Drift causes anomalous exponents in growth processes

The effect of a drift term in the presence of fixed boundaries is studied for the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism that causes a change of exponents for a very broad class of growth processes. This mechanism represents a relevant perturbation and therefore is important for the interpretation of experimental and numerical results. In effect, the mechanism leads to the roughness exponent assuming the same value as the growth exponent. In the case of the Edwards-Wilkinson equation this implies exponents deviating from those expected by dimensional analysis.Comment: 4 pages, 1 figure, REVTeX; accepted for publication in PRL; added note and reference

Enhanced effects from tiny flexible in-wall blips and shear flow

Fluid motion at high Reynolds number over a flexible in-wall blip (a compliant bump or dip in an otherwise fixed wall) is considered theoretically for a very short blip buried low inside a boundary layer. Only the near-wall shear of the oncoming flow affects the local motion past the tiny blip. Slowly evolving features are examined first to allow for variations in the incident flow. Linear and nonlinear solutions show that at certain parameter values (eigenvalues) intensifications occur in which the interactive effect on flow and blip shape is larger by an order of magnitude than at most parameter values. Similar findings apply to the boundary layer with several tiny blips present or to channel flows with blips of almost any length. These intensifications lead on to fully nonlinear unsteady motion as a second stage, after some delay, thus combining with finite-time breakups to form a distinct path into transition of the flow

Critical Behaviour of the Drossel-Schwabl Forest Fire Model

We present high statistics Monte Carlo results for the Drossel-Schwabl forest fire model in 2 dimensions. They extend to much larger lattices (up to $65536\times 65536$) than previous simulations and reach much closer to the critical point (up to $\theta \equiv p/f = 256000$). They are incompatible with all previous conjectures for the (extrapolated) critical behaviour, although they in general agree well with previous simulations wherever they can be directly compared. Instead, they suggest that scaling laws observed in previous simulations are spurious, and that the density $\rho$ of trees in the critical state was grossly underestimated. While previous simulations gave $\rho\approx 0.408$, we conjecture that $\rho$ actually is equal to the critical threshold $p_c = 0.592...$ for site percolation in $d=2$. This is however still far from the densities reachable with present day computers, and we estimate that we would need many orders of magnitude higher CPU times and storage capacities to reach the true critical behaviour -- which might or might not be that of ordinary percolation.Comment: 8 pages, including 9 figures, RevTe

Does No-Tillage Mitigate Stover Removal in Irrigated Continuous Corn? A Multi-Location Assessment

No-tillage (NT) may ameliorate negative effects on soil properties from corn (Zea mays L.) stover harvest, but few long-term irrigated continuous corn production systems have been evaluated to test this hypothesis. We evaluated three long-term no-tillage sites (4–13 yr) in Nebraska and Colorado that spanned a range of precipitation and soil organic carbon (SOC) levels. We measured SOC, d13C of SOC, soil microbial biomass (SMB) and composition (i.e., phospholipid fatty acids, PLFAs), and water stable aggregation at all sites under stover retention vs. removal (~60%). Surface SOC stocks (0–30- cm depth) increased across the gradient and were 46.4, 57.4, and 63.1 Mg C ha–1 for Colorado, central Nebraska, and eastern Nebraska, respectively. Overall, residue removal decreased SOC stocks by 6% and soil aggregation by 12% in the 0- to 30-cm depth. The d13C signature of SOC indicated less new surface C storage under residue removal in Colorado, but not at the two Nebraska sites. Residue harvest did not decrease SMB or change soil microbial community structure, suggesting that high plant productivity buffered community composition from stover harvest impacts under NT but stimulated microbial activity levels that led to SOC loss. The high rates of stover removal used in this study decreased SOC stocks and aggregation at all sites compared to residue retained treatments, suggesting that no-tillage alone was not sufficient to maintain erosion protection and soil function

Abelian Manna model on various lattices in one and two dimensions

We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish universality of exponents and moment ratios across different lattices and a good survey for the strength of corrections to scaling which are notorious in the Manna universality class. The results are compared against previous work done on Manna model, Oslo model and directed percolation. We also confirm hypothesis of various scaling relations.Comment: 16 pages, 3 figures, 7 tables, submitted to Journal of Statistical Mechanic

The origin of power-law distributions in self-organized criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in J. Phys.

A field-theoretic approach to the Wiener Sausage

The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a single loop renormalised perturbation theory of a stochastic process closely related to the Wiener Sausage, which, however, proves to be exact for the exponents and some amplitudes. The field-theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem. While we recover a number of known, classical results, the field-theoretic techniques deployed provide a particularly versatile framework, which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions. At the same time, we provide a highly instructive, non-trivial example for some of the technical particularities of the field-theoretic description of stochastic processes, such as excluded volume, lack of translational invariance and immobile particles. The aim of the present work is not to improve upon the well-established results for the Wiener Sausage, but to provide a field-theoretic approach to it, in order to gain a better understanding of the field-theoretic obstacles to overcome.Comment: 45 pages, 3 Figures, Springer styl

Self-organization without conservation: Are neuronal avalanches generically critical?

