This paper deals with the asymptotic behavior of solutions of the stochastic g-Navier-Stokes equation driven by nonlinear noise.The existence and uniqueness of weak pullback mean random attractors for the equation in ...This paper deals with the asymptotic behavior of solutions of the stochastic g-Navier-Stokes equation driven by nonlinear noise.The existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear functions.Furthermore,we also establish the existence of invariant measures for the equation.展开更多
A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented....A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable's moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.展开更多
The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on...The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.展开更多
We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(o(x)↓△u) and multiplicative noises. Under some mild conditions on the diffusion variable o(x) an...We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(o(x)↓△u) and multiplicative noises. Under some mild conditions on the diffusion variable o(x) and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2(DN, σ) space, where DN is an arbitrary (bounded or unbounded) domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.展开更多
In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors ...In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.展开更多
Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method(PEM)is an effective method for calculation of random vibration.Due to complicated an...Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method(PEM)is an effective method for calculation of random vibration.Due to complicated and coupling random vibration in rocket or shuttle launching,the new staging white noise mathematical model is deduced according to the practical launch environment.This deduced model is applied for PEM to calculate the specific structure of Time of Flight Counter(ToFC).The responses of power spectral density and the relevant dynamic characteristic parameters of ToFC are obtained in terms of the flight acceptance test level.Considering stiffness of fixture structure,the random vibration experiments are conducted in three directions to compare with the revised PEM.The experimental results show the structure can bear the random vibration caused by launch without any damage and key dynamical parameters of ToFC are obtained.The revised PEM is similar with random vibration experiment in dynamical parameters and responses are proved by comparative results.The maximum error is within 9%.The reasons of errors are analyzed to improve reliability of calculation.This research provides an effective method for solutions of computing dynamical characteristic parameters of complicated structure in the process of rocket or shuttle launching.展开更多
We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D(μω) be its dimension of the sample measure, then we pr...We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D(μω) be its dimension of the sample measure, then we prove a formula relating D(μω) to the entropy and Lyapunov exponents of the random system, where D (μω) is dimHμω, dimBμm, or dimBμm.展开更多
In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also o...In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also obtain some properties of omega-limit sets, as well as connectedness of random attractors. A simple deterministic example is given to illustrate some confusing problems.展开更多
Demand assignment MAC protocols have been used widely in wireless networks. It can effectively utilize wireless bandwidth. Some strategies can he used by demand assignment MAC protocols to further improve their effici...Demand assignment MAC protocols have been used widely in wireless networks. It can effectively utilize wireless bandwidth. Some strategies can he used by demand assignment MAC protocols to further improve their efficiency. The concept of transmit probability is introduced. This concept allows a request slot to be assigned to many different traffic classes at the same time. Based on it, the dynamic random channel reservation (DRCR) protocol is proposed. The DRCR protocol operates dynamically by observing the traffic conditions. It uses information about the recent traffic conditions to assign transmit probability with which an mobile station can select request slots with lower traffic. The performance of DRCR is evaluated and compared with RSCA. The results show that DRCR is more stable than RSCA, it offers shorter delays of requests than RSCA and can relieve heavily stressed traffic classes faster than RSCA.展开更多
We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds...We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10^(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the展开更多
The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in ...The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in these systems has a topological origin. In this paper, we focus on the rotational stretched exponential relaxation behavior in complex-disordered systems and introduce a simple phase space model to understand the mechanism of the non-exponential relaxation of these systems. By employing the Monte Carlo simulation method to the model, we obtain the rotational relaxation function as a function of temperature. We show that the relaxation function has a stretched exponential form under the critical temperature while it obeys the Debye law above the critical temperature.展开更多
In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by...In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.展开更多
The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical ...The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.展开更多
Opening the silicon oxide mask of a capacitor in dynamic random access memory is a critical process on a capacitive coupled plasma(CCP)etch tool.Three steps,dielectric anti-reflective coating(DARC)etch back,silicon ox...Opening the silicon oxide mask of a capacitor in dynamic random access memory is a critical process on a capacitive coupled plasma(CCP)etch tool.Three steps,dielectric anti-reflective coating(DARC)etch back,silicon oxide etch and strip,are contained.To acquire good performance,such as low leakage current and high capacitance,for further fabricating capacitors,we should firstly optimize DARC etch back.We developed some experiments,focusing on etch time and chemistry,to evalu-ate the profile of a silicon oxide mask,DARC remain and critical dimension.The result shows that etch back time should be con-trolled in the range from 50 to 60 s,based on the current equipment and condition.It will make B/T ratio higher than 70%mean-while resolve the DARC remain issue.We also found that CH_(2)F_(2) flow should be~15 sccm to avoid reversed CD trend and keep in-line CD.展开更多
Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method (LBM) and random walk (RW), respectively. The numerical implementation isdeveloped and validat...Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method (LBM) and random walk (RW), respectively. The numerical implementation isdeveloped and validated on general purpose graphic processing units (GPGPUs). Both the LBM and RWmethod are well suited to parallel implementation on GPGPUs because they require only next-neighbourcommunication and thus can reduce expenses. The LBM model is an order of magnitude faster onGPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified forparallel plate flow, backward facing step and single fracture flow; and the RWmodel is verified for pointsourcediffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithmsplace limitations on the discrete displacement of fluid or particle transport per time step to minimise thenumerical error that must be considered during implementation. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.展开更多
A computer software named VDAS (Vehicle Dynamic Analysis Simulation) is presented.Based on the mathematical modelling for a military vehicle as a 3-D dynamic system, the softwarecreates random excitation resulting fro...A computer software named VDAS (Vehicle Dynamic Analysis Simulation) is presented.Based on the mathematical modelling for a military vehicle as a 3-D dynamic system, the softwarecreates random excitation resulting from double side road-surface roughness by statisticalsimulation, and solves for the time series of the system response from the system state equations,and gives out the results in probability statistics as well as performance evaluations.展开更多
We study the random dynamical system (RDS) generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS.
In this paper, Brin-Katok local entropy formula and Katok's definition of the measuretheoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.
In this paper,we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces.We discuss on the effect of temperedness and the sp...In this paper,we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces.We discuss on the effect of temperedness and the spectral gaps in the nonuniform pseudo-hyperbolicity so as to prove the existence of invariant manifolds and invariant foliations,which preserve the CN,τ;(ω)Holder smoothness of the random system in the space variable and the measurability of the random system in the sample point.Moreover,we also prove that the stable foliation is CN-1;(ω)in the base point.展开更多
基金supported by the National NaturalScience Foundation of China(11871138)the Sichuan Science and Technology Program(2023NSFSC0076)。
文摘This paper deals with the asymptotic behavior of solutions of the stochastic g-Navier-Stokes equation driven by nonlinear noise.The existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear functions.Furthermore,we also establish the existence of invariant measures for the equation.
基金Project supported by the Natural Science Foundation of Shaanxi Province of China (No,A200214)
文摘A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices axe constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic axe then derived by using the random variable's moment function method and algebra synthesis method. Two examples axe used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.
基金the National NSFC under grant No.50579022the Foundation of Pre-973 Program of China under grant No.2004CCA02500+1 种基金the SRF for the ROCS,SEMthe Talent Recruitment Foundation of HUST
文摘The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.
基金supported by China NSF(11271388)Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1400430)Basis and Frontier Research Project of Chongqing(cstc2014jcyj A00035)
文摘We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(o(x)↓△u) and multiplicative noises. Under some mild conditions on the diffusion variable o(x) and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2(DN, σ) space, where DN is an arbitrary (bounded or unbounded) domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.
文摘In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.
基金Supported by National Natural Science Foundation of China(Grant No.51105025)International Science & Technology Cooperation Program of China(Grant No.2013DFB70110)
文摘Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method(PEM)is an effective method for calculation of random vibration.Due to complicated and coupling random vibration in rocket or shuttle launching,the new staging white noise mathematical model is deduced according to the practical launch environment.This deduced model is applied for PEM to calculate the specific structure of Time of Flight Counter(ToFC).The responses of power spectral density and the relevant dynamic characteristic parameters of ToFC are obtained in terms of the flight acceptance test level.Considering stiffness of fixture structure,the random vibration experiments are conducted in three directions to compare with the revised PEM.The experimental results show the structure can bear the random vibration caused by launch without any damage and key dynamical parameters of ToFC are obtained.The revised PEM is similar with random vibration experiment in dynamical parameters and responses are proved by comparative results.The maximum error is within 9%.The reasons of errors are analyzed to improve reliability of calculation.This research provides an effective method for solutions of computing dynamical characteristic parameters of complicated structure in the process of rocket or shuttle launching.
基金Partially supported by NSFC(10571130)NSFC(10501033) and SRFDP of China.
文摘We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D(μω) be its dimension of the sample measure, then we prove a formula relating D(μω) to the entropy and Lyapunov exponents of the random system, where D (μω) is dimHμω, dimBμm, or dimBμm.
