.Specifically,the emergence of one and two sharp localized peaks was observed within a one-wavelength domain.We observed notable influences of the intensity of the control field,probe field detuning and decay rates on atomic localization.Ultimately,we have achieved an unprecedented level of ultrahigh resolution and precision in localizing an atom within an area smaller thanλ/35×λ/35.These findings hold promise for potential applications in fields such as Bose-Einstein condensation,nanolithography,laser cooling,trapping of neutral atoms and the measurement of center-of-mass wave functions.展开更多
In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercriti...In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.展开更多
It was attempted to enhance and accelerate the separation of oxidation inclusions from magnesium alloy melt by virtue of ultrasonic agglomeration technology.In order to investigate the feasibility and effectiveness of...It was attempted to enhance and accelerate the separation of oxidation inclusions from magnesium alloy melt by virtue of ultrasonic agglomeration technology.In order to investigate the feasibility and effectiveness of standing waves for ultrasonic purification of magnesium alloy melt,numerical simulation and relevant experiment were carried out.The numerical simulation was broken into two main aspects.On one hand,the ultrasonic field propagations within the cells with various shapes were characterized by numerical solutions of the wave equation and with a careful choice of geometry a nearly idealized standing wave field was finally obtained.On the other hand,within such a standing wave field the agglomeration behavior of oxidation inclusions in magnesium alloy melt was analyzed and discussed.The agglomeration time and agglomeration position of oxidation inclusions were predicted with numerical simulation method.The results show that the oxidation inclusions whose apparent densities are close to the density of the melt can agglomerate at wave nodes in a short time which to a great extent enhances and accelerates the separation of oxidation inclusions from magnesium alloy melt.展开更多
Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which ca...Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.展开更多
We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first est...We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the SchrSdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2.展开更多
In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" ...In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.展开更多
The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder,insonified by acoustic...The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder,insonified by acoustic standing waves having an arbitrary angle of incidence in the polar(transverse)plane.The host medium of wave propagation and the eccentric liquid-like cylinder are non-viscous.Numerical computations illustrate the theoretical analysis with particular emphases on the eccentricity of the cylinder,the angle of incidence and the dimensionless size parameters of the inner and coating cylindrical fluid materials.The method to derive the acoustical scattering,and radiation force and torque components conjointly uses modal matching with the addition theorem,which adequately account for the multiple wave interaction effects between the layer and core fluid materials.The results demonstrate that longitudinal and lateral radiation force components arise.Moreover,an axial radiation torque component is quantified and computed for the non-absorptive compound cylinder,arising from geometrical asymmetry considerations as the eccentricity increases.The computational results reveal the emergence of neutral,positive,and negative radiation force and torque depending on the size parameter of the cylinder,the eccentricity,and the angle of incidence of the insonifying field.Moreover,based on the law of energy conservation applied to scattering,numerical verification is accomplished by computing the extinction/scattering energy efficiency.The results may find some related applications in fluid dynamics,particle trapping,mixing and manipulation using acoustical standing waves.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
The existence and orbital instability of standing waves for the generalized three- dimensional nonlocal nonlinear SchrSdinger equations is studied. By defining some suitable functionals and a constrained variational p...The existence and orbital instability of standing waves for the generalized three- dimensional nonlocal nonlinear SchrSdinger equations is studied. By defining some suitable functionals and a constrained variational problem, we first establish the existence of standing waves, which relys on the inner structure of the equations under consideration to overcome the drawback that nonlocal terms violate the space-scale invariance. We then show the orbital instability of standing waves. The arguments depend upon the conservation laws of the mass and of the energy.展开更多
We present examples of a controlled numerical experiment that contribute towards understanding of the physical phenomena that lead to the reduction of coherency of strong earthquake ground motion.We show examples for ...We present examples of a controlled numerical experiment that contribute towards understanding of the physical phenomena that lead to the reduction of coherency of strong earthquake ground motion.We show examples for separation distance of 100 m between the two points on the ground surface,which is in the range of engineering interest.Our examples illustrate the consequences of:(a)standing waves that result from interference of the incident and reflected waves from a near vertical contrast in material properties,(b)standing waves within a concave inhomogeneity(a semi-circular valley in our examples),and(c)smaller motions in the diffraction zone,behind the inhomogeneity.We show that it is possible to reduce coherency,to the extent observed for recorded strong earthquake ground motion,even by a single inclusion in a half space,for incident ground motion that is coherent.We also illustrate the combined effects of geometric spreading and finite fault width,superimposed on the otherwise dominating effects caused by interference.Our examples show reduction of coherence for specific angles of incident waves,while,for other angles of incidence,the coherence remains essentially equal to one.展开更多
