Orthogonal polynomials for area-type measures and image recovery

Let $G$ be a finite union of disjoint and bounded Jordan domains in the complex plane, let $\mathcal{K}$ be a compact subset of $G$ and consider the set $G^\star$ obtained from $G$ by removing $\mathcal{K}$; i.e., $G^\star:=G\setminus \mathcal{K}$. We refer to $G$ as an archipelago and $G^\star$ as an archipelago with lakes. Denote by $\{p_n(G,z)\}_{n=0}^\infty$ and $\{p_n(G^\star,z)\}_{n=0}^\infty$, the sequences of the Bergman polynomials associated with $G$ and $G^\star$, respectively; that is, the orthonormal polynomials with respect to the area measure on $G$ and $G^\star$. The purpose of the paper is to show that $p_n(G,z)$ and $p_n(G^\star,z)$ have comparable asymptotic properties, thereby demonstrating that the asymptotic properties of the Bergman polynomials for $G^\star$ are determined by the boundary of $G$. As a consequence we can analyze certain asymptotic properties of $p_n(G^\star,z)$ by using the corresponding results for $p_n(G,z)$, which were obtained in a recent work by B. Gustafsson, M. Putinar, and two of the present authors. The results lead to a reconstruction algorithm for recovering the shape of an archipelago with lakes from a partial set of its complex moments.Comment: 24 pages, 9 figure

Dust Formation and He II 4686 emission in the Dense Shell of the Peculiar Type Ib Supernova 2006jc

We present evidence for the formation of dust grains in an unusual Type Ib SN based on late-time spectra of SN 2006jc. The progenitor suffered an LBV-like outburst just 2 yr earlier, and we propose that the dust formation is a consequence of the SN blast wave overtaking that LBV-like shell. The key evidence for dust formation is (a) the appearance of a red/near-IR continuum source fit by 1600 K graphite grains, and (b) fading of the redshifted sides of He I emission lines, yielding progressively more asymmetric blueshifted lines as dust obscures receding material. This provides the strongest case yet for dust formation in any SN Ib/c. Both developments occurred between 51 and 75 d after peak, while other SNe observed to form dust did so after a few hundred days. Geometric considerations indicate that dust formed in the dense swept-up shell between the forward and reverse shocks, and not in the freely expanding SN ejecta. Rapid cooling leading to dust formation may have been aided by extremely high shell densities, as indicated by He I line ratios. The brief epoch of dust formation is accompanied by He II 4686 emission and enhanced X-ray emission. These clues suggest that the unusual dust formation in this object was not due to properties of the SN itself, but instead -- like most peculiarities of SN 2006jc -- was a consequence of the dense environment created by an LBV-like eruption 2 yr before the SN.Comment: ApJ, accepted. added some discussion and 2 figures, better title, conclusions same as previous version. 12 pages, 4 color fig

Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons

Runaway electrons with strongly anisotropic distributions present in post-disruption tokamak plasmas can destabilize the extraordinary electron (EXEL) wave. The present work investigates the dynamics of the quasi-linear evolution of the EXEL instability for a range of different plasma parameters using a model runaway distribution function valid for highly relativistic runaway electron beams produced primarily by the avalanche process. Simulations show a rapid pitch-angle scattering of the runaway electrons in the high energy tail on the $100-1000\;\rm \mu s$ time scale. Due to the wave-particle interaction, a modification to the synchrotron radiation spectrum emitted by the runaway electron population is foreseen, exposing a possible experimental detection method for such an interaction

The 2006 hot phase of Romano's star (GR 290) in M33

Understanding the nature of the instabilities of LBVs is important to understand the late evolutionary stages of very massive stars. We investigate the long term, S Dor-type variability of the luminous blue variable GR290 (Romano's star) in M33, and its 2006 minimum phase. New spectroscopic and photometric data taken in November and December 2006 were employed in conjunction with already published data on GR290 to derive the physical structure of GR290 in different phases and the time scale of the variability. We find that by the end of 2006, GR 290 had reached the deepest visual minimum so far recorded. Its present spectrum resembles closely that of the Of/WN9 stars, and is the hottest so far recorded in this star (and in any LBV as well), while its visual brightness decreased by about 1.4 mag. This first spectroscopic record of GR290 during a minimum phase confirms that, similarly to AG Car and other LBVs, the star is subject to ample S Dor-type variations, being hotter at minimum, suggesting that the variations take place at constant bolometric luminosity.Comment: 4 figures, 1 table, accepted for publication in A&A Letter

Data-driven Control Method for Impinging Jets

A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The approach, based on a dynamic mode decomposition reduced order model (DMD-ROM), determines forcing receptivity in an economical manner by projecting flow and actuator-specific forcing snapshots onto a reduced subspace and then evolving the results forward in time. Since it effectively determines a linear response around the unsteady flow in the time-domain, the method differs materially from typical techniques that use steady basic states, such as stability or input-output approaches that employ linearized Navier-Stokes operators in the frequency-domain. The method naturally accounts for factors inherent to the snapshot basis, including configuration complexity and flow parameters such as Reynolds number. Furthermore, gain metrics calculated in the reduced subspace facilitate rapid assessments of flow sensitivities to a wide range of forcing parameters, from which optimal actuator inputs may be selected and results confirmed in scale-resolved simulations or experiments. The DMD-ROM approach is demonstrated from two different perspectives. The first concerns asymptotic feedback resonance, where the effects of harmonic pressure forcing are estimated and verified with nonlinear simulations using a blowing-suction actuator. The second examines time-local behavior within critical feedback events, where the phase of actuation becomes important. For this, a conditional space-time mode is used to identify the optimal forcing phase that minimizes convective instability initiation within the resonance cycle.Comment: 10 pages, 7 figure

