Nonlinear Diffusion and Image Contour Enhancement

The theory of degenerate parabolic equations of the forms $$u_t=(\Phi(u_x))_{x} \quad {\rm and} \quad v_{t}=(\Phi(v))_{xx}$$ is used to analyze the process of contour enhancement in image processing, based on the evolution model of Sethian and Malladi. The problem is studied in the framework of nonlinear diffusion equations. It turns out that the standard initial-value problem solved in this theory does not fit the present application since it it does not produce image concentration. Due to the degenerate character of the diffusivity at high gradient values, a new free boundary problem with singular boundary data can be introduced, and it can be solved by means of a non-trivial problem transformation. The asymptotic convergence to a sharp contour is established and rates calculated.Comment: 29 pages, includes 6 figure

Hybrid Natural Inflation

We construct two simple effective field theory versions of {\it Hybrid Natural Inflation (HNI)} that illustrate the range of its phenomenological implications. The resulting inflationary sector potential, $V=\Delta^4(1+a\cos(\phi/f))$, arises naturally, with the inflaton field a pseudo-Nambu-Goldstone boson. The end of inflation is triggered by a waterfall field and the conditions for this to happen are determined. Also of interest is the fact that the slow-roll parameter $\epsilon$ (and hence the tensor $r$) is a non-monotonic function of the field with a maximum where observables take universal values that determines the maximum possible tensor to scalar ratio $r$. In one of the models the inflationary scale can be as low as the electroweak scale. We explore in detail the associated HNI phenomenology, taking account of the constraints from Black Hole production, and perform a detailed fit to the Planck 2015 temperature and polarisation data.Comment: V2: 19 pages, 2 figures, 1 table. Extended discussions and new references added. Version accepted for publication in JHE

Étude du processus de nitratation avec des boues activées : effet inhibiteur de l'ammoniac sur les bactéries nitratantes

Cet article porte sur l'étude de la réaction de nitratation (oxydation de nitrites en nitrates) par voie biologique aérobie avec des bactéries autotrophes nitratantes. Les phénomènes d'inhibition de l'ammoniac sur l'activité nitratante de populations microbiennes issues de boues activées (populations mixtes ou enrichies en bactéries nitratantes) ont été caractérisés.A l'aide d'une méthodologie faisant appel à la respirométrie, les caractéristiques de la population enrichie ont été définies :- les conditions optimales de mise en oeuvre sont un pH de 7,8 et une température de 29·C- les paramètres cinétiques définissant les performances sont QSmax=61 mgN-NO2-/gMVS×h et KS=3,04 mgN-NO2-/l- cette population présente une bonne tolérance vis-à-vis de NH3, une inhibition de 60% de la respiration des bactéries nitratantes ayant été obtenue pour 11,4 mgN-NH3/l.Les mêmes effets inhibiteurs ont été observés lors de la mise en culture discontinue de populations mixtes dans les conditions optimales de pH et température. Dans ces conditions de mise en oeuvre, différentes cultures dont les concentrations en biomasse totale ont varié de 0,1 à 2 gMVS/l, en présence de 3 mgN-NH3/l, ont présenté la même vitesse spécifique de nitratation. Ces phénomènes d'inhibition de la nitratation par NH3 paraissent complexes et fortement dépendant de facteurs environnementaux qui agissent sur la dynamique de croissance de ces bactéries.This paper focuses both on nitrification and on inhibition by ammonia of the bacteria responsible for this process in activated sludge (nitrifying bacteria). Nitrification (autotrophic nitrite oxidation to nitrate) is the limiting step in wastewater treatment plants during nitrogen biological treatment (ammonia is known as the major inhibitor). To assess the effects of environmental conditions on nitrification, respirometric measurements of a nitrifying bacteria-enriched activated sludge were carried out using a chemostat providing a stable nitrite-oxidizing population. The influence of pH, temperature, and the free ammonia concentration [NH3-N] was studied. The maximum activity of the nitrifying bacteria was found at pH 7.8 and at 29 oC, with the 90% range of maximum activity lying between pH values of 7.5 and 8.1. Activation and deactivation energies for nitrification were estimated by Arrhenius analysis to be 12.2 and - 41.5 kcal/mol, respectively. A Q10 value (multiplicative factor of oxygen consumption rate for each 10oC increase) of 2.8 was determined. Saturation or half-velocity coefficient (Ks) and maximum specific rate of nitrite oxidation (QSmax) were calculated by respirometric measurements, and are 3.04 mg NO2--N/l and 61 mg NO2--N/g VSS.h, respectively. In the study of effect of free ammonia, respirometric measurements were performed at ammonia concentrations ranging from 0.1 to 70 mg NH3-N/l. For a concentration of 11.4 mg NH3-N/l, a nitrification inhibition degree of 60% was reached. Contrary to the work of Anthonisen et al. (1976), which showed total inhibition of nitrifying bacteria at a concentration of 1 mg NH3-N/l, our results indicate a residual respiration, even at a concentration of 70 mg NH3-N/l. This displacement of total inhibition could be due to the predominance of nitrifying bacteria in the activated sludge used.In the second phase of the present research, our results were validated for another mixed bacterial population that was not enriched in nitrifying bacteria. Different concentrations of NH3 were imposed in flask cultures of nitrifying activated sludge, to assess the inhibition thresholds for ammonia. Between 0 and 10 mg NH3-N/l, the degrees of inhibition were inferior to those obtained by respirometric measurements for cultures enriched with nitrifying bacteria, except at 10 mg NH3-N/l, where about 58% inhibition was achieved. The effect of the total biomass concentration of nitrifying activated sludge was also studied. An ammonia concentration of 3 mg NH3-N/l was used in flask cultures with different biomass concentrations (0.1 to 2 g VSS/l). This variable was not significant as similar specific nitrite oxidation rates were measured in all cultures. Inhibitory effects of ammonia on nitrifying bacteria activity seem to be complex and strongly dependent on other environmental factors which modify the dynamics of biomass growth

