Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Organic Matter Fractions and Quality of the Surface Layer of a Constructed and Vegetated Soil After Coal Mining. I - Humic Substances and Chemical Characterization

After open coal mining, soils are “constructed”, which usually contain low levels and quality of organic matter (OM). Therefore, the use of plant species for revegetation and reclamation of degraded areas is essential. This study evaluated the distribution of carbon (C) in the chemical fractions as well as the chemical characteristics and humification degree of OM in a soil constructed after coal mining under cultivation of perennial grasses. The experiment was established in 2003 with the following treatments: Hemarthria altissima (T1), Paspalum notatum (T2), Cynodon dactilon (T3), Urochloa brizantha (T4), bare constructed soil (T5), and natural soil (T6). In 2009, soil samples were collected from the 0.00-0.03 m layer and the total organic carbon stock (TOC) and C stock in the chemical fractions: acid extract (CHCl), fulvic acid (CFA), humic acid (CHA), and humin (CHU) were determined. The humic acid (HA) fraction was characterized by infrared spectroscopy and the laser-induced fluorescence index (ILIF) of OM was also calculated. After six years, differences were only observed in the CHA stocks, which were highest in T1 (0.89 Mg ha-1) and T4 (1.06 Mg ha-1). The infrared spectra of HA in T1, T2 and T4 were similar to T6, with greater contribution of aliphatic organic compounds than in the other treatments. In this way, ILIF decreased in the sequence T5>T3>T4>T1>T2>T6, indicating higher OM humification in T3 and T5 and more labile OM in the other treatments. Consequently, the potential of OM quality recovery in the constructed soil was greatest in treatments T1 and T4.

Organic Matter Fractions and Quality of the Surface Layer of a Constructed and Vegetated Soil After Coal Mining. II - Physical Compartments and Carbon Management Index

Soils constructed after mining often have low carbon (C) stocks and low quality of organic matter (OM). Cover crops are decisive for the recovery process of these stocks, improving the quality of constructed soils. Therefore, the goal of this study was to evaluate the effect of cover crops on total organic C (TOC) stocks, C distribution in physical fractions of OM and the C management index (CMI) of a soil constructed after coal mining. The experiment was initiated in 2003 with six treatments: Hemarthria altissima (T1), Paspalum notatum (T2), Cynodon dactylon (T3), Urochloa brizantha (T4), bare constructed soil (T5), and natural soil (T6). Soil samples were collected in 2009 from the 0.00-0.03 m layer, and the TOC and C stocks in the physical particle size fractions (carbon in the coarse fraction - CCF, and mineral-associated carbon - MAC) and density fractions (free light fraction - FLF; occluded light fraction - OLF, and heavy fraction - HF) of OM were determined. The CMI components: carbon pool index (CPI), lability (L) and lability index (LI) were estimated by both fractionation methods. No differences were observed between TOC, CCF and MAC stocks. The lowest C stocks in FLF and OLF fractions were presented by T2, 0.86 and 0.61 Mg ha-1, respectively. The values of TOC stock, C stock in physical fractions and CMI were intermediate, greater than T5 and lower than T6 in all treatments, indicating the partial recovery of soil quality. As a result of the better adaptation of the species Hemarthria and Brizantha, resulting in greater accumulation of labile organic material, the CPI, L, LI and CMI values were higher in these treatments, suggesting a greater potential of these species for recovery of constructed soils.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Sampling Position under No-Tillage System Affects the Results of Soil Physical Properties

ABSTRACT Understanding the spatial behavior of soil physical properties under no-tillage system (NT) is required for the adoption and maintenance of a sustainable soil management system. The aims of this study were to quantify soil bulk density (BD), porosity in the soil macropore domain (PORp) and in the soil matrix domain (PORm), air capacity in the soil matrix (ACm), field capacity (FC), and soil water storage capacity (FC/TP) in the row (R), interrow (IR), and intermediate position between R and IR (designated IP) in the 0.0-0.10 and 0.10-0.20 m soil layers under NT; and to verify if these soil properties have systematic variation in sampling positions related to rows and interrows of corn. Soil sampling was carried out in transect perpendicular to the corn rows in which 40 sampling points were selected at each position (R, IR, IP) and in each soil layer, obtaining undisturbed samples to determine the aforementioned soil physical properties. The influence of sampling position on systematic variation of soil physical properties was evaluated by spectral analysis. In the 0.0-0.1 m layer, tilling the crop rows at the time of planting led to differences in BD, PORp, ACm, FC and FC/TP only in the R position. In the R position, the FC/TP ratio was considered close to ideal (0.66), indicating good water and air availability at this sampling position. The R position also showed BD values lower than the critical bulk density that restricts root growth, suggesting good soil physical conditions for seed germination and plant establishment. Spectral analysis indicated that there was systematic variation in soil physical properties evaluated in the 0.0-0.1 m layer, except for PORm. These results indicated that the soil physical properties evaluated in the 0.0-0.1 m layer were associated with soil position in the rows and interrows of corn. Thus, proper assessment of soil physical properties under NT must take into consideration the sampling positions and previous location of crop rows and interrows.

