On some problems involving Hardy's function

Some problems involving the classical Hardy function $$Z(t) := \zeta(1/2+it)\bigl(\chi(1/2+it)\bigr)^{-1/2}, \quad \zeta(s) = \chi(s)\zeta(1-s)$$ are discussed. In particular we discuss the odd moments of $Z(t)$, the distribution of its positive and negative values and the primitive of $Z(t)$. Some analogous problems for the mean square of $|\zeta(1/2+it)|$ are also discussed.Comment: 15 page

Cellular Models for River Networks

A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks.Comment: 7 pages, revtex style, 14 figure

Biological life-history and farming scenarios of marine aquaculture to help reduce wild marine fishing pressure

Aquaculture (freshwater and marine) has largely supplemented fisheries, but in theory could help reduce fishing pressure on wild stocks. Although not the sole factors, some potential benefits depend on aquaculture pressures on fished species, including collection of wild ‘seed’ material—earlier to later life stages—for rearing in captivity and the capacity of aquaculture to increase. Here we first classify 203 marine (saltwater and brackish) animal species as being produced by either open-cycle capture-based aquaculture (CBA) or closed-cycle domesticated aquaculture (DA)—based on their likely reliance on wild seed—and assess the extent to which these forms of aquaculture could support seafood production and greater wild biomass. Using a data-limited modelling approach, we find evidence that current aquaculture practices are not necessarily helping reduce fishing to sustainable levels for their wild counterparts—consistent with emerging scientific research. However, if some wild capture species (87 equivalent spp.) were instead produced through CBA, almost a million extra tonnes could theoretically be left in the wild, without reducing seafood production. Alternatively, if reliance on wild seed inputs is further reduced by shifting to DA production, then a little less than doubling of aquaculture of the overexploited species in our study could help fill the ‘production gap’ to support fishing at maximum sustainable levels. While other ecological (e.g. escapes), social and economic considerations (e.g. market substitution) are important, we focused on a critical biological linkage between wild fisheries and aquaculture that provides another aspect on how to improve management alignment of the sectors

Anion exchange membrane soil nitrate predicts turfgrass color and yield.

Desirable nitrogen (N) management practices for turfgrass supply sufficient N for high quality turf while limiting excess soil N. Previous studies suggested the potential of anion exchange membranes (AEMs) for predicting turfgrass color, quality, or yield. However, these studies suggested a wide range of critical soil nitrate-nitrogen (NO3-N) values across sample dates. A field experiment, in randomized complete block design with treatments consisting of nine N application rates, was conducted on a mixed species cool-season turfgrass lawn across two growing seasons. Every 2 wk from May to October, turfgrass color was assessed with three different reflectance meters, and soil NO3-N was measured with in situ AEMs. Cate-Nelson models were developed comparing relative reflectance value and yield to AEM desorbed soil NO3-N pooled across all sample dates. These models predicted critical AEM soil NO3-N values from 0. 45 to 1.4 micro g cm-2 d-1. Turf had a low probability of further positive response to AEM soil NO3-N greater than these critical values. These results suggest that soil NO3-N critical values from AEMs may be applicable across sample dates and years and may serve to guide N fertilization to limit excess soil NO3-N

Hydromorphological, hydraulic and ecological effects of restored wood: findings and reflections from an academic partnership approach

This is the peer reviewed version of the following article: Pinto, C. , Ing, R. , Browning, B. , Delboni, V. , Wilson, H. , Martyn, D. and Harvey, G. L. (2019), Hydromorphological, hydraulic and ecological effects of restored wood: findings and reflections from an academic partnership approach. Water and Environment Journal. doi:10.1111/wej.12457, which has been published in final form at https://doi.org/10.1111/wej.12457. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions© 2019 CIWEM Large wood (re)introduction can deliver multiple benefits in river restoration, but there is a dearth of the detailed and longer-term post-project monitoring and evaluation required for improving best practice. We present findings from an academic partnership approach to post-project evaluation, based on successive MSc research projects on restored large wood in the Loddon catchment, UK. Field and modelling data reveal: (i) key differences in large wood features between restored and natural reaches; (ii) increased hydraulic retention and changes to mesohabitats associated with large wood; (iii) differences in macroinvertebrate community composition around large wood but a lack of site-level effects; (iv) interactions between macrophytes and large wood that may be specific to restored reaches; (v) a need for further field and modelling studies to inform the accurate representation of large wood in hydraulic models. Some key challenges in partnership working are identified to aid planning and effectiveness of future collaborations

Order and Chaos in some Trigonometric Series: Curious Adventures of a Statistical Mechanic

This paper tells the story how a MAPLE-assisted quest for an interesting undergraduate problem in trigonometric series led some "amateurs" to the discovery that the one-parameter family of deterministic trigonometric series \pzcS_p: t\mapsto \sum_{n\in\Nset}\sin(n^{-{p}}t), $p>1$, exhibits both order and apparent chaos, and how this has prompted some professionals to offer their expert insights. It is proved that \pzcS_p(t) = \alpha_p\rm{sign}(t)|t|^{1/{p}}+O(|t|^{1/{(p+1)}})\;\forall\;t\in\Rset, with explicitly computed constant $\alpha_p$. Experts' commentaries are reproduced stating the fluctuations of \pzcS_p(t) - \alpha_p{\rm{sign}}(t)|t|^{1/{p}} are presumably not Gaussian. Inspired by a central limit type theorem of Marc Kac, a well-motivated conjecture is formulated to the effect that the fluctuations of the $\lceil t^{1/(p+1)}\rceil$-th partial sum of \pzcS_p(t), when properly scaled, do converge in distribution to a standard Gaussian when $t\to\infty$, though --- provided that $p$ is chosen so that the frequencies \{n^{-p}\}_{n\in\Nset} are rationally linear independent; no conjecture has been forthcoming for rationally dependent \{n^{-p}\}_{n\in\Nset}. Moreover, following other experts' tip-offs, the interesting relationship of the asymptotics of \pzcS_p(t) to properties of the Riemann $\zeta$ function is exhibited using the Mellin transform.Comment: Based on the invited lecture with the same title delivered by the author on Dec.19, 2011 at the 106th Statistical Mechanics Meeting at Rutgers University in honor of Michael Fisher, Jerry Percus, and Ben Widom. (19 figures, colors online). Comments of three referees included. Conjecture 1 revised. Accepted for publication in J. Stat. Phy