Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

Numerical study of a model for nonequilibrium wetting

We revisit the scaling properties of a model for nonequilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special point in the phase diagram, where the model exhibits a roughening transition related to directed percolation. We argue that in the vicinity of this point evaporation from the middle of plateaus can be interpreted as an external field in the language of directed percolation. This analogy allows us to compute the crossover exponent and to predict the form of the phase transition line close to its terminal point.

Network of recurrent events for the Olami-Feder-Christensen model

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder, and Christensen (OFC) to mimic earthquakes and investigate to what extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicity. Following a recently proposed method to characterize such clustering by networks of recurrent events [J. Davidsen, P. Grassberger, and M. Paczuski, Geophys. Res. Lett. 33, L11304 (2006)], we find that for synthetic catalogs generated by the OFC model these networks have many nontrivial statistical properties. This includes characteristic degree distributions, very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs, indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

An opinion dynamics model for the diffusion of innovations

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data. (C) 2009 Elsevier B.V. All rights reserved.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

A Markovian model market-Akerlof`s lemons and the asymmetry of information

In this work we study an agent based model to investigate the role of asymmetric information degrees for market evolution. This model is quite simple and may be treated analytically since the consumers evaluate the quality of a certain good taking into account only the quality of the last good purchased plus her perceptive capacity beta. As a consequence, the system evolves according to a stationary Markov chain. The value of a good offered by the firms increases along with quality according to an exponent alpha, which is a measure of the technology. It incorporates all the technological capacity of the production systems such as education, scientific development and techniques that change the productivity rates. The technological level plays an important role to explain how the asymmetry of information may affect the market evolution in this model. We observe that, for high technological levels, the market can detect adverse selection. The model allows us to compute the maximum asymmetric information degree before the market collapses. Below this critical point the market evolves during a limited period of time and then dies out completely. When beta is closer to 1 (symmetric information), the market becomes more profitable for high quality goods, although high and low quality markets coexist. The maximum asymmetric information level is a consequence of an ergodicity breakdown in the process of quality evaluation. (C) 2011 Elsevier B.V. All rights reserved.

On the accuracy of two-fluid model predictions for a particular gas-solid riser flow

Literature presents a huge number of different simulations of gas-solid flows in risers applying two-fluid modeling. In spite of that, the related quantitative accuracy issue remains mostly untouched. This state of affairs seems to be mainly a consequence of modeling shortcomings, notably regarding the lack of realistic closures. In this article predictions from a two-fluid model are compared to other published two-fluid model predictions applying the same Closures, and to experimental data. A particular matter of concern is whether the predictions are generated or not inside the statistical steady state regime that characterizes the riser flows. The present simulation was performed inside the statistical steady state regime. Time-averaged results are presented for different time-averaging intervals of 5, 10, 15 and 20 s inside the statistical steady state regime. The independence of the averaged results regarding the time-averaging interval is addressed and the results averaged over the intervals of 10 and 20 s are compared to both experiment and other two-fluid predictions. It is concluded that the two-fluid model used is still very crude, and cannot provide quantitative accurate results, at least for the particular case that was considered. (C) 2009 Elsevier Inc. All rights reserved.

MULTIVARIATE STATISTICAL METHOD IN OPTIMIZATION OF PROTEIN EXTRACTION FROM SOYBEAN FLOUR WITH DAIRY WHEY

The aim objective of this project was to evaluate the protein extraction of soybean flour in dairy whey, by the multivariate statistical method with 2(3) experiments. Influence of three variables were considered: temperature, pH and percentage of sodium chloride against the process specific variable ( percentage of protein extraction). It was observed that, during the protein extraction against time and temperature, the treatments at 80 degrees C for 2h presented great values of total protein (5.99%). The increasing for the percentage of protein extraction was major according to the heating time. Therefore, the maximum point from the function that represents the protein extraction was analysed by factorial experiment 2(3). By the results, it was noted that all the variables were important to extraction. After the statistical analyses, was observed that the parameters as pH, temperature, and percentage of sodium chloride, did not sufficient for the extraction process, since did not possible to obtain the inflection point from mathematical function, however, by the other hand, the mathematical model was significant, as well as, predictive.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

A split-pot experiment with sorghum to test a root water uptake partitioning model

Correct modeling of root water uptake partitioning over depth is an important issue in hydrological and crop growth models. Recently a physically based model to describe root water uptake was developed at single root scale and upscaled to the root system scale considering a homogeneous distribution of roots per soil layer. Root water uptake partitioning is calculated over soil layers or compartments as a function of respective soil hydraulic conditions, specifically the soil matric flux potential, root characteristics and a root system efficiency factor to compensate for within-layer root system heterogeneities. The performance of this model was tested in an experiment performed in two-compartment split-pot lysimeters with sorghum plants. The compartments were submitted to different irrigation cycles resulting in contrasting water contents over time. The root system efficiency factor was determined to be about 0.05. Release of water from roots to soil was predicted and observed on several occasions during the experiment; however, model predictions suggested root water release to occur more often and at a higher rate than observed. This may be due to not considering internal root system resistances, thus overestimating the ease with which roots can act as conductors of water. Excluding these erroneous predictions from the dataset, statistical indices show model performance to be of good quality.

Norwegian long-distance reflexives: Lectal variation and speaker attitudes

10 lectal variables were examined with respect to Norwegian speakers' acceptance of long-distance reflexives (LDR), using a questionnaire to elicit grammaticality judgements on 50 potential LDR sentences. A sample of 180 speakers completed the questionnaire. The data was analysed using a general linear model univariate model, and Spearman's correlation. In this sample the results showed that dialect and level of education had significant effects on speakers' acceptance of long-distance reflexives, while sex, age, being a native speaker, having both native-speaker parents, living in the city or the country, and the speaker's attitudes to the two Norwegian writing languages had no influence on speakers' acceptance of long-distance reflexives. It is suggested that the influence of Danish on Norwegian writing and on the southern dialects may be the cause of the observed variation with respect to LDR in Norwegian.

A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

RWMODEL II: Computer simulation of the Rescorla-Wagner model of Pavlovian conditioning

RWMODEL II simulates the Rescorla-Wagner model of Pavlovian conditioning. It is written in Delphi and runs under Windows 3.1 and Windows 95. The program was designed for novice and expert users and can be employed in teaching, as well as in research. It is user friendly and requires a minimal level of computer literacy but is sufficiently flexible to permit a wide range of simulations. It allows the display of empirical data, against which predictions from the model can be validated.