The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consis...The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate (1 + t)^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate (1 + t)^-1/4 which is slower than the rate (1 + t)^-3/4 for the compressible Navier-Stokes equations (NS). In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate (1 + t)^-3/4+ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.展开更多
The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data...The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l(R3) ∩ B˙ s 1,1 (R3) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t) 1 4 s 2 in L2 -norm, which is slower than the rate (1+t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t) 3 4 due to the cancellation effect from the interplay interaction of the charged particles.展开更多
In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. ...In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.展开更多
We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] prov...We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] proved that(Pλ)with p∈ (2, 5) has always a positive radial solution, but (Pλ) with p E (1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that(Pλ)with p ∈(1+∞)has alaways a bound state(H^1(R^3)solution for λ∈[0,λ0)and certain functions V(x)and Q(x)in L^∞(R^3).Moreover,for every λ∈[0,λ0),the solutions uλ of (Pλ)converges,along a subsequence,to a solution of (P0)in H^1 as λ→0展开更多
The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being ...The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl(R3) (R3) for 1 〉 4 and s E (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t)-3/4, but the momentum for each particle decays at the optimal rate (1 + t)-1/4-3/2 which is slower than the rate (1 + t)-3/4-3/2 for the compressible Navier-Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1 +t)-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.展开更多
When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poiss...When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.展开更多
In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.
In this paper, the properties ofthe solutions ofBoltzm ann-Poisson system in three di- m ensions are considered. The estim ates ofthe energies (the kinetic and the potentialenergies) and the γ-th m om ents w ith γ...In this paper, the properties ofthe solutions ofBoltzm ann-Poisson system in three di- m ensions are considered. The estim ates ofthe energies (the kinetic and the potentialenergies) and the γ-th m om ents w ith γ∈[2,3) are obtained. The latter answ ers an open problem .展开更多
This paper is concerned with the quasi-neutral limit of the bipolar NavierStokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that ...This paper is concerned with the quasi-neutral limit of the bipolar NavierStokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible NavierStokes equations as the Debye length goes to zero. Moreover, if we let the viscous coefficients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations.展开更多
This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. ...This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.展开更多
This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the ...This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.展开更多
This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We stud...This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.展开更多
Based on Nehari manifold, Schwarz symmetric methods and critical point theory, we prove the existence of positive radial ground states for a class of Schrodinger-Poisson systems in , which doesn’t require any symmetr...Based on Nehari manifold, Schwarz symmetric methods and critical point theory, we prove the existence of positive radial ground states for a class of Schrodinger-Poisson systems in , which doesn’t require any symmetry assumptions on all potentials. In particular, the positive potential is interesting in physical applications.展开更多
In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages...In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.展开更多
Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non...Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.展开更多
In the tag recommendation task on academic platforms,existing methods disregard users’customized preferences in favor of extracting tags based just on the content of the articles.Besides,it uses co-occurrence techniq...In the tag recommendation task on academic platforms,existing methods disregard users’customized preferences in favor of extracting tags based just on the content of the articles.Besides,it uses co-occurrence techniques and tries to combine nodes’textual content for modelling.They still do not,however,directly simulate many interactions in network learning.In order to address these issues,we present a novel system that more thoroughly integrates user preferences and citation networks into article labelling recommendations.Specifically,we first employ path similarity to quantify the degree of similarity between user labelling preferences and articles in the citation network.Then,the Commuting Matrix for massive node pair paths is used to improve computational performance.Finally,the two commonalities mentioned above are combined with the interaction paper labels based on the additivity of Poisson distribution.In addition,we also consider solving the model’s parameters by applying variational inference.Experimental results demonstrate that our suggested framework agrees and significantly outperforms the state-of-the-art baseline on two real datasets by efficiently merging the three relational data.Based on the Area Under Curve(AUC)and Mean Average Precision(MAP)analysis,the performance of the suggested task is evaluated,and it is demonstrated to have a greater solving efficiency than current techniques.展开更多
基金The research of the first author was partially supported by the NNSFC No.10871134the NCET support of the Ministry of Education of China+4 种基金the Huo Ying Dong Fund No.111033the Chuang Xin Ren Cai Project of Beijing Municipal Commission of Education #PHR201006107the Instituteof Mathematics and Interdisciplinary Science at CNUThe research of the second author was supported by the General Research Fund of Hong Kong (CityU 103109)the National Natural Science Foundation of China,10871082
文摘The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate (1 + t)^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate (1 + t)^-1/4 which is slower than the rate (1 + t)^-3/4 for the compressible Navier-Stokes equations (NS). In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate (1 + t)^-3/4+ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.
