Abstract: This article presents the complete study of the long-time evolution of random waves of a vibrating thin elastic plate in the limit of small plate deformation so that modes of oscillations interact weakly. According to the wave turbulence theory a nonlinear wave system evolves in longtime creating a slow redistribution of the spectral energy from one mode to another. We derive step by step, following the method of cumulants expansion and multiscale asymptotic perturbations, the kinetic equation for the second order cumulants as well as the second and fourth order renormalization of the dispersion relation of the waves. We characterize the non-equilibrium evolution to an equilibrium wave spectrum, which happens to be the well known Rayleigh-Jeans distribution. Moreover we show the existence of an energy cascade, often called the Kolmogorov-Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh Jeans distribution. We perform numerical simulations confirming these scenarii, namely the equilibrium relaxation for closed systems and the existence of an energy cascade wave spectrum. Both show a good agreement between theoretical predictions and numerics. We show also some other relevant features of vibrating elastic plates, such as the existence of a self-similar wave action inverse cascade which happens to blow-up in finite time. We discuss the mechanism of the wave breakdown phenomena in elastic plates as well as the limit of strong turbulence which arises as the thickness of the plate vanishes. Finally, we discuss the role of dissipation and the connection with experiments, and the generalization of the wave turbulence theory to elastic shells. (C) 2017 Elsevier B.V. All rights reserved.

Abstract: In this paper, we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long-scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in (h) over bar. Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasidistribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is nontrivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as “hidden momentum” and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

Abstract: The family F-lambda of orientation-preserving harmonic functions f = h + (g) over bar in the unit disc D (normalised in the standard way) satisfying h' (z) + g' (z) = 1/(1 + lambda z)(1 + (lambda) over barz), z is an element of D, for some lambda is an element of partial derivative D, along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in F-lambda are convex.

Abstract: The identification of environmental barriers which govern species distribution is a fundamental concern in ecology. Even though salt was previously identified as a major transition boundary for micro- and macroorganisms alike, the salinities causing species turnover in protistan communities are unknown. We investigated 4.5 million high-quality protistan metabarcodes (V4 region of the SSU rDNA) obtained from 24 shallow salt ponds (salinities 4%-44%) from South America and Europe. Statistical analyses of protistan community profiles identified four salinity classes, which strongly selected for different protistan communities: 4-9%, 14-24%, 27-36% and 38-44%. The proportion of organisms unknown to science is highest in the 14-24% salinity class, showing that environments within this salinity range are an unappreciated reservoir of as yet undiscovered organisms. Distinct higher-rank taxon groups dominated in the four salinity classes in terms of diversity. As increasing salinities require different cellular responses to cope with salt, our results suggest that different evolutionary lineages of protists have evolved distinct haloadaptation strategies. Salinity appears to be a stronger selection factor for the structuring of protistan communities than geography. Yet, we find a higher degree of endemism in shallow salt ponds compared with less isolated ecosystems such as the open ocean. Thus, rules for biogeographic structuring of protistan communities are not universal, but depend on the ecosystem under consideration.

Abstract: Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered-which is extremely important for agricultural management.

Abstract: A large variety of antipredator defenses are exhibited by plants, animals and microbes in nature. A deep understanding of the dynamic consequences of prey responses to predation risk is essential for building a comprehensive theory of food webs. Here we present a simple classification of prey defenses based on the sensitivity of prey immunity to predation respect to abundances of prey and predators. Only three out of six defense types have been analytically studied in the context of predator-prey dynamics, which reveals a serious gap in our current knowledge of ecological interactions. In this study we present a mathematical analysis on a widely occurring type of prey defense whose behavior has not been established in exact terms. The study model considers prey whose average immunity to predators is enhanced by predator abundance. This case, known as inducible defenses, has been reported for a wide array of species. Our results reveal a rich dynamic behavior, in which the predator-prey system exhibits either one, two or three positive equilibrium points, with up to two attractors. Thus, inducible defenses constitute a mechanism that could drive alternative stable states even in very simple food web models. (C) 2017 Elsevier B.V. All rights reserved.

Abstract: Recent experimental work has determined that free falling Rb-87 atoms on Earth, with vertically aligned spins, follow geodesics, thus apparently ruling out spin-gravitation interactions. It is showed that while some spinning matter models coupled to gravitation referenced to in that work seem to be ruled out by the experiment, those same experimental results confirm theoretical results derived from a Lagrangian description of spinning particles coupled to gravity constructed over forty years ago. A proposal to carry out (similar but) different experiments which will help to test the validity of the universality of free fall as opposed to the correctness of the aforementioned Lagrangian theory, is presented.

Abstract: In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.

Abstract: Background: Nannochloropsis salina (= Eustigmatophyceae) is a marine microalga which has become a biotechnological target because of its high capacity to produce polyunsaturated fatty acids and triacylglycerols. It has been used as a source of biofuel, pigments and food supplements, like Omega 3. Only some Nannochloropsis species have been sequenced, but none of them benefit from a genome-scale metabolic model (GSMM), able to predict its metabolic capabilities. Results: We present iNS934, the first GSMM for N. salina, including 2345 reactions, 934 genes and an exhaustive description of lipid and nitrogen metabolism. iNS934 has a 90% of accuracy when making simple growth/no-growth predictions and has a 15% error rate in predicting growth rates in different experimental conditions. Moreover, iNS934 allowed us to propose 82 different knockout strategies for strain optimization of triacylglycerols. Conclusions: iNS934 provides a powerful tool for metabolic improvement, allowing predictions and simulations of N. salina metabolism under different media and genetic conditions. It also provides a systemic view of N. salina metabolism, potentially guiding research and providing context to -omics data.

Abstract: Peracetic acid (PM) is an alternative disinfectant that may be effective for combined sewer overflow (CSO) disinfection, but little is known about the effect of particle size on PM disinfection efficiency. In this work, PM and hypochlorite were compared as disinfectants, with a focus on the effect of wastewater particles. Inactivation experiments were conducted on suspended cultures of Escherichia coli and wastewater suspended solids. Tested size fractions included particle diameters <10 μm, <100 μm, and raw wastewater. Chlorine disinfection efficiency decreased with increasing solids size. However, solids size had little effect on PM disinfection. The PM disinfection efficiency decreased at pH values above 7.5. Live/dead staining revealed that PM disinfection leaves most cells in a viable but non-culturable condition. Fourier transform infrared spectroscopy (FTIR) analyses suggests that PAA and hypochlorite may inactivate E. coli bacteria by similar mechanisms. (C) 2017 Elsevier B.V. All rights reserved.