Simple model for nonexponential relaxation in complex fluids

The nonexponential relaxation occurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in any time scale becomes apparent in an effective temperature field, which leads to a hierarchy of relaxation times responsible for the slow relaxation phenomena.

Percolation transition and the onset of nonexponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in two and three dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the large scale effects of frustration, present below the percolation threshold. Moreover, these results are consistent with the picture suggested by Campbell et al. [J. Phys. C 20, L47 (1987)] in the space of configurations.

Relaxation dynamics in suspensions of ferromagnetic particles

We have studied the relaxation dynamics of a dilute assembly of ferromagnetic particles in suspension. A formalism based on the Smoluchowski equation, describing the evolution of the probability density for the directions of the magnetic moment and of the axis of easy magnetization of the particles, has been developed. We compute the rotational viscosity from a Green-Kubo formula and give an expression for the relaxation time of the particles which comes from the dynamic equations of the correlation functions. Concerning the relaxation time for the particles, our results agree quite well with experiments performed on different samples of ferromagnetic particles for which the magnetic energy, associated with the interaction between the magnetic moments and the external field, or the energy of anisotropy plays a dominant role.

EFFECT OF SOIL TILLAGE AND PLANT RESIDUE ON SURFACE ROUGHNESS OF AN OXISOL UNDER SIMULATED RAIN

Surface roughness of the soil is formed by mechanical tillage and is also influenced by the kind and amount of plant residue, among other factors. Its persistence over time mainly depends on the fundamental characteristics of rain and soil type. However, few studies have been developed to evaluate these factors in Latossolos (Oxisols). In this study, we evaluated the effect of soil tillage and of amounts of plant residue on surface roughness of an Oxisol under simulated rain. Treatments consisted of the combination of the tillage systems of no-tillage (NT), conventional tillage (CT), and minimum tillage (MT) with rates of plant residue of 0, 1, and 2 Mg ha-1 of oats (Avena strigosa Schreb) and 0, 3, and 6 Mg ha-1 of maize (Zea mays L.). Seven simulated rains were applied on each experimental plot, with intensity of 60±2 mm h-1 and duration of 1 h at weekly intervals. The values of the random roughness index ranged from 2.94 to 17.71 mm in oats, and from 5.91 to 20.37 mm in maize, showing that CT and MT are effective in increasing soil surface roughness. It was seen that soil tillage operations carried out with the chisel plow and the leveling disk harrow are more effective in increasing soil roughness than those carried out with the heavy disk harrow and leveling disk harrow. The roughness index of the soil surface decreases exponentially with the increase in the rainfall volume applied under conditions of no tillage without soil cover, conventional tillage, and minimum tillage. The oat and maize crop residue present on the soil surface is effective in maintaining the roughness of the soil surface under no-tillage.

Magnetic relaxation of a one-dimensional model for small particle systems with dipolar interactions: Monte Carlo simulation

Atribution as a function of the time are analyzed and this study leads to a deeper knowledge of the microscopic processes involved in the magnetic relaxation

Computational calculations of magnetic relaxation and viscosity in small magnetic grains

In this article we present a phenomenological model which simulates very well the mag¿ netic relaxation behavior experimentally observed in small magnetic grains and single domain particles. In this model, the occurrence of quantum tunneling of magnetization below a certain temperature is taken into account. Experimental results for different materials are presented to illustrate the most important behavior deduced from our model

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.

Magnetic field scaling of relaxation curves in small particle systems

We study the effects of the magnetic field on the relaxation of the magnetization of smallmonodomain noninteracting particles with random orientations and distribution of anisotropyconstants. Starting from a master equation, we build up an expression for the time dependence of themagnetization which takes into account thermal activation only over barriers separating energyminima, which, in our model, can be computed exactly from analytical expressions. Numericalcalculations of the relaxation curves for different distribution widths, and under different magneticfields H and temperatures T, have been performed. We show how a T ln(t/t0) scaling of the curves,at different T and for a given H, can be carried out after proper normalization of the data to theequilibrium magnetization. The resulting master curves are shown to be closely related to what wecall effective energy barrier distributions, which, in our model, can be computed exactly fromanalytical expressions. The concept of effective distribution serves us as a basis for finding a scalingvariable to scale relaxation curves at different H and a given T, thus showing that the fielddependence of energy barriers can be also extracted from relaxation measurements.