Standing waves in the cylinder hasins with inhomogeneous bottom are considered in this paper. We assume that the inviscid, incompressible fluid is in irrotational undulatory motion. For convenience sake, cylindrical c...Standing waves in the cylinder hasins with inhomogeneous bottom are considered in this paper. We assume that the inviscid, incompressible fluid is in irrotational undulatory motion. For convenience sake, cylindrical coordinates are chosen. The velocitv potentials, the wave profiles and the modified frequencies are determined (to the third order) as power series in terms of the amplitude divided by the wavelength. Axisymmetrical analytical solutions are worked out. When w=0 , the second order frequency are gained.As an example, we assume that cylinder bottom is an axisymmetricat paraboloid. We find out that the uneven bottom has influences on standing waves. In the end. we go into detail on geometric factors.展开更多
In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L<sup>2</sup>-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At firs...In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L<sup>2</sup>-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At first, by the classical minimizing argument, we obtain a ground state solution to the above problem for sufficiently small ρwhen . Secondly, in the case p = 6, we show the nonexistence of positive solutions by using a Liouville-type result. Finally, we argue by contradiction to investigate the orbital stability of standing waves for .展开更多
Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstan...Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge code. The mode transitions, also known as density jumps, of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude standing helicon waves(SHWs) are responsible for the mode transitions, similar to those of a resonant cavity for laser generation.This paper intends to give a complete and quantitative SHW resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.展开更多
The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when the...The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when there were neither external background magnetic field or other factors that destroyed the poloidal symmetry of the tube.The formation mechanism and chirality of helical streamers are discussed according to the surface electromagnetic standing wave theory.The shape of the helical streamers and the characteristics of helical branches are quantitatively analyzed to further expand the application of plasma and streamer theory in the helix problem and chiral catalytic synthesis.展开更多
The motion and the energy of electrons driven by the ponderomotive force in linearly polarized high-intensity laser standing wave fields are considered. The results show that there exists a threshold laser intensity, ...The motion and the energy of electrons driven by the ponderomotive force in linearly polarized high-intensity laser standing wave fields are considered. The results show that there exists a threshold laser intensity, above which the motion of electrons incident parallel to the electric field of the laser standing waves undergoes a transition from regulation to chaos. We propose that the huge energy exchange between the electrons and the strong laser standing waves is triggered by inelastic scattering, which is related to the chaos patterns. It is shown that an electron＇s energy gain of tens of MeV can be realized for a laser intensity of 10^20 W/cm^2.展开更多
The recording and playback of information using a reverse stimulated photon—echo hologram when exposed to the recording medium pulse of non-resonant electromagnetic standing wave was considered. It was shown that the...The recording and playback of information using a reverse stimulated photon—echo hologram when exposed to the recording medium pulse of non-resonant electromagnetic standing wave was considered. It was shown that the spatial intensity distribution in stimulated echo hologram response depended on the electric field intensity of non-resonant standing wave that allowed controlling by a reproducible image.展开更多
This study is devoted to the global existence,blow-up and orbital stability of standing waves for the Schröinger equation with mixed nonlinearities.Firstly,we derive some criteria for global existence and blow-up...This study is devoted to the global existence,blow-up and orbital stability of standing waves for the Schröinger equation with mixed nonlinearities.Firstly,we derive some criteria for global existence and blow-up of the solutions by making use of the ground state and scaling techniques.Secondly,by taking advantage of the refined compactness argument,scaling techniques and the variational characterization of ground state solutions,we explore the L^(2)-concentration phenomenon and limiting behavior of blow-up solutions in the L^(2)-critical case withμ=±1 and 1<q<p=1+4/N.Finally,we research the orbital stability of standing waves in the cases withμ=−1,1<q<p≤1+4/Norμ=1,1+4/N=p<q<N+2/N-2,by combining the variational methods,profile decomposition and the arguments of concentration compactness.Our study complements the conclusions of some known works.展开更多
