Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

The first real-time worldwide ionospheric predictions network: an advance in support of spaceborne experimentation, on-line model validation, and space weather

We report on the first realtime ionospheric predictions network and its capabilities to ingest a global database and forecast F-layer characteristics and "in situ" electron densities along the track of an orbiting spacecraft. A global network of ionosonde stations reported around-the-clock observations of F-region heights and densities, and an on-line library of models provided forecasting capabilities. Each model was tested against the incoming data; relative accuracies were intercompared to determine the best overall fit to the prevailing conditions; and the best-fit model was used to predict ionospheric conditions on an orbit-to-orbit basis for the 12-hour period following a twice-daily model test and validation procedure. It was found that the best-fit model often provided averaged (i.e., climatologically-based) accuracies better than 5% in predicting the heights and critical frequencies of the F-region peaks in the latitudinal domain of the TSS-1R flight path. There was a sharp contrast however, in model-measurement comparisons involving predictions of actual, unaveraged, along-track densities at the 295 km orbital altitude of TSS-1R In this case, extrema in the first-principle models varied by as much as an order of magnitude in density predictions, and the best-fit models were found to disagree with the "in situ" observations of Ne by as much as 140%. The discrepancies are interpreted as a manifestation of difficulties in accurately and self-consistently modeling the external controls of solar and magnetospheric inputs and the spatial and temporal variabilities in electric fields, thermospheric winds, plasmaspheric fluxes, and chemistry.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

Control of flowering time in temperate cereals: genes, domestication, and sustainable productivity

The control of flowering is central to reproductive success in plants, and has a major impact on grain yield in crop species. The global importance of temperate cereal crops such as wheat and barley has meant emphasis has long been placed on understanding the genetics of flowering in order to enhance yield. Leads gained from the dissection of the molecular genetics of model species have combined with comparative genetic approaches, recently resulting in the isolation of the first flowering time genes in wheat and barley. This paper reviews the genetics and genes involved in cereal flowering pathways and the current understanding of how two of the principal genes, Vrn and Ppd, have been involved in domestication and adaptation to local environments, and the implications for future breeding programmes are discussed.

Sudden stratospheric warmings as noise-induced transitions

Sudden stratospheric warmings (SSWs) are usually considered to be initiated by planetary wave activity. Here it is asked whether small-scale variability (e.g., related to gravity waves) can lead to SSWs given a certain amount of planetary wave activity that is by itself not sufficient to cause a SSW. A highly vertically truncated version of the Holton–Mass model of stratospheric wave–mean flow interaction, recently proposed by Ruzmaikin et al., is extended to include stochastic forcing. In the deterministic setting, this low-order model exhibits multiple stable equilibria corresponding to the undisturbed vortex and SSW state, respectively. Momentum forcing due to quasi-random gravity wave activity is introduced as an additive noise term in the zonal momentum equation. Two distinct approaches are pursued to study the stochastic system. First, the system, initialized at the undisturbed state, is numerically integrated many times to derive statistics of first passage times of the system undergoing a transition to the SSW state. Second, the Fokker–Planck equation corresponding to the stochastic system is solved numerically to derive the stationary probability density function of the system. Both approaches show that even small to moderate strengths of the stochastic gravity wave forcing can be sufficient to cause a SSW for cases for which the deterministic system would not have predicted a SSW.

Influence of gut morphology on passive transport of freshwater bryozoans by waterfowl in Donana (southwestern Spain)

Waterbirds have been proposed as important vectors for the passive dispersal of those aquatic invertebrates and plants that lack a capacity for active dispersal between isolated water bodies. We analysed the frequency of internal transport of bryozoan propagules (statoblasts) by waterbirds in Donana, Spain, by examining their presence in the intestines and ceca of dead birds and analysing the role of different aspects of gut characteristics in explaining variation in the presence/absence and abundance of statoblasts. Of the 228 samples examined, 7.9% presented intact statoblasts of Plumatella fungosa (Pallas, 1768), Plumatella emarginata Allman, 1844, and two unidentified Plumatella species. For a given bird species, individuals with heavier gizzards and shorter ceca had a lower incidence and abundance of statoblasts in the lower gut. Grit mass and intestine length were unrelated to the presence or abundance of statoblasts. Our results suggest that waterbirds frequently transport bryozoans on a local scale, with lighter gizzards and longer ceca favouring such transport. Lighter gizzards are likely to destroy fewer propagules before they reach the lower gut. Species and individuals with longer ceca are particularly good candidates for long-distance dispersal of bryozoans, given the longer passage time of propagules that enter the ceca.

