Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate

We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space is the largest one in which we can expect convergence to the steady size distribution. Although this convergence is known to occur under fairly general conditions on the coefficients of the equation, we prove that it does not happen uniformly with respect to the initial data when the fragmentation rate in bounded. First we get the result for fragmentation kernels which do not form arbitrarily small fragments by taking advantage of the Dyson-Phillips series. Then we extend it to general kernels by using the notion of quasi-compactness and the fact that it is a topological invariant

Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts

We study the asymptotic behaviour of the following linear growth-fragmentation equation$$\dfrac{\partial}{\partial t} u(t,x) + \dfrac{\partial}{\partial x} \big(x u(t,x)\big) + B(x) u(t,x) =4 B(2x)u(t,2x),$$ and prove that under fairly general assumptions on the division rate $B(x),$ its solution converges towards an oscillatory function,explicitely given by the projection of the initial state on the space generated by the countable set of the dominant eigenvectors of the operator. Despite the lack of hypo-coercivity of the operator, the proof relies on a general relative entropy argument in a convenient weighted $L^2$ space, where well-posedness is obtained via semigroup analysis. We also propose a non-dissipative numerical scheme, able to capture the oscillations

Correction of upstream flow and hydraulic state with data assimilation in the context of flood forecasting

The present study describes the assimilation of river water level observations and the resulting improvement in flood forecasting. The Kalman Filter algorithm was built on top of a one-dimensional hydraulic model which describes the Saint-Venant equations. The assimilation algorithm folds in two steps: the first one was based on the assumption that the upstream flow can be adjusted using a three-parameter correction; the second one consisted of directly correcting the hydraulic state. This procedure was applied using a four- day sliding window over the flood event. The background error covariances for water level and discharge were repre- sented with anisotropic correlation functions where the cor- relation length upstream of the observation points is larger than the correlation length downstream of the observation points. This approach was motivated by the implementation of a Kalman Filter algorithm on top of a diffusive flood wave propagation model. The study was carried out on the Adour and the Marne Vallage (France) catchments. The correction of the upstream flow as well as the control of the hydraulic state during the flood event leads to a significant improve- ment in the water level and discharge in both analysis and forecast modes

Appariements sur le Marché du Logement.

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Appariements sur le Marché du Logement

Cet article souhaite contribuer à une théorie du marché du logement locatif où les frictions de recherche sont rendues endogènes par une fonction d’appariement entre propriétaires et locataires potentiels. Le loyer est déterminé par une négociation à la Nash entre propriétaires et locataires ou choisi par le propriétaire ex ante. L’introduction de frictions de recherche modifie largement les résultats traditionnels et la statique comparative de l’état stationnaire est menée dans cette perspective. On étudie, notamment, un équilibre de court terme (le cas d’une ville fermée) et un autre de moyen terme (le cas d’une ville ouverte où l’offre de logements est fixe et les travailleurs libres d’entrer, ou non, sur le marché). Dans les deux cas, on discute les conséquences d’une taxation des appartements vacants. On retrouve un résultat relativement général en présence de frictions importantes : les mesures qui tendent à protéger les agents d’un certain type (employés, locataires) le font au détriment de ceux qui aspirent à accéder à ce statut (chômeurs, personnes ayant des difficultés à se loger)

On the influence of geometry updating on modal correlation of brake components.

In most industries dealing with vibration, test/analysis correlation of modal properties is considered a key aspect of the design process. The success of test/analysis methods however often show mixed results. The aim of this paper is to assess and answer some classical correlation problems in structural dynamics. First an investigation of correlation problems from tests is proposed. Tools based on the modal assurance criterion are presented to provide a deeper analysis of correlation and results improvement. In a second part, the need of FEM topology correlation and update is demonstrated, using an efficient morphing technique. Tolerances in the manufacturing process that are well accepted in design and production stages are shown to lead to significant degradation of the test/analysis correlation. An application to an industrial brake part is eventually presented, in an approach of correlation procedure automatization for recurrent use

Spontaneous demagnetization of a dipolar spinor Bose gas at ultra-low magnetic field

