Heat transfer simulation of evacuated tube collectors (ETC): An application to a prototype

Since fossil fuels shortages are predicted for the forthcoming generations, the use of renewable energy sources is playing a key role and is strongly recommended worldwide by national and international regulations. In this scenario, solar collectors for hot water preparation, space heating and cooling are becoming an increasingly interesting alternative, especially in the building sector because of population growth. Thus, the present paper is addressed to numerically investigate the thermal behaviour of a prototypal evacuated tube by solving the heat transfer differential equations using the Finite Element Method. This is to reproduce the heat transfer process occurring within the real system, helping the industry improve the prototype

On Singularity formation for the L^2-critical Boson star equation

We prove a general, non-perturbative result about finite-time blowup solutions for the $L^2$-critical boson star equation $i\partial_t u = \sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under the sole assumption that the solution blows up in $H^{1/2}$ at finite time, we show that $u(t)$ has a unique weak limit in $L^2$ and that $|u(t)|^2$ has a unique weak limit in the sense of measures. Moreover, we prove that the limiting measure exhibits minimal mass concentration. A central ingredient used in the proof is a "finite speed of propagation" property, which puts a strong rigidity on the blowup behavior of $u$. As the second main result, we prove that any radial finite-time blowup solution $u$ converges strongly in $L^2$ away from the origin. For radial solutions, this result establishes a large data blowup conjecture for the $L^2$-critical boson star equation, similar to a conjecture which was originally formulated by F. Merle and P. Raphael for the $L^2$-critical nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704]. We also discuss some extensions of our results to other $L^2$-critical theories of gravitational collapse, in particular to critical Hartree-type equations.Comment: 24 pages. Accepted in Nonlinearit

Sowing density effect on common bean leaf area development

Sowing density is a major management factor that affects growth and development of grain crops by modifying the canopy light environment and interplant competition for water and nutrients. While the effects of sowing density and plant architecture on static vegetative and reproductive growth traits have been explored previously in the common bean, few studies have focused on the impacts of sowing density on the dynamics of node addition and leaf area development. We present the results from two sites of field experiments where the effects of sowing densities (5, 10, 15, 20, 25 and 35 plants m-2) and genotypes with contrasting plant architectures (two each from growth habits I through III) on the dynamics of node addition and leaf area were assessed. Analysis of the phyllochron (°C node-1) indicated genotype and density effects (but no interaction) on the rate of node addition. While significant, these differences amounted to less than two days of growth at either site. In terms of leaf area development, analysis using a power function reflected large differences in the dynamics and final size of individual plant leaf area between the lower density (20 plants m-2) at the growth habit, but not genotype level. These differences in node addition and leaf development dynamics translated to marked differences between growth habits and sowing densities in estimated leaf area indices, and consequently, in the estimated fraction of intercepted light at lower densities

Rate of Convergence Towards Semi-Relativistic Hartree Dynamics

We consider the semi-relativistic system of $N$ gravitating Bosons with gravitation constant $G$. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where $N \to \infty$ and $G \to 0$ while $GN = \lambda$ fixed. In the super-critical regime of large $\lambda$, we introduce the regularized interaction where the cutoff vanishes as $N \to \infty$. We show that the difference between the many-body semi-relativistic Schr\"{o}dinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order $N^{-1}$ for all $\lambda$, i.e., the result covers the sub-critical regime and the super-critical regime. The $N$ dependence of the bound is optimal.Comment: 29 page

Dynamical Collapse of Boson Stars

We study the time evolution in system of $N$ bosons with a relativistic dispersion law interacting through an attractive Coulomb potential with coupling constant $G$. We consider the mean field scaling where $N$ tends to infinity, $G$ tends to zero and $\lambda = G N$ remains fixed. We investigate the relation between the many body quantum dynamics governed by the Schr\"odinger equation and the effective evolution described by a (semi-relativistic) Hartree equation. In particular, we are interested in the super-critical regime of large $\lambda$ (the sub-critical case has been studied in \cite{ES,KP}), where the nonlinear Hartree equation is known to have solutions which blow up in finite time. To inspect this regime, we need to regularize the Coulomb interaction in the many body Hamiltonian with an $N$ dependent cutoff that vanishes in the limit $N\to \infty$. We show, first, that if the solution of the nonlinear equation does not blow up in the time interval $[-T,T]$, then the many body Schr\"odinger dynamics (on the level of the reduced density matrices) can be approximated by the nonlinear Hartree dynamics, just as in the sub-critical regime. Moreover, we prove that if the solution of the nonlinear Hartree equation blows up at time $T$ (in the sense that the $H^{1/2}$ norm of the solution diverges as time approaches $T$), then also the solution of the linear Schr\"odinger equation collapses (in the sense that the kinetic energy per particle diverges) if $t \to T$ and, simultaneously, $N \to \infty$ sufficiently fast. This gives the first dynamical description of the phenomenon of gravitational collapse as observed directly on the many body level.Comment: 40 page

