赤道东太平洋海气耦合振荡的非线性分析及ENSO循环的极限环理论

把赤道东太平洋地区大气对流层,海洋混合层看作是在定常热源（太阳辐射）驱动下的动力系统,利用一个局域平均的热力学气候模式,建立了海气耦合自激振荡模型,得到了一个封闭的自治的二次系统,对系统进行了线性和非线性分析．结合系统稳定的极限环解,对海气耦合的物理机制进行了探讨．和观测事实的比较表明,在赤道东太平洋区域平均的以500 hPa为代表的大气对流层的温度距平和海表温度距平,在相平面上和极限环解定性上很一致．这为研究热带海气相互作用的年际变化提供了一个理论模型．     

海-气耦合气候系统非线性扰动模式的周期正解

与ENSO相关的热带大尺度海-气相互作用是影响全球气候年际变化的主要过程之一.该文从一个海-气相互作用方程组出发,推广了一个具有一般形式的海 气耦合气候系统非线性扰动模式.运用拓扑度理论,从数学上严格证明了一定条件下该模式存在周期正解的结果,并分析了所得结果潜在的应用价值.海-气相互作用研究,有助于理解气候变化过程,为气候模拟和预报提供理论基础.     

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

The Jin-Neelin model for the El Ni$\wt{\rm n}$o--Southern Oscillation (ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO dynamics. From the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length $k$ and on each sub-interval to solve successively the oceanic component, using the temperature $T$ calculated on the previous sub-interval, to then solve the sea-surface temperature (SST for short) equation on the current sub-interval. The passage to the limit as $k$ tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.     

Asymptotic solution for EI Nino-southern oscillation of nonlinear model

A class of nonlinear coupled system for El Nino-Southern Oscillation(ENSO) model is considered.Using the asymptotic theory and method of variational iteration,the asymptotic expansion of the solution for ENSO models is obtained.     

PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE EL NINO/LA NINO-SOUTHERN OSCILLATION MECHANISM

A class of coupled system to oscillate of the E1 Nino/La Nino-Southern Oscillation （ENSO） mechanism is studied. Using the perturbed theory, the asymptotic expansions and asymptotic behavior of the solution for an ENSO model are obtained.     

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

研究了基于Navier-Stokes方程的脉动速度方程的最优低维动力系统建模理论.最优目标泛函为脉动速度基函数的不可压缩性和正交性.数值计算了充分发展的并排双方柱绕流问题,并基于双尺度全局最优化方法,建立了它的脉动速度的最优动力系统模型.对其相空间轨道、Poincaré截面、分岔特性、功率谱和Lyapunov指数集等动力学特性进行了分析.随着Reynolds数的增加,双方柱绕流的脉动速度方程最优动力系统具有复杂的类倍周期分岔行为.     

Asymptotic solution for EI Ni$$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{n} $$o-southern oscillation of nonlinear model

A class of nonlinear coupled system for EI Nino-Southern Oscillation （ENSO） model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.     

厄尔尼诺/拉尼娜-南方海涛模型的变分迭代解法

研究了-类厄尔尼诺-南方海涛（ENSO）振子的模型，利用变分迭代方法求出了ENSO模型的近似解。     

A mathematical framework for stochastic climate models

There has been a recent burst of activity in the atmosphere‐ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degrees of freedom in stochastic climate prediction. Here a systematic mathematical strategy for stochastic climate modeling is developed, and some of the new phenomena in the resulting equations for the climate variables alone are explored. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean variables and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. All of these phenomena are derived from a systematic self‐consistent mathematical framework for eliminating the unresolved stochastic modes that is mathematically rigorous in a suitable asymptotic limit. The theory is illustrated for general quadratically nonlinear equations where the explicit nature of the stochastic climate modeling procedure can be elucidated. The feasibility of the approach is demonstrated for the truncated equations for barotropic flow with topography. Explicit concrete examples with the new phenomena are presented for the stochastically forced three‐mode interaction equations. The conjecture of Smith and Waleffe [Phys. Fluids 11 (1999), 1608–1622] for stochastically forced three‐wave resonant equations in a suitable regime of damping and forcing is solved as a byproduct of the approach. Examples of idealized climate models arising from the highly inhomogeneous equilibrium statistical mechanics for geophysical flows are also utilized to demonstrate self‐consistency of the mathematical approach with the predictions of equilibrium statistical mechanics. In particular, for these examples, the reduced stochastic modeling procedure for the climate variables alone is designed to reproduce both the climate mean and the energy spectrum of the climate variables. © 2001 John Wiley & Sons, Inc.     

Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Recently, techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. The probability distribution functions (PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models. Asymptotic Gaussian lower bounds are also established under suitable hypotheses.     

Geometric Ergodicity for Piecewise Contracting Processes with Applications for Tropical Stochastic Lattice Models

Stochastic lattice models are increasingly prominent as a way to capture highly intermittent unresolved features of moist tropical convection in climate science and as continuum mesoscopic models in material science. Stochastic lattice models consist of suitably discretized continuum partial differential equations interacting with Markov jump processes at each lattice site with transition rates depending on the local value of the continuum equation; they are a special case of piecewise deterministic Markov processes but often have an infinite state space and unbounded transition rates. Here a general theorem on geometric ergodicity for piecewise deterministic contracting processes is developed with full generality to apply to stochastic lattice models. A highly nontrivial application to the stochastic skeleton model for the Madden‐Julian oscillation (Thual et al., 2013) is developed here where there is an infinite state space with unbounded and also degenerate transition rates. Geometric ergodicity for the stochastic skeleton model guarantees exponential convergence to a unique invariant measure that defines the statistical tropical climate of the model. Another application of the general framework is developed here for stochastic lattice models designed to capture intermittent fluctuation in the simplest tropical climate models. Other straightforward applications to models motivated by material science are mentioned briefly here. © 2016 Wiley Periodicals, Inc.     

不完备质量下的报童问题及其评估机制

在产品质量不完备的环境下,考虑了需求依赖于质量水平的报童问题。本文主要利用马氏理论刻画质量水平与需求之间关联性的动态演变过程,并将“不完备质量”的决策理念纳入报童问题的理论框架,进而提出了新的随机库存系统的优化模型及其决策机制。同时,利用随机质量过程中的首达性、遍历性、不可约性等基本属性,构建了随机库存系统在运作和管理过程中的可靠性及其收益评估机制。模型的相关结论表明:在不完备质量的环境下,零售商的最优订购决策是由各个质量状态的转移概率所确定,若由质量水平的波动性所导出的随机过程为不可约遍历马氏链时,则库存系统的决策机制具有良好的稳定性。     

A CLASS OF HOMOTOPIC SOLVING METHOD FOR ENSO MODEL

The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...     

Positive Harris recurrence for degenerate diffusions with internal variables and randomly perturbed time-periodic input

We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations, which is driven by possibly very low-dimensional noise. Equations of this type commonly occur in biology when modeling neurons or in statistical mechanics for certain Hamiltonian systems. We provide verifiable conditions on the original deterministic dynamical system under which the solution to the respective stochastic system features a point in the interior of its state space, which can be proved to be attainable by deterministic control arguments, and at which a local Hörmander condition holds. Together with a Lyapunov condition, it follows that the corresponding process is positive Harris recurrent.     

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland’s variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.     

倒向随机微分方程与巴黎期权的非线性定价

巴黎期权是一种复杂的奇异期权. 本文基于倒向随机微分方程, 定义了巴黎期权的非线性价格过程, 分析其性质, 并且给出巴黎期权非线性定价的偏微分方程表达式. 在金融市场收益率不确定的情形以及存贷利率不同的情形下分别对连续巴黎期权进行定价和具体的数值分析, 结论显示巴黎期权的非线性定价机制更具合理性.     

A stochastic Lagrangian proof of global existence of the Navier–Stokes equations for flows with small Reynolds number

We consider the incompressible Navier–Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time Hölder continuous solutions. Our proof uses a stochastic representation formula to obtain a decay estimate for heat flows in Hölder spaces, and a stochastic Lagrangian formulation of the Navier–Stokes equations.     

SPT: a stochastic tunneling algorithm for global optimization

A stochastic approach to solving unconstrained continuous-function global optimization problems is presented. It builds on the tunneling approach to deterministic optimization presented by Barhen and co-workers (Bahren and Protopopescu, in: State of the Art in Global Optimization, Kluwer, 1996; Barhen et al., Floudas and Pardalos (eds.), TRUST: a deterministic algorithm for global optimization, 1997) by combining a series of local descents with stochastic searches. The method uses a rejection-based stochastic procedure to locate new local minima descent regions and a fixed Lipschitz-like constant to reject unpromising regions in the search space, thereby increasing the efficiency of the tunneling process. The algorithm is easily implemented in low-dimensional problems and scales easily to large problems. It is less effective without further heuristics in these latter cases, however. Several improvements to the basic algorithm which make use of approximate estimates of the algorithms parameters for implementation in high-dimensional problems are also discussed. Benchmark results are presented, which show that the algorithm is competitive with the best previously reported global optimization techniques. A successful application of the approach to a large-scale seismology problem of substantial computational complexity using a low-dimensional approximation scheme is also reported.     

Stochasticity in the image greenhouse model

The potential impacts of climate change are a major issue in the Greenhouse debate. Various models and particularly IMAGE (Integrated Model to Assess the Greenhouse Effect), are being used by the IPCC to investigate climate change. The IMAGE model has been reduced to a system of differential equations and incorporates various initial conditions and model parameters. These initial conditions and parameter values are not known precisely and are subject to variability of various forms. This paper briefly describes the mathematical form of IMAGE and then investigates the stochastic properties of the model. Particular attention is paid to the propagation and amplification of assumed distributions for the initial conditions and certain key physical parameters. The IMAGE model appears to be quite robust with respect to these stochastic characteristics.     

Existence of the universal attractor for the 3-D viscous primitive equations of large-scale moist atmosphere

In this paper, we consider the initial-boundary value problem for the three-dimensional viscous primitive equations of large-scale moist atmosphere which are used to describe the turbulent behavior of long-term weather prediction and climate changes. By obtaining the existence and uniqueness of global strong solutions for the problem and studying the long-time behavior of strong solutions, we prove the existence of the universal attractor for the dynamical system generated by the primitive equations of large-scale moist atmosphere.