AN EXPLICIT EXPRESSION FOR k-NEGATIONS

Abstract We give a new proof for the existence and the uniqueness of k-negations. With the aid of a generalised dyadic representation system is possible to give an explicit expression for k-negations and it is possible to showing that there exists a set of measure 1 where knegations have derivatives with zero values

Unstable and stable regimes of polariton condensation

Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform.Comment: 7 pages, 5 figure

Un proyecto escultórico: la tortuga

En enero de 2003, los escultores Pablo de Arriba del Amo y José de las Casas Gómez presentaron la idea de una posible creación escultórica a la Junta municipal de Villaverde Alto. Este proyecto fue aprobado; por tanto, contó con la financiación necesaria para llevarlo a cabo, posteriormente fue instalado en la localización final propuesta, que era en la plaza Ágata de ese mismo distrito. En este artículo se van a desarrollar pormenorizadamente todos los pasos que se siguieron en el proceso de creación de este monumento, el cual por su envergadura era especialmente complejo. Desde la elección del tema, los materiales y los procesos hasta el desarrollo y estudio de la cimentación, todo ello será explicado para dar cuenta de un proyecto de máximo interés no sólo para los propios escultores, sino que, para el público general, la aproximación a este procedimiento puede hacer valorar el universo de la escultura mucho más. Hay que tener en consideración que ambos escultores se inventaron un procedimiento escultórico mediante la aplicación de sus conocimientos en una configuración novedosa, tanto por el procedimiento como por el método de aplicación de los materiales. Durante las páginas que siguen se verán y comprenderán las dificultades que tuvieron que afrontar no sólo a nivel técnico, sino a nivel conceptual para hilvanar todos los aspectos del proyecto, viéndose, así mismo, los ámbitos en los que este proyecto concreto es singular.In January 2003, the sculptors Pablo de Arriba del Amo and José de las Casas Gómez, presented the idea of a possible sculptural creation to the Municipal Board of Villaverde Alto, this project was approved, therefore, it had the necessary financing to carry it out. It was later installed in the proposed final location, which was in Plaza Ágata in that same district. In this article, all the steps that were followed in the process of creating this monument, which was especially complex due to its size, will be developed in detail. From the choice of theme, materials and processes to the development and study of the foundation, all of this will be explained to account for a project of maximum interest not only for the sculptors themselves, but also for the general public. The approach to this procedure can make the universe of sculpture much more appreciated. It must be taken into account, that both sculptors invented a sculptural procedure by applying their knowledge in a novel configuration, both in terms of the procedure and the method of applying the materials. During the following pages you will see and understand the difficulties they had to face not only at a technical level but also at a conceptual level to put together all the aspects of the project, seeing, likewise, the areas in which this specific project is unique

How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Sculpting oscillators with light within a nonlinear quantum fluid

Seeing macroscopic quantum states directly remains an elusive goal. Particles with boson symmetry can condense into such quantum fluids producing rich physical phenomena as well as proven potential for interferometric devices [1-10]. However direct imaging of such quantum states is only fleetingly possible in high-vacuum ultracold atomic condensates, and not in superconductors. Recent condensation of solid state polariton quasiparticles, built from mixing semiconductor excitons with microcavity photons, offers monolithic devices capable of supporting room temperature quantum states [11-14] that exhibit superfluid behaviour [15,16]. Here we use microcavities on a semiconductor chip supporting two-dimensional polariton condensates to directly visualise the formation of a spontaneously oscillating quantum fluid. This system is created on the fly by injecting polaritons at two or more spatially-separated pump spots. Although oscillating at tuneable THz-scale frequencies, a simple optical microscope can be used to directly image their stable archetypal quantum oscillator wavefunctions in real space. The self-repulsion of polaritons provides a solid state quasiparticle that is so nonlinear as to modify its own potential. Interference in time and space reveals the condensate wavepackets arise from non-equilibrium solitons. Control of such polariton condensate wavepackets demonstrates great potential for integrated semiconductor-based condensate devices.Comment: accepted in Nature Physic

