Entropy and spatial disorder

The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions.     

Entropy and spatial disorder

The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions.     

Entropy and Information Content of Geostatistical Models

Mathematical Geosciences - Geostatistical models quantify spatial relations between model parameters and can be used to estimate and simulate properties away from known observations. The underlying...     

Lunar materials: Their mineralogy,petrology and chemistry

The manned Apollo 11, 12, 14 and 15 and the automated Luna 16 lunar missions have provided us with lunar rock and regolith (soil) samples from a number of geologically distinct sites. The mare regions were sampled by Apollo 11, 12 and Luna 16, whereas Apollo 14 landed on a terrain with more relief, the Fra Mauro Formation which represents an ejecta blanket from the Imbrian Basin, and Apollo 15 touched down near the lunar highlands. The samples collected consist of a mixture, mainly of basalt, breccia and regolith (soil-particulate matter, generally < 1 cm in size). The basalts show considerable variation in texture, mineralogy and chemistry and probably represent fragments from various parts of relatively thin and extensive lava flows in the maria. The breccias represent regolith material which was indurated to varying degrees by impact events. The regolith is a product of the breakdown, again by impact, of coherent rock masses of basalt and breccia.     

信息熵在水系统中的应用研究综述

在介绍信息熵基本概念作理论的基础上，对其在水系统中的应用研究，主要从概率分布和参数估计，熵谱预报，水文（水质）站网布设评估，水质水环境的预测预报评估，水系统建模评估，水力学，河流地貌学等问题进行了综述，并对今后的研究进行了展望。     

Complementary Entropy and Wavelet Analysis of Drilling-Ability Data

The paper combines wavelet and entropy analysis of nonstationary drilling-ability data in order to obtain optimum information on the mechanical behavior of different geological formations. Both methods are multiscale in nature, and while entropy analysis provides information on stationary subdomains, wavelet analysis identifies dominant scales or range of scales at which the entropy analysis is most useful. The combination of the techniques yields relatively simple results that can aid the drilling process by providing information on delays to be expected.     

Entropy and structure of oxidized and reduced iron-bearing silicate glasses

The influence of ferrous and ferric iron on the low-temperature heat capacity and vibrational entropy of silicate glasses has been determined by adiabatic calorimetry. Two pairs of samples based on sodium disilicate and calcium Tschermak molecule compositions have been studied. Along with previous data for another Fe-bearing glass, these results have been used to complement the available set of composition independent partial molar relative entropies of oxides in silicate glasses with S₂₉₈ − S₀ values of 56.7 and 116 J/mol for FeO and Fe₂O₃, respectively. The calorimetric data indicate that the fraction of fivefold coordinated Al is significant in the CaO-“FeO”-Al₂O₃-SiO₂ system and that association of Ca²⁺ and Na⁺ with Fe³⁺ in tetrahedral coordination for charge compensation does not entail significant changes in coordination for these two cations. At very low temperatures, however, the heat capacity is no longer an additive function of composition because of unexpectedly high positive deviations from Debye laws. These anomalies are stronger for the reduced than the oxidized glasses and considerably larger than for iron-free glasses, but their origin cannot be established from the present measurements.     

Creative spoil: Design concepts,construction techniques,and disposal of excavated materials

The author discusses some of the construction methods used in building the Tennessee-Tombigbee Waterway, the disposal of surplus excavated materials, and the reclamation of disposal areas along the waterway Emphasis is placed on the steps taken to assure protection of natural resources and to promote overall environmental quality.     

基于Halphen分布和最大熵的洪水频率分析

设计洪水估算值对水利水电工程的设计规划至关重要,其关键是选择合适的分布线型和参数估计方法。目前采用单一的频率曲线进行水文分析计算,其设计结果具有较大的不确定性。引入Halphen分布函数进行洪水频率分析,并提出了基于最大熵原理的参数估计方法。利用丹江口水库1929~2014年的年最大日流量资料系列,分析检验Halphen分布的拟合效果,并与传统的分布进行比较。结果表明,Halphen函数具有灵活的形式和较好的尾部特征,适合于水文频率分析,其拟合结果基本优于其他的传统分布。     

轻质土密度、强度与材料组成的关系研究

论述了轻质土试样的制备方法,对轻质土密度、无侧限抗压强度与材料组成之间的关系进行的研究表明：密度主要受到EPS颗粒添加量的影响;无侧限抗压强度主要受到水泥添加量、EPS颗粒添加量的影响。在此基础上给出了适合于工程应用的轻质土的配方公式。     

Heat Dissipation and Entropy Variation of the Earth System

The Earth system is characterized by the contradiction between increasing disorderness of the nature and increasing orderness of life evolution. The second law of thermodynamics shows that the irreversible process of heat dissipation of the Earth takes place naturally in only one direction, while paleontology shows that life on the Earth proceeds toward a state of increasing order. Why the life could be flourishing on the Earth in some periods or rapid extinction in some other times while the…     

Entropy in Markov analysis of late paleozoic cyclical coal measures of East Bokaro basin, Bihar, India

Randomness in the occurrence of lithologies in a cyclical succession is evaluated in terms of entropies which can be calculated from a Markov chain matrix. Two types of entropies are linked with every lithologic state; one is the entropy before deposition E ^(pre) and the other is that after deposition E ^(post),which together form an entropy set. The entropy sets for pebbly sandstone, sandstone, shale, and coal for the Karharbari coal measures, and sandstone, shale, carbonaceous shale, and coal for the Barakar coal measures were plotted separately and compared with Hattori's idealized plots. These coal measures probably were essentially of symmetrical cyclical pattern (Type-B)of Hattori. The entropy of the whole sedimentation unit readily fits under the broad framework of fluvial cycles.     

矿井断层构造复杂程度的GIS与熵值耦合评价研究

基于GIS与熵值耦合理论的矿井断层构造复杂程度的综合评价方法,建立了断层构造的非线性特征值、断层规模指数、煤层底板倾角指数、断层断距指数等与矿井构造复杂程度相关的评价指标体系。并以河南某矿为例,对矿井断层构造复杂程度进行多因素评价综合分区。结果显示:该矿井构造以中等和简单为主;在构造简单-中等区,构造对煤层开采基本无影响,而在构造复杂区,断层可导致水文地质条件变得较为复杂,影响煤层安全开采。     

基于熵权正态云模型的软岩等级评价

软岩是地下工程施工中常见的复杂地质情况之一,科学准确的对其分类是进行安全施工的重要前提。针对软岩环境的复杂性和不确定性,选取单轴抗压强度σ_c、完整性系数K_v、黏聚力σ_n、软化系数K_f和软化指数f_s 5项定量化指标建立软岩评价指标体系,采用熵权法确定各指标权重,结合云理论建立熵权-正态云模型,对软岩的类型进行分级评价。以4组软岩工程实例对所建立模型进行检验,并与未确知度法、模糊评价法和BQ法的判别结果进行对比。研究结果表明,熵权-正态云模型在软岩等级判别中具有良好的实用性和可靠性,可为软岩类型预测提供一种新思路。     

Relict olivine grains, chondrule recycling, and implications for the chemical, thermal, and mechanical processing of nebular materials

Chondrules and isolated forsterites in five low-subtype ordinary chondrites [NWA 3127 (LL3.1), Sahara 97210 (LL3.2), Wells (LL3.3), Chainpur (LL3.4), and Sahara 98175 (LL3.5)] were studied using petrographic, EMPA, and SIMS techniques to better constrain the origin of chondrules and the olivine grains within them. Our results imply that igneous crystallization, vapor fractionation, redox effects, and open-system behavior were important processes. All olivine grains, including normal, relict, and isolated forsterite grains, show evidence for igneous fractionation under disequilibrium conditions, with olivine crystallizing during rapid cooling (closer to 2000 °C/h than to 100 °C/h). Vapor fractionation is manifested by anti-correlated abundances between refractory elements (Al, Sc, Y, Ti, Ca, V) and volatile elements (Cr, Mn, P, Rb, Fe) in olivine. Redox effects are evidenced in various ways, and imply that Fe, Co, Ni, and P were partitioned more into metal, and V was partitioned more into olivine, under reducing conditions in the most FeO-poor melts. There is no obvious evidence for systematic variations in olivine composition according to meteorite subtype, but shock melting in Sahara 97210 resulted in the injection of glass-derived melt into olivine, resulting in artificially high abundances of Ba, Sr, Na, Ti, and some other incompatible elements in olivine. Terrestrial weathering in a hot desert environment may have mobilized Ba and Sr in some glasses.Our data suggest that chondrules in ordinary chondrites experienced repeated thermal, chemical, and mechanical processing during a “recycling” process over an extended time period, which involved multiple episodes of melting under fluctuating redox and heating conditions, and multiple episodes of chondrule break-up in some cases. Forsterite grains, including normal grains in forsterite-bearing type I chondrules, the cores of isolated forsterites, and relict forsterite in type II chondrules, all crystallized from similar, refractory melts under reducing conditions; relict Mg-olivine and isolated forsterite grains were thus derived from type I chondrules. Olivine in type II chondrules, including normal grains and ferroan overgrowths on relict Mg-olivine, crystallized from more volatile-rich, oxidized, and relatively unfractionated melts. Relict dusty olivine grains in type I chondrules were derived from type II chondrules during incomplete melting episodes involving reduction and some vaporization, with clear (non-dusty) grains in dusty olivine-bearing chondrules crystallizing from the reduced and partly vaporized melts. Melt compositions parental to normal olivine grains in type I and II chondrules are systematically enriched in refractory elements compared to bulk chondrule compositions, implying that chondrules often experienced open-system exchange with more volatile-rich surroundings after some olivine had crystallized, possibly while the chondrules were still partly molten. Type II chondrules could have been derived from type I chondrules by the addition of relatively volatile-rich material, followed by re-melting and little evaporation under oxidizing conditions. In contrast, type I chondrules could have been derived from type II chondrules by re-melting involving more-or-less evaporation under reducing conditions. Chemical, oxygen isotope, and petrographic data are best accommodated by a model in which there were several (>2-3, sometimes ?4-5) melting episodes for most chondrules in ordinary chondrites.     

利用有序熵法进行煤层对比

煤层的对比方法很多,但适用范围各有所限。古生代煤田多为海陆交互相,具明显的旋回特征,使用传统的方法基本上是可行的;而中生代煤田多为陆相,沉积变化大,煤层不稳定,又缺标志层,仅用传统的煤层对比方法,就显得困难。     

Entropy as criterion of heterogeneity of rocks

Statistical entropy of a multicomponent material (mechanical) system, such as sediments or rocks, particularly the relative entropy, is shown to be an easily calculable, simple and meaningful index of heterogeneity of the system, well suited for diagrammatic representations and for stratigraphic and/or lithological mapping. – V. P. Sokoloff.     

Morphological characteristics of gully networks and their relationship to host materials,Baringo District,Kenya

The morphological characteristics of gully networks in Baringo District, Kenya are described in relation to host materials. All gullies studied were part of a well integrated network characterised by a high drainage density. Causes of network rejuvenation leading to gullying are postulated. The morphology of the individual gullies were found to be related to the most material. Gullies formed on weathered bedrock had a dendritic drainage network with convex slopes. The morphology of gullies developed in lacustrine sediments varied with sediment texture and chemistry. V-shaped dendritic gullies with a concave longitudinal profile were associated with a high clay content and high sodium content whereas entrenched gullies were associated with a high silt content and low sodium content. Process inferences are made in order to explain the variation in gully morphology.     

静电自组装制备斜发沸石负载纳米TiO2吸附及光催化降解甲基橙染料研究

为了实现纳米TiO2的固定化负载,提高材料对污染物的光催化效率,采用静电自组装方法制备了天然斜发沸石负载纳米TiO2光催化材料。采用硅烷偶联剂(OCH3)3Si(CH2)3SH干法改性斜发沸石,采用30%H2O2/HOAc氧化剂将偶联剂巯基基团(—SH)氧化为易电离的磺酸基基团(—SO3H),带负电荷的沸石与钛聚合阳离子在静电引力的作用下自发地组装在一起,经一定温度的焙烧得到斜发沸石负载纳米TiO2光催化材料。采用XRD和SEM对材料进行分析和表征,采用甲基橙染料评价材料的吸附和光催化性能,结果表明:沸石负载纳米TiO2对甲基橙染料具有吸附与光催化的协同作用,静电自组装方法制备的材料的光催化性能较传统方法有所提高。