基金supported by NSFC (10872004)National Basic Research Program of China (2010CB731500)the China Ministry of Education (200800010013)
文摘The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l(R3) ∩ B˙ s 1,1 (R3) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t) 1 4 s 2 in L2 -norm, which is slower than the rate (1+t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t) 3 4 due to the cancellation effect from the interplay interaction of the charged particles.
基金supported by the National Natural Science Foundation of China(11331005,11471134)the Program for Changjiang Scholars and Innovative Research Team in University(IRT13066)the Scientific Research Funds of Huaqiao University(15BS201,15BS309)
文摘In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.
基金Supported by NSFC(10631030) and CAS-KJCX3-SYW-S03
文摘We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] proved that(Pλ)with p∈ (2, 5) has always a positive radial solution, but (Pλ) with p E (1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that(Pλ)with p ∈(1+∞)has alaways a bound state(H^1(R^3)solution for λ∈[0,λ0)and certain functions V(x)and Q(x)in L^∞(R^3).Moreover,for every λ∈[0,λ0),the solutions uλ of (Pλ)converges,along a subsequence,to a solution of (P0)in H^1 as λ→0
基金supported by the NSFC (10871134)supported by the NSFC (10871134,10910401059)+1 种基金the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107)supported by the General Research Fund of Hong Kong,City Univ.103108
文摘The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl(R3) (R3) for 1 〉 4 and s E (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t)-3/4, but the momentum for each particle decays at the optimal rate (1 + t)-1/4-3/2 which is slower than the rate (1 + t)-3/4-3/2 for the compressible Navier-Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1 +t)-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.
文摘When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform. Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.
文摘In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.
文摘In this paper, the properties ofthe solutions ofBoltzm ann-Poisson system in three di- m ensions are considered. The estim ates ofthe energies (the kinetic and the potentialenergies) and the γ-th m om ents w ith γ∈[2,3) are obtained. The latter answ ers an open problem .
基金supported by the Science Fund for Young Scholars of Nanjing University of Aeronautics and Astronautics
文摘This paper is concerned with the quasi-neutral limit of the bipolar NavierStokes-Poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible NavierStokes equations as the Debye length goes to zero. Moreover, if we let the viscous coefficients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations.
文摘This paper deals with a class of Schr¨odinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature.
基金1. The NNSF (0111051400) of Henan Province2. The OYF (0016) of Henan Province.
文摘This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.
文摘This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.
文摘Based on Nehari manifold, Schwarz symmetric methods and critical point theory, we prove the existence of positive radial ground states for a class of Schrodinger-Poisson systems in , which doesn’t require any symmetry assumptions on all potentials. In particular, the positive potential is interesting in physical applications.
文摘In this paper, the global existence of weak s olutions to the initial boundary value problem for Boltzmann-Poisson system is proved. The proof is based on the regularization and the stability of the veloci ty averages and the compactness results on L 1-theory.
基金the National Natural Science Foundation of China(No.12072118)the Natural Science Funds for Distinguished Young Scholar of Fujian Province of China(No.2021J06024)the Project for Youth Innovation Fund of Xiamen of China(No.3502Z20206005)。
文摘Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.
基金supported by the National Natural Science Foundation of China(No.62271274).
文摘In the tag recommendation task on academic platforms,existing methods disregard users’customized preferences in favor of extracting tags based just on the content of the articles.Besides,it uses co-occurrence techniques and tries to combine nodes’textual content for modelling.They still do not,however,directly simulate many interactions in network learning.In order to address these issues,we present a novel system that more thoroughly integrates user preferences and citation networks into article labelling recommendations.Specifically,we first employ path similarity to quantify the degree of similarity between user labelling preferences and articles in the citation network.Then,the Commuting Matrix for massive node pair paths is used to improve computational performance.Finally,the two commonalities mentioned above are combined with the interaction paper labels based on the additivity of Poisson distribution.In addition,we also consider solving the model’s parameters by applying variational inference.Experimental results demonstrate that our suggested framework agrees and significantly outperforms the state-of-the-art baseline on two real datasets by efficiently merging the three relational data.Based on the Area Under Curve(AUC)and Mean Average Precision(MAP)analysis,the performance of the suggested task is evaluated,and it is demonstrated to have a greater solving efficiency than current techniques.