A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

From Full stopping to transparency in a holographic model of heavy ion collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Tailoring the surface density of silicon nanocrystals embedded in SiOx single layers

In this article, we explore the possibility of modifying the silicon nanocrystal areal density in SiOx single layers, while keeping constant their size. For this purpose, a set of SiOx monolayers with controlled thickness between two thick SiO2 layers has been fabricated, for four different compositions (x=1, 1.25, 1.5, or 1.75). The structural properties of the SiO x single layers have been analyzed by transmission electron microscopy (TEM) in planar view geometry. Energy-filtered TEM images revealed an almost constant Si-cluster size and a slight increase in the cluster areal density as the silicon content increases in the layers, while high resolution TEM images show that the size of the Si crystalline precipitates largely decreases as the SiO x stoichiometry approaches that of SiO2. The crystalline fraction was evaluated by combining the results from both techniques, finding a crystallinity reduction from 75% to 40%, for x = 1 and 1.75, respectively. Complementary photoluminescence measurements corroborate the precipitation of Si-nanocrystals with excellent emission properties for layers with the largest amount of excess silicon. The integrated emission from the nanoaggregates perfectly scales with their crystalline state, with no detectable emission for crystalline fractions below 40%. The combination of the structural and luminescence observations suggests that small Si precipitates are submitted to a higher compressive local stress applied by the SiO2 matrix that could inhibit the phase separation and, in turn, promotes the creation of nonradiative paths.

Microwave spectrometry for the Evaluation of the structural integrity of metallic stents

Purpose: To assess the feasibility of a method based on microwave spectrometry to detect structural distortions of metallic stents in open air conditions and envisage the prospects of this approach toward possible medical applicability for the evaluation of implanted stents. Methods: Microwave absorbance spectra between 2.0 and 18.0 GHz were acquired in open air for the characterization of a set of commercial stents using a specifically design setup. Rotating each sample over 360º, 2D absorbance diagrams were generated as a function of frequency and rotation angle. To check our approach for detecting changes in stent length (fracture) and diameter (recoil), two specific tests were performed in open air. Finally, with a few adjustments, this same system provides 2D absorbance diagrams of stents immersed in a water-based phantom, this time over a bandwidth ranging from 0.2 to 1.8 GHz. Results: The authors show that metallic stents exhibit characteristic resonant frequencies in their microwave absorbance spectra in open air which depend on their length and, as a result, may reflect the occurrence of structural distortions. These resonances can be understood considering that such devices behave like dipole antennas in terms of microwave scattering. From fracture tests, the authors infer that microwave spectrometry provides signs of presence of Type I to Type IV stent fractures and allows in particular a quantitative evaluation of Type III and Type IV fractures. Recoil tests show that microwave spectrometry seems able to provide some quantitative assessment of diametrical shrinkage, but only if it involves longitudinal shortening. Finally, the authors observe that the resonant frequencies of stents placed inside the phantom shift down with respect to the corresponding open air frequencies, as it should be expected considering the increase of dielectric permittivity from air to water. Conclusions: The evaluation of stent resonant frequencies provided by microwave spectrometry allows detection and some quantitative assessment of stent fracture and recoil in open air conditions. Resonances of stents immersed in water can be also detected and their characteristic frequencies are in good agreement with theoretical estimates. Although these are promising results, further verifica tion in a more relevant phantom is required in order to foresee the real potential of this approach.

Effect of the surface charge discretization on electric double layers. A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups,a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

Architectural characterization of a delta-front reservoir analogue combining ground penetrating radar and electrical resistivity tomography: Roda Sandstone (Lower Eocene, Graus-Tremp basin, Spain)

Three-dimensional reconstruction of reservoir analogues can be improved combining data from different geophysical methods. Ground Penetrating Radar (GPR) and Electrical Resistivity Tomography (ERT) data are valuable tools, since they provide subsurface information from internal architecture and facies distribution of sedimentary rock bodies, enabling the upgrading of depositional models and heterogeneity reconstruction. The Lower Eocene Roda Sandstone is a well-known deltaic complex widely studied as a reservoir analogue that displays a series of sandstone wedges with a general NE to SW progradational trend. To provide a better understanding of internal heterogeneity of a 10m-thick progradational delta-front sandstone unit, 3D GPR data were acquired. In addition, common midpoints (CMP) to measure the sandstone subsoil velocity, test profiles with different frequency antennas (25, 50 and 100MHz) and topographic data for subsequent correction in the geophysical data were also obtained. Three ERT profiles were also acquired to further constrain GPR analysis. These geophysical results illustrate the geometry of reservoir analogue heterogeneities both depositional and diagenetic in nature, improving and complementing previous outcrop-derived data. GPR interpretation using radar stratigraphy principles and attributes analysis provided: 1)tridimensional geometry of major stratigraphic surfaces that define four units in the GPR Prism, 2) image the internal architecture of the units and their statistical study of azimuth and dips, useful for a quick determination of paleocurrent directions. These results were used to define the depositional architecture of the progradational sandbody that shows an arrangement in very-high-frequency sequences characterized by clockwise paleocurrent variations and decrease of the sedimentary flow, similar to those observed at a greater scale in the same system. This high-frequency sequential arrangement has been attributed to the autocyclic dynamics of a supply-dominated delta- front where fluvial and tidal currents are in competition. The resistivity models enhanced the viewing of reservoir quality associated with cement distribution caused by depositional and early diagenetic processes related to the development of transgressive and regressive systems tracts in igh-frequency sequences.

