We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain...We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain the Jacobi's elliptic solution of the defocusing Hirota equation,and solve the related linear matrix eigenvalue problem on elliptic function background.The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique.The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t→±∞are studied.Through numerical plots of the elliptic one-,two-and three-dark solitons,the amplification effect on the velocity of elliptic dark solitons,and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.展开更多
In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^...In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation.With the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.展开更多
The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses...The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.展开更多
The conversion efficiency of stimulated Raman scattering （SRS） in CH4 is studied by using a single longitudinal mode second-harmonic Nd：YAG laser （532 nm, linewidth 0.003 cm^-1, pulse-width （FWHM） 6.5 ns）. Due ...The conversion efficiency of stimulated Raman scattering （SRS） in CH4 is studied by using a single longitudinal mode second-harmonic Nd：YAG laser （532 nm, linewidth 0.003 cm^-1, pulse-width （FWHM） 6.5 ns）. Due to the heat release from vibrationally excited particles, SRS processes often suffer from the thermal defocusing effect （TDE）. In view of 6.5 ns laser pulse width is much shorter than the vibrational relaxation time of CH4 molecules, TDE can only affect the SRS processes afterwards. In the cases of low laser repetition, TDE will be not serious, because it will be removed by the thermal diffusion in Raman medium before the next pulse arrives. At the laser repetition rate 2 Hz, CH4 pressure 1.1 MPa and pump laser energy 95 mJ, the quantum conversion efficiency of backward first-Stokes （BS1） has attained 73%. This represents the highest first-stokes conversion efficiency in CH4. Furthermore, due to the relaxation oscillation, the BS1 pulses are narrowed to about 1.2 ns. As a result, the BS1 peak power turns out to be 2.7 times that of the pump. Its beam quality is also much better and is only slightly affected by TDE. This reason is that BS1 represents a wave-front-reversed replica of the pump beam, which can compensate the thermal distortions in Raman amplify process. Under the same conditions, but pump laser repetition rate as 10 Hz, the conversion efficiency of BS1 goes down to 36% due to TDE. From this study, we expect that a well-behaved 630 nm Raman laser may be designed by using a closed CH4/He circulating-cooling system, which may have some important applications.展开更多
The femtosecond filamentation in the classical and high-order Kerr （HOK） models is numerically investigated by adopting multi-photon ionization （MPI） cross section with different values. It is found that in the ca...The femtosecond filamentation in the classical and high-order Kerr （HOK） models is numerically investigated by adopting multi-photon ionization （MPI） cross section with different values. It is found that in the case that the MPI cross section is relatively small, there exists a big difference between the electron density as well as clamped intensity calculated in the classical model and those calculated in the HOK one, while in the case that the MPI cross section is relatively large, the electron density and clamped intensity calculated in the two models are nearly in agreement with each other, and under this circumstance, even if the higher-order nonlinear terms do exist, the free-charge generation and the associated defocusing in a filament are enough to mask their effects. The different behaviors of the maximum intensity and on-axis electron density at the collapse position with the pulse duration provides an approach to determine which effect plays the dominant defocusing role. These results demonstrate that it is ionization that results in the difference between the two models.展开更多
The semi-classical limit in the cubic defocusing nonlinear Schrodinger system in the whole space is proven.The electron and current densities,defined by the solution of the Schrodinger sys-tem,converge to a solution o...The semi-classical limit in the cubic defocusing nonlinear Schrodinger system in the whole space is proven.The electron and current densities,defined by the solution of the Schrodinger sys-tem,converge to a solution of the compressible Euler equation with nonlinear pressure.The corre-sponding Wigner fanction of the Schrodinger system converges to a solution of a nonlincar Vlasov equation.The proof of these results is based on estimates of a modulated energy funtional and on the Wigner measure method.展开更多
We study the existence of dark solitons of the defocusing cubic nonlinear Schr¨odinger(NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower sol...We study the existence of dark solitons of the defocusing cubic nonlinear Schr¨odinger(NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincar′e map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.展开更多
In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data ...In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].展开更多
