A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation

We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the solution to a linear Schr\"odinger equation as $t\to \pm \infty$. The criteria is expressed in terms of the scale-invariant quantities $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2}$ and $M[u]E[u]$, where $u_0$ denotes the initial data, and $M[u]$ and $E[u]$ denote the (conserved in time) mass and energy of the corresponding solution $u(t)$. The focusing NLS possesses a soliton solution $e^{it}Q(x)$, where $Q$ is the ground-state solution to a nonlinear elliptic equation, and we prove that if $M[u]E[u]<M[Q]E[Q]$ and $\|u_0\|_{L^2}\|\nabla u_0\|_{L^2} < \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution $u(t)$ is globally well-posed and scatters. This condition is sharp in the sense that the soliton solution $e^{it}Q(x)$, for which equality in these conditions is obtained, is global but does not scatter. We further show that if $M[u]E[u] \|Q\|_{L^2}\|\nabla Q\|_{L^2}$, then the solution blows-up in finite time. The technique employed is parallel to that employed by Kenig-Merle \cite{KM06a} in their study of the energy-critical NLS

Control and stabilization of waves on 1-d networks

We present some recent results on control and stabilization of waves on 1-d networks.The fine time-evolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a subtle manner on the topology of the network under consideration and also on the number theoretical properties of the lengths of the strings entering in it. Therefore, the overall picture is quite complex.In this paper we summarize some of the existing results on the problem of controllability that, by classical duality arguments in control theory, can be reduced to that of observability of the adjoint uncontrolled system. The problem of observability refers to that of recovering the total energy of solutions by means of measurements made on some internal or external nodes of the network. They lead, by duality, to controllability results guaranteeing that L 2-controls located on those nodes may drive sufficiently smooth solutions to equilibrium at a final time. Most of our results in this context, obtained in collaboration with R. Dáger, refer to the problem of controlling the network from one single external node. It is, to some extent, the most complex situation since, obviously, increasing the number of controllers enhances the controllability properties of the system. Our methods of proof combine sidewise energy estimates (that in the particular case under consideration can be derived by simply applying the classical d'Alembert's formula), Fourier series representations, non-harmonic Fourier analysis, and number theoretical tools.These control results belong to the class of the so-called open-loop control systems.We then discuss the problem of closed-loop control or stabilization by feedback. We present a recent result, obtained in collaboration with J. Valein, showing that the observability results previously derived, regardless of the method of proof employed, can also be recast a posteriori in the context of stabilization, so to derive explicit decay rates (as) for the energy of smooth solutions. The decay rate depends in a very sensitive manner on the topology of the network and the number theoretical properties of the lengths of the strings entering in it.In the end of the article we also present some challenging open problems

Behavioural indicators of welfare in farmed fish

Behaviour represents a reaction to the environment as fish perceive it and is therefore a key element of fish welfare. This review summarises the main findings on how behavioural changes have been used to assess welfare in farmed fish, using both functional and feeling-based approaches. Changes in foraging behaviour, ventilatory activity, aggression, individual and group swimming behaviour, stereotypic and abnormal behaviour have been linked with acute and chronic stressors in aquaculture and can therefore be regarded as likely indicators of poor welfare. On the contrary, measurements of exploratory behaviour, feed anticipatory activity and reward-related operant behaviour are beginning to be considered as indicators of positive emotions and welfare in fish. Despite the lack of scientific agreement about the existence of sentience in fish, the possibility that they are capable of both positive and negative emotions may contribute to the development of new strategies (e. g. environmental enrichment) to promote good welfare. Numerous studies that use behavioural indicators of welfare show that behavioural changes can be interpreted as either good or poor welfare depending on the fish species. It is therefore essential to understand the species-specific biology before drawing any conclusions in relation to welfare. In addition, different individuals within the same species may exhibit divergent coping strategies towards stressors, and what is tolerated by some individuals may be detrimental to others. Therefore, the assessment of welfare in a few individuals may not represent the average welfare of a group and vice versa. This underlines the need to develop on-farm, operational behavioural welfare indicators that can be easily used to assess not only the individual welfare but also the welfare of the whole group (e. g. spatial distribution). With the ongoing development of video technology and image processing, the on-farm surveillance of behaviour may in the near future represent a low-cost, noninvasive tool to assess the welfare of farmed fish.Fundação para a Ciência e Tecnologia, Portugal [SFRH/BPD/42015/2007]info:eu-repo/semantics/publishedVersio

Activity patterns, home-range size, and habitat utilization of Sarpa salpa (Teleostei : Sparidae) in the Mediterranean Sea

