In order to obtain a lower frequency band gap,this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor.An improved camroller structure is designed in this meta-beam to achieve ...In order to obtain a lower frequency band gap,this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor.An improved camroller structure is designed in this meta-beam to achieve the softening nonlinear stiffness of the local oscillators.Firstly,based on Hamilton's principle and the Galerkin method,the control equations for the coupled system are established.The theoretical band gap boundary is then derived with the modal analysis method.The theoretical results reveal that the band gap of the meta-beam shifts towards lower frequencies due to the presence of a softening nonlinear factor,distinguishing it from both linear metamaterials and those with hardening nonlinear characteristics.Then,the vibration attenuation characteristics of a finite size meta-beam are investigated through numerical calculation,and are verified by the theoretical results.Furthermore,parameter studies indicate that the reasonable design of the local oscillator parameters based on lightweight principles helps to achieve further broadband and efficient vibration reduction in the low-frequency region.Finally,a prototype of the meta-beam is fabricated and assembled,and the formations of the low-frequency band gap and the amplitude-induced band gap phenomenon are verified through experiments.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
We introduce a novel scheme for achieving quantum entanglement and Einstein–Podolsky–Rosen(EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom–optomechanical system. The system...We introduce a novel scheme for achieving quantum entanglement and Einstein–Podolsky–Rosen(EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom–optomechanical system. The system comprises an optical cavity, a two-level atomic ensemble and a mechanical resonator that possesses Duffing nonlinearity. The interaction between these components is mediated by the cavity mode, which is driven by an external laser. Our findings indicate that optimizing the coupling strengths between photons and phonons, as well as between atoms and the cavity,leads to maximal entanglement and EPR steering. The amplitude of the driving laser plays a pivotal role in enhancing the coupling between photons and phonons, and the system maintains robust entanglement and EPR steering even under high dissipation, thereby mitigating the constraints on initial conditions and parameter precision. Remarkably, the Duffing nonlinearity enhances the system's resistance to thermal noise, ensuring its stability and entanglement protection. Our analysis of EPR steering conditions reveals that the party with lower dissipation exhibits superior stability and a propensity to steer the party with higher dissipation. These discoveries offer novel perspectives for advancing quantum information processing and communication technologies.展开更多
We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We s...We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We show that all the horizontal symmetric waves for this equation must be traveling waves.This extends the previous results for the Camassa-Holm and Novikov equations.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
Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting ...Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.展开更多
We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the ...We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the Kerr effect increases,the absorption curve exhibits an asymmetric-symmetric-asymmetric transition,and the zero absorption point shifts with the increase of the Kerr effect.Furthermore,by changing the strength of the Kerr effect,we can control the width of the transparent window,and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak.The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak.The simple dependence of the zeroabsorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.展开更多
We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavio...We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.展开更多
Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(...Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.展开更多
For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-ex...For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-expansion method along with the novel ansatz of F-base function.Furthermore,we extend the analytical study of soliton dynamics to higher(2+1)and(3+1)dimensions by using the self-similar method,and demonstrate the soliton behavior via graphical illustration.Moreover,we investigate the effect of the resonance term on bright soliton solution in(1+1)dimensions.Additionally,we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional(1D)to three-dimensional(3D)cases.The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model.展开更多
The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide...The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12172014,U224126412332001)。
文摘In order to obtain a lower frequency band gap,this paper proposes a novel locally resonant meta-beam incorporating a softening nonlinear factor.An improved camroller structure is designed in this meta-beam to achieve the softening nonlinear stiffness of the local oscillators.Firstly,based on Hamilton's principle and the Galerkin method,the control equations for the coupled system are established.The theoretical band gap boundary is then derived with the modal analysis method.The theoretical results reveal that the band gap of the meta-beam shifts towards lower frequencies due to the presence of a softening nonlinear factor,distinguishing it from both linear metamaterials and those with hardening nonlinear characteristics.Then,the vibration attenuation characteristics of a finite size meta-beam are investigated through numerical calculation,and are verified by the theoretical results.Furthermore,parameter studies indicate that the reasonable design of the local oscillator parameters based on lightweight principles helps to achieve further broadband and efficient vibration reduction in the low-frequency region.Finally,a prototype of the meta-beam is fabricated and assembled,and the formations of the low-frequency band gap and the amplitude-induced band gap phenomenon are verified through experiments.