This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter ...This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter by using WKB and paraxial approximations and solved it numerically. The effect of chirp and other laser plasma parameters is seen on the behavior of beam width parameter with dimensionless distance of propagation. The results are discussed and presented graphically. Our simulation results show that the amplitude of oscillations decreases with the distance of propagation. Due to collisional frequency, the laser beam shows fast divergence which can be minimized by the introduction of chirp parameter. The chirp decreases the effect of defocusing and increases the ability of self-focusing of laser beam in collisional plasma.展开更多
The method of nonlinearization of spectral problems is developed to the defocusing nonlinear Schr(o|¨)dingerequation.As an application,an integrable decomposition of the defocusing nonlinear Schr(o|¨)dinger ...The method of nonlinearization of spectral problems is developed to the defocusing nonlinear Schr(o|¨)dingerequation.As an application,an integrable decomposition of the defocusing nonlinear Schr(o|¨)dinger equation is presented.展开更多
We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized wav...We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intrigu- ing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is estab- lished in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.展开更多
AIM:To compare the clinical outcomes of extended depth-of-focus intraocular lenses(EDOF IOLs)using either micromonovision implantation or mixed implantation of EDOF and diffractive bifocal IOLs.METHODS:This retrospect...AIM:To compare the clinical outcomes of extended depth-of-focus intraocular lenses(EDOF IOLs)using either micromonovision implantation or mixed implantation of EDOF and diffractive bifocal IOLs.METHODS:This retrospective clinical trial included 130 patients(260 eyes),who were divided into two groups.Group RR comprised 70 patients(140 eyes)bilaterally implanted with ZXR00 IOLs(Tecnis ZXR00,where one target was-0.5 D to-0.75 D and the other was 0 to-0.25 D).Group RM comprised 60 patients(120 eyes)unilaterally implanted with both ZXR00 and ZMB00 IOLs(Tecnis ZMB00,0 to-0.25 D).Postoperative outcomes were compared after 3 mo,including visual acuity,defocus curves,stereoacuity,modulation transfer functions(MTFs),higher-order aberrations,and Visual Function-14(VF-14)questionnaire responses.RESULTS:Group RR had superior bilateral intermediate vision,while the group RM had superior bilateral near vision(both P<0.05).Group RM also exhibited superior MTFs and reduced higher-order aberrations(both P<0.05).Stereoacuity and VF-14 questionnaire results showed no statistically significant difference between groups(P>0.05).CONCLUSION:The implantation of micromonovision has significantly improved near vision.IOLs and their collocation can be customized according to individual patient needs to achieve precise treatment and provide cataract patients with high-quality vision.展开更多
For different dimensions, heights and irregular shapes, small and large particles cannot be viewed simultaneously as sharp images under the microscope due to optical defocusing effects. Bi-orthogonal wavelet transform...For different dimensions, heights and irregular shapes, small and large particles cannot be viewed simultaneously as sharp images under the microscope due to optical defocusing effects. Bi-orthogonal wavelet transform is used in this paper to depress such defocusing effect by merging the wavelet coefficients of the image series. The algorithm is presented in detail, using SWE（13,7） and CDF（2,2）, and a few particle images are provided to validate the proposed method.展开更多
AIM:To evaluate the effects of microlens design of peripheral defocus modifying spectacle lenses(PDMSLs)and non-microlens design of PDMSLs on controlling myopia progression in children and adolescents.METHODS:A system...AIM:To evaluate the effects of microlens design of peripheral defocus modifying spectacle lenses(PDMSLs)and non-microlens design of PDMSLs on controlling myopia progression in children and adolescents.METHODS:A systematic search was carried out in the PubMed,Cochrane Library,Embase,CNKI,and Web of Science databases.The search targeted randomized controlled trials(RCTs)and cohort studies(CTs)that explored the effects of PDMSLs on myopia control among children and adolescents.The Cochrane risk-of-bias tool and the Newcastle-Ottawa Scale were employed to evaluate the risk of bias in the included studies.The published biases of the included studies were evaluated using Egger’s test.RESULTS:Nine studies(7 RCTs,2 CTs)were included,involving 4332 participants in the PDMSLs group and 7317 participants in the single vision lenses(SVLs)group.Metaanalysis showed that PDMSLs with microlens design had lower change in spherical equivalent refraction(SER)than SVLs at 6,12,18,and 24mo after wearing glasses,with reductions of 0.19 D(95%CI:0.14 to 0.24,P<0.00001),0.36 D(95%CI:0.25 to 0.46,P<0.00001),0.43 D(95%CI:0.32 to 0.55,P<0.00001),and 0.51 D(95%CI:0.33 to 0.69,P<0.00001),respectively.The changes in axial length(AL)were also lower in PDMSLs compared to SVLs,with reductions of-0.09 mm(95%CI:-0.13 to-0.04,P=0.0002),-0.15 mm(95%CI:-0.21 to-0.08,P<0.00001),-0.27 mm(95%CI:-0.34 to-0.20,P<0.00001),and-0.29 mm(95%CI:-0.38 to-0.20,P<0.00001),respectively.There was no significant difference between the non-microlens group and SVLs in controlling the changes of SER and AL in myopia(both P>0.05).CONCLUSION:The synthesized evidence indicates superior myopia management outcomes with microlens design of PDMSLs compared to both SVLs and nonmicrolens design of PDMSLs in children and adolescents.展开更多
