In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
In a recent paper published in Phys.Rev.Lett.133,152503(2024),H.Zhang,T.Li,and X.Wang predicted that modern intense lasers can induce highly nonlinear responses in the 229 Th nucleus for the first time,which is an ast...In a recent paper published in Phys.Rev.Lett.133,152503(2024),H.Zhang,T.Li,and X.Wang predicted that modern intense lasers can induce highly nonlinear responses in the 229 Th nucleus for the first time,which is an astonishing effect of light-nucleus interactions.This phenomenon is underpinned by two key factors:(1)the presence of a very low-lying nuclear excited state and(2)a nuclear hyperfine mixing effect that significantly enhances light-nucleus coupling.The resulting highly nonlinear responses facilitate efficient nuclear excitation and enable coherent light emission from the nucleus,resulting in high harmonic generation.229 Th presents a promising platform for advancements in both laser-nuclear physics and nuclear clock development.The pioneering work by Zhang et al.marks a new frontier in light-matter interactions.展开更多
The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant ...The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.展开更多
Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the developm...Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.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
The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported d...The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.展开更多
Nonlinear Hall effect(NLHE)has been detected in various of condensed matter systems.Unlike linear Hall effect,NLHE may exist in physical systems with broken inversion symmetry in crystals.On the other hand,real space ...Nonlinear Hall effect(NLHE)has been detected in various of condensed matter systems.Unlike linear Hall effect,NLHE may exist in physical systems with broken inversion symmetry in crystals.On the other hand,real space spin texture may also break inversion symmetry and result in NLHE.We employ the Feynman diagrammatic technique to calculate non-linear Hall conductivity(NLHC)in three-dimensional magnetic systems.The results connect NLHE with the physical quantity of emergent electrodynamics which originates from the magnetic texture.The leading order contribution of NLHC,χ_(abb),is proportional to the emergent toroidal moment T_(α)^(e),which reflects how the spin textures wind in three dimensions.展开更多
The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics,which still remain hidden from us.We consider the main cornerstones of the concept of no...The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics,which still remain hidden from us.We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons.On the base of this model,we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton selfinduced sub-barrier transparency effect.We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions.The main finding of this study concerns the conservation of total number of nucleons(or the baryon number)in nuclear-like soliton reactions.We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a“cloud”of“dressing”spectral side-bands appears in the frequency spectra of the solitons.This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter.Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors.We show that the nuclear-like reactions between well-dressed solitons are realized by“exchange”between“particle-like”side bands in their spectra.展开更多
When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order non...When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schr¨odinger equation, we analytically explore the evolution of optical solitons in the presence of highorder nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.展开更多
The ultrashort lasers working in pulse-burst mode reveal great machining performance in recent years. The number of pulses in bursts effects greatly on the removal rate and roughness. To generate a more equal amplitud...The ultrashort lasers working in pulse-burst mode reveal great machining performance in recent years. The number of pulses in bursts effects greatly on the removal rate and roughness. To generate a more equal amplitude of pulses in burst with linear polarization output and time gap adjustable, we propose a new method by the harmonic beam combining(HBC).The beam combining is commonly used in adding pulses into the output beam while maintaining the pulse waveform and beam quality. In the HBC, dichroic mirrors are used to combine laser pulses of fundamental wave(FW) into harmonic wave(HW), and nonlinear crystals are used to convert the FW into HW. Therefore, HBC can add arbitrarily more HW pulses to generate pulse-burst in linear polarization with simple structure. The amplitude of each pulse in bursts can be adjusted the same to increase the stability of the burst, the time gap of each pulse can be adjusted precisely by proper time delay. Because HBC adds pulses sequentially, the peak power density of the burst is the same as each pulse, pulses can be combined without concern of back-conversion which often occurs in high peak power density. In the demonstration, the extendibility of HBC was verified by combining two beams with a third beam. The combined efficiency rates were larger than 99%, and the beam quality of each beam was maintained at M^(2)≈1.4.展开更多
This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers...This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.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
We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Co...We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.展开更多
Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high v...Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.展开更多
We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipati...We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipative vector vortices(DVVs)that possess diverse vorticity values.Numerous fundamental characteristics of the DVVs are examined,encompassing amplitude profiles,energy fluxes,parameter effects,as well as linear and dynamic stability.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
Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep lea...Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.展开更多
The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direc...The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.展开更多
We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that t...We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient(thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.展开更多
In this paper,we apply the three circle type method and a Hardy type inequality to a nonlinear Dirac type equation on surfaces,and provide alternative proofs to the energy quantization results.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
文摘In a recent paper published in Phys.Rev.Lett.133,152503(2024),H.Zhang,T.Li,and X.Wang predicted that modern intense lasers can induce highly nonlinear responses in the 229 Th nucleus for the first time,which is an astonishing effect of light-nucleus interactions.This phenomenon is underpinned by two key factors:(1)the presence of a very low-lying nuclear excited state and(2)a nuclear hyperfine mixing effect that significantly enhances light-nucleus coupling.The resulting highly nonlinear responses facilitate efficient nuclear excitation and enable coherent light emission from the nucleus,resulting in high harmonic generation.229 Th presents a promising platform for advancements in both laser-nuclear physics and nuclear clock development.The pioneering work by Zhang et al.marks a new frontier in light-matter interactions.