Nanoantenna enhanced emission of lightharvesting complex 2: the role of resonance, polarization, and radiative and non-radiative rates

Nanoantennae show potential for photosynthesis research for two reasons; first by spatially confining light for experiments which require high spatial resolution, and second by enhancing the photon emission of single light-harvesting complexes. For effective use of nanoantennae a detailed understanding of the interaction between the nanoantenna and the light-harvesting complex is required. Here we report how the excitation and emission of multiple purple bacterial LH2s (light-harvesting complex 2) are controlled by single gold nanorod antennae. LH2 complexes were chemically attached to such antennae, and the antenna length was systematically varied to tune the resonance with respect to the LH2 absorption and emission. There are three main findings. (i) The polarization of the LH2 emission is fully controlled by the resonant nanoantenna. (ii) The largest fluorescence enhancement, of 23 times, is reached for excitation with light at λ = 850 nm, polarized along the long antenna-axis of the resonant antenna. The excitation enhancement is found to be 6 times, while the emission efficiency is increased 3.6 times. (iii) The fluorescence lifetime of LH2 depends strongly on the antenna length, with shortest lifetimes of [similar]40 ps for the resonant antenna. The lifetime shortening arises from an 11 times resonant enhancement of the radiative rate, together with a 2–3 times increase of the non-radiative rate, compared to the off-resonant antenna. The observed length dependence of radiative and non-radiative rate enhancement is in good agreement with simulations. Overall this work gives a complete picture of how the excitation and emission of multi-pigment light-harvesting complexes are influenced by a dipole nanoantenna.

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system

An octree isosurface codification based on discrete planes

Describes a method to code a decimated model of an isosurface on an octree representation while maintaining volume data if it is needed. The proposed technique is based on grouping the marching cubes (MC) patterns into five configurations according the topology and the number of planes of the surface that are contained in a cell. Moreover, the discrete number of planes on which the surface lays is fixed. Starting from a complete volume octree, with the isosurface codified at terminal nodes according to the new configuration, a bottom-up strategy is taken for merging cells. Such a strategy allows one to implicitly represent co-planar faces in the upper octree levels without introducing any error. At the end of this merging process, when it is required, a reconstruction strategy is applied to generate the surface contained in the octree intersected leaves. Some examples with medical data demonstrate that a reduction of up to 50% in the number of polygons can be achieved

Disseny pràctic d'un transmissor d'àudio complert utilitzant una modulació AM

Un transmissor d’AM (modulació per amplitud), utilitza una de les moltes tècniques de modulació existents avui en dia. És molta la importància que té la modulació de senyals i aquests en són alguns exemples: -Facilita la propagació del senyal per cable o per aire. -Ordena l’espectre, distribuint Canals a les diferents informacions. -Disminueix la dimensió de les antenes. -Optimitza l’ample de banda de cada canal. -Evita interferències entre Canals. -Protegeix la informació de les degradacions per soroll. -Defineix la qualitat de la informació transmesa. L’objectiu principal d’aquest treball, serà realitzar un transmissor d’AM utilitzant components electrònics disponibles al mercat. Això es realitzarà mitjançant diversos procediments de disseny. Es realitzarà un procediment de disseny teòric, tot utilitzant els “datasheets” dels diferents components. Es realitzarà un procediment de disseny mitjançant la simulació, gràcies al qual es podrà provar el disseny del dispositiu i realitzar-ne algunes parts impossibles a reproduir teòricament. I finalment es realitzarà el dispositiu a la pràctica. Entre les conclusions més rellevants obtingudes en aquest treball, voldríem destacar la importància de la simulació per poder dissenyar circuits de radiofreqüència. En aquest treball s’ha demostrat que gràcies a una bona simulació, el primer prototip de dispositiu creat ens ha funcionat a la perfecció. D’altre banda, també comentar la importància d’un disseny adequat d’antena per poder aprofitar al màxim el rendiment del nostre dispositiu. Per concloure, la realització d’un aparell transmissor aporta unes nocions equilibrades d’electrònica i telecomunicacions importants per al disseny de dispositius de comunicació.