Diffusion Spectrum Imaging after stroke shows structural changes in the contra-lateral motor network correlating with functional recovery

There is growing interest in understanding the role of the non-injured contra-lateral hemisphere in stroke recovery. In the experimental field, histological evidence has been reported that structural changes occur in the contra-lateral connectivity and circuits during stroke recovery. In humans, some recent imaging studies indicated that contra-lateral sub-cortical pathways and functional and structural cortical networks are remodeling, after stroke. Structural changes in the contra-lateral networks, however, have never been correlated to clinical recovery in patients. To determine the importance of the contra-lateral structural changes in post-stroke recovery, we selected a population of patients with motor deficits after stroke affecting the motor cortex and/or sub-cortical motor white matter. We explored i) the presence of Generalized Fractional Anisotropy (GFA) changes indicating structural alterations in the motor network of patientsâeuro? contra-lateral hemisphere as well as their longitudinal evolution ii) the correlation of GFA changes with patientsâeuro? clinical scores, stroke size and demographics data iii) and a predictive model.

Extraction and concentration of vapors from fire debris for forensic purposes: evaluation of the use of Radiello Passive Air Sampler

The Radiello Passive Air Sampler is one of the latest innovations developed for the sampling of pollutants in the air by passive headspace. It has been reported that its properties allow an enhanced sensitivity, reproducibility and adsorption capacity. It therefore appears to be of interest in the extraction of potential residues of ignitable liquids present in fire debris when arson is suspected. A theoretical approach and several laboratory tests have made it possible to precisely characterize in a forensic perspective the potential of the device in extracting and concentrating the vapors of ignitable liquids found in fire debris. Despite some advantages, the Radiello device appears to be less efficient than traditional axial symmetry samplers.

Evaluation of the RapidAir 457 Air Void Analyzer, March 2012

An adequate air void system is imperative to produce concrete with freeze-thaw durability in a wet freeze environment such as found in Iowa. Specifications rely on a percentage of air obtained in the plastic state by the pressure meter. Actual, in place air contents, of some concrete pavements in Iowa, have been found with reduced air content due to a number of factors such as excessive vibration and inadequate mixing. Determining hardened air void parameters is a time consuming process involving potential for human error. The RapidAir 457 air void analyzer is an automated device used to determine hardened air void parameters. The device is used in Europe and has been shown to quickly produce accurate and repeatable hardened air results. This research investigates how well the RapidAir 457 results correlate to plastic air content and the image analysis air technique. The repeatability and operator variation were also investigated, as well as, the impact of aggregate porosity and selection of threshold value on hardened air results.

Reelin regulates the development and synaptogenesis of the layer-specific entorhino-hippocampal connections

Here we examine the role of Reelin, an extracellular protein involved in neuronal migration, in the formation of hippocampal connections. Both at prenatal and postnatal stages, the general laminar and topographic distribution of entorhinal projections is preserved in the hippocampus of reeler mutant mice, in the absence of Reelin. However, developing and adult entorhinal afferents show severe alterations, including increased numbers of misrouted fibers and the formation of abnormal patches of termination from the medial and lateral entorhinal cortices. At perinatal stages, single entorhinal axons in reeler mice are grouped into thick bundles, and they have decreased axonal branching and decreased extension of axon collaterals. We also show that the number of entorhino-hippocampal synapses is lower in reeler mice than in control animals during development. Studies performed in mixed entorhino-hippocampal co-cultures combining slices from reeler and wild-type mice indicate that these abnormalities are caused by the lack of Reelin in the target hippocampus. These findings imply that Reelin fulfills a modulatory role during the formation of layer-specific and topographic connections in the hippocampus. They also suggest that Reelin promotes maturation of single fibers and synaptogenesis by entorhinal afferents.