Physical Sciences and Mathematics Commons^™

When Does Linear Stability Not Exclude Nonlinear Instability?, Panos Kevrekidis, D. E. Pelinovsky, A. Saxena

Panos Kevrekidis

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensional lattice with cubic …

The Expected Total Curvature Of Random Polygons, Jason Cantarella, Alexander Y. Grosberg, Robert Kusner, Clayton Shonkwiler

Robert Kusner

We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference between the expected total curvature of a random closed polygon and a random open polygon with the same number of turning angles approaches a positive constant. We show that this is true for a natural class of probability measures on polygons, and give a formula for the constant in terms of the moments of the edgelength distribution.

We then consider the symmetric measure on closed polygons of fixed total length constructed by …

Stability And Tunneling Dynamics Of A Dark-Bright Soliton Pair In A Harmonic Trap, E. T. Karamatskos, J. Stockhofe, Panos Kevrekidis, P. Schmelcher

Panos Kevrekidis

http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.043637

Mirror Symmetry For Log Calabi-Yau Surfaces I, Mark Gross, Paul Hacking, Sean Keel

Paul Hacking

We give a cononical sythetic construction of the mirror family to pairs (Y,D) where Y is a smooth projective surface and D is an anti-canonical cycle of rational curves. This mirror family is constructed as the spectrum of an explicit algebra structure on a vector space with canonical basis and multiplication rule defined in terms of counts of rational curves on Y meeting D in a single point. The elements of the canonical basis are called theta functions. Their construction depends crucially on the Gromov-Witten theory of the pair (Y,D)

Highly Nonlinear Wave Propagation In Elastic Woodpile Periodic Structures, Panos Kevrekidis

Panos Kevrekidis

In the present work, we experimentally implement, numerically compute with, and theoretically analyze a configuration in the form of a single column woodpile periodic structure. Our main finding is that a Hertzian, locally resonant, woodpile lattice offers a test bed for the formation of genuinely traveling waves composed of a strongly localized solitary wave on top of a small amplitude oscillatory tail. This type of wave, called a nanopteron, is not only motivated theoretically and numerically, but is also visualized experimentally by means of a laser Doppler vibrometer. This system can also be useful for manipulating stress waves at will, …

The Jcmt Gould Belt Survey: Evidence For Radiative Heating In Serpens Mwc 297 And Its Influence On Local Star Formation, D. Rumble, J. Hatchell, R. A. Gutermuth, H. Kirk, J. Buckle, S.F. Beaulieu, D.S. Berry, H. Broekhoven-Fiene, M.J. Currie, M. Fich, T. Jenness, D. Johnstone, J.C. Mottram, D. Nutter, K. Pattle, J.E. Pineda, C. Quinn, C. Salji, S. Tisi, S. Walker-Smith, J. Di Francesco, M.R. Hogerheijde, D. Ward-Thompson, L.E. Allen, L.A. Cieza, M.M. Dunham, P.M. Harvey, K.R. Stapelfeldt, P. Bastien, H. Bunter, M. Chen, A. Chrysostomou, S. Coude, C.J. Davis, E. Drabek-Maunder, A. Duarte-Cabral, J. Greaves, J. Gregson, W. Holland, G. Joncas, J.M. Kirk, L.B.G. Knee, S. Mairs, K. Marsh, B.C. Matthews, G. Moriarty-Schieven, J. Rawlings, J. Richer, D. Robertson, E. Rosolowsky, S. Sadavoy, H. Thomas, N. Tothill, S. Viti, G.J. White, C.D. Wilson, J. Wouterloot, J. Yates, M. Zhu

Robert A. Gutermuth

We present SCUBA-2 450 and 850 μm observations of the Serpens MWC 297 region, part of the James Clerk Maxwell Telescope (JCMT) Gould Belt Survey of nearby star-forming regions. Simulations suggest that radiative feedback influences the star formation process and we investigate observational evidence for this by constructing temperature maps. Maps are derived from the ratio of SCUBA-2 fluxes and a two-component model of the JCMT beam for a fixed dust opacity spectral index of β = 1.8. Within 40 arcsec of the B1.5Ve Herbig star MWC 297, the submillimetre fluxes are contaminated by free–free emission with a spectral index …

Dark-Bright Solitons And Their Lattices In Atomic Bose-Einstein Condensates, D. Yan, F. Tsitoura, Panos Kevrekidis, D. J. Frantzeskakis

Panos Kevrekidis

In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients gij. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even …

Indentation Of Ultrathin Elastic Films And The Emergence Of Asymptotic Isometry, Dominic Vella, Jianghui Huang, Narayanan Menon, Thomas P. Russell, Benny Davidovitch

Benny Davidovitch

We study the indentation of a thin elastic film floating at the surface of a liquid. We focus on the onset of radial wrinkles at a threshold indentation depth and the evolution of the wrinkle pattern as indentation progresses far beyond this threshold. Comparison between experiments on thin polymer films and theoretical calculations shows that the system very quickly reaches the far from threshold regime, in which wrinkles lead to the relaxation of azimuthal compression. Furthermore, when the indentation depth is sufficiently large that the wrinkles cover most of the film, we recognize a novel mechanical response in which the …

A 24Μm Point Source Catalog Of The Galactic Plane From Spitzer/Mipsgal, R. A. Gutermuth, Mark Heyer

Robert A. Gutermuth

In this contribution, we describe the applied methods to construct a 24 μm based point source catalog derived from the image data of the MIPSGAL 24 μm Galactic Plane Survey and the corresponding data products. The high quality catalog product contains 933,818 sources, with a total of 1,353,228 in the full archive catalog. The source tables include positional and photometric information derived from the 24 μm images, source quality and confusion flags, and counterpart photometry from matched 2MASS, GLIMPSE, and WISE point sources. Completeness decay data cubes are constructed at 1' angular resolution that describe the varying background levels over …

The Red Radio Ring: A Gravitationally Lensed Hyperluminous Infrared Radio Galaxy At Z=2.553 Discovered Through Citizen Science, J. E. Geach, A. More, A. Verma, P.J. Marshall, N. Jackson, P. E. Belles, R. Beswick, E. Baeten, M. Chavez, C. Cornen, B. E. Cox, T. Erben, N. J. Erickson, S. Garrington, P. A. Harrison, K. Harrington, D. H. Hughes, R. J. Ivison, C. Jordan, Y. T. Lin, A. Leauthaud, C. Lintott, S. Lynn, A. Kapadia, J. P. Kneib, C. Macmillan, M. Makler, G. Miller, A. Montana, R. Mujica, T. Muxlow, Gopal Narayanan, D. O Briain, T. O'Brien, M. Oguri, E. Paget, M. Parrish, N.P. Ross, E. Rozo, E. Rusu, E. S. Rykoff, D. Sanchez-Arguelles, R. Simpson, C. Snyder, F. P. Schloerb, M. Tecza, L. Van Waerbeke, J. Wilcox, M. Viero, G. W. Wilson, M. S. Yun, M. Zeballos

Gopal Narayanan

We report the discovery of a gravitationally lensed hyperluminous infrared galaxy (L_IR~10^13 L_sun) with strong radio emission (L_1.4GHz~10^25 W/Hz) at z=2.553. The source was identified in the citizen science project SpaceWarps through the visual inspection of tens of thousands of iJKs colour composite images of Luminous Red Galaxies (LRGs), groups and clusters of galaxies and quasars. Appearing as a partial Einstein ring (r_e~3") around an LRG at z=0.2, the galaxy is extremely bright in the sub-millimetre for a cosmological source, with the thermal dust emission approaching 1 Jy at peak. The redshift of the lensed galaxy is determined through the …

The Herschel View Of The Dominant Mode Of Galaxy Growth From Z=4 To The Present Day, C. Schreiber, M. Pannella, D. Elbaz, M. Bethermin, H. Inami, M. Dickinson, B. Magnelli, T. Wang, H. Aussel, E. Daddi, S Juneau, X. Shu, M. T. Sargent, V. Buat, S.M. Faber, H.C. Ferguson, Mauro Giavalisco, A.M. Koekemoer, G. Magdis, G.E. Morrison, C. Papovich, P. Santini, D. Scott

Mauro Giavalisco

No abstract provided.

Torque-Limited Growth Of Massive Black Holes In Galaxies Across Cosmic Tim, Daniel Angles-Alcazar, Feryal Ozel, Romeel Dave, Neal S. Katz, Juna Kollmeier, Benjamin D. Oppenheimer

Neal S. Katz

We combine cosmological hydrodynamic simulations with analytic models to evaluate the role of galaxy-scale gravitational torques on the evolution of massive black holes at the centers of star-forming galaxies. We confirm and extend our earlier results to show that torque-limited growth yields black holes and host galaxies evolving on average along the M BH-M bulge relation from early times down to z = 0 and that convergence onto the scaling relation occurs independent of the initial conditions and with no need for mass averaging through mergers or additional self-regulation processes. Smooth accretion dominates the long-term evolution, with black hole mergers …

Csi 2264: Characterizing Young Stars In Ngc 2264 With Short-Duration, Periodic Flux Dips In Their Light Curves, John Stauffer, Ann Marie Cody, Pauline Mcginnis, Luisa Rebull, Lynne A. Hillenbrand, Neal. J. Turner, John Carpenter, Peter Plavchan, Sean Carey, Susan Terebey, Maria Morales-Calderon, Silvia H.P. Alencar, Jerome Bouvier, Laura Venuti, Lee Hartmann, Nuria Calvet, Giushi Micela, Ettore Flaccomio, Inseok Song, R. A. Gutermuth, David Barrado, Frederick J. Vrba, Kevin Covey, Debbie Padgett, William Herbst, Edward Gillen, Wladimir Lyra, Marcelo Medeiros Guimaraes, Herve Bouy, Fabio Favata

Robert A. Gutermuth

We identify nine young stellar objects (YSOs) in the NGC 2264 star-forming region with optical CoRoT light curves exhibiting short-duration, shallow periodic flux dips. All of these stars have infrared excesses that are consistent with their having inner disk walls near the Keplerian co-rotation radius. The repeating photometric dips have FWHMs generally less than 1 day, depths almost always less than 15%, and periods (3 < P < 11 days) consistent with dust near the Keplerian co-rotation period. The flux dips vary considerably in their depth from epoch to epoch, but usually persist for several weeks and, in two cases, were present in data collected in successive years. For several of these stars, we also measure the photospheric rotation period and find that the rotation and dip periods are the same, as predicted by standard "disk-locking" models. We attribute these flux dips to clumps of material in or near the inner disk wall, passing through our line of sight to the stellar photosphere. In some cases, these dips are also present in simultaneous Spitzer IRAC light curves at 3.6 and 4.5 microns. We characterize the properties of these dips, and compare the stars with light curves exhibiting this behavior to other classes of YSOs in NGC 2264. A number of physical mechanisms could locally increase the dust scale height near the inner disk wall, and we discuss several of those mechanisms; the most plausible mechanisms are either a disk warp due to interaction with the stellar magnetic field or dust entrained in funnel-flow accretion columns arising near the inner disk wall.

Elevation-Dependent Warming In Mountain Regions Of The World, Mountain Research Institute, Nicolas Pepin, Raymond S. Bradley

Raymond S Bradley

"There is growing evidence that the rate of warming is amplified with elevation, such that high-mountain environments experience more rapid changes in temperature than environments at lower elevations. Elevation-dependent warming (EDW) can accelerate the rate of change in mountain ecosystems, cryospheric systems, hydrological regimes and biodiversity. Here we review important mechanisms that contribute towards EDW: snow albedo and surface-based feedbacks; water vapour changes and latent heat release; surface water vapour and radiative flux changes; surface heat loss and temperature change; and aerosols. All lead to enhanced warming with elevation (or at a critical elevation), and it is believed that combinations …

Winter Climate Extremes Over The Northeastern United States And Southeastern Canada And Teleconnections With Large-Scale Modes Of Climate Variability, Liang Ning, Raymond S. Bradley

Raymond S Bradley

The relationship between winter climate extremes across the northeastern United States and adjacent parts of Canada and some important modes of climate variability are examined to determine how these circulation patterns are related to extreme events. Linear correlations between 15 extreme climate indices related to winter daily precipitation, maximum and minimum temperature, and three dominant large-scale patterns of climate variability [the North Atlantic Oscillation (NAO), Pacific–North American (PNA) pattern, and El Niño–Southern Oscillation (ENSO)] were analyzed for the period 1950–99. The mechanisms behind these teleconnections are analyzed by applying composite analysis to the geopotential height, sea level pressure (SLP), moisture …

Transitions From Order To Disorder In Multi-Dark And Multi-Dark-Bright Soliton Atomic Clouds, Wenlong Wang, Panos Kevrekidis

Panos Kevrekidis

We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a “crystalline” configuration to that of a disordered state that can be characterized as a soliton “gas.” As our illustrative examples, we use both one-component, as well as two-component, one-dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial …

Fluctuation-Induced First Order Phase Transitions In Type-1.5 Superconductors In Zero External Field, Hannes Meier, Egor Babaev, Mats Wallin

Egor Babaev

No abstract provided.

Pathwise Sensitivity Analysis In Transient Regimes, Georgios Arampatzis, Markos Katsoulakis, Yannis Pantazis

Markos Katsoulakis

The instantaneous relative entropy (IRE) and the corresponding instantaneous Fisher information matrix (IFIM) for transient stochastic processes are presented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corresponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example.

Birational Geometry Of Cluster Algebras, Mark Gross, Paul Hacking, Sean Keel

Paul Hacking

We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric type), extend Speyer's example [Spe13] of upper cluster algebras which are not finitely generated, and show that the Fock-Goncharov dual basis conjecture is usually false.

