In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems ...In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.展开更多
The condensation of DNA induced by spermine is studied by atomic force microscopy （AFM） and molecular dynamics （MD） simulation in this paper. In our experiments, an equivalent amount of multivalent cations is adde...The condensation of DNA induced by spermine is studied by atomic force microscopy （AFM） and molecular dynamics （MD） simulation in this paper. In our experiments, an equivalent amount of multivalent cations is added to the DNA solutions in different numbers of steps, and we find that the process of DNA condensation strongly depends on the speed of adding cations. That is, the slower the spermine cations are added, the slower the DNA aggregates. The MD and steered molecular dynamics （SMD） simulation results agree well with the experimental results, and the simulation data also show that the more steps of adding multivalent cations there are, the more compact the condensed DNA structure will be. This investigation can help us to control DNA condensation and understand the complicated structures of DNA--cation complexes.展开更多
We study the effect of Landau-Zener （LZ） tunneling caused by the varying sweeping rate of the external field, and solve the problem about the LZ tunneling rate among many levels. The LZ tunneling rate is essentially...We study the effect of Landau-Zener （LZ） tunneling caused by the varying sweeping rate of the external field, and solve the problem about the LZ tunneling rate among many levels. The LZ tunneling rate is essentially changed by the unsteady variation of the time-dependent sweeping field and is different from the steadily varying sweeping field, which makes the particles in lower states transit periodically to upper states within a finite time.展开更多
The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a pri...The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of eommu- tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.展开更多
The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influen...The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density （bulk pressure）. If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows.展开更多
The static electric dipole polarizabilities of the ground state and n ≤ 3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium...The static electric dipole polarizabilities of the ground state and n ≤ 3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium. The plasma screening of the Coulomb interaction is described by the Debye-Hiickel potential and the interaction between the valence electron and the atomic core is described by a model potential. The electron energies and wave functions for both the bound and continuum states are calculated by solving the SchrSdinger equation numerically using the symplectic integrator. The oscillator strengths, partial-wave, and total static dipole polarizabilities of the ground state and n ≤ 3 excited states of the lithium atom are calculated. Comparison of present results with those of other authors, when available, is made. The results for the 2s ground state demonstrated that the oscillator strengths and the static dipole polarizabilities from np orbitals do not always increase or decrease with the plasma screening effect increasing, unlike that for hydrogen-like ions, especially for 2s→3p transition there is a zero value for both the oscillator strength and the static dipole polarizability for screening length D = 10.3106a0, which is associated with the Cooper minima.展开更多
The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an ...The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an operator from Bω to Bμ is denoted by ｜｜Tφ｜｜e,Bω→Bμ. The purpose of this paper is to prove that, for w, ω normal and φ ∈ H（B）｜｜Tφ｜｜e,Bω→Bμ≈lim sup｜z｜→1μ（z）｜Rφ（z）｜∫0^｜z｜dt/ω（t）.展开更多
The ionization process of B2＋ by H＋ impact is studied using the continuum-distorted-wave eikonal-initial-state （CDW-EIS） method and the modified free electron peak approximation （M-FEPA）, respectively. Total, si...The ionization process of B2＋ by H＋ impact is studied using the continuum-distorted-wave eikonal-initial-state （CDW-EIS） method and the modified free electron peak approximation （M-FEPA）, respectively. Total, single-, and double- differential cross sections from ls and 2s orbitals are presented for the energy range from 10 keV/u to 10 MeV/u. Com- parison between the results from the two methods demonstrates that the total and single-differential cross sections for the high-energy incident projectile case can be well evaluated using the simple M-FEPA model. Moreover, the M-FEPA model reproduces the essential features of the binary-encounter （BE） bump in the double-differential cross sections. Thus, the BE ionization mechanism is discussed in detail by adopting the M-FEPA model. In particular, the double- and single- differential cross sections from the 2s orbital show a high-energy hip, which is different from those from the ls orbital. Based on Ref. [1], the Compton profiles of B2＋ for ls and 2s orbitals are given, and the hips in DDCS and SDCS from the 2s orbital are explained.展开更多
An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assulued that some particles in porous media do not overlap and that fluid in porous media is inco...An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assulued that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as： φc = 0.32, DT,： = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.展开更多
In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We...In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of ｜ det（f＇（z））｜and Rdet（f＇（z）） for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given.展开更多
Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this ...Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this paper, we prove the existence of decreasing solutions for a general iterative equation, which was proposed as an open problem in [J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. （China） 24 （1995） 385-405] （or [W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 （2000） 29-36]）.展开更多
Many animals can detect the multi-frequency signals from their external surroundings.The understanding for underlying mechanism of signal detection can apply the theory of vibrational resonance,in which the moderate h...Many animals can detect the multi-frequency signals from their external surroundings.The understanding for underlying mechanism of signal detection can apply the theory of vibrational resonance,in which the moderate high frequency driving can maximize the nonlinear system's response to the low frequency subthreshold signal.In this work,we study the roles of chemical autapse on the vibrational resonance in a single neuron for signal detection.We reveal that the vibrational resonance is strengthened significantly by the inhibitory autapse in the neuron,while it is weakened typically by the excitatory autapse.It is generally believed that the inhibitory synapse has a suppressive effect in neuronal dynamics.However,we find that the detection of the neuron to the low frequency subthreshold signal can be improved greatly by the inhibitory autapse.Our finding indicates that the inhibitory synapse may act constructively on the detection of weak signal in the brain and neuronal system.展开更多
