The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω i...The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω is a bounded open set in Rn with smoothbonndary and the nonlinearity bu+ crosses eigenvalues of △2 ＋c△. They investigate therelatiolls when the source term is constant and when it is generated by two eigenfuntions.展开更多
In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method...In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.展开更多
In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, wher...In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.展开更多
This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity ...This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity transformations have been used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. These equations are then solved numerically using a very efficient implicit finite difference method. Favorable comparison with previously published work is performed and it is found to be in excellent agreement. The results of this parametric study are shown in several plots and tables and the physical aspects of the problem are highlighted and discussed.展开更多
The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid beha...The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of justified similarity transformations the governing equations were reduced to couple nonlinear ordinary differential equations. The effective numerical technique Keller Box method is used to solve these equations. The variations in velocity, temperature profiles were presented with the various values of nonlinear stretching parameter n and Casson parameter β. The nature of Skinfriction and Local nusselt number has presented. Effects of radiation and heat source/sink on temperature profiles have been discussed.展开更多
This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient co...This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.展开更多
This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t...This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t） = u^q（1,t）, （｜ux｜^m-1ux）（0,t） = O, and positive initial data u（x,0） = uo（x）, where the parameters va, n, p, q 〉0. It is proved that the problem possesses global solutions if and only if p ≤ n and q〈min {n,m（n＋1）/m＋1}.展开更多
This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Cr...This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Criteria for global existence of the solution and for quenching are investigated.展开更多
We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black h...We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.展开更多
In this work,a new structure is used to enhance the nonlinear effect in the cavity,which improvesthe performance of the 1.3μm broadband swept source.The swept source adopts a semiconductoroptical amplifier(SOA),a cir...In this work,a new structure is used to enhance the nonlinear effect in the cavity,which improvesthe performance of the 1.3μm broadband swept source.The swept source adopts a semiconductoroptical amplifier(SOA),a circulator,a coupler,and a tunable filter.In the structure,the lightpasses through the nonlinear medium(SOA)twice in two opposite directions,which excites thenonlinear ffect and increases the performance of the swept source.The tunable filter is based on apolygon rotating mirror and gratings.Traditionally,multiple SOAs are adopted to improve thesweep range and the optical power,which increases the cost and complexity of the swept source.The method proposed in this paper can improve the spectral range and optical power of the sweptsources without additional accessories.For the short-cavity swept source,the power increasesfrom 6 mW to 7.7 mW,and the sweep range increases from 98 nm to 120 nm.The broadband swept sources could have wide applications in biomedical imaging,sensor system,measurementand so on.展开更多
In this paper we study existence of solutions of a class of Cauchy problems for porous medium equations with strongly nonlinear sources or absorptions and convections when the initial trace is a Radon measure μ on RN.
The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computat...The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computational fluid dynamics(CFD)and other mathematical techniques.In this paper,the hull form optimization method based on the Rankine source method and nonlinear programming(NLP)is discussed;in the optimization process,a hull form modification function is introduced to represent an improved hull surface and to generate a new smooth hull surface by changing its frame lines and bow stem profiles under the prescribed design constraints. Numerical example is given for a practical container hull form.Finally,shape optimization of bow bulls is shown for non-protruding and protruding bow bulls.This study presents a simplified and practical design method to the select frame lines of bow bulls.展开更多
The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault par...The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault parameters inversion has nonlinear characteristics, and the gradient-based optimizer(GBO) has the characteristics of fast convergence speed and falling into local optimum hardly. This paper applies GBO algorithm to simulated earthquakes and real LuShan earthquakes in the nonlinear inversion of the Okada model to obtain the source parameters. The simulated earthquake experiment results show that the algorithm is stable, and the seismic source parameters obtained by GBO are slightly closer to the true value than the multi peak particle swarm optimization(MPSO). In the 2013 LuShan earthquake experiment, the root mean square error between the deformation after forwarding of fault parameters obtained by the introduced GBO algorithm and the surface observation deformation was 3.703 mm, slightly better than 3.708 mm calculated by the MPSO. Moreover, the inversion result of GBO algorithm is better than MPSO algorithm in stability. The above results show that the introduced GBO algorithm has a certain practical application value in seismic fault source parameters inversion.展开更多
