8,557 research outputs found

    Fractional Operators, Dirichlet Averages, and Splines

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    Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

    The Detection of Outflows in the IR-Quiet Molecular Core NGC 6334 I(North)

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    We find strong evidence for outflows originating in the dense molecular core NGC 6334 I(North): a 1000 Msol molecular core distinguished by its lack of HII regions and mid-IR emission. New observations were obtained of the SiO 2-1 and 5-4 lines with the SEST 15-m telescope and the H2 (1-0) S(1) line with the ESO 2.2-m telescope. The line profiles of the SiO transitions show broad wings extending from -50 to 40 km/s, and spatial maps of the line wing emission exhibit a bipolar morphology with the peaks of the red and blue wing separated by 30". The estimated mass loss rate of the outflow is comparable to those for young intermediate to high-mass stars. The near-IR images show eight knots of H2 emission. Five of the knots form a linear chain which is displaced from the axis of the SiO outflow; these knots may trace shock excited gas along the path of a second, highly collimated outflow. We propose that I(N) is a rare example of a molecular core in an early stage of cluster formation.Comment: 4 pages, LaTeX, 3 ps figures, accepted by ApJ

    Resting state correlates of subdimensions of anxious affect

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    Resting state fMRI may help identify markers of risk for affective disorder. Given the comorbidity of anxiety and depressive disorders and the heterogeneity of these disorders as defined by DSM, an important challenge is to identify alterations in resting state brain connectivity uniquely associated with distinct profiles of negative affect. The current study aimed to address this by identifying differences in brain connectivity specifically linked to cognitive and physiological profiles of anxiety, controlling for depressed affect. We adopted a two-stage multivariate approach. Hierarchical clustering was used to independently identify dimensions of negative affective style and resting state brain networks. Combining the clustering results, we examined individual differences in resting state connectivity uniquely associated with subdimensions of anxious affect, controlling for depressed affect. Physiological and cognitive subdimensions of anxious affect were identified. Physiological anxiety was associated with widespread alterations in insula connectivity, including decreased connectivity between insula subregions and between the insula and other medial frontal and subcortical networks. This is consistent with the insula facilitating communication between medial frontal and subcortical regions to enable control of physiological affective states. Meanwhile, increased connectivity within a frontoparietal-posterior cingulate cortex-precunous network was specifically associated with cognitive anxiety, potentially reflecting increased spontaneous negative cognition (e.g., worry). These findings suggest that physiological and cognitive anxiety comprise subdimensions of anxiety-related affect and reveal associated alterations in brain connectivity

    The Supercooling of a Nematic Liquid Crystal

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    We investigate the supercooling of a nematic liquid crystal using fluctuating non-linear hydrodynamic equations. The Martin-Siggia-Rose formalism is used to calculate renormalized transport coefficients to one-loop order. Similar theories for isotropic liquids have shown substantial increases of the viscosities as the liquid is supercooled or compressed due to feedback from the density fluctuations which are freezing. We find similar results here for the longitudinal and various shear viscosities of the nematic. However, the two viscosities associated with the nematic director motion do not grow in any dramatic way; i.e.\ there is no apparent freezing of the director modes within this hydrodynamic formalism. Instead a glassy state of the nematic may arise from a ``random anisotropy" coupling of the director to the frozen density.Comment: Late

    Finite Temperature Spectral Densities of Momentum and R-Charge Correlators in N=4\N=4 Yang Mills Theory

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    We compute spectral densities of momentum and R-charge correlators in thermal N=4\N=4 Yang Mills at strong coupling using the AdS/CFT correspondence. For ωT\omega \sim T and smaller, the spectral density differs markedly from perturbation theory; there is no kinetic theory peak. For large ω\omega, the spectral density oscillates around the zero-temperature result with an exponentially decreasing amplitude. Contrast this with QCD where the spectral density of the current-current correlator approaches the zero temperature result like (T/ω)4(T/\omega)^4. Despite these marked differences with perturbation theory, in Euclidean space-time the correlators differ by only 10\sim 10% from the free result. The implications for Lattice QCD measurements of transport are discussed.Comment: 18 pages, 3 figure

    The size-star formation relation of massive galaxies at 1.5<z<2.5

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    We study the relation between size and star formation activity in a complete sample of 225 massive (M > 5 x 10^10 Msun) galaxies at 1.5<z<2.5, selected from the FIREWORKS UV-IR catalog of the CDFS. Based on stellar population synthesis model fits to the observed restframe UV-NIR SEDs, and independent MIPS 24 micron observations, 65% of galaxies are actively forming stars, while 35% are quiescent. Using sizes derived from 2D surface brightness profile fits to high resolution (FWHM_{PSF}~0.45 arcsec) groundbased ISAAC data, we confirm and improve the significance of the relation between star formation activity and compactness found in previous studies, using a large, complete mass-limited sample. At z~2, massive quiescent galaxies are significantly smaller than massive star forming galaxies, and a median factor of 0.34+/-0.02 smaller than galaxies of similar mass in the local universe. 13% of the quiescent galaxies are unresolved in the ISAAC data, corresponding to sizes <1 kpc, more than 5 times smaller than galaxies of similar mass locally. The quiescent galaxies span a Kormendy relation which, compared to the relation for local early types, is shifted to smaller sizes and brighter surface brightnesses and is incompatible with passive evolution. The progenitors of the quiescent galaxies, were likely dominated by highly concentrated, intense nuclear star bursts at z~3-4, in contrast to star forming galaxies at z~2 which are extended and dominated by distributed star formation.Comment: 6 pages, 4 figures, accepted for publication in Ap

    Single-particle and collective excitations in a charged Bose gas at finite temperature

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    The main focus of this work is on the predictions made by the dielectric formalism in regard to the relationship between single-particle and collective excitation spectra in a gas of point-like charged bosons at finite temperature TT below the critical region of Bose-Einstein condensation. Illustrative numerical results at weak coupling (rs=1r_s = 1) are presented within the Random Phase Approximation. We show that within this approach the single-particle spectrum forms a continuum extending from the transverse to the longitudinal plasma mode frequency and leading to a double-peak structure as TT increases, whereas the density fluctuation spectrum consists of a single broadening peak. We also discuss the momentum distribution and the superfluidity of the gas.Comment: 15 pages, 5 figure

    Breakdown of Hydrodynamic Transport Theory in the Ordered Phase of Helimagnets

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    It is shown that strong fluctuations preclude a hydrodynamic description of transport phenomena in helimagnets, such as MnSi, at T>0. This breakdown of hydrodynamics is analogous to the one in chiral liquid crystals. Mode-mode coupling effects lead to infinite renormalizations of various transport coefficients, and the actual macroscopic description is nonlocal. At T=0 these effects are weakened due to the fluctuation-dissipation theorem, and the renormalizations remain finite. Observable consequences of these results, as manifested in the neutron scattering cross-section, are discussedComment: 4pp., 1 eps figur
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