Generating Functions, Polynomials And Vortices With Alternating Signs In Bose-Einstein Condensates, Anna M. Barry, Farshid Hajir, P. G. Kevrekidis

Farshid Hajir

In this work, we construct suitable generating functions for vortices of alternating signs in the realm of quasi-two-dimensional Bose–Einstein condensates in the large density (so-called Thomas–Fermi) limit, where the vortices can be treated as effective particles. In addition to the vortex–vortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, so-called, Tkachenko differential equation. From that equation, we reconstruct collinear few-vortex equilibria obtained in earlier work, as well as extend …

Dynamics Of Vortex Dipoles In Anisotropic Bose-Einstein Condensates, Roy H. Goodman, Panos Kevrekidis, R. Carretero-Gonzalez

Panos Kevrekidis

We study the motion of a vortex dipole in a Bose--Einstein condensate confined to an anisotropic trap. We focus on a system of ODEs describing the vortices' motion, which is in turn a reduced model of the Gross--Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction …

Vortex Chains Due To Nonpairwise Interactions And Field-Induced Phase Transitions Between States With Different Broken Symmetry In Superconductors With Competing Order Parameters, Julien Garaud, Egor Babaev

Egor Babaev

We study superconductors with two order components and phase separation driven by intercomponent density-density interaction, focusing on the phase where only one condensate has nonzero ground-state density and a competing order parameter exists only in vortex cores. We demonstrate there that multibody intervortex interactions can be strongly nonpairwise, leading to some unusual vortex patterns in an external field, such as vortex pairs and vortex chains. We demonstrate that in an external magnetic field such a system undergoes a field-driven phase transition from (broken) U(1) to (broken) U(1)×U(1) symmetries when a subdominant order parameter in the vortex cores acquires global coherence. …

Canonical Bases For Cluster Algebras, Mark Gross, Paul Hacking, Sean Keel, Maxim Kontesevich

Paul Hacking

In GHK11, Conjecture 0.6, the first three authors conjectured the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral tropical points of the mirror. Further, the structure constants for the multiplication rule in this basis should be given by counting broken lines (certain combinatorial objects, morally the tropicalisations of holomorphic discs). Here we prove the conjecture in the case of cluster varieties, where the statement is a more precise form of the Fock-Goncharov dual basis conjecture, FG06, Conjecture 4.3. In particular, under …

Spontaneous Breakdown Of Time-Reversal Symmetry Induced By Thermal Fluctuations, Johan Carlström, Egor Babaev

Egor Babaev

In systems with broken U(1) symmetry, such as superfluids, superconductors or magnets, the symmetry restoration is driven by proliferation of topological defects in the form of vortex loops. Here we discuss that in certain systems the proliferation of topological defects can, by contrast, lead to the breakdown of an additional symmetry. As a particular example we demonstrate that this effect should take place in s + is superconductors, which are widely discussed in connection with the Iron-based materials. In these systems a vortex excitation can create a “bubble" of fluctuating Z2 order parameter. Thermal excitation of vortices then leads to …

Scattering Of Matter-Waves In Spatially Inhomogeneous Environments, F. Tsitoura, P. Kruger, Panos Kevrekidis, D. J. Frantzeskakis

Panos Kevrekidis

We study scattering of quasi-one-dimensional matter waves at an interface of two spatial domains, one with repulsive and one with attractive interatomic interactions. It is shown that the incidence of a Gaussian wave packet from the repulsive to the attractive region gives rise to generation of a soliton train. More specifically, the number of emergent solitons can be controlled, e.g., by the variation of the amplitude or the width of the incoming wave packet. Furthermore, we study the reflectivity of a soliton incident from the attractive region to the repulsive one. We find the reflection coefficient numerically and employ analytical …

Moduli Of Surfaces With An Anti-Canonical Cycle, Mark Gross, Paul Hacking, Sean Keel

Paul Hacking

We prove a global torelli theorem for pairs (Y,D) where Y is a smooth projective rational surface and D ∈ |−Ky | is a cycle of rational curves, as conjectured by Friedman in 1984. In addition, we construct natural universal families for such pairs.

Solitons And Vortices In Two-Dimensional Discrete Nonlinear Schrodinger Systems With Spatially Modulated Nonlinearity, Panos Kevrekidis

Panos Kevrekidis

We consider a two-dimensional (2D) generalization of a recently proposed model [Gligorić et al., Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anticontinuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual “extended” unstaggered bright solitons, in which all sites are excited in the …

Validation Of Recent Shear Wave Velocity Models In The United States With Full-Wave Simulation, Haiying Gao, Yang Shen

Haiying Gao

Interpretations of dynamic processes and the thermal and chemical structure of the Earth depend on the accuracy of Earth models. With the growing number of velocity models constructed with different tomographic methods and seismic data sets, there is an increasing need for a systematic way to validate model accuracy and resolution. This study selects five shear wave velocity models in the U.S. and simulates full wave propagation within the 3-D structures. Surface-wave signals extracted from ambient seismic noise and regional earthquakes are compared with synthetic waveforms at multiple-frequency bands. Phase delays and cross-correlation coefficients between observed and synthetic waveforms allow …