Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the ease of exponential saturable ...Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the ease of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.展开更多
In this paper,we construct sign-changing radial solutions for a class of Schrodinger equations with saturable nonlinearity which arises from several models in mathematical physics.More precisely,for any given nonnegat...In this paper,we construct sign-changing radial solutions for a class of Schrodinger equations with saturable nonlinearity which arises from several models in mathematical physics.More precisely,for any given nonnegative integer k,by using a minimization argument,we first obtain a sign-changing minimizer with k nodes of a constrained minimization problem,and show,by a deformation lemma and Miranda's theorem,that the minimizer is the desired solution.展开更多
We investigate the higher-order topological laser in the two-dimensional(2D) coupled-cavity array. By adding staggered on-site gain and loss to the 2D Hermitian array with a trivial phase, the system will emerge degen...We investigate the higher-order topological laser in the two-dimensional(2D) coupled-cavity array. By adding staggered on-site gain and loss to the 2D Hermitian array with a trivial phase, the system will emerge degenerate topological corner modes, which are protected by bulk band gap. For such a non-Hermitian model, by adjusting the parameters of the system and introducing the pumping into the cavity at the corner, a single-mode lasing with topological protection emerges.Furthermore, single-mode lasing exists over a wide range of pumping strengths. No matter where the cavity is initially stimulated, after enough time evolution, all the cavities belonging to the topological corner mode can emit a stable laser.展开更多
In this paper, we introduce and propose exact and explicit analytical solutions to a novel model of the nonlinear Schr¨odinger(NLS) equation. This model is derived as the equation governing the dynamics of modula...In this paper, we introduce and propose exact and explicit analytical solutions to a novel model of the nonlinear Schr¨odinger(NLS) equation. This model is derived as the equation governing the dynamics of modulated cutoff waves in a discrete nonlinear electrical lattice. It is characterized by the addition of two terms that involve time derivatives to the classical equation. Through those terms, our model is also tantamount to a generalized NLS equation with saturable;which suggests that the discrete electrical transmission lines can potentially be used to experimentally investigate wave propagation in media that are modeled by such type of nonlinearity. We demonstrate that the new terms can enlarge considerably the forms of the solutions as compared to similar NLS-type equations. Sine–Gordon expansion-method is used to derive numerous kink, antikink, dark, and bright soliton solutions.展开更多
On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability(MI) have b...On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability(MI) have been analyzed and calculated for negative-refractive metamaterials(MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.展开更多
A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components, i.e. turbine, PID t^^pe governor with saturatio...A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components, i.e. turbine, PID t^^pe governor with saturation part and generator included in the model. Existence, stability and direction of Hopf bifurcation of an example HTGS are investigated in detail and presented in forms of bifurcation diagrams and time "wavefomis. The analysis show,that a supercritical Hopf bifurcation may exist in hydraulic turbine systems in some certain conditions. Moreover, the dynaiidc behavior of system with different parameters such as Tw, Tab, Ty and 尺 are studied extensively. An example with numerical simulations is presented to illustrate the theoretical results. The researches provide a reasonable explanation for the Hopf phenomenon happened in operation of hydroelectric generating unit.展开更多
In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic ...In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.展开更多
We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several fa...We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.展开更多
A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case o...A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′<SUB> i </SUB>at any time.展开更多
It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and tes...It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.展开更多
On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is...On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance展开更多
The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering th...The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the ro/λ(λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When ro/λ is large enough (r0 〉〉 λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.展开更多