AIM:To investigate the impact of multifocal gas permeable contact lens(MFGPCL)in various add power and distance/near area allocation on short-term changes of choroidal thickness(ChT),axial length(AL),and retinal defoc...AIM:To investigate the impact of multifocal gas permeable contact lens(MFGPCL)in various add power and distance/near area allocation on short-term changes of choroidal thickness(ChT),axial length(AL),and retinal defocus profile in young adults.METHODS:Seventeen young adults(2 males and 15 females;age 23.17±4.48y)were randomly assigned to wear two designs binocularly with a one-week washout period in between.Total of four MFGPCL designs were assessed.All designs were distance-center that varied in two add power(+1.50 and 3.00 D)and/or two distance zone(DZ)diameters(1.50 and 3.00 mm;design A:DZ 1.5/add 3.0,B:DZ 1.5/add 1.5,C:DZ 3.0/add 3.0,D:DZ 3.0/add 1.5).ChT,AL,and peripheral refraction data were collected on each subject at baseline,on days 1 and 7 of MFGPCL daily wear.ChT was assessed in four quadrants using a spectraldomain optical coherence tomography.RESULTS:AL was shortened by-26±44μm with lens C,-18±27μm with lens D,-13±29μm with lens A,and-8±30μm with lens B(all P<0.05).A significant overall increase in ChT was observed with all 4 designs(lens A:+6±6μm,B:+3±7μm,C:+8±7μm,and D:+8±7μm).Temporal and superior choroid exhibited more choroidal thickening associated with MFGPCL.All designs induced significant relative peripheral myopia(RPM)beyond the central 20o across the horizontal meridian in both nasal and temporal fields(P<0.05).CONCLUSION:MFGPCLs show a significant influence on ChT and AL,which are associated with significant increase in RPM after short-term wear.The reliability and feasibility of quantifying short-term changes in ChT support its use as a promising marker for the long-term efficacy of myopia-controlling treatments.展开更多
The plasma sheath can induce radar signal modulation,causing not only ineffective target detection,but also defocusing in inverse synthetic aperture radar(ISAR)imaging.In this paper,through establishing radar echo mod...The plasma sheath can induce radar signal modulation,causing not only ineffective target detection,but also defocusing in inverse synthetic aperture radar(ISAR)imaging.In this paper,through establishing radar echo models of the reentry object enveloped with time-varying plasma sheath,we simulated the defocusing of ISAR images in typical environment.Simulation results suggested that the ISAR defocusing is caused by false scatterings,upon which the false scatterings’formation mechanism and distribution property are analyzed and studied.The range of false scattering correlates with the electron density fluctuation frequency.The combined value of the electron density fluctuation and the pulse repetition frequency jointly determines the Doppler of false scattering.Two measurement metrics including peak signal-to-noise ratio and structural similarity are used to evaluate the influence of ISAR imaging.展开更多
The present study is concerned with laser beam welding and its effect on size and microstructure of fusion zone then, on mechanical and corrosion properties of duplex stainless steel welded joints. In this regard, inf...The present study is concerned with laser beam welding and its effect on size and microstructure of fusion zone then, on mechanical and corrosion properties of duplex stainless steel welded joints. In this regard, influence of different laser welding parameters was clarified. Both bead-on-plate and autogenously butt welded joints were made using carbon dioxide laser with a maximum output of 9 kW in the continuous wave mode. Welded joints were subjected to visual, dye penetrant and radiography tests before sectioning it for different destructive tests. Accelerated corrosion test was carried out based on tafel plot technique. The results achieved in this investigation disclosed that welding parameters play an important role in obtaining satisfactory properties of welded joint. High laser power and/or high welding speed together with adjusting laser focused spot at specimen surface have produced welded joints with a remarkable decrease in fusion zone size and an acceptable weld profile with higher weld depth/width ratio. Besides, acceptable mechanical and corrosion properties were obtained. Using nitrogen as a shielding gas has resulted in improving mechanical and corrosion properties of welded joints in comparison with argon shielding. This is related to maintaining proper ferrite/austenite balance in both weld metal and HAZ in case of nitrogen shielding. As a conclusion, laser power, welding speed, defocusing distance and type of shielding gas combination have to be optimized for obtaining welded joints with acceptable profile as well as mechanical and corrosion properties.展开更多