We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several fa...We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.展开更多
This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system...This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system is symmetric and positive definite,and thus the algorithm is easy to implement and analyze.Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular polygonal mesh.A superconvergence result is proved when the coefficient matrix is constant or piecewise constant.Numerical examples are performed which not only verify the theoretical results but also reveal some unexpected superconvergence phenomena.展开更多
A dynamic network Qo S control mechanism was proposed based on traffic prediction. It first predicts network traffic flow and then dynamically distributes network resources, which makes full use of network flow self-s...A dynamic network Qo S control mechanism was proposed based on traffic prediction. It first predicts network traffic flow and then dynamically distributes network resources, which makes full use of network flow self-similarity and chaos. So it can meet changing network needs very well. The simulation results show that the dynamic Qo S control mechanism based on prediction has better network performance than that based on measurement.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10926066 and 11026182)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6100007)+3 种基金the Zhejiang Educational Committee,China(Grant No.Y200805720)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010408)the Innovation Fund of Basic Scientific Research Operating Expenses,China(Grant No.3207010501)the Alexander von Humboldt Foundation of Germany
文摘In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.
基金supported by the National Natural Science Foundation of China (Grant Nos. 20974081, 20934004, 21174131, and 21104060)the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y4110357)
文摘The condensation of DNA induced by spermine is studied by atomic force microscopy （AFM） and molecular dynamics （MD） simulation in this paper. In our experiments, an equivalent amount of multivalent cations is added to the DNA solutions in different numbers of steps, and we find that the process of DNA condensation strongly depends on the speed of adding cations. That is, the slower the spermine cations are added, the slower the DNA aggregates. The MD and steered molecular dynamics （SMD） simulation results agree well with the experimental results, and the simulation data also show that the more steps of adding multivalent cations there are, the more compact the condensed DNA structure will be. This investigation can help us to control DNA condensation and understand the complicated structures of DNA--cation complexes.
基金Project supported by the National Natural Science Foundation of China (Grant No. 20804039)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y4080300)
文摘We study the effect of Landau-Zener （LZ） tunneling caused by the varying sweeping rate of the external field, and solve the problem about the LZ tunneling rate among many levels. The LZ tunneling rate is essentially changed by the unsteady variation of the time-dependent sweeping field and is different from the steadily varying sweeping field, which makes the particles in lower states transit periodically to upper states within a finite time.
基金Sponsored by the Fundamental Research Funds for the Central Universities(2010QS04)the National Science Foundation of China(11201475,11126160,11201185)Zhejiang Provincial Natural Science Foundation of China under Grant(LQ12A01013)
文摘The Boussinesq approximation finds more and more frequent use in geologi- cal practice. In this paper, the asymptotic behavior of solution for fractional Boussinesq approximation is studied. After obtaining some a priori estimates with the aid of eommu- tator estimate, we apply the Galerkin method to prove the existence of weak solution in the case of periodic domain. Meanwhile, the uniqueness is also obtained. Because the results obtained are independent of domain, the existence and uniqueness of the weak solution for Cauchy problem is also true. Finally, we use the Fourier splitting method to prove the decay of weak solution in three cases respectively.
基金Supported by the One-Hundred Talents Project of Chinese Academy of Sciences, the National Natural Science Foundation of China under Grant Nos 10474109, 10674146 and 10447001, the Guangxi Science Foundation under Grant No 0640064, the National Basic Research Programme of China under Grant No 2006CB708612, Zhejiang Funding Scheme to Young College Teachers and Shanghai Supercomputer Center of China. We thank Professor Fang Haiping for useful discussion and Shanghai Supercomputer Centre of China for the support of computation.
文摘The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density （bulk pressure）. If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11005049,10979007,and 10974021)
文摘The static electric dipole polarizabilities of the ground state and n ≤ 3 excited states of a lithium atom embedded in a weekly coupled plasma environment are investigated as a function of the plasma screening radium. The plasma screening of the Coulomb interaction is described by the Debye-Hiickel potential and the interaction between the valence electron and the atomic core is described by a model potential. The electron energies and wave functions for both the bound and continuum states are calculated by solving the SchrSdinger equation numerically using the symplectic integrator. The oscillator strengths, partial-wave, and total static dipole polarizabilities of the ground state and n ≤ 3 excited states of the lithium atom are calculated. Comparison of present results with those of other authors, when available, is made. The results for the 2s ground state demonstrated that the oscillator strengths and the static dipole polarizabilities from np orbitals do not always increase or decrease with the plasma screening effect increasing, unlike that for hydrogen-like ions, especially for 2s→3p transition there is a zero value for both the oscillator strength and the static dipole polarizability for screening length D = 10.3106a0, which is associated with the Cooper minima.
