Brownian motion in short range random potentials

A numerical study of Brownian motion of noninteracting particles in random potentials is presented. The dynamics are modeled by Langevin equations in the high friction limit. The random potentials are Gaussian distributed and short ranged. The simulations are performed in one and two dimensions. Different dynamical regimes are found and explained. Effective subdiffusive exponents are obtained and commented on.

An analytical approach to sorting in periodic and random potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

Pedotransfer functions to estimate retention and availability of water in soils of the state of Santa Catarina, Brazil

Studies on water retention and availability are scarce for subtropical or humid temperate climate regions of the southern hemisphere. The aims of this study were to evaluate the relations of the soil physical, chemical, and mineralogical properties with water retention and availability for the generation and validation of continuous point pedotransfer functions (PTFs) for soils of the State of Santa Catarina (SC) in the South of Brazil. Horizons of 44 profiles were sampled in areas under different cover crops and regions of SC, to determine: field capacity (FC, 10 kPa), permanent wilting point (PWP, 1,500 kPa), available water content (AW, by difference), saturated hydraulic conductivity, bulk density, aggregate stability, particle size distribution (seven classes), organic matter content, and particle density. Chemical and mineralogical properties were obtained from the literature. Spearman's rank correlation analysis and path analysis were used in the statistical analyses. The point PTFs for estimation of FC, PWP and AW were generated for the soil surface and subsurface through multiple regression analysis, followed by robust regression analysis, using two sets of predictive variables. Soils with finer texture and/or greater organic matter content retain more moisture, and organic matter is the property that mainly controls the water availability to plants in soil surface horizons. Path analysis was useful in understanding the relationships between soil properties for FC, PWP and AW. The predictive power of the generated PTFs to estimate FC and PWP was good for all horizons, while AW was best estimated by more complex models with better prediction for the surface horizons of soils in Santa Catarina.

Silicate fertilization of tropical soils: silicon availability and recovery index of sugarcane

Sugarcane is considered a Si-accumulating plant, but in Brazil, where several soil types are used for cultivation, there is little information about silicon (Si) fertilization. The objectives of this study were to evaluate the silicon availability, uptake and recovery index of Si from the applied silicate on tropical soils with and without silicate fertilization, in three crops. The experiments in pots (100 L) were performed with specific Si rates (0, 185, 370 and 555 kg ha-1 Si), three soils (Quartzipsamment-Q, 6 % clay; Rhodic Hapludox-RH, 22 % clay; and Rhodic Acrudox-RA, 68 % clay), with four replications. The silicon source was Ca-Mg silicate. The same Ca and Mg quantities were applied to all pots, with lime and/or MgCl2, when necessary. Sugarcane was harvested in the plant cane and first- and second-ratoon crops. The silicon rates increased soil Si availability and Si uptake by sugarcane and had a strong residual effect. The contents of soluble Si were reduced by harvesting and increased with silicate application in the following decreasing order: Q>RH>RA. The silicate rates promoted an increase in soluble Si-acetic acid at harvest for all crops and in all soils, except RA. The amounts of Si-CaCl2 were not influenced by silicate in the ratoon crops. The plant Si uptake increased according to the Si rates and was highest in RA at all harvests. The recovery index of applied Si (RI) of sugarcane increased over time, and was highest in RA.

Adding functionalities to precomputed holograms with random mask multiplexing in holographic optical tweezers

In this study, we present a method designed to generate dynamic holograms in holographic optical tweezers. The approach combines our random mask encoding method with iterative high-efficiency algorithms. This hybrid method can be used to dynamically modify precalculated holograms, giving them new functionalities¿temporarily or permanently¿with a low computational cost. This allows the easy addition or removal of a single trap or the independent control of groups of traps for manipulating a variety of rigid structures in real time.

