Phase-driven interaction of widely separated nonlinear Schr\"odinger solitons

We show that, for the 1d cubic NLS equation, widely separated equal amplitude in-phase solitons attract and opposite-phase solitons repel. Our result gives an exact description of the evolution of the two solitons valid until the solitons have moved a distance comparable to the logarithm of the initial separation. Our method does not use the inverse scattering theory and should be applicable to nonintegrable equations with local nonlinearities that support solitons with exponentially decaying tails. The result is presented as a special case of a general framework which also addresses, for example, the dynamics of single solitons subject to external forces

Fourth Amendment Accommodations: (UN)Compelling Public Needs, Balancing Acts, and the Fiction of Consent

The problems of public housing-including crime, drugs, and gun violence- have received an enormous amount of national attention. Much attention has also focused on warrantless searches and consent searches as solutions to these problems. This Note addresses the constitutionality of these proposals and asserts that if the Supreme Court\u27s current Fourth Amendment jurisprudence is taken to its logical extremes, warrantless searches in public housing can be found constitutional. The author argues, however, that such an interpretation fails to strike the proper balance between public need and privacy in the public housing context. The Note concludes by proposing alternative consent-based regimes that would pass constitutional muster

Réponse à Didier Fassin

L’argumentation de mon collègue Didier Fassin s’attache dans le détail à dire que Le déni des cultures est un travail « scientifiquement infondé », elle ne propose pas une ligne d’interprétation alternative. Je vais aborder les remarques sur la cohérence puis j’essaierai de montrer que, au-delà des points de méthode et d’analyse statistique, c’est l’ensemble de ma démarche qui a peut-être été mal comprise par l’auteur. Ce que suggèrent aussi quelques citations tronquées. [Premier paragraphe

On the 2d Zakharov system with L^2 Schr\"odinger data

We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L^2-based Sobolev scale. Moreover, it is a natural space for the Cauchy problem in view of the subsonic limit equation, namely the focusing cubic nonlinear Schroedinger equation. The existence time we obtain depends only upon the corresponding norms of the initial data - a result which is false for the cubic nonlinear Schroedinger equation in dimension two - and it is optimal because Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change

Blue carbon stocks in Baltic Sea eelgrass (Zostera marina) meadows

Although seagrasses cover only a minor fraction of the ocean seafloor, their carbon sink capacity accounts for nearly one-fifth of the total oceanic carbon burial and thus play a critical structural and functional role in many coastal ecosystems. We sampled 10 eelgrass (<i>Zostera marina</i>) meadows in Finland and 10 in Denmark to explore seagrass carbon stocks (C_org stock) and carbon accumulation rates (C_org accumulation) in the Baltic Sea area. The study sites represent a gradient from sheltered to exposed locations in both regions to reflect expected minimum and maximum stocks and accumulation. The C_org stock integrated over the top 25 cm of the sediment averaged 627 g C m⁻² in Finland, while in Denmark the average C_org stock was over 6 times higher (4324 g C m⁻²). A conservative estimate of the total organic carbon pool in the regions ranged between 6.98 and 44.9 t C ha⁻¹. Our results suggest that the Finnish eelgrass meadows are minor carbon sinks compared to the Danish meadows, and that majority of the C_org produced in the Finnish meadows is exported. Our analysis further showed that &gt; 40 % of the variation in the C_org stocks was explained by sediment characteristics, i.e. dry density, porosity and silt content. In addition, our analysis show that the root : shoot ratio of <i>Z. marina</i> explained &gt; 12 % and the contribution of <i>Z. marina</i> detritus to the sediment surface C_org pool explained &gt; 10 % of the variation in the C_org stocks. The mean monetary value for the present carbon storage and carbon sink capacity of eelgrass meadows in Finland and Denmark, were 281 and 1809 EUR ha⁻¹, respectively. For a more comprehensive picture of seagrass carbon storage capacity, we conclude that future blue carbon studies should, in a more integrative way, investigate the interactions between sediment biogeochemistry, seascape structure, plant species architecture and the hydrodynamic regime