SOIL PHOSPHORUS THRESHOLDS IN EVALUATING RISK OF ENVIRONMENTAL TRANSFER TO SURFACE WATERS IN SANTA CATARINA, BRAZIL

The State of Santa Catarina, Brazil, has agricultural and livestock activities, such as pig farming, that are responsible for adding large amounts of phosphorus (P) to soils. However, a method is required to evaluate the environmental risk of these high soil P levels. One possible method for evaluating the environmental risk of P fertilization, whether organic or mineral, is to establish threshold levels of soil available P, measured by Mehlich-1 extractions, below which there is not a high risk of P transfer from the soil to surface waters. However, the Mehlich-1 extractant is sensitive to soil clay content, and that factor should be considered when establishing such P-thresholds. The objective of this study was to determine P-thresholds using the Mehlich-1 extractant for soils with different clay contents in the State of Santa Catarina, Brazil. Soil from the B-horizon of an Oxisol with 800 g kg-1 clay was mixed with different amounts of sand to prepare artificial soils with 200, 400, 600, and 800 g kg-1 clay. The artificial soils were incubated for 30 days with moisture content at 80 % of field capacity to stabilize their physicochemical properties, followed by additional incubation for 30 days after liming to raise the pH(H2O) to 6.0. Soil P sorption curves were produced, and the maximum sorption (Pmax) was determined using the Langmuir model for each soil texture evaluated. Based on the Pmax values, seven rates of P were added to four replicates of each soil, and incubated for 20 days more. Following incubation, available P contents (P-Mehlich-1) and P dissolved in the soil solution (P-water) were determined. A change-point value (the P-Mehlich-1 value above which P-water starts increasing sharply) was calculated through the use of segmented equations. The maximum level of P that a soil might safely adsorb (P-threshold) was defined as 80 % of the change-point value to maintain a margin for environmental safety. The P-threshold value, in mg dm-3, was dependent on the soil clay content according to the model P-threshold = 40 + Clay, where the soil clay content is expressed as a percentage. The model was tested in 82 diverse soil samples from the State of Santa Catarina and was able to distinguish samples with high and low environmental risk.

Surface Complexation Modeling in Variable Charge Soils: Charge Characterization by Potentiometric Titration

ABSTRACT Intrinsic equilibrium constants of 17 representative Brazilian Oxisols were estimated from potentiometric titration measuring the adsorption of H+ and OH− on amphoteric surfaces in suspensions of varying ionic strength. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. The former was fitted by calculating total site concentration from curve fitting estimates and pH-extrapolation of the intrinsic equilibrium constants to the PZNPC (hand calculation), considering one and two reactive sites, and by the FITEQL software. The latter was fitted only by FITEQL, with one reactive site. Soil chemical and physical properties were correlated to the intrinsic equilibrium constants. Both surface complexation models satisfactorily fit our experimental data, but for results at low ionic strength, optimization did not converge in FITEQL. Data were incorporated in Visual MINTEQ and they provide a modeling system that can predict protonation-dissociation reactions in the soil surface under changing environmental conditions.

Surface Complexation Modeling in Variable Charge Soils: Prediction of Cadmium Adsorption

ABSTRACT Intrinsic equilibrium constants for 22 representative Brazilian Oxisols were estimated from a cadmium adsorption experiment. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. Intrinsic equilibrium constants were optimized by FITEQL and by hand calculation using Visual MINTEQ in sweep mode, and Excel spreadsheets. Data from both models were incorporated into Visual MINTEQ. Constants estimated by FITEQL and incorporated in Visual MINTEQ software failed to predict observed data accurately. However, FITEQL raw output data rendered good results when predicted values were directly compared with observed values, instead of incorporating the estimated constants into Visual MINTEQ. Intrinsic equilibrium constants optimized by hand calculation and incorporated in Visual MINTEQ reliably predicted Cd adsorption reactions on soil surfaces under changing environmental conditions.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.