In the paper, Ablowitz–Ladik hierarchy with new self-consistent sources is investigated. First the source in the hierarchy is described as φnφn+1, where φnis related to the Ablowitz–Ladik spectral problem, instea...In the paper, Ablowitz–Ladik hierarchy with new self-consistent sources is investigated. First the source in the hierarchy is described as φnφn+1, where φnis related to the Ablowitz–Ladik spectral problem, instead of the corresponding adjoint spectral problem. Then by means of the inverse scattering transform, the multi-soliton solutions for the hierarchy are obtained. Two reductions to the discrete mKdV and nonlinear Schr¨odinger hierarchies with selfconsistent sources are considered by using the uniqueness of the Jost functions, as well as their N-soliton solutions.展开更多
In this paper,by utilizing the angle of arrivals(AOAs) and imprecise positions of the sensors,a novel modified Levenberg-Marquardt algorithm to solve the source localization problem is proposed.Conventional source loc...In this paper,by utilizing the angle of arrivals(AOAs) and imprecise positions of the sensors,a novel modified Levenberg-Marquardt algorithm to solve the source localization problem is proposed.Conventional source localization algorithms,like Gauss-Newton algorithm and Conjugate gradient algorithm are subjected to the problems of local minima and good initial guess.This paper presents a new optimization technique to find the descent directions to avoid divergence,and a trust region method is introduced to accelerate the convergence rate.Compared with conventional methods,the new algorithm offers increased stability and is more robust,allowing for stronger non-linearity and wider convergence field to be identified.Simulation results demonstrate that the proposed algorithm improves the typical methods in both speed and robustness,and is able to avoid local minima.展开更多
For the 22-year solar cycle oscillation there is no external time dependent source. A nonlinear oscillation, the solar cycle must be generated internally, and Babcock-Leighton models apply an artificial nonlinear sour...For the 22-year solar cycle oscillation there is no external time dependent source. A nonlinear oscillation, the solar cycle must be generated internally, and Babcock-Leighton models apply an artificial nonlinear source term that can simulate the observations—which leaves open the question of the actual source mechanism for the solar cycle. Addressing this question, we propose to take guidance from the wave mechanism that generates the 2-year Quasi-biennial Oscillation (QBO) in the Earth atmosphere. Upward propagating gravity waves, eastward and westward, deposit momentum to generate the observed zonal wind oscillation. On the Sun, helioseismology has provided a thorough understanding of the acoustic p-waves, which propagate down into the convective envelope guided by the increasing temperature and related propagation velocity. Near the tachocline with low turbulent viscosity, the waves propagating eastward and westward can produce an axisymmetric 22-year oscillation of the zonal flow velocities that can generate the magnetic solar dynamo. Following the Earth model, waves in opposite directions can generate in the Sun wind and magnetic field oscillations in opposite directions, the proposition of a potential solar cycle mechanism.展开更多
文摘The authors investigatc relations between multiplicity of solutions and sourceterms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition △2u＋c△u = bu+＋f inΩ, wherc Ω is a bounded open set in Rn with smoothbonndary and the nonlinearity bu+ crosses eigenvalues of △2 ＋c△. They investigate therelatiolls when the source term is constant and when it is generated by two eigenfuntions.
基金Supported by the National Natural Science Foundation of China (50736002,61072005)the Youth Backbone Teacher Project of University,Ministry of Education,China+1 种基金the Scientific Research Foundation of the Department of Science and Technology of Liaoning Province (20102082)the Changjiang Scholars and Innovative Team Development Plan (IRT0952)
文摘In order to overcome the disturbance of noise,this paper presented a method to measure two-phase flow velocity using particle swarm optimization algorithm,nonlinear blind source separation and cross correlation method.Because of the nonlinear relationship between the output signals of capacitance sensors and fluid in pipeline,nonlinear blind source separation is applied.In nonlinear blind source separation,the odd polynomials of higher order are used to fit the nonlinear transformation function,and the mutual information of separation signals is used as the evaluation function.Then the parameters of polynomial and linear separation matrix can be estimated by mutual information of separation signals and particle swarm optimization algorithm,thus the source signals can be separated from the mixed signals.The two-phase flow signals with noise which are obtained from upstream and downstream sensors are respectively processed by nonlinear blind source separation method so that the noise can be effectively removed.Therefore,based on these noise-suppressed signals,the distinct curves of cross correlation function and the transit times are obtained,and then the velocities of two-phase flow can be accurately calculated.Finally,the simulation experimental results are given.The results have proved that this method can meet the measurement requirements of two-phase flow velocity.