A Continuum Robot and Control Interface for Surgical Assist in Fetoscopic Interventions

Twin-twin transfusion syndrome requires interventional treatment using a fetoscopically introduced laser to sever the shared blood supply between the fetuses. This is a delicate procedure relying on small instrumentation with limited articulation to guide the laser tip and a narrow field of view to visualize all relevant vascular connections. In this letter, we report on a mechatronic design for a comanipulated instrument that combines concentric tube actuation to a larger manipulator constrained by a remote centre of motion. A stereoscopic camera is mounted at the distal tip and used for imaging. Our mechanism provides enhanced dexterity and stability of the imaging device. We demonstrate that the imaging system can be used for computing geometry and enhancing the view at the operating site. Results using electromagnetic sensors for verification and comparison to visual odometry from the distal sensor show that our system is promising and can be developed further for multiple clinical needs in fetoscopic procedures

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Analysis of the radiative decays among the charmonium states

In this article, we study the radiative decays among the charmonium states with the heavy quark effective theory, and make predictions for the ratios among the radiative decay widths of an special multiplet to another multiplet. The predictions can be confronted with the experimental data in the future and put additional constraints in identifying the $X$, $Y$, $Z$ charmonium-like mesons.Comment: 12 pages, revised revisio

Regional circulation patterns of Mediterranean Outflow Water near the Iberian and African continental slopes

The Mediterranean Outflow Water (MOW) is a dense water mass originated in the Strait of Gibraltar. Downstream of the Gulf of Cádiz, the MOW forms a reservoir region west of the Iberian continental slopes at a buoyant depth of approximately 1000&thinsp;m. This region plays a key role as the main centre where the MOW is mixed and distributed into the North Atlantic. The seafloor in this area is characterized by the presence of a complex bathymetry with three abyssal plains separated by mountain chains. Although the topographic features do not reach the surface, they influence ocean flows at intermediate and deep ocean layers, conditioning the distribution and circulation of MOW. The Copernicus Marine Environmental Monitoring Service (CMEMS) Iberian–Biscay–Ireland (IBI) ocean reanalysis is used to provide a detailed view of the circulation and mixing processes of MOW near the Iberian and African continental slopes. This work emphasizes the relevance of the complex bathymetric features defining the circulation processes of MOW in this region. The high resolution of the IBI reanalysis allows us to make a description of the mesoscale features forced by the topography. The temperature, salinity, velocity, transport, and vorticity fields are analysed to understand the circulation patterns of MOW. The high-resolution circulation patterns reveal that Horseshoe Basin and the continental slope near Cape Ghir (a.k.a. Cap Rhir or Cabo de Aguer) are key areas controlling the mixing processes of MOW with the surrounding water masses, mainly North Atlantic Central Water (NACW) and Antarctic Intermediate Water (AAIW). The water mass variability is also analysed by means of composite analysis. Results indicate the existence of a variability in the MOW tongue which retracts and expands westwards in opposition to the movement of the underlying North Atlantic Deep Water.</p

All -optical control of the quantum flow of a polariton condensate

Although photons in vacuum are massless particles that do not appreciably interact with each other, significant interactions appear in suitable nonlinear media, leading to hydrodynamic behaviours typical of quantum fluids(1-6). Here, we show the generation and manipulation of vortex-antivortex pairs in a coherent gas of strongly dressed photons (polaritons) flowing against an artificial potential barrier created and controlled by a light beam in a semiconductor microcavity. The optical control of the polariton flow allows us to reveal new quantum hydrodynamical phenomenologies such as the formation of vortex pairs upstream from the optical barrier, a case of ultra-short time excitation of the quantum flow, and the generation of vortices with counterflow trajectories. Additionally, we demonstrate how to permanently trap and store quantum vortices hydrodynamically generated in the wake of a defect. These observations are supported by time-dependent simulations based on the non-equilibrium Gross-Pitaevskii equation(7)