An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach. Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking loca...An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach. Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking location induce alongshore non-uniformities of wave setup and nearshore circulation, e.g., rip currents and alongshore currents, in the surfzone. A simplified analytic model for nearshore circulation generated by focused/defocused waves on a planar beach is developed and theoretical solutions are obtained using transport stream function and perturbations in alongshore distributions of wave height and wave angle at the breaker line. The analytic model suggests that alongshore currents are strongly affected by a pair of counter-rotating vortices generated shoreward of the wave focal zone. The vortices are persistent, and their strengths depend on the amplitudes of alongshore variations in wave height and wave angle. The alongshore gradient in wave height tends to intensify the vortices while the convergence of wave angle tends to weaken the vortices. Divergent flows associated with the vortices in the surfzone are intense, strengthening alongshore currents in the downstream of the wave focal zone and weakening alongshore currents or causing flows reversal in the upstream. Alongshore currents are modulated by rip currents associated with the wave focusing/defocusing patterns.展开更多
Propagation of intense femtosecond laser pulses （60 fs, 800 nm, 120 m J, 6 × 10^17 W/cm^2 in vacuum） in supersonic （CD4）N and （D2）N cluster jets at different backing pressures was studied. Pump-probe interf...Propagation of intense femtosecond laser pulses （60 fs, 800 nm, 120 m J, 6 × 10^17 W/cm^2 in vacuum） in supersonic （CD4）N and （D2）N cluster jets at different backing pressures was studied. Pump-probe interferometry is employed to investigate the propagation of laser beams in dense cluster jets by examining the electron density distribution of plasma chan- nels. It was found that propagation effects, including ionization-induced defocusing and laser attenuation of incident pulses, are very different in the （CD4）N and （D2）N cluster jets. Different ionization states of CD4 and D2 molecules were observed by analyzing the transverse electron density profiles of the plasma channels and should be considered as a major reason for the differences in the propagation effects. Numerical simulations of the nonlinear propagation of femtosecond laser pulses in （CD4）N and （D2）N cluster jets were performed, and the results indicated a good reproduction of the experimental data.展开更多
The purpose of this paper is to present a comparison between the modified nonlinear SchrSdinger （MNLS） equation and the focusing and defocusing variants of the （unmodified） nonlinear SchrSdinger （NLS） equation i...The purpose of this paper is to present a comparison between the modified nonlinear SchrSdinger （MNLS） equation and the focusing and defocusing variants of the （unmodified） nonlinear SchrSdinger （NLS） equation in the semiclassical limit. We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretically through inverse-scattering and noncommutative steepest descent methods. The main message is that, depending on initial data, the MNLS equation can behave either like the defocusing NLS equation, like the focusing NLS equation （in both cases the analogy is asymptotically accurate in the semiclassical limit when the NLS equation is posed with appropriately modified initial data）, or like an interesting mixture of the two. In the latter case, we identify a feature of the dynamics analogous to a sonic line in gas dynamics, a free boundary separating subsonic flow from supersonic flow.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12326304,12326305,12071304)the Shenzhen Natural Science Fund(the Stable Support Plan Program)(Grant No.20220809163103001)+2 种基金the Natural Science Foundation of Henan Province(Grant No.232300420119)the Excellent Science and Technology Innovation Talent Support Program of ZUT(Grant No.K2023YXRC06)Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。
文摘We investigate dark solitons lying on elliptic function background in the defocusing Hirota equation with third-order dispersion and self-steepening terms.By means of the modified squared wavefunction method,we obtain the Jacobi's elliptic solution of the defocusing Hirota equation,and solve the related linear matrix eigenvalue problem on elliptic function background.The elliptic N-dark soliton solution in terms of theta functions is constructed by the Darboux transformation and limit technique.The asymptotic dynamical behaviors for the elliptic N-dark soliton solution as t→±∞are studied.Through numerical plots of the elliptic one-,two-and three-dark solitons,the amplification effect on the velocity of elliptic dark solitons,and the compression effect on the soliton spatiotemporal distributions produced by the third-order dispersion and self-steepening terms are discussed.
