In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced...In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.展开更多
This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by sj the speed of each machine, j = 1, 2, 3. Assume 0 〈 s1 = s2 = r 〈 t = s3, a...This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by sj the speed of each machine, j = 1, 2, 3. Assume 0 〈 s1 = s2 = r 〈 t = s3, and let s = t/r be the speed ratio. An algorithm with competitive ratio max(2, 3s+6/s+6 is presented. We also show the lower bound is at least max(2, 38 3s/s+6). For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun.展开更多
In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element i...In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.展开更多
This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of fin...This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of finite elements.This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition.The stability of the discrete scheme is derived under some regularity assumptions.Optimal error estimates are obtained by applying the standard Galerkin techniques.Finally,the numerical illustrations agree completely with the theoretical expectations.展开更多
In this work,two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered.These methods are based on the local Gauss integration technique and the lowest equal-order finite ...In this work,two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered.These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair.Moreover,the two-level stabilized finite volume methods involve solving one small NavierStokes problem on a coarse mesh with mesh size H,a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^(2))or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|logh|^(1/2)H^(3)).These methods we studied provide an approximate solution(ue v h,pe v h)with the convergence rate of same order as the standard stabilized finite volume method,which involve solving one large nonlinear problem on a fine mesh with mesh size h.Hence,our methods can save a large amount of computational time.展开更多
基金Project supported by the National Natural Science Foundation of China(No.12072264)the Fundamental Research Funds for the Central Universities+3 种基金the Research Funds for Interdisciplinary Subject of Northwestern Polytechnical Universitythe Shaanxi Project for Distinguished Young Scholarsthe National Key Research and Development Program of China(No.2018AAA0102201)the Shaanxi Provincial Key R&D Program(Nos.2020KW-013 and 2019TD-010)。
文摘In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.
基金Supported by the National Natural Science Foundation of China (No. 60674071)
文摘This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by sj the speed of each machine, j = 1, 2, 3. Assume 0 〈 s1 = s2 = r 〈 t = s3, and let s = t/r be the speed ratio. An algorithm with competitive ratio max(2, 3s+6/s+6 is presented. We also show the lower bound is at least max(2, 38 3s/s+6). For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun.
文摘In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.
基金the NSF of China(No.10971166)the National High Technology Research and Development Program of China(863 Program,No.2009AA01A135).
文摘This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conductionconvection equations by using the lowest equal-order pairs of finite elements.This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition.The stability of the discrete scheme is derived under some regularity assumptions.Optimal error estimates are obtained by applying the standard Galerkin techniques.Finally,the numerical illustrations agree completely with the theoretical expectations.
基金supported by the Natural Science Foundation of China(No.11126117)Doctor Fund of Henan Polytechnic University(B2011-098).
文摘In this work,two-level stabilized finite volume formulations for the 2D steady Navier-Stokes equations are considered.These methods are based on the local Gauss integration technique and the lowest equal-order finite element pair.Moreover,the two-level stabilized finite volume methods involve solving one small NavierStokes problem on a coarse mesh with mesh size H,a large general Stokes problem for the Simple and Oseen two-level stabilized finite volume methods on the fine mesh with mesh size h=O(H^(2))or a large general Stokes equations for the Newton two-level stabilized finite volume method on a fine mesh with mesh size h=O(|logh|^(1/2)H^(3)).These methods we studied provide an approximate solution(ue v h,pe v h)with the convergence rate of same order as the standard stabilized finite volume method,which involve solving one large nonlinear problem on a fine mesh with mesh size h.Hence,our methods can save a large amount of computational time.