Phosphorus availability in oxidic soils treated with lime and silicate applications

Based on the assumption that silicate application can raise soil P availability for crops, the aim of this research was to compare the effect of silicate application on soil P desorption with that of liming, in evaluations based on two extractors and plant growth. The experiment was carried out in randomized blocks with four replications, in a 3 × 3 × 5 factorial design, in which three soil types, three P rates, and four soil acidity correctives were evaluated in 180 experimental plots. Trials were performed in a greenhouse using corn plants in 20-dm³ pots. Three P rates (0, 50 and 150 mg dm-3) were applied in the form of powder triple superphosphate and the soil was incubated for 90 days. After this period, soil samples were collected for routine chemical analysis and P content determination by the extraction methods resin, Mehlich-1 and remaining P. Based on the results, acidity correctives were applied at rates calculated for base saturation increased to 70 %, with subsequent incubation for 60 more days, when P content was determined again. The acidity correctives consisted of: dolomitic lime, steelmaking slag, ladle furnace slag, and wollastonite. Therefore, our results showed that slags raised the soil P content more than lime, suggesting a positive correlation between P and Si in soil. Silicon did not affect the extractor choice since both Mehlich-1 and resin had the same behavior regarding extracted P when silicon was applied to the soil. For all evaluated plant parameters, there was significant interaction between P rates and correctives; highest values were obtained with silicate.

Soil phosphorus availability and soybean response to phosphorus starter fertilizer

Phosphorus fixation in tropical soils may decrease under no-till. In this case, P fertilizer could be surface-spread, which would improve farm operations by decreasing the time spend in reloading the planter with fertilizers. In the long term, less soluble P sources could be viable. In this experiment, the effect of surface-broadcast P fertilization with both soluble and reactive phosphates on soil P forms and availability to soybean was studied with or without fertilization with soluble P in the planting furrow in a long-term experiment in which soybean was grown in rotation with Ruzigrass (Brachiaria ruziziensis). No P or 80 kg ha-1 of P2O5 in the form of triple superphosphate or Arad reactive rock phosphate was applied on the surface of a soil with variable P fertilization history. Soil samples were taken to a depth of 60 cm and soil P was fractionated. Soybean was grown with 0, 30, and 60 kg ha-1 of P2O5 in the form of triple phosphate applied in the seed furrow. Both fertilizers applied increased available P in the uppermost soil layers and the moderately labile organic and inorganic forms of P in the soil profile, probably as result of root decay. Soybean responded to phosphates applied on the soil surface or in the seed furrow; however, application of soluble P in the seed furrow should not be discarded. In tropical soils with a history of P fertilization, soluble P sources may be substituted for natural reactive phosphates broadcast on the surface. The planting operation may be facilitated through reduction in the rate of P applied in the planting furrow in relation to the rates currently applied.

Solvable dynamics in a system of interacting random tops

A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an explicit study of orientational effects in synchronization phenomena as well as nonlinear processes in resonance phenomena in strongly coupled magnetic systems. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with orientational disorder always synchronizes in the absence of noise.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Continuous-time random-walk model for financial distributions

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollardeutsche mark future exchange, finding good agreement between theory and the observed data.

Tuning clustering in random networks with arbitrary degree distributions

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

Occupancy of a single site by many random walkers

We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin, which is unoccupied. The random-walk model is taken to be a continuous-time random walk and the pausing-time density at the target site is allowed to differ from the pausing-time density at other sites. We calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time T. We also find the variance for the cumulative time during which the site is unoccupied. The large-T behavior of the variance differs according as the random walk is transient or recurrent. It is shown that the variance is proportional to T at large T in three or more dimensions, it is proportional to T3/2 in one dimension and to TlnT in two dimensions.

Synchronization, diversity, and topology of networks of integrate and fire oscillators

We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention on the interplay between topological disorder and synchronization features of networks. First, we analyze synchronization time T in random networks, and find a scaling law which relates T to network connectivity. Then, we compare synchronization time for several other topological configurations, characterized by a different degree of randomness. The analysis shows that regular lattices perform better than a disordered network. This fact can be understood by considering the variability in the number of links between two adjacent neighbors. This phenomenon is equivalent to having a nonrandom topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings.