Biogenic calcium phosphate transformation in soils over millennial time scales

Changes in bioavailability of phosphorus (P) during pedogenesis and ecosystem development have been shown for geogenic calcium phosphate (Ca-P). However, very little is known about long-term changes of biogenic Ca-P in soil. Long-term transformation characteristics of biogenic Ca-P were examined using anthropogenic soils along a chronosequence from centennial to millennial time scales. Phosphorus fractionation of Anthrosols resulted in overall consistency with the Walker and Syers model of geogenic Ca-P transformation during pedogenesis. The biogenic Ca-P (e.g., animal and fish bones) disappeared to 3% of total P within the first ca. 2,000 years of soil development. This change concurred with increases in P adsorbed on metal-oxides surfaces, organic P, and occluded P at different pedogenic time. Phosphorus K-edge X-ray absorption near-edge structure (XANES) spectroscopy revealed that the crystalline and therefore thermodynamically most stable biogenic Ca-P was transformed into more soluble forms of Ca-P over time. While crystalline hydroxyapatite (34% of total P) dominated Ca-P species after about 600-1,000 years, beta-tricalcium phosphate increased to 16% of total P after 900-1,100 years, after which both Ca-P species disappeared. Iron-associated P was observable concurrently with Ca-P disappearance. Soluble P and organic P determined by XANES maintained relatively constant (58-65%) across the time scale studied. Disappearance of crystalline biogenic Ca-P on a time scale of a few thousand years appears to be ten times faster than that of geogenic Ca-P.

Measure functional differential equations and functional dynamic equations on time scales

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.

On Fermat's principle for causal curves in time oriented Finsler spacetimes

In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the second variation of the time arrival functional along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765066]

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

Macrofaunal succession in sediments around kelp and wood falls in the deep NE Pacific and community overlap with other reducing habitats

Sunken parcels of macroalgae and wood provide important oases of organic enrichment at the deep-sea floor, yet sediment community structure and succession around these habitat islands are poorly evaluated. We experimentally implanted 100-kg kelp falls and 200 kg wood falls at 1670 m depth in the Santa Cruz Basin to investigate (1) macrofaunal succession and (2) species overlap with nearby whale-fall and cold-seep communities over time scales of 0.25-5.5 yr. The abundance of infaunal macrobenthos was highly elevated after 0.25 and 0.5 yr near kelp parcels with decreased macrofaunal diversity and evenness within 0.5 m of the falls. Apparently opportunistic species (e.g., two new species of cumaceans) and sulfide tolerant microbial grazers (dorvilleid polychaetes) abounded after 0.25-0.5 yr. At wood falls, opportunistic cumaceans become abundant after 0.5 yr, but sulfide tolerant species only became abundant after 1.8-5.5 yr, in accordance with the much slower buildup of porewater sulfides at wood parcels compared with kelp falls. Species diversity decreased significantly over time in sediments adjacent to the wood parcels, most likely due to stress resulting from intense organic loading of nearby sediments (up to 20-30% organic carbon). Dorvilleid and ampharetid polychaetes were among the top-ranked fauna at wood parcels after 3.0-5.5 yr. Sediments around kelp and wood parcels provided low-intensity reducing conditions that sustain a limited chemoautrotrophically-based fauna. As a result, macrobenthic species overlap among kelp, wood, and other chemosynthetic habitats in the deep NE Pacific are primarily restricted to apparently sulfide tolerant species such as dorvilleid polychaetes, opportunistic cumaceans, and juvenile stages of chemosymbiont containing vesicomyid bivalves. We conclude that organically enriched sediments around wood falls may provide important habitat islands for the persistence and evolution of species dependent on organic- and sulfide-rich conditions at the deep-sea floor and contribute to beta and gamma diversity in deep-sea ecosystems. (C) 2010 Elsevier Ltd. All rights reserved.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Perfomance of methods for estimating reference evapotranspiration in the municipalities of Frederico Westphalen and Palmeira das Missoes, State of Rio Grande do Sul, Brazil

The estimation of reference evapotranspiration (ETo), used in water balance, allows to determine soil water content, assisting on irrigation management. The present study aimed to compare simple ETo estimating methods with the Penman-Monteith (FAO), in the folowing time scales: daily, 5, 10, 15 and 30 days and monthly in the counties of Frederico Westphalen and Palmeira das Missoes, in the Rio Grande do Sul state, Brazil. The methods tested had their efficiency improved by increasing the time scale of analysis, keeping the same performance for both locations. The highest and lowest ETo values occurred in December and June, respectively. Most methods underestimated ETo. For any of the time scales Makking and Radiaton FAO24 methods can replace the Penman-Monteith for estimating ETo.

Non-mean-field effects in systems with long-range forces in competition

We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Atomistic Study of Water Confined in Silica.

In this work, we have used a combined of atomistic simulation methods to explore the effects of confinement of water molecules between silica surfaces. Firstly, the mechanical properties of water severe confined (~3A) between two silica alpha-quartz was determined based on first principles calculations within the density functional theory (DFT). Simulated annealing methods were employed due to the complex potential energry surface, and the difficulties to avoid local minima. Our results suggest that much of the stiffness of the material (46%) remains, even after the insertion of a water monolayer in the silica. Secondly, in order to access typical time scales for confined systems, classical molecular dynamics was used to determine the dynamical properties of water confined in silica cylindrical pores, with diameters varying from 10 to 40A. in this case we have varied the passivation of the silica surface, from 13% to 100% of SiOH, and the other terminations being SiOH2 and SiOH3, the distribution of the different terminations was obtained with a Monte Carlo simulation. The simulations indicates a lowering of the diffusion coefficientes as the diameter decreases, due to the structuration of hydrogen bonds of water molecules; we have also obtained the density profiles of the confined water and the interfacial tension.