一类海-气耦合振子模型行波解的渐近解法

热带海-气振子是一个复杂的自然现象.本文是对一个海-气耦合振子模型,利用一个待定系数和摄动理论相结合的新方法,得到了相应模型的行波渐近解.     

赤道东太平洋SST的海-气振子模型

研究了一个海-气振子的非线性耦合系统的模型.利用变分迭代原理，首先构造了相应的一组泛函.其次选取其Lagrange乘子.再用广义变分迭代方法得到了海-气振子模型一组解的近似序列. 关键词： 海-气振子 非线性 耦合系统 厄尔尼诺模型     

厄尔尼诺-南方涛动时滞海-气振子耦合模型

研究了一个时滞海-气振子模型.利用摄动理论和方法，得到了海-气振子模型解的渐近展开式. 关键词： 非线性 时滞 厄尔尼诺-南方涛动 海-气振子     

基于水平集的两步MCMC方法对河道形态的识别

首先运用符号距离函数刻画河道的复杂几何形态，然后通过求解水平集演化方程和两步马尔科夫链蒙特卡罗（MCMC）算法拟合生产历史数据，逐步更新河道的边界.在两步MCMC方法的第一步，应用流线模拟计算的敏感性矩阵获取近似的似然函数，修改MCMC的推荐概率分布；第二步，为确保MCMC算法的严密性，对通过第一步的油藏模型进行完整的数值模拟以获取精准的似然函数，并用更改的接受概率作为模型接受的判断准则.最后通过二维计算实例验证该方法的有效性.     

一类扰动海-气耦合振子机理的近似解

考虑了一个全球气候扰动海-气热盐循环的箱域模型.利用同伦映射方法,研究了一类非线性模型.得到了模型的近似解.同伦映射求解方法是一个解析方法,得到的解还能继续进行解析运算.从而再可研究有关物理量的各种定性、定量的性态.     

一类扰动海-气耦合振子机理的近似解

考虑了一个全球气候扰动海-气热盐循环的箱域模型.利用同伦映射方法,研究了一类非线性模型.得到了模型的近似解.同伦映射求解方法是一个解析方法,得到的解还能继续进行解析运算.从而再可研究有关物理量的各种定性、定量的性态.     

海-气耦合动力系统的改进变分迭代解法

研究了一个描述厄尔尼诺和南方涛动振荡物理机理的海-气耦合动力系统.利用改进变分迭代方法 (MVIM)简捷地得到了该非线性模型近似解的展开式.通过与特殊情形下模型精确解的比较,说明获得的MVIM 近似解具有非常好的准确度.     

环境因素对海-气界面低频异常声透射的影响研究

针对海中声源在海-气界面低频异常声透射问题, 根据两层媒质声传输模型, 分析了大气声速和密度与气压、气温、湿度及海水中声速和密度与海温、盐度间的关系, 研究了低频声透射和传输受温度、气压、盐度、湿度等因素的影响, 分析了各因素对声透射和传输的影响程度. 结果表明: 1) 声透射到大气中的声功率与气温、湿度负相关, 与海温、盐度、气压正相关; 2) 单极子与水平偶极子声源辐射到海中的声功率与海温、盐度负相关, 而垂直偶极子声源辐射到海中的声功率与海温、盐度正相关; 3) 声透射指向性与海温正相关, 与气温负相关; 4) 低频声透射受温度影响最大, 其次是盐度, 受气压和湿度影响较小, 垂直偶极子声源的声透射受温度影响大于水平偶极子和单极子声源.     

一类全球气候气-海耦合振子机理的近似解析解

考虑了一个全球气候两半球间气-海热盐循环(THC)的箱域模型. 利用同伦映射方法,研究了一类简化型非线性模型. 得到了模型的近似解. 同伦映射求解方法是一个解析方法,得到的解还能继续进行解析运算. 从而可再研究有关物理量的各种定性、定量的性态. 关键词： 气-海 厄尔尼诺-南方涛动 同伦映射 近似解     