Enhancement in the Photoluminescence Properties of SiO2:Ge Embedded in a Polymeric Matrix

Polymer films of styrene butadiene copolymer (SBC) mixed with SiO2:Ge powder were successfully obtained by the drop casting method. The SBC concentration (in chloroform solution) was 10%w/v and the SiO2:Ge powder was mixed (mass ratio 80:20 respectively). The thicknesses of the films obtained were 50, 100, and 200 μm. In addition, polymer films of polytetrafluoroethylene (PTFE) preparation (60% dispersion in water), were obtained mixing 2 ml of PTFE and 0.05g of SiO2:Ge powder with a mass relation of 98% polymer and 2% SiO2:Ge. The photoluminescence emission spectra (PL) of SBC doped with SiO2:Ge resulted in similar characteristics to those for SiO2:Ge powders, although their intensity shows an increase 3.5 times approximately, compared with the pure powder. On the other hand, the PTFE films with SiO2:Ge present just one peak in the PL emission at 439 nm but their intensity increases 18 times respect to the powder. The photoluminescence excitation (PLE) spectra of the SiO2:Ge powders show the characteristic peaks at 248 nm (most intense) and at 366 nm. However, when the powder is embedded either in SBC or PTFE the peak at 366 nm shows an important increase which seems to indicate an energy transfer from the polymer to the SiO2:Ge

CMOS-3D smart imager architectures for feature detection

This paper reports a multi-layered smart image sensor architecture for feature extraction based on detection of interest points. The architecture is conceived for 3-D integrated circuit technologies consisting of two layers (tiers) plus memory. The top tier includes sensing and processing circuitry aimed to perform Gaussian filtering and generate Gaussian pyramids in fully concurrent way. The circuitry in this tier operates in mixed-signal domain. It embeds in-pixel correlated double sampling, a switched-capacitor network for Gaussian pyramid generation, analog memories and a comparator for in-pixel analog-to-digital conversion. This tier can be further split into two for improved resolution; one containing the sensors and another containing a capacitor per sensor plus the mixed-signal processing circuitry. Regarding the bottom tier, it embeds digital circuitry entitled for the calculation of Harris, Hessian, and difference-of-Gaussian detectors. The overall system can hence be configured by the user to detect interest points by using the algorithm out of these three better suited to practical applications. The paper describes the different kind of algorithms featured and the circuitry employed at top and bottom tiers. The Gaussian pyramid is implemented with a switched-capacitor network in less than 50 μs, outperforming more conventional solutions.Xunta de Galicia 10PXIB206037PRMinisterio de Ciencia e Innovación TEC2009-12686, IPT-2011-1625-430000Office of Naval Research N00014111031