基金supported by the National Science Foundation of China(Grant No.12271104,51879045)。
文摘In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS equation.With the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.
文摘The conversion efficiency of stimulated Raman scattering （SRS） in CH4 is studied by using a single longitudinal mode second-harmonic Nd：YAG laser （532 nm, linewidth 0.003 cm^-1, pulse-width （FWHM） 6.5 ns）. Due to the heat release from vibrationally excited particles, SRS processes often suffer from the thermal defocusing effect （TDE）. In view of 6.5 ns laser pulse width is much shorter than the vibrational relaxation time of CH4 molecules, TDE can only affect the SRS processes afterwards. In the cases of low laser repetition, TDE will be not serious, because it will be removed by the thermal diffusion in Raman medium before the next pulse arrives. At the laser repetition rate 2 Hz, CH4 pressure 1.1 MPa and pump laser energy 95 mJ, the quantum conversion efficiency of backward first-Stokes （BS1） has attained 73%. This represents the highest first-stokes conversion efficiency in CH4. Furthermore, due to the relaxation oscillation, the BS1 pulses are narrowed to about 1.2 ns. As a result, the BS1 peak power turns out to be 2.7 times that of the pump. Its beam quality is also much better and is only slightly affected by TDE. This reason is that BS1 represents a wave-front-reversed replica of the pump beam, which can compensate the thermal distortions in Raman amplify process. Under the same conditions, but pump laser repetition rate as 10 Hz, the conversion efficiency of BS1 goes down to 36% due to TDE. From this study, we expect that a well-behaved 630 nm Raman laser may be designed by using a closed CH4/He circulating-cooling system, which may have some important applications.
基金supported by the National Basic Research Program of China(Grant No.2013CB922200)the National Natural Science Foundation of China(Grant Nos.11034003 and 11474129)+1 种基金the Research Fund for the Doctoral Program of Higher Education in China(Grant No.20130061110021)the Graduate Innovation Fund of Jilin University,China(Grant No.2015091)
文摘The femtosecond filamentation in the classical and high-order Kerr （HOK） models is numerically investigated by adopting multi-photon ionization （MPI） cross section with different values. It is found that in the case that the MPI cross section is relatively small, there exists a big difference between the electron density as well as clamped intensity calculated in the classical model and those calculated in the HOK one, while in the case that the MPI cross section is relatively large, the electron density and clamped intensity calculated in the two models are nearly in agreement with each other, and under this circumstance, even if the higher-order nonlinear terms do exist, the free-charge generation and the associated defocusing in a filament are enough to mask their effects. The different behaviors of the maximum intensity and on-axis electron density at the collapse position with the pulse duration provides an approach to determine which effect plays the dominant defocusing role. These results demonstrate that it is ionization that results in the difference between the two models.
基金Supported by the National Youth Natural Science Foundation(10001034)of ChinaSupported by the FWF-Projekt"14876-MAT""Fokker Planck and Miulere-Feld-Gleichungen"(Austria).
文摘The semi-classical limit in the cubic defocusing nonlinear Schrodinger system in the whole space is proven.The electron and current densities,defined by the solution of the Schrodinger sys-tem,converge to a solution of the compressible Euler equation with nonlinear pressure.The corre-sponding Wigner fanction of the Schrodinger system converges to a solution of a nonlincar Vlasov equation.The proof of these results is based on estimates of a modulated energy funtional and on the Wigner measure method.
基金Supported by the National Natural Science Foundation of China under Grant No.61178091the National Key Basic Research Program of China under Grant No.2011CB302400the Open Project Program of State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,China under Grant No.Y4KF211CJ1
文摘We study the existence of dark solitons of the defocusing cubic nonlinear Schr¨odinger(NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincar′e map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity.
基金supported by Hunan Provincial Natural Science Foundation of China(2016JJ2061)Scientific Research Fund of Hunan Provincial Education Department(15B102)+3 种基金China Postdoctoral Science Foundation(2013M532169,2014T70991)NNSF of China(11671101,11371367,11271118)the Construct Program of the Key Discipline in Hunan Province(201176)the aid program for Science and Technology Innovative Research Team in Higher Education Institutions of Hunan Province(2014207)
文摘In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].