基金Supported by the NNSF of China（10771064） Supported by the Natural Science Foundation of Zhejiang Province（YT080197, Y6090036, Y6100219） Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province（T200924） Acknowledgement The author would like to express her thanks to her supervisor, Prof HU Zhang-jian, for his guidance.
文摘The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an operator from Bω to Bμ is denoted by ｜｜Tφ｜｜e,Bω→Bμ. The purpose of this paper is to prove that, for w, ω normal and φ ∈ H（B）｜｜Tφ｜｜e,Bω→Bμ≈lim sup｜z｜→1μ（z）｜Rφ（z）｜∫0^｜z｜dt/ω（t）.
基金Project supported by the National Basic Research Program of China (Grant No. 2013CB922200)the National Natural Science Foundation of China (Grant Nos. 11005049, 11025417, 10979007, and 10974021)
文摘The ionization process of B2＋ by H＋ impact is studied using the continuum-distorted-wave eikonal-initial-state （CDW-EIS） method and the modified free electron peak approximation （M-FEPA）, respectively. Total, single-, and double- differential cross sections from ls and 2s orbitals are presented for the energy range from 10 keV/u to 10 MeV/u. Com- parison between the results from the two methods demonstrates that the total and single-differential cross sections for the high-energy incident projectile case can be well evaluated using the simple M-FEPA model. Moreover, the M-FEPA model reproduces the essential features of the binary-encounter （BE） bump in the double-differential cross sections. Thus, the BE ionization mechanism is discussed in detail by adopting the M-FEPA model. In particular, the double- and single- differential cross sections from the 2s orbital show a high-energy hip, which is different from those from the ls orbital. Based on Ref. [1], the Compton profiles of B2＋ for ls and 2s orbitals are given, and the hips in DDCS and SDCS from the 2s orbital are explained.
基金supported by the National Natural Science Foundation of China(Grant No.10932010,10972199,11005093,11072220, and 11079029)the Natural Science Foundation of Zhejiang Province of China (Grant No. Z6090556 and Y6100384)the Research Project for the Higher Educational Institutions of Inner Mongolia Autonomous Region (Grant No. NJZZ11284)
文摘An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assulued that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as： φc = 0.32, DT,： = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.
基金partly supported by the National Natural Science Foundation of China(10826083,10971063)NSF of Zhejiang Province (D7080080, Y606197,Y6090694)Scientific Research Fund of Zhejiang Provincial Education Department (Y200805520)
文摘In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of ｜ det（f＇（z））｜and Rdet（f＇（z）） for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given.
基金supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LY18A010017the National Science Foundation of China(11101105,11301226)
文摘Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this paper, we prove the existence of decreasing solutions for a general iterative equation, which was proposed as an open problem in [J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. （China） 24 （1995） 385-405] （or [W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 （2000） 29-36]）.
基金Project supported partially by the National Natural Science Foundation of China(Grant Nos.11675112,11705116,11675134,and 11874310)the National Natural Science Foundation of China for the 111 Project(Grant No.B16029).
文摘Many animals can detect the multi-frequency signals from their external surroundings.The understanding for underlying mechanism of signal detection can apply the theory of vibrational resonance,in which the moderate high frequency driving can maximize the nonlinear system's response to the low frequency subthreshold signal.In this work,we study the roles of chemical autapse on the vibrational resonance in a single neuron for signal detection.We reveal that the vibrational resonance is strengthened significantly by the inhibitory autapse in the neuron,while it is weakened typically by the excitatory autapse.It is generally believed that the inhibitory synapse has a suppressive effect in neuronal dynamics.However,we find that the detection of the neuron to the low frequency subthreshold signal can be improved greatly by the inhibitory autapse.Our finding indicates that the inhibitory synapse may act constructively on the detection of weak signal in the brain and neuronal system.
基金supported by the National Natural Science Foundation of China (Grant No. 10704067)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6100381)
文摘We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.
基金supported by Zhejiang Provincial Natural Science Foundation of China(LY19A010008).
文摘This article is devoted to establishing a least square based weak Galerkin method for second order elliptic equations in non-divergence form using a discrete weak Hessian operator.Naturally,the resulting linear system is symmetric and positive definite,and thus the algorithm is easy to implement and analyze.Convergence analysis in the H2 equivalent norm is established on an arbitrary shape regular polygonal mesh.A superconvergence result is proved when the coefficient matrix is constant or piecewise constant.Numerical examples are performed which not only verify the theoretical results but also reveal some unexpected superconvergence phenomena.
基金Funded by the National Natural Science Foundation of China(No.41301084)the Scientific Research Project of Hunan Province Education Department,China(No.13C713)the Natural Science Foundation of Hunan Province,China(No.13JJ6075)
文摘A dynamic network Qo S control mechanism was proposed based on traffic prediction. It first predicts network traffic flow and then dynamically distributes network resources, which makes full use of network flow self-similarity and chaos. So it can meet changing network needs very well. The simulation results show that the dynamic Qo S control mechanism based on prediction has better network performance than that based on measurement.