We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedde...We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.展开更多
On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is inve...On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.展开更多
In this paper,we study the existence and concentration behavior of the semiclassical states with L2-constraints for the following saturable nonlinear Schr?dinger equation:-ε2Δv+Γ(I(x)+v^(2))/(1+I(x)+v^(2))v=λv fo...In this paper,we study the existence and concentration behavior of the semiclassical states with L2-constraints for the following saturable nonlinear Schr?dinger equation:-ε2Δv+Γ(I(x)+v^(2))/(1+I(x)+v^(2))v=λv for x∈R2.For a negatively large coupling constantΓ,we show that there exists a family of normalized positive solutions(i.e.,with the L2-constraint)whenεis small,which concentrate around local maxima of the intensity function I(x)asε→0.We also consider the case where I(x)may tend to-1 at infinity and the existence of multiple solutions.The proof of our results is variational and the novelty of the work lies in the development of a new truncation-type method for the construction of the desired solutions.展开更多
In recent years,image processing based on stochastic resonance(SR)has received more and more attention.In this paper,a new model combining dynamical saturating nonlinearity with regularized variational term for enhanc...In recent years,image processing based on stochastic resonance(SR)has received more and more attention.In this paper,a new model combining dynamical saturating nonlinearity with regularized variational term for enhancement of low contrast image is proposed.The regularized variational term can be setting to total variation(TV),second order total generalized variation(TGV)and non-local means(NLM)in order to gradually suppress noise in the process of solving the model.In addition,the new model is tested on a mass of gray-scale images from standard test image and low contrast indoor color images from Low-Light dataset(LOL).By comparing the new model and other traditional image enhancement models,the results demonstrate the enhanced image not only obtain good perceptual quality but also get more excellent value of evaluation index compared with some previous methods.展开更多
Two-dimensional semiconductors such as transition metal dichalcogenides(TMDs)have attracted much interest in the past decade.Herein,we present an all-physical top-down method for the scalable production of the intrins...Two-dimensional semiconductors such as transition metal dichalcogenides(TMDs)have attracted much interest in the past decade.Herein,we present an all-physical top-down method for the scalable production of the intrinsic TMD quantum sheets(QSs).The phases of the TMDs(e.g.,2H-MoSe_(2),2H-WSe_(2),and Td-WTe2)remain stable during the transformation from bulk to QSs.However,phase transition(from Td to 2H)is detected in MoTe2.Such phase-modulation by size-reduction has never been reported before.The TMD QSs can be well dispersed in solvents,resulting in remarkable photoluminescence with excitation wavelength-,concentration-,and solvent-dependence.Meanwhile,the TMD QSs can be readily solution-processed into hybrid thin films,which demonstrate exceptional nonlinear saturation absorption(NSA).Notably,2H-MoTe2 QSs in poly(methyl methacrylate)show extremely high NSA performance with(absolute)modulation depth up to 46.6%and saturation intensity down to 0.81 MW·cm^(−2).Our work paves the way towards quantum-sized TMDs.展开更多
The production of two-dimensional nanosheets(2D NSs)with all sizes(1-100 nm)and few(<10)layers is highly desired but far from satisfactory.Herein,we report an all-physical top-down method to produce indium chalcoge...The production of two-dimensional nanosheets(2D NSs)with all sizes(1-100 nm)and few(<10)layers is highly desired but far from satisfactory.Herein,we report an all-physical top-down method to produce indium chalcogenide(In2X3(X=S,Se,Te))NSs with wide-range(150-3.0 nm)controlled sizes.The method combines silica-assisted ball-milling and sonication-assisted solvent exfoliation to fabricate multiscale NSs with varying distributions,which are then precisely separated by cascade centrifugation.Multiple characterization techniques reveal that the as-produced In2X3 NSs are intrinsic and defect-free and remainβ-phase during the whole process.The redispersions of In2X3 NSs exhibit prominent excitation wavelength-,solvent-,concentration-,and size-dependent photoluminescence.The NSs-poly(methyl methacrylate)(PMMA)hybrid thin films demonstrate strong size effects in nonlinear saturation absorption.The absolute modulation depths of 35.4%,43.3%,47.2%and saturation intensities of 1.63,1.05,0.83 MW·cm^(−2)(i.e.,163,105,and 83 nJ·cm^(−2))are derived for the In_(2)S_(3),In_(2)Se_(3),and In2Te3 quantum sheets,respectively.Our method paves the way for mass production and full exploration of full-scale 2D NSs.展开更多
