Stochastic Multiscale Heat Transfer Analysis of Heterogeneous Materials with Multiple Random Configurations

This study presents a new stochastic multiscale analysis approach to analyze the heat transfer performance of heterogeneous materials with random structures at different length scales. The heterogeneities of the materials are taken into account by periodic layouts of unit cells, consisting of randomly distributed inclusion dispersions and homogeneous matrix on the microscale and mesoscale. Based on the reiterated homogenization, a novel unified micro-meso-macro stochastic multiscale formulation is established and the scale gap is correlated by means of two-scale asymptotic expansions. Also, the stochastic multiscale formulae for computing the effective thermal property and temperature field are derived successively. Then, the stochastic prediction algorithm coupled with the finite element method is brought forward in details. The accuracy of the implemented stochastic multiscale analysis is verified by comparing the results against the experimental data for three scales heterogeneous materials with several different material combinations. The comparison demonstrates the usability of the proposed stochastic multiscale method for the determination of the thermal behaviors. This study offers a unified multiscale framework that enables heat transfer behavior analysis of heterogeneous materials with multiple random configurations.     

Constrained Markov control processes with randomized discounted cost criteria: infinite linear programming approach

In this paper, we study constrained Markov control processes on Borel spaces with possibly unbounded one‐stage cost, under a discounted optimality criterion with random discount factor and restrictions of the same kind. We prove that the corresponding optimal control problem is equivalent to an infinite‐dimensional linear programming problem. In addition, considering the dual program, we show that there is no duality gap, and moreover, the strong duality condition holds. Hence, both programs are solvable, and their optimal values coincide. Copyright © 2013 John Wiley & Sons, Ltd.     

EPR Spectroscopy as a Tool to Characterize the Maturity Degree of Humic Acids

The major indicator of soil fertility and productivity are humic acids (HAs) arising from decomposition of organic matter. The structure and properties of HAs depend, among others climate factors, on soil and anthropogenic factors, i.e., methods of soil management. The purpose of the research undertaken in this paper is to study humic acids resulting from the decomposition of crop residues of wheat (Triticum aestivum L.) and plant material of thuja (Thuja plicata D.Don.ex. Lamb) using electron paramagnetic resonance (EPR) spectroscopy. In the present paper, we report EPR studies carried out on two types of HAs extracted from forest soil and incubated samples of plant material (mixture of wheat straw and roots), both without soil and mixed with soil. EPR signals obtained from these samples were subjected to numerical analysis, which showed that the EPR spectra of each sample could be deconvoluted into Lorentzian and Gaussian components. It can be shown that the origin of HAs has a significant impact on the parameters of their EPR spectra. The parameters of EPR spectra of humic acids depend strongly on their origin. The HA samples isolated from forest soils are characterized by higher spin concentration and lower peak-to-peak width of EPR spectra in comparison to those of HAs incubated from plant material.     

不同地理株杂交培育的柔嫩艾美球虫及其免疫保护率

目的　培育 3个不同地理株柔嫩艾美球虫 (Eimeriatenella)的杂交株 ,以探讨研制球虫疫苗的可能性。　方法　通过免疫试验 ,从 5个不同地理株中选择 3株作为杂交亲本株 ,对此 3株分别进行两次杂交 ,获得的后代混合卵囊经单卵囊分离、扩增 ,分别提取卵囊DNA ,利用随机扩增多态性DNA(RAPD)进行分析 ( 3 0条引物 ) ,分离、培育出两代杂交株。再进行免疫试验 ,比较杂交株与亲本株的免疫保护性。　结果　选择了免疫原性较好、免疫保护率较高的广州株、保定株、长春株作为杂交亲本 ,分别进行保定株×长春株、广州株×F1株两次杂交 ,获得的后代卵囊 ,提取卵囊DNA ,RAPD分析后 ,得到了保定株×长春株的杂交株F1(F1Z7)和广州株×F1株的杂交株F2 (F2Z3 )。免疫试验结果 ,杂交株F1与F2的免疫保护率分别为 80 %和 84% ;亲本株广州株为 77% ,保定株为 69% ,长春株为 63 %。　结论　分离、培育出了F1、F2两代杂交虫株。其免疫保护率均高于各亲本株 ,提示杂交株获得了亲本株的部分保护性 ,其免疫的雏鸡对各虫株的攻击均有好的保护力。尤其是F2株 ,免疫保护率平均达到 84%。     

Soil animals alter plant litter diversity effects on decomposition

Most of the terrestrial net primary production enters the decomposer system as dead organic matter, and the subsequent recycling of C and nutrients are key processes for the functioning of ecosystems and the delivery of ecosystem goods and services. Although climatic and substrate quality controls are reasonably well understood, the functional role of biodiversity for biogeochemical cycles remains elusive. Here we ask how altering litter species diversity affects species-specific decomposition rates and whether large litter-feeding soil animals control the litter diversity-function relationship in a temperate forest ecosystem. We found that decomposition of a given litter species changed greatly in the presence of litters from other cooccurring species despite unaltered climatic conditions and litter chemistry. Most importantly, soil fauna determined the magnitude and direction of litter diversity effects. Our data show that litter species richness and soil fauna interactively determine rates of decomposition in a temperate forest, suggesting a combination of bottom-up and top-down controls of litter diversity effects on ecosystem C and nutrient cycling. These results provide evidence that, in ecosystems supporting a well developed soil macrofauna community, animal activity plays a fundamental role for altered decomposition in response to changing litter diversity, which in turn has important implications for biogeochemical cycles and the long-term functioning of ecosystems with ongoing biodiversity loss.     