基金Partially Supported by the SRFDP (20070183053) and the Young Fund of the College of Mathematics at Jilin University.
文摘In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also obtain some properties of omega-limit sets, as well as connectedness of random attractors. A simple deterministic example is given to illustrate some confusing problems.
文摘Demand assignment MAC protocols have been used widely in wireless networks. It can effectively utilize wireless bandwidth. Some strategies can he used by demand assignment MAC protocols to further improve their efficiency. The concept of transmit probability is introduced. This concept allows a request slot to be assigned to many different traffic classes at the same time. Based on it, the dynamic random channel reservation (DRCR) protocol is proposed. The DRCR protocol operates dynamically by observing the traffic conditions. It uses information about the recent traffic conditions to assign transmit probability with which an mobile station can select request slots with lower traffic. The performance of DRCR is evaluated and compared with RSCA. The results show that DRCR is more stable than RSCA, it offers shorter delays of requests than RSCA and can relieve heavily stressed traffic classes faster than RSCA.
基金Foundation item:The work was supported in part by the NSFC(No.90511009).
文摘We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10^(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the
基金Project supported by Istanbul University(Grant Nos.28432 and 45662)
文摘The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in these systems has a topological origin. In this paper, we focus on the rotational stretched exponential relaxation behavior in complex-disordered systems and introduce a simple phase space model to understand the mechanism of the non-exponential relaxation of these systems. By employing the Monte Carlo simulation method to the model, we obtain the rotational relaxation function as a function of temperature. We show that the relaxation function has a stretched exponential form under the critical temperature while it obeys the Debye law above the critical temperature.
文摘In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.
基金supported by the National Natural Science Foundation of China (No. 10661002)the NaturalScience Foundation of Guangxi (No. 0832065)the Excellent Talents Fund of Guangxi (No. 0825)
文摘The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.
文摘Opening the silicon oxide mask of a capacitor in dynamic random access memory is a critical process on a capacitive coupled plasma(CCP)etch tool.Three steps,dielectric anti-reflective coating(DARC)etch back,silicon oxide etch and strip,are contained.To acquire good performance,such as low leakage current and high capacitance,for further fabricating capacitors,we should firstly optimize DARC etch back.We developed some experiments,focusing on etch time and chemistry,to evalu-ate the profile of a silicon oxide mask,DARC remain and critical dimension.The result shows that etch back time should be con-trolled in the range from 50 to 60 s,based on the current equipment and condition.It will make B/T ratio higher than 70%mean-while resolve the DARC remain issue.We also found that CH_(2)F_(2) flow should be~15 sccm to avoid reversed CD trend and keep in-line CD.
文摘Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method (LBM) and random walk (RW), respectively. The numerical implementation isdeveloped and validated on general purpose graphic processing units (GPGPUs). Both the LBM and RWmethod are well suited to parallel implementation on GPGPUs because they require only next-neighbourcommunication and thus can reduce expenses. The LBM model is an order of magnitude faster onGPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified forparallel plate flow, backward facing step and single fracture flow; and the RWmodel is verified for pointsourcediffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithmsplace limitations on the discrete displacement of fluid or particle transport per time step to minimise thenumerical error that must be considered during implementation. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.
文摘A computer software named VDAS (Vehicle Dynamic Analysis Simulation) is presented.Based on the mathematical modelling for a military vehicle as a 3-D dynamic system, the softwarecreates random excitation resulting from double side road-surface roughness by statisticalsimulation, and solves for the time series of the system response from the system state equations,and gives out the results in probability statistics as well as performance evaluations.
基金Supported by the China Postdoctoral Science Foundation (No. 2005038326)
文摘We study the random dynamical system (RDS) generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS.
基金the National Natural Science Foundation of China(No.10701032)Natural Science Foundation of Hebei Province(No.A2008000132)
文摘In this paper, Brin-Katok local entropy formula and Katok's definition of the measuretheoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.11501549,11331007,11971330,11771307,11831012 and 11726623)the Fundamental Research Funds for the Central Universities(Grant No.YJ201646).
文摘In this paper,we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces.We discuss on the effect of temperedness and the spectral gaps in the nonuniform pseudo-hyperbolicity so as to prove the existence of invariant manifolds and invariant foliations,which preserve the CN,τ;(ω)Holder smoothness of the random system in the space variable and the measurability of the random system in the sample point.Moreover,we also prove that the stable foliation is CN-1;(ω)in the base point.