Recent experiments on cortical neural networks have revealed the existence of well-defined avalanches of electrical activity. Such avalanches have been claimed to be generically scale-invariant -- i.e. power-law distributed -- with many exciting implications in Neuroscience. Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel to justify such an empirical finding. Given that (i) neural dynamics is dissipative and (ii) there is a loading mechanism "charging" progressively the background synaptic strength, this model/dynamics is very similar in spirit to forest-fire and earthquake models, archetypical examples of non-conserving self-organization, which have been recently shown to lack true criticality. Here we show that cortical neural networks obeying (i) and (ii) are not generically critical; unless parameters are fine tuned, their dynamics is either sub- or super-critical, even if the pseudo-critical region is relatively broad. This conclusion seems to be in agreement with the most recent experimental observations. The main implication of our work is that, if future experimental research on cortical networks were to support that truly critical avalanches are the norm and not the exception, then one should look for more elaborate (adaptive/evolutionary) explanations, beyond simple self-organization, to account for this.Comment: 28 pages, 11 figures, regular pape

Salience versus magnitude in the measurement of the cortisol awakening response

Pulsatile ultradian secretion of cortisol, rarely studied in salivary data, has functional importance in hypothalamic pituitary adrenal (HPA) axis regulation. The first daily ultradian episode, the cortisol awakening response (CAR), was examined in healthy adults, in 5-min secretion rates of salivary cortisol from electronically monitored awakening time to 1.25 h. Aggregated rates revealed a cubic trend, with wave-length of almost exactly 1 h, as predicted from known ultradian periodicity. Peak secretion rate occurred 20-min post-awakening. Peak (20-min) to trough (59-min) amplitude (PTA) expressed a salient signal shape. Rates rose steeply to and from peak, and major secretion was packaged into a few 5-min intervals, inconsistent with normal or uniform distribution of 5-min rates, but consistent with known pulsatile cortisol delivery. Null hypotheses asserting normal or uniform distributions were rejected. Maximal rates overwhelmingly occurred before and minimal rates after 30-mins, with degree of extremity at each polarity significantly positively correlated. To demonstrate utility and reliability of PTA estimation in a clinically relevant domain, re- analyses of a previously published study were conducted. Data from only three saliva samples were used, given importance of cost considerations for many CAR researchers. Difference between mean rates before and after 30-min yielded a simple salience index, highly correlated with PTA derived from full 5-min interval data. CAR salience performed significantly better than traditional AUCi magnitude in discriminating control cases (higher inferred amplitude) and cases with Seasonal Affective Disorder (lower inferred amplitude). Evidence suggested that low AUCi may be more sensitive in identifying within-subject changes (e.g. more depressed mood in winter among SAD cases) and low CAR salience better at revealing enduring between-subjects associations (e.g. underlying disorder vulnerability). Since both PTA salience and AUCi magnitude can be analysed and compared using exactly the same data from the same commonly used saliva sampling points, further research is warranted into the importance of individual differences in patterns of cortisol delivery, not just how much is delivered

Seasonal switchgrass ecotype contributions to soil organic carbon, deep soil microbial community composition and rhizodeposit uptake during an extreme drought

The importance of rhizodeposit C and associated microbial communities in deep soil C stabilization is relatively unknown. Phenotypic variability in plant root biomass could impact C cycling through belowground plant allocation, rooting architecture, and microbial community abundance and composition. We used a pulse-chase 13C labeling experiment with compound-specific stable-isotope probing to investigate the importance of rhizodeposit C to deep soil microbial biomass under two switchgrass ecotypes (Panicum virgatum L., Kanlow and Summer) with contrasting root morphology. We quantified root phenology, soil microbial biomass (phospholipid fatty acids, PLFA), and microbial rhizodeposit uptake (13C-PLFAs) to 150 cm over one year during a severe drought. The lowland ecotype, Kanlow, had two times more root biomass with a coarser root system compared to the upland ecotype, Summer. Over the drought, Kanlow lost 78% of its root biomass, while Summer lost only 60%. Rhizosphere microbial communities associated with both ecotypes were similar. However, rhizodeposit uptake under Kanlow had a higher relative abundance of gram-negative bacteria (44.1%), and Summer rhizodeposit uptake was primarily in saprotrophic fungi (48.5%). Both microbial community composition and rhizodeposit uptake shifted over the drought into gram-positive communities. Rhizosphere soil C was greater one year later under Kanlow due to turnover of unlabeled structural root C. Despite a much greater root biomass under Kanlow, rhizosphere δ13C was not significantly different between the two ecotypes, suggesting greater microbial C input under the finer rooted species, Summer, whose microbial associations were predominately saprotrophic fungi. Ecotype specific microbial communities can direct rhizodeposit C flow and C accrual deep in the soil profile and illustrate the importance of the microbial community in plant strategies to survive environmental stress such as drought