医院门诊处方质量控制抽样体系的研究及构建

目的：探究医院门诊处方点评过程中,科学的处方抽样方法。方法：通过引入GB/T 2828.1-2012国家抽样标准,结合随机抽样理论,采用SPSS13.0统计软件包Rv.Normal功能辅助完成抽样过程。结果：结合处方抽样实例,通过科学抽样体系,实践抽样过程,为门诊处方点评工作实现科学抽样提供理论依据。结论：该抽样方法能够提高处方抽样的科学性,使门诊处方点评结果更能体现医院处方总体质量。     

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann–Gibbs–Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon–Khinchin axioms, the -entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.Many statistical systems can be characterized by a macrostate for which many microconfigurations exist that are compatible with it. The number of configurations associated with the macrostate is called the phase-space volume or multiplicity, M. Boltzmann entropy is the logarithm of the multiplicity,and has the same properties as the thermodynamic (Clausius) entropy for systems such as the ideal gas (1). We set . Boltzmann entropy scales with the degrees of freedom f of the system. For example, for N noninteracting point particles in three dimensions, . Systems where scales with system size are called extensive. The entropy per degree of freedom is a system-specific constant. Many complex systems are nonextensive, meaning that if two initially insulated systems A and B, with multiplicities and , respectively, are brought into contact, the multiplicity of the combined system is . For such systems, which are typically strongly interacting, non-Markovian, or nonergodic, and the effective degrees of freedom do no longer scale as N. Given the appropriate scaling for , the entropy is a finite and nonzero constant in the thermodynamic limit, .A crucial observation in statistical mechanics is that the distribution of all macrostate variables gets sharply peaked and narrow as system size N increases. The reason behind this is that the multiplicities for particular macrostates grow much faster with N than those for other states. In the limit the probability of measuring a macrostate becomes a Dirac delta, which implies that one can replace the expectation value of a macrovariable by its most likely value. This is equivalent to maximizing the entropy in Eq. 1 with respect to the macrostate. By maximizing entropy one identifies the “typical” microconfigurations compatible with the macrostate. This typical region of phase space dominates all other possibilities and therefore characterizes the system. Probability distributions associated with these typical microconfigurations can be obtained in a constructive way by the maximum entropy principle (MEP), which is closely related to the question of finding the most likely distribution functions (histograms) for a given system.We demonstrate the MEP in the example of coin tossing. Consider a sequence of N independent outcomes of coin tosses, , where is either head or tail. The sequence x contains heads and tails. The probability of finding a sequence with exactly heads and tails iswhere is the binomial factor. We use the shorthand notation for the histogram of heads and tails and for the marginal probabilities for throwing head or tail. For the relative frequencies we write . We also refer to θ as the “biases” of the system. The probability of observing a particular sequence x with histogram k is given by . It is invariant under permutations of the sequence x because the coin tosses are independent. All possible sequences x with the same histogram k have identical probabilities. is the respective multiplicity, representing the number of possibilities to throw exactly heads and tails. As a consequence Eq. 2 becomes the probability of finding the distribution function p of relative frequencies for a given N. The MEP is used to find the most likely p. We denote the most likely histogram by and the most likely relative frequencies by .We now identify the two components that are necessary for the MEP to hold. The first is that in Eq. 2 factorizes into a multiplicity that depends on k only and a factor that depends on k and the biases θ. The second necessary component is that the multiplicity is related to an entropy expression. By using Stirling’s formula, the multiplicity of Eq. 2 can be trivially rewritten for large N,where an entropy functional of Shannon type (2) appears,The same arguments hold for multinomial processes with sequences x of N independent trials, where each trial takes one of W possible outcomes (3). In that case the probability for finding a given histogram k is is the multinomial factor and . Asymptotically holds. Extremizing Eq. 5 for fixed N with respect to k yields the most likely histogram, . Taking logarithms on both sides of Eq. 5 givesObviously, extremizing Eq. 6 leads to the same histogram . The term in Eq. 6 is sometimes called relative entropy or Kullback–Leibler divergence (4). We identify the first term on the right-hand side of Eq. 6 with Shannon entropy , and the second term is the so-called cross-entropy . Eq. 6 states that the cross-entropy is equal to entropy plus the relative entropy. The constraints of the MEP are related to the cross-entropy. For example, let the marginal probabilities be given by the so-called Boltzmann factor, , for the “energy levels” , where β is the inverse temperature and α the normalization constant. Inserting the Boltzmann factor into the cross-entropy, Eq. 6 becomeswhich is the MEP in its usual form, where Shannon entropy gets maximized under linear constraints. α and β are the Lagrangian multipliers for the normalization and the “energy” constraint , respectively. Note that in Eq. 6 we used to scale . Any other nonlinear would yield nonsensical results in the limit of , either 0 or ∞. Comparing with Eq. 1 shows that indeed, up to a constant multiplicative factor, . This means that the Boltzmann entropy per degree of freedom of a (uncorrelated) multinomial process is given by a Shannon-type entropy functional. Many systems that are nonergodic, are strongly correlated, or have long memory will not be of multinomial type, implying that is not invariant under permutations of a sequence x. For this situation it is not a priori evident that a factorization of into a θ-independent multiplicity and a θ-dependent term, as in Eq. 5, is possible. Under which conditions such a factorization is both feasible and meaningful is discussed in the next section.