In this paper,we study the following three-dimensional Schrodinger equation with combined Hartree-type and power-type nonlinearities i∂ψ+△ψ+(|x|^(-2)*|ψ|^(2))ψ+|ψ|^(p-1)=0 with 1<p<5.Using standard variati...In this paper,we study the following three-dimensional Schrodinger equation with combined Hartree-type and power-type nonlinearities i∂ψ+△ψ+(|x|^(-2)*|ψ|^(2))ψ+|ψ|^(p-1)=0 with 1<p<5.Using standard variational arguments,the existence of ground state solutions is obtained.And then we prove that when p≥3,the standing wave solution e^(1ωt)u_(ω)(x)is strongly unstable for the frequencyω>0.展开更多
In this paper,inspired by the running motion gait of a cheetah,an H-shaped bionic piezoelectric robot(H-BPR)based on the standing wave principle is proposed and designed.The piezoelectric robot realizes linear motion,...In this paper,inspired by the running motion gait of a cheetah,an H-shaped bionic piezoelectric robot(H-BPR)based on the standing wave principle is proposed and designed.The piezoelectric robot realizes linear motion,turning motion,and turning motion with different radi by the voltage differential driving method.A prototype with a weight of 38 g and dimensions of 150×80×31 mm^(3) was fabricated.Firstly,the dynamics and kinematics of the piezoelectric robot were analyzed to obtain the trajectory of a point at the end of the piezoelectric robot leg.The motion principle of the piezo-electric robot was analyzed,and then the piezoelectric robot's modal analysis and harmonic response analysis were carried out using finite element analysis software.Finally,an experimental setup was built to verify the effectiveness and high efficiency of the robot's motion,and the effects of frequency,voltage,load,and height of the driving leg on the robot's motion performance were discussed.The performance test results show that the piezoelectric robot has a maximum veloc-ity of 66.79 mm/s at an excitation voltage of 320 V and a load capacity of 55 g.In addition,the H-BPR with unequal drive legs has better climbing performance,and the obtained conclusions are informative for selecting leg heights for piezoelectric robots.展开更多
In this paper bottom scours in front of vertical breakwaters by standing waves are systematically investigated, the scouring patterns, criterion for differentiating the scouring patterns and scouring mechanism are dis...In this paper bottom scours in front of vertical breakwaters by standing waves are systematically investigated, the scouring patterns, criterion for differentiating the scouring patterns and scouring mechanism are discussed ; a formula of maximum depth of scouring trough considering sediment size is given; and influence of mound foundation on bottom scours is investigated.展开更多
文摘In this study we theoretically demonstrate ultrahigh-resolution two-dimensional atomic localization within a three-levelλ-type atomic medium via superposition of asymmetric and symmetric standing wave fields.Our analysis provides an understanding of the precise spatial localization of atomic positions at the atomic level,utilizing advanced theoretical approaches and principles of quantum mechanics.The dynamical behavior of a three-level atomic system is thoroughly analyzed using the density matrix formalism within the realm of quantum mechanics.A theoretical approach is constructed to describe the interaction between the system and external fields,specifically a control field and a probe field.The absorption spectrum of the probe field is thoroughly examined to clarify the spatial localization of the atom within the proposed configuration.A theoretical investigation found that symmetric and asymmetric superposition phenomena significantly influence the localized peaks within a two-dimensional spatial domain.Specifically,the emergence of one and two sharp localized peaks was observed within a one-wavelength domain.We observed notable influences of the intensity of the control field,probe field detuning and decay rates on atomic localization.Ultimately,we have achieved an unprecedented level of ultrahigh resolution and precision in localizing an atom within an area smaller thanλ/35×λ/35.These findings hold promise for potential applications in fields such as Bose-Einstein condensation,nanolithography,laser cooling,trapping of neutral atoms and the measurement of center-of-mass wave functions.
文摘In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.
基金Projects(2007CB613701,2007CB613702)supported by the National Basic Research Program of ChinaProjects(50974037,50904018)supported by the National Natural Science Foundation of ChinaProject(NCET-08-0098)supported by the Program for New Century Excellent Talents in University of China
文摘It was attempted to enhance and accelerate the separation of oxidation inclusions from magnesium alloy melt by virtue of ultrasonic agglomeration technology.In order to investigate the feasibility and effectiveness of standing waves for ultrasonic purification of magnesium alloy melt,numerical simulation and relevant experiment were carried out.The numerical simulation was broken into two main aspects.On one hand,the ultrasonic field propagations within the cells with various shapes were characterized by numerical solutions of the wave equation and with a careful choice of geometry a nearly idealized standing wave field was finally obtained.On the other hand,within such a standing wave field the agglomeration behavior of oxidation inclusions in magnesium alloy melt was analyzed and discussed.The agglomeration time and agglomeration position of oxidation inclusions were predicted with numerical simulation method.The results show that the oxidation inclusions whose apparent densities are close to the density of the melt can agglomerate at wave nodes in a short time which to a great extent enhances and accelerates the separation of oxidation inclusions from magnesium alloy melt.