Curve crossing for the reflected Levy process at zero and infinity

Let $R_{t}=\sup_{0\leq s\leq t}X_{s}-X_{t}$ be a Levy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for $R_{t}$ is finite, is given. We also discuss the almost sure finiteness of $\limsup_{t\to 0}R_{t}/t^{\kappa}$, for each $\kappa\geq 0$.

Predicting fatty acid profiles in blood based on food intake and the FADS1 rs174546 SNP

SCOPE: A high intake of n-3 PUFA provides health benefits via changes in the n-6/n-3 ratio in blood. In addition to such dietary PUFAs, variants in the fatty acid desaturase 1 (FADS1) gene are also associated with altered PUFA profiles. METHODS AND RESULTS: We used mathematical modelling to predict levels of PUFA in whole blood, based on MHT and bolasso selected food items, anthropometric and lifestyle factors, and the rs174546 genotypes in FADS1 from 1,607 participants (Food4Me Study). The models were developed using data from the first reported time point (training set) and their predictive power was evaluated using data from the last reported time point (test set). Amongst other food items, fish, pizza, chicken and cereals were identified as being associated with the PUFA profiles. Using these food items and the rs174546 genotypes as predictors, models explained 26% to 43% of the variability in PUFA concentrations in the training set and 22% to 33% in the test set. CONCLUSIONS: Selecting food items using MHT is a valuable contribution to determine predictors, as our models' predictive power is higher compared to analogue studies. As unique feature, we additionally confirmed our models' power based on a test set.

First detection of methylgermylene in the gas phase and time-resolved study of some of its reactions

A new transient species has been produced and detected by the gas-phase, 193 nm laser flash photolysis of 1,3,4-trimethylgermacyclopent-3-ene, TMGCP. The species has strong visible absorptions in the wavelength region 450−520 nm (maximum at 485 nm) and is attributed to the germylene, MeGeH. Time-resolved kinetic studies have led to the first rate constants for its reactions with GeH4, Me2GeH2, C2H2, C2H4, C3H6, i-C4H8, TMGCP, MeOH, HCl, and SO2. The reactivity of MeGeH is compared to those of GeH2 and GeMe2. The Me-for-H substituent effect varies according to reaction type and is not constant from GeH2 to MeGeH to GeMe2.

Sustained monitoring of the Southern Ocean at Drake Passage: past achievements and future priorities

Drake Passage is the narrowest constriction of the Antarctic Circumpolar Current (ACC) in the Southern Ocean, with implications for global ocean circulation and climate. We review the long-term sustained monitoring programmes that have been conducted at Drake Passage, dating back to the early part of the twentieth century. Attention is drawn to numerous breakthroughs that have been made from these programmes, including (a) the first determinations of the complex ACC structure and early quantifications of its transport; (b) realization that the ACC transport is remarkably steady over interannual and longer periods, and a growing understanding of the processes responsible for this; (c) recognition of the role of coupled climate modes in dictating the horizontal transport, and the role of anthropogenic processes in this; (d) understanding of mechanisms driving changes in both the upper and lower limbs of the Southern Ocean overturning circulation, and their impacts. It is argued that monitoring of this passage remains a high priority for oceanographic and climate research, but that strategic improvements could be made concerning how this is conducted. In particular, long-term programmes should concentrate on delivering quantifications of key variables of direct relevance to large-scale environmental issues: in this context, the time-varying overturning circulation is, if anything, even more compelling a target than the ACC flow. Further, there is a need for better international resource-sharing, and improved spatio-temporal coordination of the measurements. If achieved, the improvements in understanding of important climatic issues deriving from Drake Passage monitoring can be sustained into the future.

