淮河流域洪涝变化的耗散性

混沌理论中,人们提出了一些非线性复杂现象的分析方法。在这些方法的启发下,我们曾研究了淮河流域洪涝变化的分形特征和混沌性。在先前研究的基础上,该文以淮河流域洪涝变化为对象,通过表征相空间轨道附近平均收缩(发散)特征的Lyapunov指数,定量地分析和论证了淮河流域洪涝变化的耗散性。淮河流域洪涝变化耗散性的定量论证标志着在地理系统非线性研究方面进行了新的尝试和探索     

砂岩强度MTS试验及阶段特征的混沌动力学研究

采用MTS815.03电液伺服岩石试验系统对三种强度的砂岩进行全应力-应变试验研究,得出试验曲线呈明显的分段特征,曲线的离散性发生于应变软化阶段。通过对试验数据序列的混沌动力学分析得出：随着单向抗压强度的增加,砂岩全应力-应变过程的系统状态由强混沌态逐渐演化到低混沌态,进而质变为较有序的定常态;砂岩峰后应力-应变阶段曲线的线性性质增强,裂隙系统状态由强混沌态向强有序的定常态演化;砂岩峰前阶段的裂隙系统基本呈现弱混沌状态。该试验方法可靠,对砂岩强度阶段特征的混沌分析具有一定的理论意义。     

Probabilistic collocation and lagrangian sampling for advective tracer transport in randomly heterogeneous porous media

The Karhunen-Loeve (KL) decomposition and the polynomial chaos (PC) expansion are elegant and efficient tools for uncertainty propagation in porous media. Over recent years, KL/PC-based frameworks have successfully been applied in several contributions for the flow problem in the subsurface context. It was also shown, however, that the accurate solution of the transport problem with KL/PC techniques is more challenging. We propose a framework that utilizes KL/PC in combination with sparse Smolyak quadrature for the flow problem only. In a subsequent step, a Lagrangian sampling technique is used for transport. The flow field samples are calculated based on a PC expansion derived from the solutions at relatively few quadrature points. To increase the computational efficiency of the PC-based flow field sampling, a new reduction method is applied. For advection dominated transport scenarios, where a Lagrangian approach is applicable, the proposed PC/Monte Carlo method (PCMCM) is very efficient and avoids accuracy problems that arise when applying KL/PC techniques to both flow and transport. The applicability of PCMCM is demonstrated for transport simulations in multivariate Gaussian log-conductivity fields that are unconditional and conditional on conductivity measurements.     

Approximate general solution of 2-degrees of freedom dynamical systems using `les solutions precieuses'

This paper presents the procedure of a computational scheme leading to approximate general solution of the axi-symmetric,2-degrees of freedom dynamical systems. Also the results of application of this scheme in two such systems of the non-linear double oscillator with third and fifth order potentials in position variables. Their approximate general solution is constructed by computing a dense set of families of periodic solutions and their presentation is made through plots of initial conditions. The accuracy of the approximate general solution is defined by two error parameters, one giving a measure of the accuracy of the integration and calculation of periodic solutions procedure, and the second the density in the initial conditions space of the periodic solutions calculated. Due to the need to compute families of periodic solutions of large periods the numerical integrations were carried out using the eighth order, variable step, R-K algorithm, which secured for almost all results presented here conservation of the energy constant between 10^-9 and 10^-12 for single runs of any and all solutions. The accuracy of the approximate general solution is controlled by increasing the number of family curves and also by `zooming' into parts of the space of initial conditions. All families of periodic solutions were checked for their stability. The computation of such families within areas of `deterministic chaos' did not encounter any difficulty other than poorer precision. Furthermore, on the basis of the stability study of the computed families, the boundaries of areas of `order' and `chaos' were approximately defined. On the basis of these results it is concluded that investigations in thePoincaré sections have to disclose 3 distinct types of areas of `order' and 2 distinct types of areas of `chaos'. Verification of the `order'/`chaos' boundary calculation was made by working out several Poincaré surfaces of sections. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Calculation of Lyapunov Indicators with Post-stabilization in a Weyl Field

We present details of a work aiming at the overestimation of Lyapunov exponents defined by the geodesic deviation equations in the previous work. The geodesic deviation vector with post-stabilization is used to compute the fast Lyapunov indicator, considered to be a very sensitive tool for discrimination between ordered or weakly chaotic motions. We make a detailed study of the dynamics in the superposed Weyl field between a black hole and shell of octopoles by using the fast Lyapunov indicator with the Poincare surface of section. In particular, we examine the effects on the dynamics around the fixed points, of varying one of the three parameters (specific energy E, specific angular momentum L and octopolar moment O), while keeping the other two fixed, and identify the intervals of the varying parameter where the motion is regular or chaotic.     