Discovery of Precursor LBV Outbursts in Two Recent Optical Transients: The Fitfully Variable Missing Links UGC 2773-OT and SN 2009ip

We present progenitor-star detections, light curves, and optical spectra of SN2009ip and the 2009 optical transient in UGC2773 (U2773-OT), which were not genuine SNe. Precursor variability in the decade before outburst indicates that both of the progenitor stars were LBVs. Their pre-outburst light curves resemble the S Doradus phases that preceded giant eruptions of eta Carinae and SN1954J (V12 in NGC2403), with intermediate progenitor luminosities. HST detections a decade before discovery indicate that the SN2009ip and U2773-OT progenitors were supergiants with likely initial masses of 50-80 Msun and \ga20 Msun, respectively. Both outbursts had spectra befitting known LBVs, although in different physical states. SN 2009ip exhibited a hot LBV spectrum with characteristic speeds of 550 km/s, plus faster material up to 5000 km/s, resembling the slow Homunculus and fast blast wave of eta Carinae. U2773-OT shows a forest of narrow absorption and emission lines comparable to that of S Dor in its cool state, plus [CaII] emission and an IR excess indicative of dust, similar to SN2008S and N300-OT. [CaII] emission is probably tied to a dusty pre-outburst environment, and not the outburst mechanism. SN2009ip and U2773-OT may provide a critical link between historical LBV eruptions, while U2773-OT may provide a link between LBVs and SN2008S and N300-OT. Future searches will uncover more examples of precursor LBV variability of this kind, providing key clues that may help unravel the instability driving LBVs.Comment: 18 pages, 13 Figures, accepted AJ. added significant material while revising after referee repor

MN112: a new Galactic candidate Luminous Blue Variable

We report the discovery of a new Galactic candidate Luminous Blue Variable (cLBV) via detection of an infrared circular nebula and follow-up spectroscopy of its central star. The nebula, MN112, is one of many dozens of circular nebulae detected at $24 \mu$m in the {\it Spitzer Space Telescope} archival data, whose morphology is similar to that of nebulae associated with known (c)LBVs and related evolved massive stars. Specifically, the core-halo morphology of MN112 bears a striking resemblance to the circumstellar nebula associated with the Galactic cLBV GAL 079.29+00.46, which suggests that both nebulae might have a similar origin and that the central star of MN112 is a LBV. The spectroscopy of the central star showed that its spectrum is almost identical to that of the bona fide LBV P Cygni, which also supports the LBV classification of the object. To further constrain the nature of MN112, we searched for signatures of possible high-amplitude (\ga 1 mag) photometric variability of the central star using archival and newly obtained photometric data covering a 45 year period. We found that the B magnitude of the star was constant ($\simeq$ 17.1$\pm$0.3 mag) over this period, while in the I band the star brightened by $\simeq 0.4$ mag during the last 17 years. Although the non-detection of large photometric variability leads us to use the prefix `candidate' in the classification of MN112, we remind that the long-term photometric stability is not unusual for genuine LBVs and that the brightness of P Cygni remains relatively stable during the last three centuries.Comment: 6 pages, 3 figures, accepted to MNRA

Rapid Microfluidic Preparation of Niosomes for Targeted Drug Delivery

Niosomes are non-ionic surfactant-based vesicles with high promise for drug delivery applications. They can be rapidly prepared via microfluidics, allowing their reproducible production without the need of a subsequent size reduction step, by controlled mixing of two miscible phases of an organic (lipids dissolved in alcohol) and an aqueous solution in a microchannel. The control of niosome properties and the implementation of more complex functions, however, thus far are largely unknown for this method. Here we investigate microfluidics-based manufacturing of topotecan (TPT)-loaded polyethylene glycolated niosomes (PEGNIO). The flow rate ratio of the organic and aqueous phases was varied and optimized. Furthermore, the surface of TPT-loaded PEGNIO was modified with a tumor homing and penetrating peptide (tLyp-1). The designed nanoparticular drug delivery system composed of PEGNIO-TPT-tLyp-1 was fabricated for the first time via microfluidics in this study. The physicochemical properties were determined through dynamic light scattering (DLS) and zeta potential analysis. In vitro studies of the obtained formulations were performed on human glioblastoma (U87) cells. The results clearly indicated that tLyp-1-functionalized TPT-loaded niosomes could significantly improve anti-glioma treatment

Extended Magnetic Dome Induced by Low Pressures in Superconducting FeSe1-x_\mathrm{1\text{-}x}Sx_\mathrm{x}

We report muon spin rotation ($\mu$SR) and magnetization measurements under pressure on Fe$_{1+\delta}$Se$_\mathrm{1\text{-}x}$S$_\mathrm{x}$ with x $\approx 0.11$.Above $p\approx0.6$ GPa we find microscopic coexistence of superconductivity with an extended dome of long range magnetic order that spans a pressure range between previously reported separated magnetic phases. The magnetism initially competes on an atomic scale with the coexisting superconductivity leading to a local maximum and minimum of the superconducting $T_\mathrm{c}(p)$. The maximum of $T_\mathrm{c}$ corresponds to the onset of magnetism while the minimum coincides with the pressure of strongest competition. A shift of the maximum of $T_\mathrm{c}(p)$ for a series of single crystals with x up to 0.14 roughly extrapolates to a putative magnetic and superconducting state at ambient pressure for x $\geq0.2$.Comment: 10 pages, 6 figures, including supplemental materia