Comprendre les brachiopodes linguloides : Obulus et Ungula comme exemples

EMIG (2002) a revu la taxonomie du genre Obolus EICHWALD du Cambrien moyen - Ordovician basal des régions baltes orientales dans le cadre d'un projet de révision de l'ensemble des critères de la systématique des linguloides. Il a suggéré que les études taxonomiques antérieures sur Obolus et les formes apparentées sont fondées à tort sur des caractères dépourvus de toute valeur taxonomique. La révision proposées par EMIG s'appuie principalement sur les faibles variations morphologiques observées entre taxons fossiles et récents au sein d'une seule famille de linguloide, les Lingulidae. Notre article s'attache à démontrer la validité taxonomique des critères diagnostiques utilisés dans la classification au sein des familles, pour la plupart éteintes, de la Superfamille des Linguloidea, car ils présentent une bien plus grande diversité morphologique. Cette étude montre aussi que EMIG n'a pas proposé une base satisfaisante pour étayer les changements et révisions radicaux qu'il souhaite apporter à la taxonomie, en vigueur et largement acceptée, des Obolidae des séries du Cambrien à l'Ordovician basal des régions baltes orientales. Obolus EICHWALD et Ungula PANDER sont considérés comme des genres distincts comprenant les espèces Obolus apollinis EICHWALD, O. ruchini KHAZANOVITCH et POPOV, O. transversus (PANDER), Ungula ingrica (EICHWALD), U. inornata (MICKWITZ) et U. convexa PANDER.EMIG (2002) re-examined the taxonomy of the genus Obolus EICHWALD from the Middle Cambrian - earliest Ordovician of the East Baltic region as part of a proposal for a wholesale revision of the principles of linguloid systematics. He contended that previous taxonomic studies on Obolus and related forms were carried out erroneously using characters that have no taxonomic value. EMIG´s proposed revision is based mainly on the limited morphological diversity between fossil and Recent taxa within a single linguloid Family, the Lingulidae. However, the present study demonstrates the taxonomic validity of the diagnostic characters used for classification within the mostly extinct families of the Superfamily Linguloidea, for they exhibit far more variation in morphology. This study also shows that EMIG has provided no satisfactory basis for his radical changes and revisions to the existing widely accepted taxonomy of the Cambrian to earliest Ordovician Obolidae of the East Baltic. Obolus EICHWALD and Ungula PANDER are shown to constitute distinctive and discrete genera comprising the species Obolus apollinis EICHWALD, O. ruchini KHAZANOVITCH et POPOV, O. transversus (PANDER), Ungula ingrica (EICHWALD), U. inornata (MICKWITZ), and U. convexa PANDER

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

Mussel production and Water Framework Directive targets in the Limfjord, Denmark: an integrated assessment for use in system-based management

Growth of human activities often conflict with nature conservation requirements and integrated assessments are necessary to build reliable scenarios for management. In the Limfjord, Denmark's largest estuary, nutrient loading reductions are necessary to fulfill EU regulations criteria, such as the Water Framework Directive (WFD). Cuts in nutrient loadings do not necessarily result in corresponding reductions in eutrophication impacts or in improving primary and higher trophic-level production. Similarly, the socioeconomic consequences of a mussel fishery and aquaculture production are complex and hard to predict. This study focuses on the usefulness of a System Approach Framework (SAF) implementation for stakeholder understanding of complex systems and development of sustainable management. Ecological-social-economic (ESE) model simulations clearly demonstrated the potential problems of WFD implementation for mussel fishers and mussel farmers. Simulation of mussel fishery closures resulted in a tenfold increase in the hitherto fishable mussel biomass and a similar decrease in the biomass of shallow-water mussels and medium-sized ones in deep water. A total closure of the mussel fishery could result in an annual profit loss of ~6.2 million. Scenario simulation of the introduction of one, two, three, and four mussel culture farms of ~19 ha showed that the introduction of line-mussels would decrease the biomass of wild mussels both in shallow and deep waters, affecting the catch and profit of fishers. The SAF, which included consultation with stakeholders at all stages, differs from the traditional public consultation process in that (1) communication was verbal and multilateral, (2) discussion among stakeholders was facilitated, and (3) stakeholder opinions and priorities formed the focus of the ESE assessment

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