基金supported by the 2021 Open Project Fund of Science and Technology on Electromechanical Dynamic Control Laboratory,grant number 212-C-J-F-QT-2022-0020China Postdoctoral Science Foundation,grant number 2021M701713+1 种基金Postgraduate Research&Practice Innovation Program of Jiangsu Province,grant number KYCX23_0511the Jiangsu Funding Program for Excellent Postdoctoral Talent,grant number 20220ZB245。
文摘The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes.To overcome this issue,we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm.This enhances the algorithm loading capability of the fuze.In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms,we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square(SAF-LMS)algorithm.We also designed an algorithm pause module to retain the original trend of the target echo peak,improving the time discrimination accuracy and anti-interference capability of the fuze.Finally,experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals.The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than31 d B,with an increase of up to 76%in extreme detection distance.
基金supported by the Australian Research Council(Grant No.DP210101292)the International Technology Center Indo-Pacific (ITC IPAC) via Army Research Office (contract FA520923C0023)。
文摘Nonlinear dielectric metasurfaces provide a promising approach to control and manipulate frequency conversion optical processes at the nanoscale,thus facilitating both advances in fundamental research and the development of new practical applications in photonics,lasing,and sensing.Here,we employ symmetry-broken metasurfaces made of centrosymmetric amorphous silicon for resonantly enhanced second-and third-order nonlinear optical response.Exploiting the rich physics of optical quasi-bound states in the continuum and guided mode resonances,we comprehensively study through rigorous numerical calculations the relative contribution of surface and bulk effects to second-harmonic generation(SHG)and the bulk contribution to third-harmonic generation(THG) from the meta-atoms.Next,we experimentally achieve optical resonances with high quality factors,which greatly boosts light-matter interaction,resulting in about 550 times SHG enhancement and nearly 5000-fold increase of THG.A good agreement between theoretical predictions and experimental measurements is observed.To gain deeper insights into the physics of the investigated nonlinear optical processes,we further numerically study the relation between nonlinear emission and the structural asymmetry of the metasurface and reveal that the generated harmonic signals arising from linear sharp resonances are highly dependent on the asymmetry of the meta-atoms.Our work suggests a fruitful strategy to enhance the harmonic generation and effectively control different orders of harmonics in all-dielectric metasurfaces,enabling the development of efficient active photonic nanodevices.
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 National Natural Science Foundation of China(Grant No.61975055)the Natural Science Foundation of Hunan Province,China(Grant No.2023JJ30165)+1 种基金the Natural Science Foundation of Shandong Province,China(Grant No.ZR2022QF005)the Doctoral Fund of University of Heze(Grant No.XY22BS14).
文摘The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.
基金supported by the Startup Foundation in Tiangong University(Grant No.63010201/52010399)supported by the Office of Basic Energy Sciences,Division of Materials Sciences and Engineering,U.S.Department of Energy(Grant No.DE-SC0020221)。
文摘Nonlinear Hall effect(NLHE)has been detected in various of condensed matter systems.Unlike linear Hall effect,NLHE may exist in physical systems with broken inversion symmetry in crystals.On the other hand,real space spin texture may also break inversion symmetry and result in NLHE.We employ the Feynman diagrammatic technique to calculate non-linear Hall conductivity(NLHC)in three-dimensional magnetic systems.The results connect NLHE with the physical quantity of emergent electrodynamics which originates from the magnetic texture.The leading order contribution of NLHC,χ_(abb),is proportional to the emergent toroidal moment T_(α)^(e),which reflects how the spin textures wind in three dimensions.