基金Supported by a financial grant from CSIR,New Delhi,India,under Project No.03(1277)/13/EMR-Ⅱ
文摘This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter by using WKB and paraxial approximations and solved it numerically. The effect of chirp and other laser plasma parameters is seen on the behavior of beam width parameter with dimensionless distance of propagation. The results are discussed and presented graphically. Our simulation results show that the amplitude of oscillations decreases with the distance of propagation. Due to collisional frequency, the laser beam shows fast divergence which can be minimized by the introduction of chirp parameter. The chirp decreases the effect of defocusing and increases the ability of self-focusing of laser beam in collisional plasma.
基金Supported by the National Natural Science Foundation of China under Grant No.10871165
文摘The method of nonlinearization of spectral problems is developed to the defocusing nonlinear Schr(o|¨)dingerequation.As an application,an integrable decomposition of the defocusing nonlinear Schr(o|¨)dinger equation is presented.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11475135,11547302,11434013 and 11425522
文摘We study optical localized waves on a plane-wave background in negative-index materials governed by the defocusing nonlinear Schr6dinger equation with self-steepening effect. Important characteristics of localized waves, such as the excitations, transitions, propagation stability, and mechanism, are revealed in detail. An intrigu- ing sequential transition that involves the rogue wave, antidark-dark soliton pair, antidark soliton and antidark soliton pair can be triggered as the self-steepening effect attenuates. The corresponding phase diagram is estab- lished in the defocusing regime of negative-index materials. The propagation stability of the localized waves is confirmed numerically. In particular, our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.
文摘AIM:To compare the clinical outcomes of extended depth-of-focus intraocular lenses(EDOF IOLs)using either micromonovision implantation or mixed implantation of EDOF and diffractive bifocal IOLs.METHODS:This retrospective clinical trial included 130 patients(260 eyes),who were divided into two groups.Group RR comprised 70 patients(140 eyes)bilaterally implanted with ZXR00 IOLs(Tecnis ZXR00,where one target was-0.5 D to-0.75 D and the other was 0 to-0.25 D).Group RM comprised 60 patients(120 eyes)unilaterally implanted with both ZXR00 and ZMB00 IOLs(Tecnis ZMB00,0 to-0.25 D).Postoperative outcomes were compared after 3 mo,including visual acuity,defocus curves,stereoacuity,modulation transfer functions(MTFs),higher-order aberrations,and Visual Function-14(VF-14)questionnaire responses.RESULTS:Group RR had superior bilateral intermediate vision,while the group RM had superior bilateral near vision(both P<0.05).Group RM also exhibited superior MTFs and reduced higher-order aberrations(both P<0.05).Stereoacuity and VF-14 questionnaire results showed no statistically significant difference between groups(P>0.05).CONCLUSION:The implantation of micromonovision has significantly improved near vision.IOLs and their collocation can be customized according to individual patient needs to achieve precise treatment and provide cataract patients with high-quality vision.
基金sponsored by the National Natural Science Foundation of China under Grant Nos.51138001, 90815024 and 50808032the Fundamental Research Funds for the Central Universities of China under Grant No.DUT11ZD110
文摘For different dimensions, heights and irregular shapes, small and large particles cannot be viewed simultaneously as sharp images under the microscope due to optical defocusing effects. Bi-orthogonal wavelet transform is used in this paper to depress such defocusing effect by merging the wavelet coefficients of the image series. The algorithm is presented in detail, using SWE（13,7） and CDF（2,2）, and a few particle images are provided to validate the proposed method.
基金Supported by Sichuan Province Science and Technology Plan(No.2023YFS0506)Medical Research Project of Jinniu District,Chengdu,Sichuan Province(No.JNKY2024-94)Xinglin Scholar Program at Chengdu University of Traditional Chinese Medicine(No.ZYTS2023028).