The structural,morphological,optical,and nonlinear optical properties of a lead sulfde(PbS) thin film grown by chemical bath deposition(CBD) are investigated by X-ray difraction(XRD),scanning electron microscope(SEM),...The structural,morphological,optical,and nonlinear optical properties of a lead sulfde(PbS) thin film grown by chemical bath deposition(CBD) are investigated by X-ray difraction(XRD),scanning electron microscope(SEM),ultraviolet-visible(UV-Vis),and open aperture Z-scan experiments.The band gap energy of the PbS nanocrystalline film is 1.82 eV,higher than that of bulk PbS at 300 K.The nonlinear absorption properties of the film are investigated using the open aperture Z-scan technique at 1064 nm and pulse durations of 4 ns and 65 ps.Intensity-dependent switching of the film from nonlinear absorption to saturable absorption is observed.The nonlinear absorption coefficient increases monotonically with increasing pulse duration from 65 ps to 4 ns.展开更多
In this Letter, the effects of the iron (Fe) dopant concentration on the nonlinear optical properties of iron-doped ferroelectric X-cut LiNbO3 crystals plates are studied by using the Z-scan technique with a cw lase...In this Letter, the effects of the iron (Fe) dopant concentration on the nonlinear optical properties of iron-doped ferroelectric X-cut LiNbO3 crystals plates are studied by using the Z-scan technique with a cw laser at the wave- length of 532 nm. The amount of iron in the compound is varied from 0 to 0.15 mol%. Measurements of nonlinear refractive index n2 and the nonlinear absorption coefficient β are determined. The sign of the nonlinear refractive index is found to be negative and the magnitude is on the order of 10-s cm2/W. This nonlinear effect increases as the concentration increases from 0 to 0.15 mol%. A good linear relationship is obtained between nonlinear refractive index, nonlinear absorption coefficient, and concentration.展开更多
基金Project supported by the Key Program of the Natural Science Foundation of Sichuan Provincial Education Department (Grant No. 2006A124)the Fundamental Application Research Project of the Department of Science & Technology of Sichuan Province (Grant No. 05JY029-084)
文摘Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the ease of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.
基金supported by National Natural Science Foundation of China(11971147)China Postdoctoral Science Foundation(2019M662475)Henan Postdoctoral Research Grant(201902026).
文摘In this paper,we construct sign-changing radial solutions for a class of Schrodinger equations with saturable nonlinearity which arises from several models in mathematical physics.More precisely,for any given nonnegative integer k,by using a minimization argument,we first obtain a sign-changing minimizer with k nodes of a constrained minimization problem,and show,by a deformation lemma and Miranda's theorem,that the minimizer is the desired solution.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12274326 and 12174288)the National Key R&D Program of China (Grant No. 2021YFA1400602)。
文摘We investigate the higher-order topological laser in the two-dimensional(2D) coupled-cavity array. By adding staggered on-site gain and loss to the 2D Hermitian array with a trivial phase, the system will emerge degenerate topological corner modes, which are protected by bulk band gap. For such a non-Hermitian model, by adjusting the parameters of the system and introducing the pumping into the cavity at the corner, a single-mode lasing with topological protection emerges.Furthermore, single-mode lasing exists over a wide range of pumping strengths. No matter where the cavity is initially stimulated, after enough time evolution, all the cavities belonging to the topological corner mode can emit a stable laser.
文摘In this paper, we introduce and propose exact and explicit analytical solutions to a novel model of the nonlinear Schr¨odinger(NLS) equation. This model is derived as the equation governing the dynamics of modulated cutoff waves in a discrete nonlinear electrical lattice. It is characterized by the addition of two terms that involve time derivatives to the classical equation. Through those terms, our model is also tantamount to a generalized NLS equation with saturable;which suggests that the discrete electrical transmission lines can potentially be used to experimentally investigate wave propagation in media that are modeled by such type of nonlinearity. We demonstrate that the new terms can enlarge considerably the forms of the solutions as compared to similar NLS-type equations. Sine–Gordon expansion-method is used to derive numerous kink, antikink, dark, and bright soliton solutions.
基金Project supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 210186)the Scientific Research Foundation of Chengdu University of Information Technology,China (Grant Nos. 2010d1 and J201117)
文摘On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability(MI) have been analyzed and calculated for negative-refractive metamaterials(MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.