基金This subject was partly supported by the National Excellent Youth Foundation of China (Grant No. 49825161)
文摘Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/lambda(0), ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, And the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.
基金supported by NSFC(11471331,11101418 and 11271360)
文摘We study the existence and stability of the standing waves of two coupled SchrSdinger equations with potentials ｜x｜bi（bi ∈ R,i = 1, 2）. Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the SchrSdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2.
文摘In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.
文摘The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder,insonified by acoustic standing waves having an arbitrary angle of incidence in the polar(transverse)plane.The host medium of wave propagation and the eccentric liquid-like cylinder are non-viscous.Numerical computations illustrate the theoretical analysis with particular emphases on the eccentricity of the cylinder,the angle of incidence and the dimensionless size parameters of the inner and coating cylindrical fluid materials.The method to derive the acoustical scattering,and radiation force and torque components conjointly uses modal matching with the addition theorem,which adequately account for the multiple wave interaction effects between the layer and core fluid materials.The results demonstrate that longitudinal and lateral radiation force components arise.Moreover,an axial radiation torque component is quantified and computed for the non-absorptive compound cylinder,arising from geometrical asymmetry considerations as the eccentricity increases.The computational results reveal the emergence of neutral,positive,and negative radiation force and torque depending on the size parameter of the cylinder,the eccentricity,and the angle of incidence of the insonifying field.Moreover,based on the law of energy conservation applied to scattering,numerical verification is accomplished by computing the extinction/scattering energy efficiency.The results may find some related applications in fluid dynamics,particle trapping,mixing and manipulation using acoustical standing waves.
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 National Natural Science Foundation of China(11171241)Program for New Century Excellent Talents in University(NCET-12-1058)
文摘The existence and orbital instability of standing waves for the generalized three- dimensional nonlocal nonlinear SchrSdinger equations is studied. By defining some suitable functionals and a constrained variational problem, we first establish the existence of standing waves, which relys on the inner structure of the equations under consideration to overcome the drawback that nonlocal terms violate the space-scale invariance. We then show the orbital instability of standing waves. The arguments depend upon the conservation laws of the mass and of the energy.
文摘We present examples of a controlled numerical experiment that contribute towards understanding of the physical phenomena that lead to the reduction of coherency of strong earthquake ground motion.We show examples for separation distance of 100 m between the two points on the ground surface,which is in the range of engineering interest.Our examples illustrate the consequences of:(a)standing waves that result from interference of the incident and reflected waves from a near vertical contrast in material properties,(b)standing waves within a concave inhomogeneity(a semi-circular valley in our examples),and(c)smaller motions in the diffraction zone,behind the inhomogeneity.We show that it is possible to reduce coherency,to the extent observed for recorded strong earthquake ground motion,even by a single inclusion in a half space,for incident ground motion that is coherent.We also illustrate the combined effects of geometric spreading and finite fault width,superimposed on the otherwise dominating effects caused by interference.Our examples show reduction of coherence for specific angles of incident waves,while,for other angles of incidence,the coherence remains essentially equal to one.
文摘Standing waves in the cylinder hasins with inhomogeneous bottom are considered in this paper. We assume that the inviscid, incompressible fluid is in irrotational undulatory motion. For convenience sake, cylindrical coordinates are chosen. The velocitv potentials, the wave profiles and the modified frequencies are determined (to the third order) as power series in terms of the amplitude divided by the wavelength. Axisymmetrical analytical solutions are worked out. When w=0 , the second order frequency are gained.As an example, we assume that cylinder bottom is an axisymmetricat paraboloid. We find out that the uneven bottom has influences on standing waves. In the end. we go into detail on geometric factors.
文摘In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L<sup>2</sup>-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At first, by the classical minimizing argument, we obtain a ground state solution to the above problem for sufficiently small ρwhen . Secondly, in the case p = 6, we show the nonexistence of positive solutions by using a Liouville-type result. Finally, we argue by contradiction to investigate the orbital stability of standing waves for .
基金supported by the National Key R&D Program of China(No.2017YFE0301201)National Natural Science Foundation of China(No.11975038)the funding support from the State Key Laboratory of Nuclear Physics and Technology,Peking University(No.NPT2021ZZ03)。
文摘Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge code. The mode transitions, also known as density jumps, of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude standing helicon waves(SHWs) are responsible for the mode transitions, similar to those of a resonant cavity for laser generation.This paper intends to give a complete and quantitative SHW resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.