文摘In this paper, we show the existence of the time periodic solutions to the porous medium equations of the formut= Δ (|u| m-1 u)+B(x,t,u)+f(x,t) in Ω×Rwith the Dirichlet boundary value condition, where m>1, Ω is a bounded domain in R N with smooth boundary Ω , the continuous function f and the Hlder continuous function B(x,t,u) are periodic in t with period ω and the nonlinear sources are assumed to be weaker, i.e., B(x,t,u) u≤b 0|u| α+1 with constants b 0≥0 and 0≤α<m.
文摘This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity transformations have been used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. These equations are then solved numerically using a very efficient implicit finite difference method. Favorable comparison with previously published work is performed and it is found to be in excellent agreement. The results of this parametric study are shown in several plots and tables and the physical aspects of the problem are highlighted and discussed.
文摘The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of justified similarity transformations the governing equations were reduced to couple nonlinear ordinary differential equations. The effective numerical technique Keller Box method is used to solve these equations. The variations in velocity, temperature profiles were presented with the various values of nonlinear stretching parameter n and Casson parameter β. The nature of Skinfriction and Local nusselt number has presented. Effects of radiation and heat source/sink on temperature profiles have been discussed.
基金supported by the National Natural Science Foundation of China(11471109)the Construct Program of the Key Discipline in Hunan Province and Hunan Provincial Innovation Foundation for Postgraduate(CX2017B172)
文摘This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.
文摘This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form （u^n）t = （｜ux｜^m-1ux）x ＋ u^p in （0, 1） × （0,T） subject to nonlinear boundary source （｜ux｜^m-1ux）（1,t） = u^q（1,t）, （｜ux｜^m-1ux）（0,t） = O, and positive initial data u（x,0） = uo（x）, where the parameters va, n, p, q 〉0. It is proved that the problem possesses global solutions if and only if p ≤ n and q〈min {n,m（n＋1）/m＋1}.
文摘This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Criteria for global existence of the solution and for quenching are investigated.
基金supported by NSFC under Grant No.11705107by the doctoral Sustentation Fund of Shanxi Datong University(2015-B-10).
文摘We discuss black hole solutions of Einstein-Λ gravity in the presence of nonlinear electrodynamics in dS spacetime.Considering the correlation of the thermodynamic quantities respectively corresponding to the black hole horizon and cosmological horizon of dS spacetime and taking the region between the two horizons as a thermodynamic system,we derive effective thermodynamic quantities of the system according to the first law of thermodynamics,and investigate the thermodynamic properties of the system under the influence of nonlinearity parameter α.It is shown that nonlinearity parameter α influences the position of the black hole horizon and the critical state of the system,and along with electric charge has an effect on the phase structure of the system,which is obvious,especially as the effective temperature is below the critical temperature.The critical phase transition is proved to be second-order equilibrium phase transition by using the Gibbs free energy criterion and Ehrenfest equations.
基金supported by the National Key R&D Program of China(2016YFF0102003 and 2016YFF0102000).
文摘In this work,a new structure is used to enhance the nonlinear effect in the cavity,which improvesthe performance of the 1.3μm broadband swept source.The swept source adopts a semiconductoroptical amplifier(SOA),a circulator,a coupler,and a tunable filter.In the structure,the lightpasses through the nonlinear medium(SOA)twice in two opposite directions,which excites thenonlinear ffect and increases the performance of the swept source.The tunable filter is based on apolygon rotating mirror and gratings.Traditionally,multiple SOAs are adopted to improve thesweep range and the optical power,which increases the cost and complexity of the swept source.The method proposed in this paper can improve the spectral range and optical power of the sweptsources without additional accessories.For the short-cavity swept source,the power increasesfrom 6 mW to 7.7 mW,and the sweep range increases from 98 nm to 120 nm.The broadband swept sources could have wide applications in biomedical imaging,sensor system,measurementand so on.
文摘In this paper we study existence of solutions of a class of Cauchy problems for porous medium equations with strongly nonlinear sources or absorptions and convections when the initial trace is a Radon measure μ on RN.