文摘A nonlinear mathematical model for hydro turbine governing system with saturation nonlinearity in small perturbation has been proposed with all the essential components, i.e. turbine, PID t^^pe governor with saturation part and generator included in the model. Existence, stability and direction of Hopf bifurcation of an example HTGS are investigated in detail and presented in forms of bifurcation diagrams and time "wavefomis. The analysis show,that a supercritical Hopf bifurcation may exist in hydraulic turbine systems in some certain conditions. Moreover, the dynaiidc behavior of system with different parameters such as Tw, Tab, Ty and 尺 are studied extensively. An example with numerical simulations is presented to illustrate the theoretical results. The researches provide a reasonable explanation for the Hopf phenomenon happened in operation of hydroelectric generating unit.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147,11071159)the Natural Science Foundation of Shanghai Municipality (Grant No.09ZR1410800)+1 种基金the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘In this paper, the Toda equation and the discrete nonlinear Schrdinger equation with a saturable nonlinearity via the discrete " (G′/G")-expansion method are researched. As a result, with the aid of the symbolic computation, new hyperbolic function solution and trigonometric function solution with parameters of the Toda equation are obtained. At the same time, new envelop hyperbolic function solution and envelop trigonometric function solution with parameters of the discrete nonlinear Schro¨dinger equation with a saturable nonlinearity are obtained. This method can be applied to other nonlinear differential-difference equations in mathematical physics.
基金supported by the National Natural Science Foundation of China (Grant No. 10704067)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6100381)
文摘We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.
基金This project was supported jointly by the National Natural Science Foundation of China under Grant Nos. 49455007, 40075011, and 40075014, and the China Postdoctoral Science Foundation,
文摘A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′<SUB> i </SUB>at any time.
基金Project supported by the National Natural Science Foundation of China (Nos.40202036,40572163,50579042)the Youth Science Foundation of Siehuan Province of China (No.05ZQ026-043)+1 种基金the Science Foundation of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(No.GZ2004-05)the Postdoctoral Science Foundation of China (No.35)
文摘It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.
文摘On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance
基金supported by the National Natural Science Foundation of China(Grant Nos.10835003 and 11274026)the Scientific Research Foundation of Mianyang Normal University,China(Grant No.07165411)
文摘The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the ro/λ(λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When ro/λ is large enough (r0 〉〉 λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11174147)the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2009366)
文摘We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.
文摘On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.
基金supported by National Natural Science Foundation of China(Grant No.11861053)supported by National Natural Science Foundation of China(Grant No.11831009)supported by National Natural Science Foundation of China(Grant No.11901582)。
文摘In this paper,we study the existence and concentration behavior of the semiclassical states with L2-constraints for the following saturable nonlinear Schr?dinger equation:-ε2Δv+Γ(I(x)+v^(2))/(1+I(x)+v^(2))v=λv for x∈R2.For a negatively large coupling constantΓ,we show that there exists a family of normalized positive solutions(i.e.,with the L2-constraint)whenεis small,which concentrate around local maxima of the intensity function I(x)asε→0.We also consider the case where I(x)may tend to-1 at infinity and the existence of multiple solutions.The proof of our results is variational and the novelty of the work lies in the development of a new truncation-type method for the construction of the desired solutions.
基金supported by the National Natural Science Foundation of China under Grant Nos. 61501276,61772294 and 61973179the China Postdoctoral Science Foundation under Grant No. 2016M592139the Qingdao Postdoctoral Applied Research Project under Grant No. 2015120
文摘In recent years,image processing based on stochastic resonance(SR)has received more and more attention.In this paper,a new model combining dynamical saturating nonlinearity with regularized variational term for enhancement of low contrast image is proposed.The regularized variational term can be setting to total variation(TV),second order total generalized variation(TGV)and non-local means(NLM)in order to gradually suppress noise in the process of solving the model.In addition,the new model is tested on a mass of gray-scale images from standard test image and low contrast indoor color images from Low-Light dataset(LOL).By comparing the new model and other traditional image enhancement models,the results demonstrate the enhanced image not only obtain good perceptual quality but also get more excellent value of evaluation index compared with some previous methods.