Radiation hardness of small-pitch 3D pixel sensors up to HL-LHC fluences

A new generation of 3D silicon pixel detectors with a small pixel size of 50$\times$50 and 25$\times$100 $\mu$m$^{2}$ is being developed for the HL-LHC tracker upgrades. The radiation hardness of such detectors was studied in beam tests after irradiation to HL-LHC fluences up to $1.4\times10^{16}$ n$_{\mathrm{eq}}$/cm$^2$. At this fluence, an operation voltage of only 100 V is needed to achieve 97% hit efficiency, with a power dissipation of 13 mW/cm$^2$ at -25$^{\circ}$C, considerably lower than for previous 3D sensor generations and planar sensors.Comment: 5 pages, 2 figures, Proceedings of TIPP 2017, Beijing (International Conference on The Technology and Instrumentation in Particle Physics 2017

Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation

We study qualitative and quantitative properties of local weak solutions of the fast $p$-Laplacian equation, $\partial_t u=\Delta_{p}u$, with $1<p<2$. Our main results are quantitative positivity and boundedness estimates for locally defined solutions in domains of \RR^n\times [0,T]. We combine these lower and upper bounds in different forms of intrinsic Harnack inequalities, which are new in the very fast diffusion range, that is when $1<p \le 2n/(n+1)$. The boundedness results may be also extended to the limit case $p=1$, while the positivity estimates cannot. We prove the existence as well as sharp asymptotic estimates for the so-called large solutions for any $1<p<2$, and point out their main properties. We also prove a new local energy inequality for suitable norms of the gradients of the solutions. As a consequence, we prove that bounded local weak solutions are indeed local strong solutions, more precisely $\partial_t u\in L^2_{\rm loc}$

Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic forces. For hard interaction potentials, discrete breathers in this model are known to exist either as ``optic breathers'' with frequencies above the optic band, or as ``acoustic breathers'' with frequencies in the gap between the acoustic and the optic band. In this paper, bifurcations between different types of discrete breathers are found numerically, with the mass ratio m and the breather frequency omega as bifurcation parameters. We identify a period tripling bifurcation around optic breathers, which leads to new breather solutions with frequencies in the gap, and a second local bifurcation around acoustic breathers. These results provide new breather solutions of the FPU system which interpolate between the classical acoustic and optic modes. The two bifurcation lines originate from a particular ``corner'' in parameter space (omega,m). As parameters lie near this corner, we prove by means of a center manifold reduction that small amplitude solutions can be described by a four-dimensional reversible map. This allows us to derive formally a continuum limit differential equation which characterizes at leading order the numerically observed bifurcations.Comment: 30 pages, 10 figure

Mass media destabilizes the cultural homogeneous regime in Axelrod's model

An important feature of Axelrod's model for culture dissemination or social influence is the emergence of many multicultural absorbing states, despite the fact that the local rules that specify the agents interactions are explicitly designed to decrease the cultural differences between agents. Here we re-examine the problem of introducing an external, global interaction -- the mass media -- in the rules of Axelrod's model: in addition to their nearest-neighbors, each agent has a certain probability $p$ to interact with a virtual neighbor whose cultural features are fixed from the outset. Most surprisingly, this apparently homogenizing effect actually increases the cultural diversity of the population. We show that, contrary to previous claims in the literature, even a vanishingly small value of $p$ is sufficient to destabilize the homogeneous regime for very large lattice sizes