文摘The main goal of our study is to reveal unexpected but intriguing analogies arising between optical solitons and nuclear physics,which still remain hidden from us.We consider the main cornerstones of the concept of nonlinear optics of nuclear reactions and the well-dressed repulsive-core solitons.On the base of this model,we reveal the most intriguing properties of the nonlinear tunneling of nucleus-like solitons and the soliton selfinduced sub-barrier transparency effect.We describe novel interesting and stimulating analogies between the interaction of nucleus-like solitons on the repulsive barrier and nuclear sub-barrier reactions.The main finding of this study concerns the conservation of total number of nucleons(or the baryon number)in nuclear-like soliton reactions.We show that inelastic interactions among well-dressed repulsive-core solitons arise only when a“cloud”of“dressing”spectral side-bands appears in the frequency spectra of the solitons.This property of nucleus-like solitons is directly related to the nuclear density distribution described by the dimensionless small shape-squareness parameter.Thus the Fourier spectra of nucleus-like solitons are similar to the nuclear form factors.We show that the nuclear-like reactions between well-dressed solitons are realized by“exchange”between“particle-like”side bands in their spectra.
基金supported by the Scientific Research Foundation of Weifang University of Science and Technology (Grant Nos.KJRC2022002 and KJRC2023035)。
文摘When pursuing femtosecond-scale ultrashort pulse optical communication, one cannot overlook higher-order nonlinear effects. Based on the fundamental theoretical model of the variable coefficient coupled high-order nonlinear Schr¨odinger equation, we analytically explore the evolution of optical solitons in the presence of highorder nonlinear effects. Moreover, the interactions between two nearby optical solitons and their transmission in a nonuniform fiber are investigated. The stability of optical soliton transmission and interactions are found to be destroyed to varying degrees due to higher-order nonlinear effects. The outcomes may offer some theoretical references for achieving ultra-high energy optical solitons in the future.
基金Project supported by Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No.2020029)。
文摘The ultrashort lasers working in pulse-burst mode reveal great machining performance in recent years. The number of pulses in bursts effects greatly on the removal rate and roughness. To generate a more equal amplitude of pulses in burst with linear polarization output and time gap adjustable, we propose a new method by the harmonic beam combining(HBC).The beam combining is commonly used in adding pulses into the output beam while maintaining the pulse waveform and beam quality. In the HBC, dichroic mirrors are used to combine laser pulses of fundamental wave(FW) into harmonic wave(HW), and nonlinear crystals are used to convert the FW into HW. Therefore, HBC can add arbitrarily more HW pulses to generate pulse-burst in linear polarization with simple structure. The amplitude of each pulse in bursts can be adjusted the same to increase the stability of the burst, the time gap of each pulse can be adjusted precisely by proper time delay. Because HBC adds pulses sequentially, the peak power density of the burst is the same as each pulse, pulses can be combined without concern of back-conversion which often occurs in high peak power density. In the demonstration, the extendibility of HBC was verified by combining two beams with a third beam. The combined efficiency rates were larger than 99%, and the beam quality of each beam was maintained at M^(2)≈1.4.
基金supported by the Graduate Education Innovation Funds(2022CXZZ088)at Central China Normal University in Chinasupported by the NSFC(12225106,11931012)the Fundamental Research Funds(CCNU22LJ002)for the Central Universities in China。
文摘This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.
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supported by the NSFC(12261044)the STP of Education Department of Jiangxi Province of China(GJJ210302)。
文摘We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.
基金Project supported by the National Natural Science Foundation of China(Grant No.12002089)the Science and Technology Projects in Guangzhou(Grant No.2023A04J1323)UKRI Horizon Europe Guarantee(Grant No.EP/Y016130/1)。
文摘Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.
基金supported by the National Natural Science Foundation of China(Grant Nos.11705164 and 11874324).
文摘We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique.By employing these approaches,we generate hierarchies of explicit dissipative vector vortices(DVVs)that possess diverse vorticity values.Numerous fundamental characteristics of the DVVs are examined,encompassing amplitude profiles,energy fluxes,parameter effects,as well as linear and dynamic stability.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094).
文摘Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.
基金supported by the National Natural Science Foundation of China(21627813)。
文摘The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.
基金Project supported by the National Natural Science Foundation of China(Grant No.12264037)the Innovation Team of Colleges and Universities in Guangdong Province(Grant No.2021KCXTD040)+2 种基金Guangdong Province Education Department(Grant No.2023KTSCX174)the Key Laboratory of Guangdong Higher Education Institutes(Grant No.2023KSYS011)Science and Technology Bureau of Zhongshan(Grant No.2023B2035)。
文摘We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient(thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.
基金supported in part by the Innovation Program of Shanghai Municipal Education Commission(2021-01-07-00-02-E00087)the National Natural Science Foundation of China(12171314)+2 种基金the Shanghai Frontier Science Center of Modern Analysispartially supported by STU Scientific Research Initiation Grant(NTF23034T)supported in part by the National Natural Science Foundation of China(12101255)。
文摘In this paper,we apply the three circle type method and a Hardy type inequality to a nonlinear Dirac type equation on surfaces,and provide alternative proofs to the energy quantization results.