基金supported by the National Natural Science Foundation of China(Nos.52073070,21673054,11874130,and 22073022)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB36000000)+1 种基金the National Key R&D Program of China(No.2018YFA0703700)the DNL Cooperation Fund CAS(No.DNL202016).
文摘Two-dimensional semiconductors such as transition metal dichalcogenides(TMDs)have attracted much interest in the past decade.Herein,we present an all-physical top-down method for the scalable production of the intrinsic TMD quantum sheets(QSs).The phases of the TMDs(e.g.,2H-MoSe_(2),2H-WSe_(2),and Td-WTe2)remain stable during the transformation from bulk to QSs.However,phase transition(from Td to 2H)is detected in MoTe2.Such phase-modulation by size-reduction has never been reported before.The TMD QSs can be well dispersed in solvents,resulting in remarkable photoluminescence with excitation wavelength-,concentration-,and solvent-dependence.Meanwhile,the TMD QSs can be readily solution-processed into hybrid thin films,which demonstrate exceptional nonlinear saturation absorption(NSA).Notably,2H-MoTe2 QSs in poly(methyl methacrylate)show extremely high NSA performance with(absolute)modulation depth up to 46.6%and saturation intensity down to 0.81 MW·cm^(−2).Our work paves the way towards quantum-sized TMDs.
基金supported by the National Natural Science Foundation of China(Nos.52073070,21673054,11874130,and 22073022)Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB36000000)+1 种基金National Key R&D Program of China(No.2018YFA0703700)DNL Cooperation Fund,CAS(DNL202016).
文摘The production of two-dimensional nanosheets(2D NSs)with all sizes(1-100 nm)and few(<10)layers is highly desired but far from satisfactory.Herein,we report an all-physical top-down method to produce indium chalcogenide(In2X3(X=S,Se,Te))NSs with wide-range(150-3.0 nm)controlled sizes.The method combines silica-assisted ball-milling and sonication-assisted solvent exfoliation to fabricate multiscale NSs with varying distributions,which are then precisely separated by cascade centrifugation.Multiple characterization techniques reveal that the as-produced In2X3 NSs are intrinsic and defect-free and remainβ-phase during the whole process.The redispersions of In2X3 NSs exhibit prominent excitation wavelength-,solvent-,concentration-,and size-dependent photoluminescence.The NSs-poly(methyl methacrylate)(PMMA)hybrid thin films demonstrate strong size effects in nonlinear saturation absorption.The absolute modulation depths of 35.4%,43.3%,47.2%and saturation intensities of 1.63,1.05,0.83 MW·cm^(−2)(i.e.,163,105,and 83 nJ·cm^(−2))are derived for the In_(2)S_(3),In_(2)Se_(3),and In2Te3 quantum sheets,respectively.Our method paves the way for mass production and full exploration of full-scale 2D NSs.
文摘The structural,morphological,optical,and nonlinear optical properties of a lead sulfde(PbS) thin film grown by chemical bath deposition(CBD) are investigated by X-ray difraction(XRD),scanning electron microscope(SEM),ultraviolet-visible(UV-Vis),and open aperture Z-scan experiments.The band gap energy of the PbS nanocrystalline film is 1.82 eV,higher than that of bulk PbS at 300 K.The nonlinear absorption properties of the film are investigated using the open aperture Z-scan technique at 1064 nm and pulse durations of 4 ns and 65 ps.Intensity-dependent switching of the film from nonlinear absorption to saturable absorption is observed.The nonlinear absorption coefficient increases monotonically with increasing pulse duration from 65 ps to 4 ns.
文摘In this Letter, the effects of the iron (Fe) dopant concentration on the nonlinear optical properties of iron-doped ferroelectric X-cut LiNbO3 crystals plates are studied by using the Z-scan technique with a cw laser at the wave- length of 532 nm. The amount of iron in the compound is varied from 0 to 0.15 mol%. Measurements of nonlinear refractive index n2 and the nonlinear absorption coefficient β are determined. The sign of the nonlinear refractive index is found to be negative and the magnitude is on the order of 10-s cm2/W. This nonlinear effect increases as the concentration increases from 0 to 0.15 mol%. A good linear relationship is obtained between nonlinear refractive index, nonlinear absorption coefficient, and concentration.