Quantum degenerate Bose gases with an internal degree of freedom, known as spinor condensates, are natural candidates to study the interplay between magnetism and superfluidity. In the spinor condensates made of alkali atoms studied so far, the spinor properties are set by contact interactions, while magnetization is dynamically frozen, due to small magnetic dipole-dipole interactions. Here, we study the spinor properties of S=3 $^{52}$Cr atoms, in which relatively strong dipole-dipole interactions allow changes in magnetization. We observe a phase transition between a ferromagnetic phase and an unpolarized phase when the magnetic field is quenched to an extremely low value, below which interactions overwhelm the linear Zeeman effect. The BEC magnetization changes due to magnetic dipole-dipole interactions that set the dynamics. Our work opens up the experimental study of quantum magnetism with free magnetization using ultra-cold atoms.Comment: 6 pages, 4 figures, 2 appendice

Analysis of CcDREB1D promoter region from drought-tolerant and susceptible clones of Coffea canephora by homologous genetic transformation of Coffea arabica

In several plant species, the DREB genes play a key role in responses to abiotic stress. Since the development of molecular markers is one of the major goals for accelerating breeding programs, a study was done to evaluate the sequence variability of the DREBID gene in several Coffee genotypes. The promoter and coding regions of DREBID gene were cloned and sequenced from 16 coffee plants (10 from C. arabica and 4 from C. canephora), most of them characterized by different phenotypes (tolerance vs. susceptibility) regarding to drought. This showed a high conservation of DREB1 D proteins among the homologous sequences due to the low level of diversity and the high number of synonymous mutations and neutral changes which represents the majority of sequence variations. However, several nucleic polymorphisms ("single nucleotide polymorphism" and insertion/deletion [InDels]) were found in the coffee DREBID promoters. A comparison of predicted cis-acting elements for all the promoter sequences signaled the loss of some regulatory DNA elements. The sequence variation and the loss of some regulatory DNA elements could explain the differences of DREBID gene expression previously observed in leaves of drought tolerant (clone 14) and susceptible (clone 22) clones of C. canephora. In fact, both clones 14 and 22, have one same CcDREBID allelic sequence (hp15), and diverge at a second allele. Thus, the CcDREBID allele in the tolerant 14 (hp16) was considered to be the favorable/tolerant allele and the allele in 22 (hp17) was inferior/sensitive. The capacity of CcDREBID promoter to control the expression of the uidA reporter gene is under evaluation in transgenic plants of Coffee arabica cv. caturra stably transformed by Agrobacterium tumefaciens mediated gene transfer procedure. Caturra transgenic embryos were placed on a clean bench and subjected to dehydration tests. Preliminary results of bioassays checking GUS (/3-glucuronidase) activities indicate that the observed sequence variations have a direct role in the regulation of CcDREBID expression. The proximal promoter of CcDREBID for the three alleles tested (hp15, hp16 and hp17) equally induced the uidA gene expression, however, expression of uidA under control of the complete CcDREBID promoter was significantly induced in the tolerant allele (hp16) in response to the osmotic stress, whereas, it was not significantly upregulated for the common (hp15) and sensitive alleles (hp17). These results also evidence that the sequence variation present at the first -700 by of CcDREBID promoter do not interfere the regulation activity of the promoter, probably due to the non-overlapping of SNPs and cis-regulatory elements. Though, the higher sequence variation and co-occurrence of SNPs and cis-regulatory elements observed between -700 and -1500 by seems to affect the regulation of CcDREBID promoter in response to drought stress.Support: CAPES COFECUB, INCT-Café, CNPq and ConsOrcio Pesquisa Café. (Texte intégral

The Component Mode Tuning (CMT) method. A strategy adapted to the design of assemblies applied to industrial brake squeal

Numerical prototyping is widely used in industrial design processes, allowing optimization and limiting validation costs through experimental testing. Industrial applications nowadays focus on the simulation of complex component assemblies that are generally mass produced. Coupling properties thus have to be modelled, updated and accounted for variability. For squeal applications, simulations still fail at robustly producing exploitable results due to the systems complexity, while experimentations are limited for diagnostic and design improvement. This paper presents a new application of the Component Mode Tuning, an efficient model reduction method adapted to quick system level reanalysis as function of component free modes, to study the effect of coupling. The impact of component coupling stiffness and coupling surface topology is thus assessed on a drum brake subassembly which design is sensitive to squeal. It is shown that significant system differences can come from coupling surface variations with patterns close to experimental observations. This emphases the need for refined analyses to control coupling in the perspective of robust modelling