Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $\rho<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.Comment: 7 page

The Role of Gas in the Merging of Massive Black Holes in Galactic Nuclei. I. Black Hole Merging in a Spherical Gas Cloud

Using high-resolution SPH numerical simulations, we investigate the effects of gas on the inspiral and merger of a massive black hole binary. This study is motivated by both observational and theoretical work that indicate the presence of large amounts of gas in the central regions of merging galaxies. N-body simulations have shown that the coalescence of a massive black hole binary eventually stalls in a stellar background. However, our simulations suggest that the massive black hole binary will finally merge if it is embedded in a gaseous background. Here we present results in which the gas is assumed to be initially spherical with a relatively smooth distribution. In the early evolution of the binary, the separation dimishes due to the gravitational drag exerted by the background gas. In the later stages, when the binary dominates the gravitational potential in its vicinity, the medium responds by forming an ellipsoidal density enhancement whose axis lags behind the binary axis, and this offset produces a torque on the binary that causes continuing loss of angular momentum and is able to reduce the binary separation to distances where gravitational radiation is efficient. Assuming typical parameters from observations of Ultra Luminous Infrared Galaxies, we predict that a black hole binary will merge within $10^{7}$yrs; therefore these results imply that in a merger of gas-rich galaxies, any massive central black holes will coalescence soon after the galaxies merge. Our work thus supports scenarios of massive black hole evolution and growth where hierarchical merging plays an important role. The final coalescence of the black holes leads to gravitational radiation emission that would be detectable up to high redshift by LISA. We show that similar physical effects are important for the formation of close binary stars.Comment: 38 pages, 14 figures, submitted to Ap

Dissociation cross sections of ground-state and excited charmonia with light mesons in the quark model

We present numerical results for the dissociation cross sections of ground-state, orbitally- and radially-excited charmonia in collisions with light mesons. Our results are derived using the nonrelativistic quark model, so all parameters are determined by fits to the experimental meson spectrum. Examples of dissociation into both exclusive and inclusive final states are considered. The dissociation cross sections of several C=(+) charmonia may be of considerable importance for the study of heavy ion collisions, since these states are expected to be produced more copiously than the J/psi. The relative importance of the productions of ground-state and orbitally-excited charmed mesons in a pion-charmonium collision is demonstrated through the $\sqrt {s}$-dependent charmonium dissociation cross sections.Comment: 9 pages, 8 figure

Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure

Phase-Locking of Vortex Lattices Interacting with Periodic Pinning

We examine Shapiro steps for vortex lattices interacting with periodic pinning arrays driven by AC and DC currents. The vortex flow occurs by the motion of the interstitial vortices through the periodic potential generated by the vortices that remain pinned at the pinning sites. Shapiro steps are observed for fields B_{\phi} < B < 2.25B_{\phi} with the most pronouced steps occuring for fields where the interstitial vortex lattice has a high degree of symmetry. The widths of the phase-locked current steps as a function of the magnitude of the AC driving are found to follow a Bessel function in agreement with theory.Comment: 5 pages 5 postscript figure

PEG Branched Polymer for Functionalization of Nanomaterials with Ultralong Blood Circulation

Nanomaterials have been actively pursued for biological and medical applications in recent years. Here, we report the synthesis of several new poly(ethylene glycol) grafted branched-polymers for functionalization of various nanomaterials including carbon nanotubes, gold nanoparticles (NP) and gold nanorods (NRs), affording high aqueous solubility and stability for these materials. We synthesize different surfactant polymers based upon poly-(g-glutamic acid) (gPGA) and poly(maleic anhydride-alt-1-octadecene) (PMHC18). We use the abundant free carboxylic acid groups of gPGA for attaching lipophilic species such as pyrene or phospholipid, which bind to nanomaterials via robust physisorption. Additionally, the remaining carboxylic acids on gPGA or the amine-reactive anhydrides of PMHC18 are then PEGylated, providing extended hydrophilic groups, affording polymeric amphiphiles. We show that single-walled carbon nanotubes (SWNTs), Au NPs and NRs functionalized by the polymers exhibit high stability in aqueous solutions at different pHs, at elevated temperatures and in serum. Morever, the polymer-coated SWNTs exhibit remarkably long blood circulation (t1/2 22.1 h) upon intravenous injection into mice, far exceeding the previous record of 5.4 h. The ultra-long blood circulation time suggests greatly delayed clearance of nanomaterials by the reticuloendothelial system (RES) of mice, a highly desired property for in vivo applications of nanomaterials, including imaging and drug delivery

Multi-wavelength analysis of high energy electrons in solar flares: a case study of August 20, 2002 flare

A multi-wavelength spatial and temporal analysis of solar high energy electrons is conducted using the August 20, 2002 flare of an unusually flat (gamma=1.8) hard X-ray spectrum. The flare is studied using RHESSI, Halpha, radio, TRACE, and MDI observations with advanced methods and techniques never previously applied in the solar flare context. A new method to account for X-ray Compton backscattering in the photosphere (photospheric albedo) has been used to deduce the primary X-ray flare spectra. The mean electron flux distribution has been analysed using both forward fitting and model independent inversion methods of spectral analysis. We show that the contribution of the photospheric albedo to the photon spectrum modifies the calculated mean electron flux distribution, mainly at energies below 100 keV. The positions of the Halpha emission and hard X-ray sources with respect to the current-free extrapolation of the MDI photospheric magnetic field and the characteristics of the radio emission provide evidence of the closed geometry of the magnetic field structure and the flare process in low altitude magnetic loops. In agreement with the predictions of some solar flare models, the hard X-ray sources are located on the external edges of the Halpha emission and show chromospheric plasma heated by the non-thermal electrons. The fast changes of Halpha intensities are located not only inside the hard X-ray sources, as expected if they are the signatures of the chromospheric response to the electron bombardment, but also away from them.Comment: 26 pages, 9 figures, accepted to Solar Physic

A New Class of Changing-Look LINERs

We report the discovery of six active galactic nuclei (AGN) caught "turning on" during the first nine months of the Zwicky Transient Facility (ZTF) survey. The host galaxies were classified as LINERs by weak narrow forbidden line emission in their archival SDSS spectra, and detected by ZTF as nuclear transients. In five of the cases, we found via follow-up spectroscopy that they had transformed into broad-line AGN, reminiscent of the changing-look LINER iPTF 16bco. In one case, ZTF18aajupnt/AT2018dyk, follow-up HST UV and ground-based optical spectra revealed the transformation into a narrow-line Seyfert 1 (NLS1) with strong [Fe VII, X, XIV] and He II 4686 coronal lines. Swift monitoring observations of this source reveal bright UV emission that tracks the optical flare, accompanied by a luminous soft X-ray flare that peaks ~60 days later. Spitzer follow-up observations also detect a luminous mid-infrared flare implying a large covering fraction of dust. Archival light curves of the entire sample from CRTS, ATLAS, and ASAS-SN constrain the onset of the optical nuclear flaring from a prolonged quiescent state. Here we present the systematic selection and follow-up of this new class of changing-look LINERs, compare their properties to previously reported changing-look Seyfert galaxies, and conclude that they are a unique class of transients well-suited to test the uncertain physical processes associated with the LINER accretion state.Comment: Submitted to ApJ, 31 pages, 17 Figures (excluding Appendix due to file size constraints but will be available in electronic version