碳气凝胶储氢性能的理论研究

采用基于Metropolis蒙特卡罗和Reverse蒙特卡罗的杂化逆向蒙特卡罗方法,构建碳气凝胶的微孔结构模型,根据碳气凝胶的介孔尺寸构建介孔模型.设计不同形状、不同孔径的介孔模型,使用巨正则蒙特卡罗方法详细模拟在298 K和77 K下的储氢量.结果显示,在77 K时,所设计的碳气凝胶的储氢量几乎是室温下的4倍.在77 K,100 bar时,储氢量最高可达到11.12 wt%和45.68 g·L^-1.     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

Fast Compression of MCMC Output

We propose cube thinning, a novel method for compressing the output of an MCMC (Markov chain Monte Carlo) algorithm when control variates are available. It allows resampling of the initial MCMC sample (according to weights derived from control variates), while imposing equality constraints on the averages of these control variates, using the cube method (an approach that originates from survey sampling). The main advantage of cube thinning is that its complexity does not depend on the size of the compressed sample. This compares favourably to previous methods, such as Stein thinning, the complexity of which is quadratic in that quantity.     

Adversarially Training MCMC with Non-Volume-Preserving Flows

Recently, flow models parameterized by neural networks have been used to design efficient Markov chain Monte Carlo (MCMC) transition kernels. However, inefficient utilization of gradient information of the target distribution or the use of volume-preserving flows limits their performance in sampling from multi-modal target distributions. In this paper, we treat the training procedure of the parameterized transition kernels in a different manner and exploit a novel scheme to train MCMC transition kernels. We divide the training process of transition kernels into the exploration stage and training stage, which can make full use of the gradient information of the target distribution and the expressive power of deep neural networks. The transition kernels are constructed with non-volume-preserving flows and trained in an adversarial form. The proposed method achieves significant improvement in effective sample size and mixes quickly to the target distribution. Empirical results validate that the proposed method is able to achieve low autocorrelation of samples and fast convergence rates, and outperforms other state-of-the-art parameterized transition kernels in varieties of challenging analytically described distributions and real world datasets.     

基于变分方法的混沌系统参数估计

提出一种基于变分原理的估计混沌系统未知参数的方法,对以x= F(x,θ) 为控制方程的所有混沌系统具有普适性.首先将混沌系统方程引入到目标泛函中;接着利用变分原理导出了混沌系统的伴随方程和待辨识参数泛函梯度的通用公式;然后设计了估计混沌系统未知参数的算法;最后对典型的Lorenz混沌系统和超混沌Chen系统的未知参数进行了估计.数值仿真结果表明该方法是一种非常有效的估计混沌系统未知参数的方法. 关键词： 混沌系统 参数估计 变分方法 伴随方程     

Modified variational iteration method for an El Ni no Southern Oscillation delayed oscillator

This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Niño Southern Oscillation. The approximate expansions of the delayed differential equation's solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. The development of the method in that time has been fueled by not only increasingly difficult problems but also novel techniques adopted from physics. Here, the history of Markov chain Monte Carlo is reviewed from its inception with the Metropolis method to the contemporary state‐of‐the‐art in Hamiltonian Monte Carlo, focusing on the evolving interplay between the statistical and physical perspectives of the method.     

海-气振荡子中的极限环解

运用Wang推导建立了描述ENSO事件的海气振荡子的随机动力学模式,进一步证明必含有惟一的一个极限环解,这一极限环是一个稳定的吸引子,它代表了一个内在的耦合系统的年际振荡子. 关键词： ENSO 极限环 海气振荡子 随机动力学     

Application of a probabilistic double-fibre structure model to diffusion-weighted MR images of the human brain

A Markov chain Monte Carlo (MCMC) algorithm has been reported which is capable of determining the probabilistic orientation of two-fibre populations from high angular resolution diffusion-weighted data (HARDI). We present and critically discuss the application of this algorithm to in vivo human datasets acquired in clinically realistic times. We show that by appropriate model selection areas of multiple fibre populations can be identified that correspond with those predicted from known anatomy. Quantitative maps of fibre orientation probability are derived and shown for one- and two-fibre models of neural architecture. Fibre crossings in the pons, the internal capsule and the corona radiata are shown. In addition, we demonstrate that the relative proportion of anisotropic signal may be a more appropriate measure of anisotropy than summary measures derived from the tensor model such as fractional anisotropy in areas with multi-fibre populations.