Probabilistic analysis of groundwater and radionuclide transport model from near surface disposal facilities

As per the regulatory requirements controlling the disposal of radioactive waste, the performance of waste disposal facilities needs to be assessed quantitatively using predictive models. This estimates the potential impact of disposal on the environment and public health. Near Surface Disposal Facilities (NSDFs), constructed to contain the low level radioactive waste are considered to model the radionuclide migration from the system to the geo-sphere. The radiation dose experienced by an individual through drinking water pathway is the endpoint of assessment of the model. A three dimensional groundwater contaminant transport model with a decaying source is modelled numerically to determine the radiation dose for short-lived and long-lived radionuclides. The consideration of uncertainties constitutes an intrinsic part of modelling. The uncertain input parameters include porosity, longitudinal dispersivity, transverse dispersivity, diffusion coefficient and distribution coefficient. The uncertainty propagation and quantification is carried out using collocation based stochastic response surface method (CSRSM). To run the simulations for the huge set of input, a code is developed using built-in python interface in the numerical model. The results are processed further to obtain the sensitive parameters affecting the output concentrations. Further, the probability of radiation dose exceeding permissible value is estimated by subset simulation.     

A generalized two-disk dynamo model

Abstract

A generalized two-disk dynamo model is considered that includes mechanical friction; this model is intended to simulate in its broad character the behavior of the geodynamo. Fixed points, limit cycles and chaotic attractors are located for different input parameters of the model. The chaotic regimes are of several kinds as are the “routes to chaos”. Several approximate models, helpful for studying the dynamo are discussed. A number of essential differences from the well-known Rikitake dynamo are demonstrated.     

深埋煤层应力松弛状态演化试验与动力学分析

应用Lyapunov指数法,对试验得到的深埋煤层应力松弛系统演化对应于各级应变水平的时间序列进行分析,科学重构相空间,得到了每一递进应变水平的相轨迹均不重复地围绕各自对应的历史应力中值而顺次演化。采用分形几何学方法进行时间序列分析,定量揭示出煤样应力松弛系统演化的各层次间自相似性,并部分反映了经典力学与非线性科学间的关系。得到了对应各级应变水平系统演化时间序列的非线性动力学评价指标,并判定深埋煤层应力松弛系统为复杂系统且具有典型混沌特征。深埋煤层应力松弛系统演化的混沌程度及复杂程度呈下降规律,煤体内部力学性质弱化因素与强化因素之间竞争最为激烈的阶段,其混沌程度最高,而宏观破坏后系统伴随最低的混沌程度及复杂程度。     

用混沌理论提高潮汐预报的准确度

为提高潮位预报的准确性,在具有较长潮汐观测数据的站点,基于混沌理论,对观测值与潮汐模型预测值之差所构成的余水位序列(即误差序列),采用局域线性模型的分析方法,给出可能误差预测,修正模型的预报结果,提高潮汐预报的准确性。所给例子,对预测跨度T=2 h,经局域法修正后,崇武站2007年12月份1个月预测水位统计的RMSE值减少74.7%,厦门站减少60.5%;对T=24 h,崇武、厦门两站RMSE值减小都在50%左右。     

Boundary crossing and non‐linear theory in earth‐system sciences – a proof of concept based on tsunami and post‐eruption scenarios on Java Island,Indonesia

Although volcanic eruptions are well‐known to be the trigger of some weather and climatic changes, land‐cover changes by pyroclastic‐flows and lahars do not get this recognition, neither do major hazards such as tsunami. These two earth processes are even lesser considered as being able to modify other earth processes they are not directly connected to, such as landslides or river discharge in non‐connected basins more than a hundred kilometres away. In this contribution the authors argue that these ideas are mainly driven by the process of being ‘educated’ in a single academic discipline and once put to the test interactions and retroactions between earth processes and atmospheric processes are far more reaching than commonly thought. For this study, the site of Java Island (Indonesia) was chosen to conduct (1) an analysis of a major tsunami impact – in the same area as the 2006 Java tsunami and (2) an analysis of the post‐eruption impacts of Merapi Volcano after a major eruption – excluding any ejecta in the atmosphere for the sake of the demonstration. The atmospheric feedback simulations were conducted using the regional climate model (RegCM‐4) with calibration from weather stations in Java Island. As a result, both simulations have proven that large scale deposits of pyroclasts (not introducing the ejectas sent in the atmosphere) and tsunamis can have outstanding impacts on the atmospheric situation and the bio‐geomorphologic evolution of the landscape in the following weeks to months. Interestingly enough these impacts are not limited to the area impacted by the earth process and the effect are not linear in time as they work following thresholds. These rainfalls ‘tele‐impacts’ are important enough to, in turn, modify earth‐surface processes in areas remote from the original phenomenon. This system acts in the same manner as a famous butterfly in Africa that could trigger a hurricane on the other side of the Atlantic Ocean. Copyright © 2012 John Wiley & Sons, Ltd.