基金the National Natural Science Foundation of China(No.51009087)
文摘The hull form optimization concerns one of the most important applications of wave-making resistance theories.In recent years,scholars can determine the hull form by using the optimization method based on the computational fluid dynamics(CFD)and other mathematical techniques.In this paper,the hull form optimization method based on the Rankine source method and nonlinear programming(NLP)is discussed;in the optimization process,a hull form modification function is introduced to represent an improved hull surface and to generate a new smooth hull surface by changing its frame lines and bow stem profiles under the prescribed design constraints. Numerical example is given for a practical container hull form.Finally,shape optimization of bow bulls is shown for non-protruding and protruding bow bulls.This study presents a simplified and practical design method to the select frame lines of bow bulls.
基金the National Natural Science Foundation of China(Nos.42174011and 41874001).
文摘The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault parameters inversion has nonlinear characteristics, and the gradient-based optimizer(GBO) has the characteristics of fast convergence speed and falling into local optimum hardly. This paper applies GBO algorithm to simulated earthquakes and real LuShan earthquakes in the nonlinear inversion of the Okada model to obtain the source parameters. The simulated earthquake experiment results show that the algorithm is stable, and the seismic source parameters obtained by GBO are slightly closer to the true value than the multi peak particle swarm optimization(MPSO). In the 2013 LuShan earthquake experiment, the root mean square error between the deformation after forwarding of fault parameters obtained by the introduced GBO algorithm and the surface observation deformation was 3.703 mm, slightly better than 3.708 mm calculated by the MPSO. Moreover, the inversion result of GBO algorithm is better than MPSO algorithm in stability. The above results show that the introduced GBO algorithm has a certain practical application value in seismic fault source parameters inversion.
基金Supported by the Research Foundation of Education Bureau of Jiangxi Province of China under Grant No.GJJ13459the National Natural Science Foundation of China under Grant No.11101350
文摘In the paper, Ablowitz–Ladik hierarchy with new self-consistent sources is investigated. First the source in the hierarchy is described as φnφn+1, where φnis related to the Ablowitz–Ladik spectral problem, instead of the corresponding adjoint spectral problem. Then by means of the inverse scattering transform, the multi-soliton solutions for the hierarchy are obtained. Two reductions to the discrete mKdV and nonlinear Schr¨odinger hierarchies with selfconsistent sources are considered by using the uniqueness of the Jost functions, as well as their N-soliton solutions.
基金Supported by the National High Technology Research and Development Programme of China(No.2011AA7014061)
文摘In this paper,by utilizing the angle of arrivals(AOAs) and imprecise positions of the sensors,a novel modified Levenberg-Marquardt algorithm to solve the source localization problem is proposed.Conventional source localization algorithms,like Gauss-Newton algorithm and Conjugate gradient algorithm are subjected to the problems of local minima and good initial guess.This paper presents a new optimization technique to find the descent directions to avoid divergence,and a trust region method is introduced to accelerate the convergence rate.Compared with conventional methods,the new algorithm offers increased stability and is more robust,allowing for stronger non-linearity and wider convergence field to be identified.Simulation results demonstrate that the proposed algorithm improves the typical methods in both speed and robustness,and is able to avoid local minima.
文摘For the 22-year solar cycle oscillation there is no external time dependent source. A nonlinear oscillation, the solar cycle must be generated internally, and Babcock-Leighton models apply an artificial nonlinear source term that can simulate the observations—which leaves open the question of the actual source mechanism for the solar cycle. Addressing this question, we propose to take guidance from the wave mechanism that generates the 2-year Quasi-biennial Oscillation (QBO) in the Earth atmosphere. Upward propagating gravity waves, eastward and westward, deposit momentum to generate the observed zonal wind oscillation. On the Sun, helioseismology has provided a thorough understanding of the acoustic p-waves, which propagate down into the convective envelope guided by the increasing temperature and related propagation velocity. Near the tachocline with low turbulent viscosity, the waves propagating eastward and westward can produce an axisymmetric 22-year oscillation of the zonal flow velocities that can generate the magnetic solar dynamo. Following the Earth model, waves in opposite directions can generate in the Sun wind and magnetic field oscillations in opposite directions, the proposition of a potential solar cycle mechanism.