文摘In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12204440)Fundamental Research Program of Shanxi Province (Grant Nos. 20210302123063 and 202103021223184)。
文摘We introduce a novel scheme for achieving quantum entanglement and Einstein–Podolsky–Rosen(EPR) steering between an atomic ensemble and a mechanical oscillator within a hybrid atom–optomechanical system. The system comprises an optical cavity, a two-level atomic ensemble and a mechanical resonator that possesses Duffing nonlinearity. The interaction between these components is mediated by the cavity mode, which is driven by an external laser. Our findings indicate that optimizing the coupling strengths between photons and phonons, as well as between atoms and the cavity,leads to maximal entanglement and EPR steering. The amplitude of the driving laser plays a pivotal role in enhancing the coupling between photons and phonons, and the system maintains robust entanglement and EPR steering even under high dissipation, thereby mitigating the constraints on initial conditions and parameter precision. Remarkably, the Duffing nonlinearity enhances the system's resistance to thermal noise, ensuring its stability and entanglement protection. Our analysis of EPR steering conditions reveals that the party with lower dissipation exhibits superior stability and a propensity to steer the party with higher dissipation. These discoveries offer novel perspectives for advancing quantum information processing and communication technologies.
基金partially supported by the National Natural Science Foundation of China(Grant No.12201417)the Project funded by the China Postdoctoral Science Foundation(Grant No.2023M733173)partially supported by the National Natural Science Foundation of China(Grant No.12375006)。
文摘We are concerned with a Camassa-Holm type equation with higher-order nonlinearity including some integrable peakon models such as the Camassa-Holm equation,the Degasperis-Procesi equation,and the Novikov equation.We show that all the horizontal symmetric waves for this equation must be traveling waves.This extends the previous results for the Camassa-Holm and Novikov equations.
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Project supported by the National Natural Science Foundation of China(Grant No.62071411)the Research Foundation of Education Department of Hunan Province,China(Grant No.20B567).
文摘Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)the National Natural Science Foundation of China(11965017)。
文摘We theoretically study the effect of Kerr effect on the second-order nonlinearity induced transparency in a double-resonant optical cavity system.We show that in the presence of the Kerr effect,as the strength of the Kerr effect increases,the absorption curve exhibits an asymmetric-symmetric-asymmetric transition,and the zero absorption point shifts with the increase of the Kerr effect.Furthermore,by changing the strength of the Kerr effect,we can control the width of the transparent window,and the position of the zero-absorption point and meanwhile change the left and right width of the absorption peak.The asymmetry absorption curve can be employed to improve the quality factor of the cavity when the frequency detuning is tuned to be around the right peak.The simple dependence of the zeroabsorption point on the strength of Kerr effect suggests that the strength of Kerr effect can be measured by measuring the position of the zero-absorption point in a possible application.
基金supported by the JSPS KAKENHI(JP22K03386)supported by the JST SPRING(JPMJSP2132)。
文摘We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62273115,62173105)the Fundamental Research Funds for the Central Universities (Grant No.3072022FSC0401)。
文摘Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.
基金Project supported by the National Natural Science Foundation of China(Grant No.11547024)。
文摘For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-expansion method along with the novel ansatz of F-base function.Furthermore,we extend the analytical study of soliton dynamics to higher(2+1)and(3+1)dimensions by using the self-similar method,and demonstrate the soliton behavior via graphical illustration.Moreover,we investigate the effect of the resonance term on bright soliton solution in(1+1)dimensions.Additionally,we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional(1D)to three-dimensional(3D)cases.The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model.
文摘The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.