文摘AIM:To evaluate the effects of microlens design of peripheral defocus modifying spectacle lenses(PDMSLs)and non-microlens design of PDMSLs on controlling myopia progression in children and adolescents.METHODS:A systematic search was carried out in the PubMed,Cochrane Library,Embase,CNKI,and Web of Science databases.The search targeted randomized controlled trials(RCTs)and cohort studies(CTs)that explored the effects of PDMSLs on myopia control among children and adolescents.The Cochrane risk-of-bias tool and the Newcastle-Ottawa Scale were employed to evaluate the risk of bias in the included studies.The published biases of the included studies were evaluated using Egger’s test.RESULTS:Nine studies(7 RCTs,2 CTs)were included,involving 4332 participants in the PDMSLs group and 7317 participants in the single vision lenses(SVLs)group.Metaanalysis showed that PDMSLs with microlens design had lower change in spherical equivalent refraction(SER)than SVLs at 6,12,18,and 24mo after wearing glasses,with reductions of 0.19 D(95%CI:0.14 to 0.24,P<0.00001),0.36 D(95%CI:0.25 to 0.46,P<0.00001),0.43 D(95%CI:0.32 to 0.55,P<0.00001),and 0.51 D(95%CI:0.33 to 0.69,P<0.00001),respectively.The changes in axial length(AL)were also lower in PDMSLs compared to SVLs,with reductions of-0.09 mm(95%CI:-0.13 to-0.04,P=0.0002),-0.15 mm(95%CI:-0.21 to-0.08,P<0.00001),-0.27 mm(95%CI:-0.34 to-0.20,P<0.00001),and-0.29 mm(95%CI:-0.38 to-0.20,P<0.00001),respectively.There was no significant difference between the non-microlens group and SVLs in controlling the changes of SER and AL in myopia(both P>0.05).CONCLUSION:The synthesized evidence indicates superior myopia management outcomes with microlens design of PDMSLs compared to both SVLs and nonmicrolens design of PDMSLs in children and adolescents.
基金the Deputyship for Research and Innovation,Ministry of Education in Saudi Arabia for funding this research work through the project(No.IFKSUOR3-433-1)。
文摘AIM:To investigate the impact of multifocal gas permeable contact lens(MFGPCL)in various add power and distance/near area allocation on short-term changes of choroidal thickness(ChT),axial length(AL),and retinal defocus profile in young adults.METHODS:Seventeen young adults(2 males and 15 females;age 23.17±4.48y)were randomly assigned to wear two designs binocularly with a one-week washout period in between.Total of four MFGPCL designs were assessed.All designs were distance-center that varied in two add power(+1.50 and 3.00 D)and/or two distance zone(DZ)diameters(1.50 and 3.00 mm;design A:DZ 1.5/add 3.0,B:DZ 1.5/add 1.5,C:DZ 3.0/add 3.0,D:DZ 3.0/add 1.5).ChT,AL,and peripheral refraction data were collected on each subject at baseline,on days 1 and 7 of MFGPCL daily wear.ChT was assessed in four quadrants using a spectraldomain optical coherence tomography.RESULTS:AL was shortened by-26±44μm with lens C,-18±27μm with lens D,-13±29μm with lens A,and-8±30μm with lens B(all P<0.05).A significant overall increase in ChT was observed with all 4 designs(lens A:+6±6μm,B:+3±7μm,C:+8±7μm,and D:+8±7μm).Temporal and superior choroid exhibited more choroidal thickening associated with MFGPCL.All designs induced significant relative peripheral myopia(RPM)beyond the central 20o across the horizontal meridian in both nasal and temporal fields(P<0.05).CONCLUSION:MFGPCLs show a significant influence on ChT and AL,which are associated with significant increase in RPM after short-term wear.The reliability and feasibility of quantifying short-term changes in ChT support its use as a promising marker for the long-term efficacy of myopia-controlling treatments.
基金supported in part by National Natural Science Foundation of China(Nos.61971330,61701381,and 61627901)in part by the Natural Science Basic Research Plan in Shaanxi Province of China(No.2019JM-177)in part by the Chinese Postdoctoral Science Foundation。
文摘The plasma sheath can induce radar signal modulation,causing not only ineffective target detection,but also defocusing in inverse synthetic aperture radar(ISAR)imaging.In this paper,through establishing radar echo models of the reentry object enveloped with time-varying plasma sheath,we simulated the defocusing of ISAR images in typical environment.Simulation results suggested that the ISAR defocusing is caused by false scatterings,upon which the false scatterings’formation mechanism and distribution property are analyzed and studied.The range of false scattering correlates with the electron density fluctuation frequency.The combined value of the electron density fluctuation and the pulse repetition frequency jointly determines the Doppler of false scattering.Two measurement metrics including peak signal-to-noise ratio and structural similarity are used to evaluate the influence of ISAR imaging.