Acoustic telemetry was used to record diel movement and habitat utilization of the salema (Sarpa salpa) (Teleostei: Sparidae) during three consecutive summers from 2000 to 2002 in the Calvi and Achiarina bays of Corsica in the Mediterranean Sea. A total of 18 fish was equipped with acoustic transmitters inserted in the body cavity, 13 were tracked in the Bay of Calvi (275 mm +/- 26.9 L-F), and 5 in Achiarina Bay (260 mm +/- 33.6 LF). Two different systems were used to track the fish. The one used in the Bay of Calvi was a manual receiver and a directional hydrophone. The second system, used in Achiarina Bay, was a radioacoustic-positioning (RAP) system that continuously monitored the movements of the fish. Fish positions were put in a geographic information system (GIS) with information on the substratum and depth. Two patterns of behaviour could be identified in the three years. Either the fish had clearly defined daytime as opposed to night-time areas of residency, characterized by different depths and substrata or the fish persistently occupied the same sites during both day and night. In the Bay of Calvi, six fish were released I km from the capture site. All of them showed homing ability and returned to the site within 48 h

Advances in invertebrates and fish telemetry

This paper analyses acoustic tagging of 8 yellowfin tunas (#Thunnus albacares$, Bonnaterre, 1788) undertaken around Fish Aggregating Devices (FADs) in La Reunion island (Indian Ocean). Emphasis is laid on the horizontal movements and thus complete previous studies on vertical movements around the same FADs. The first result of the present study deals with the relative dwelling time of yellowfin over the distance to FAD where tagged, in 0.9 km intervals. Distributions of dwelling time are different between day and night. During daytime, the fishes remain in the close vicinity of the FAD (mostly within a 1.8 km radius), whilst a drastic disassociation to the FAD occurs at night. During the day, the attractive influence of the FAD disappears 9.3 km away ; this finding leads to the suggestion that a minimum distance of 18 km between neighbouring FADs should be applied in La Reunion to avoid overlapping radii of influence. The second group of results points out the potential use of the vertical and total swimming speeds as indicators of the foraging activity of the fish and of the type of movements (behaviour of tight association to FAD, transit among FADs or offshore migration, away from the area of FADs). The day/night change affects the vertical activity, with large magnitude of vertical movements exhibited at night. The total speed during the offshore movements is estimated about 1.2 m/s : the shift from a phase of tight association to FAD toward a phase of transit movement is characterised by an increase of the total speed. A typology of the relationships between swimming speed and feeding activity is proposed and discussed. (Résumé d'auteur

Genome-wide gene expression analysis during solea sp. embryo- larval development

A combination of 454 and Illumina sequencing has allowed the increase in the knowledge of Solea sp. transcriptomes with the identification of ca. 600.000 unigenes for each species. This has allowed the development of several tools suitable for genes expression analysis (&micro;array, openarray) and has made easier the use of classical methods (qPCR, ish). The use of several developmental stages and embryos or larvae manipulation (RA/DEAB but also salinity, temperature) will allow the deciphering of particular pathways in response to these factors and will give indications to improve or adapt rearing. &nbsp; This study has been co-funded by project AQUAGENET (SOE2/P1/ E287) program INTERREG IVB SUDOE, and by project RTA2009-00066-00-00 from the Instituto Nacional de Investigaci&oacute;n y Tecnolog&iacute;a Agraria y Alimentaria (INIA, Spain), and FEDER (EU).www.juntadeandalucia.es/agriculturaypesca/ifapa/aquagenetA combination of 454 and Illumina sequencing has allowed the increase in the knowledge of Solea sp. transcriptomes with the identification of ca. 600.000 unigenes for each species. This has allowed the development of several tools suitable for genes expression analysis (&micro;array, openarray) and has made easier the use of classical methods (qPCR, ish). The use of several developmental stages and embryos or larvae manipulation (RA/DEAB but also salinity, temperature) will allow the deciphering of particular pathways in response to these factors and will give indications to improve or adapt rearing. &nbsp; This study has been co-funded by project AQUAGENET (SOE2/P1/ E287) program INTERREG IVB SUDOE, and by project RTA2009-00066-00-00 from the Instituto Nacional de Investigaci&oacute;n y Tecnolog&iacute;a Agraria y Alimentaria (INIA, Spain), and FEDER (EU).www.juntadeandalucia.es/agriculturaypesca/ifapa/aquagenet</p

Génération POP – Effet d'une exposition précoce d'embryons de poissons aux polluants organiques persistants et conséquence sur la population par étude des effets sur plusieurs générations

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