Influence of time on the plant availability of Cd, Ni and Zn after sewage sludge has been applied to soils

A pot experiment was conducted to test the hypothesis that decomposition of organic matter in sewage sludge and the consequent formation of dissolved organic compounds (DOC) would lead to an increase in the bioavailability of the heavy metals. Two Brown Earth soils, one with clayey loam texture (CL) and the other a loamy sand (LS) were mixed with sewage sludge at rates equivalent to 0, 10 and 50 1 dry sludge ha(-1) and the pots were sown with ryegrass (Lolium perenne L.). The organic matter content and heavy metal availability assessed with soil extractions with 0.05 M CaCl2 were monitored over a residual time of two years, while plant uptake over one year, after addition of the sludge. It was found that the concentrations of Cd and Ni in both the ryegrass and the soil extracts increased slightly but significantly during the first year. In most cases, this increase was most evident especially at the higher sludge application rate (50 t ha(-1)). However, in the second year metal availability reached a plateau. Zinc concentrations in the ryegrass did not show an increase but the CaCl2 extracts increased during the first year. In contrast, organic matter content decreased rapidly in the first months of the first year and much more slowly in the second (total decrease of 16%). The concentrations of DOC increased significantly in the more organic rich CL soil in the course of two years. The pattern followed by the decomposition of organic matter with time and the production of DOC may provide at least a partial explanation for trend towards increased metal availability.

Quantifying time scales of pedogenic calcrete formation using U-series disequilibria

Time scales of pedogenic calcrete development are quantified by subsampling carbonate from within a mature (stage V) pedogenic calcrete profile from southeast Spain and dating the material by U-series disequilibria. The location of the earliest and latest cements can be estimated by comparing previous studies of calcrete morphological development with micromorphological analysis of the study profile. Carbonate was sampled and dated from three locations within the profile: (1) below the lower surface of clasts within the hardpan (representing the earliest cement present-207 +/- 11 ka), (2) from the centre of cement filled pores within the hardpan (reflecting the final plugging of the calcrete hardpan-155 +/- 9 ka) and (3) from the laminar calcrete overlying the hardpan (representing the latest cement-112 +/- 15 ka). These results show that the hardpan took between 73 and 31 ka to form, whilst the mature stage V profile took between 121 and 69 ka to form. This is the first time that rates of mature calcrete development have been established by direct radiometric dating of the authigenic carbonate. The technique is appropriate for dating mature calcretes in dryland regions worldwide and offers the opportunity of increasing our understanding of the spatial and temporal variability in rates of pedogenic calcrete development. (C) 2004 Elsevier B.V. All rights reserved.

The influence of time on lead toxicity and bioaccumulation determined by the OECD earthworm toxicity test

Internationally agreed standard protocols for assessing chemical toxicity of contaminants in soil to worms assume that the test soil does not need to equilibrate with the chemical to be tested prior to the addition of the test organisms and that the chemical will exert any toxic effect upon the test organism within 28 days. Three experiments were carried out to investigate these assumptions. The first experiment was a standard toxicity test where lead nitrate was added to a soil in solution to give a range of concentrations. The mortality of the worms and the concentration of lead in the survivors were determined. The LC(50)s for 14 and 28 days were 5311 and 5395 mug(Pb) g(soil)(-1) respectively. The second experiment was a timed lead accumulation study with worms cultivated in soil containing either 3000 or 5000 mug(Pb) g(soil)(-1). The concentration of lead in the worms was determined at various sampling times. Uptake at so' Sol both concentrations was linear with time. Worms in the 5000 mug g(-1) soil accumulated lead at a faster rate (3.16 mug Pb g(tissue)(-1) day(-1)) tiss than those in the 3000 mug g(-1) soil (2.21 mug Pb-tissue g(-1) day(-1)). The third experiment was a timed experiment with worms cultivated in tiss soil containing 7000 mugPb g(soil)(-1). Soil and lead nitrate solution were mixed and stored at 20 degreesC. Worms were added at various times over a 35-day period. The time to death increased from 23 h, when worms were added directly after the lead was added to the soil, to 67 It when worms were added after the soil had equilibrated with the lead for 35 days. In artificially Pb-amended soils the worms accumulate Pb over the duration of their exposure to the Pb. Thus time limited toxicity tests may be terminated before worm body load has reached a toxic level. This could result in under-estimates of the toxicity of Pb to worms. As the equilibration time of artificially amended Pb-bearing soils increases the bioavailability of Pb decreases. Thus addition of worms shortly after addition of Pb to soils may result in the over-estimate of Pb toxicity to worms. The current OECD acute worm toxicity test fails to take these two phenomena into account thereby reducing the environmental relevance of the contaminant toxicities it is used to calculate. (C) 2002 Elsevier Science Ltd. All rights reserved.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.