文摘The present study is concerned with laser beam welding and its effect on size and microstructure of fusion zone then, on mechanical and corrosion properties of duplex stainless steel welded joints. In this regard, influence of different laser welding parameters was clarified. Both bead-on-plate and autogenously butt welded joints were made using carbon dioxide laser with a maximum output of 9 kW in the continuous wave mode. Welded joints were subjected to visual, dye penetrant and radiography tests before sectioning it for different destructive tests. Accelerated corrosion test was carried out based on tafel plot technique. The results achieved in this investigation disclosed that welding parameters play an important role in obtaining satisfactory properties of welded joint. High laser power and/or high welding speed together with adjusting laser focused spot at specimen surface have produced welded joints with a remarkable decrease in fusion zone size and an acceptable weld profile with higher weld depth/width ratio. Besides, acceptable mechanical and corrosion properties were obtained. Using nitrogen as a shielding gas has resulted in improving mechanical and corrosion properties of welded joints in comparison with argon shielding. This is related to maintaining proper ferrite/austenite balance in both weld metal and HAZ in case of nitrogen shielding. As a conclusion, laser power, welding speed, defocusing distance and type of shielding gas combination have to be optimized for obtaining welded joints with acceptable profile as well as mechanical and corrosion properties.
基金financially supported by the Tianjin Municipal Science and Technology Commission(Grant No.19JCYBJC22000)
文摘An offshore shoal or bar refracts ocean surface waves and causes wave focusing/defocusing on the adjacent beach. Wave focal patterns characterized by alongshore variations in wave height, wave angle, and breaking location induce alongshore non-uniformities of wave setup and nearshore circulation, e.g., rip currents and alongshore currents, in the surfzone. A simplified analytic model for nearshore circulation generated by focused/defocused waves on a planar beach is developed and theoretical solutions are obtained using transport stream function and perturbations in alongshore distributions of wave height and wave angle at the breaker line. The analytic model suggests that alongshore currents are strongly affected by a pair of counter-rotating vortices generated shoreward of the wave focal zone. The vortices are persistent, and their strengths depend on the amplitudes of alongshore variations in wave height and wave angle. The alongshore gradient in wave height tends to intensify the vortices while the convergence of wave angle tends to weaken the vortices. Divergent flows associated with the vortices in the surfzone are intense, strengthening alongshore currents in the downstream of the wave focal zone and weakening alongshore currents or causing flows reversal in the upstream. Alongshore currents are modulated by rip currents associated with the wave focusing/defocusing patterns.
基金supported by the National Basic Pesearch Program of China (No. 2006CB806000)National Natural Science Foundation of China (Nos. 10674145, 60921004, 10974214)
文摘Propagation of intense femtosecond laser pulses （60 fs, 800 nm, 120 m J, 6 × 10^17 W/cm^2 in vacuum） in supersonic （CD4）N and （D2）N cluster jets at different backing pressures was studied. Pump-probe interferometry is employed to investigate the propagation of laser beams in dense cluster jets by examining the electron density distribution of plasma chan- nels. It was found that propagation effects, including ionization-induced defocusing and laser attenuation of incident pulses, are very different in the （CD4）N and （D2）N cluster jets. Different ionization states of CD4 and D2 molecules were observed by analyzing the transverse electron density profiles of the plasma channels and should be considered as a major reason for the differences in the propagation effects. Numerical simulations of the nonlinear propagation of femtosecond laser pulses in （CD4）N and （D2）N cluster jets were performed, and the results indicated a good reproduction of the experimental data.
基金supported by the National Science Foundation under grant DMS-0807653
文摘The purpose of this paper is to present a comparison between the modified nonlinear SchrSdinger （MNLS） equation and the focusing and defocusing variants of the （unmodified） nonlinear SchrSdinger （NLS） equation in the semiclassical limit. We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretically through inverse-scattering and noncommutative steepest descent methods. The main message is that, depending on initial data, the MNLS equation can behave either like the defocusing NLS equation, like the focusing NLS equation （in both cases the analogy is asymptotically accurate in the semiclassical limit when the NLS equation is posed with appropriately modified initial data）, or like an interesting mixture of the two. In the latter case, we identify a feature of the dynamics analogous to a sonic line in gas dynamics, a free boundary separating subsonic flow from supersonic flow.