A two-tier bioinformatic pipeline to develop probes for target capture of nuclear loci with applications in Melastomataceae

Putatively single-copy nuclear (SCN) loci, which are identified using genomic resources of closely related species, are ideal for phylogenomic inference. However, suitable genomic resources are not available for many clades, including Melastomataceae. We introduce a versatile approach to identify SCN loci for clades with few genomic resources and use it to develop probes for target enrichment in the distantly related Memecylon and Tibouchina (Melastomataceae)

Influence of plant density and growth habit of common bean on leaf area development and N accumulation

Crop yield requires leaf area to intercept solar radiation and to undertake photosynthesis, both of which depend on nitrogen (N) accumulation. Further, the amount of accumulated plant N at the beginning of seed fill serves as the reservoir for N required in synthesizing the proteins in developing seeds. For common bean (Phaseolus vulgaris L.), resolution of the basic characteristics limiting production is challenging because of variation in plant growth-habit and in wide-ranging plant spacing. Field experiments were undertaken at two low-latitude locations with three plant growth-habit types and six plant densities to measure canopy leaf area and leaf N accumulation at the beginning of seed fill. Plant spacing of 20 plants m−2 or more was sufficient to result in equal leaf area and N accumulation for all six plant genotypes at each location. However, the low-altitude, higher-temperature location had lower accumulated leaf N and yield than the high-altitude, cooler-temperature location. These results indicate attention needs to be given to physiological or agronomic approaches to overcome the negative impact of high temperature on N accumulation by common bean

Characterizing, modelling and understanding the climate variability of the deep water formation in the North-Western Mediterranean Sea

Observing, modelling and understanding the climate-scale variability of the deep water formation (DWF) in the North-Western Mediterranean Sea remains today very challenging. In this study, we first characterize the interannual variability of this phenomenon by a thorough reanalysis of observations in order to establish reference time series. These quantitative indicators include 31 observed years for the yearly maximum mixed layer depth over the period 1980–2013 and a detailed multi-indicator description of the period 2007–2013. Then a 1980–2013 hindcast simulation is performed with a fully-coupled regional climate system model including the high-resolution representation of the regional atmosphere, ocean, land-surface and rivers. The simulation reproduces quantitatively well the mean behaviour and the large interannual variability of the DWF phenomenon. The model shows convection deeper than 1000 m in 2/3 of the modelled winters, a mean DWF rate equal to 0.35 Sv with maximum values of 1.7 (resp. 1.6) Sv in 2013 (resp. 2005). Using the model results, the winter-integrated buoyancy loss over the Gulf of Lions is identified as the primary driving factor of the DWF interannual variability and explains, alone, around 50 % of its variance. It is itself explained by the occurrence of few stormy days during winter. At daily scale, the Atlantic ridge weather regime is identified as favourable to strong buoyancy losses and therefore DWF, whereas the positive phase of the North Atlantic oscillation is unfavourable. The driving role of the vertical stratification in autumn, a measure of the water column inhibition to mixing, has also been analyzed. Combining both driving factors allows to explain more than 70 % of the interannual variance of the phenomenon and in particular the occurrence of the five strongest convective years of the model (1981, 1999, 2005, 2009, 2013). The model simulates qualitatively well the trends in the deep waters (warming, saltening, increase in the dense water volume, increase in the bottom water density) despite an underestimation of the salinity and density trends. These deep trends come from a heat and salt accumulation during the 1980s and the 1990s in the surface and intermediate layers of the Gulf of Lions before being transferred stepwise towards the deep layers when very convective years occur in 1999 and later. The salinity increase in the near Atlantic Ocean surface layers seems to be the external forcing that finally leads to these deep trends. In the future, our results may allow to better understand the behaviour of the DWF phenomenon in Mediterranean Sea simulations in hindcast, forecast, reanalysis or future climate change scenario modes. The robustness of the obtained results must be however confirmed in multi-model studies