基金This work was supported by National Natural Science Foundation of China(Nos.12005061,12065019)the Natural Science Foundation of Jiangxi Province(No.20202 BABL214036).
文摘The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when there were neither external background magnetic field or other factors that destroyed the poloidal symmetry of the tube.The formation mechanism and chirality of helical streamers are discussed according to the surface electromagnetic standing wave theory.The shape of the helical streamers and the characteristics of helical branches are quantitatively analyzed to further expand the application of plasma and streamer theory in the helix problem and chiral catalytic synthesis.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10775165 and 11104168)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2009AQ009)the National Basic Research Program of China(Grant No.2011CB808100)
文摘The motion and the energy of electrons driven by the ponderomotive force in linearly polarized high-intensity laser standing wave fields are considered. The results show that there exists a threshold laser intensity, above which the motion of electrons incident parallel to the electric field of the laser standing waves undergoes a transition from regulation to chaos. We propose that the huge energy exchange between the electrons and the strong laser standing waves is triggered by inelastic scattering, which is related to the chaos patterns. It is shown that an electron＇s energy gain of tens of MeV can be realized for a laser intensity of 10^20 W/cm^2.
文摘The recording and playback of information using a reverse stimulated photon—echo hologram when exposed to the recording medium pulse of non-resonant electromagnetic standing wave was considered. It was shown that the spatial intensity distribution in stimulated echo hologram response depended on the electric field intensity of non-resonant standing wave that allowed controlling by a reproducible image.
文摘This study is devoted to the global existence,blow-up and orbital stability of standing waves for the Schröinger equation with mixed nonlinearities.Firstly,we derive some criteria for global existence and blow-up of the solutions by making use of the ground state and scaling techniques.Secondly,by taking advantage of the refined compactness argument,scaling techniques and the variational characterization of ground state solutions,we explore the L^(2)-concentration phenomenon and limiting behavior of blow-up solutions in the L^(2)-critical case withμ=±1 and 1<q<p=1+4/N.Finally,we research the orbital stability of standing waves in the cases withμ=−1,1<q<p≤1+4/Norμ=1,1+4/N=p<q<N+2/N-2,by combining the variational methods,profile decomposition and the arguments of concentration compactness.Our study complements the conclusions of some known works.
文摘In this paper,we study the following three-dimensional Schrodinger equation with combined Hartree-type and power-type nonlinearities i∂ψ+△ψ+(|x|^(-2)*|ψ|^(2))ψ+|ψ|^(p-1)=0 with 1<p<5.Using standard variational arguments,the existence of ground state solutions is obtained.And then we prove that when p≥3,the standing wave solution e^(1ωt)u_(ω)(x)is strongly unstable for the frequencyω>0.
基金supported by the National Natural Science Foundation of China(No.12372005)the Aeronautical Science Foundation of China(No.ASFC-2024Z070050001)the Natural Science Foundation of Liaoning Province(2024-MSBA-32).
文摘In this paper,inspired by the running motion gait of a cheetah,an H-shaped bionic piezoelectric robot(H-BPR)based on the standing wave principle is proposed and designed.The piezoelectric robot realizes linear motion,turning motion,and turning motion with different radi by the voltage differential driving method.A prototype with a weight of 38 g and dimensions of 150×80×31 mm^(3) was fabricated.Firstly,the dynamics and kinematics of the piezoelectric robot were analyzed to obtain the trajectory of a point at the end of the piezoelectric robot leg.The motion principle of the piezo-electric robot was analyzed,and then the piezoelectric robot's modal analysis and harmonic response analysis were carried out using finite element analysis software.Finally,an experimental setup was built to verify the effectiveness and high efficiency of the robot's motion,and the effects of frequency,voltage,load,and height of the driving leg on the robot's motion performance were discussed.The performance test results show that the piezoelectric robot has a maximum veloc-ity of 66.79 mm/s at an excitation voltage of 320 V and a load capacity of 55 g.In addition,the H-BPR with unequal drive legs has better climbing performance,and the obtained conclusions are informative for selecting leg heights for piezoelectric robots.
文摘In this paper bottom scours in front of vertical breakwaters by standing waves are systematically investigated, the scouring patterns, criterion for differentiating the scouring patterns and scouring mechanism are discussed ; a formula of maximum depth of scouring trough considering sediment size is given; and influence of mound foundation on bottom scours is investigated.
