On Cournot-Nash equilibria with exogenous uncertainty

A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash equilibrium. We also allowp to depend on the behaviors of the participating agents. We apply the analysis to two models, one of a Cournot oligopoly, the other of a cooperative of individuals where there is uncertainty in the return to communal work

Quasi-periodic pulsations in solar and stellar flares: re-evaluating their nature in the context of power-law flare Fourier spectra

The nature of quasi-periodic pulsations in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra, also referred to as 'red' noise processes, are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPP is needed. Here we adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power law properties of flare signals. Using data from the PROBA2/LYRA, Fermi/GBM, Nobeyama Radioheliograph and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as QPP events. Additionally we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required in order to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum, rather than a direct signature of oscillating components or structures. However, for the flare of 1998 May 8, strong evidence for the existence of an explicit oscillation with P ~ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh HXT data. We conclude that, most likely, many previously analysed events in the literature may be similarly described in terms of power laws in the flare Fourier power spectrum, without the need to invoke a narrowband, oscillatory component. As a result the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.Comment: 11 pages, 7 figures, 1 table. Accepted for publication in The Astrophysical Journa

Observable Effects of Dust Formation in Dynamic Atmospheres of M-type Mira Variables

The formation of dust with temperature-dependent non-grey opacity is considered in a series of self-consistent model atmospheres at different phases of an O-rich Mira variable of mass 1.2 $M_\odot$. Photometric and interferometric properties of these models are predicted under different physical assumptions regarding the dust formation. The iron content of the initial silicate that forms and the availability of grain nuclei are found to be critical parameters that affect the observable properties. In particular, parameters were found where dust would form at 2-3 times the average continuum photospheric radius. This work provides a consistent physical explanation for the larger apparent size of Mira variables at wavelengths shorter than 1 $\mu$m than that predicted by dust free fundamental-mode pulsation models.Comment: Accepted for MNRAS; 9 pages, 5 figure

Two Wide Planetary-mass Companions to Solar-type Stars in Upper Scorpius

At wide separations, planetary-mass and brown dwarf companions to solar-type stars occupy a curious region of parameter space not obviously linked to binary star formation or solar system scale planet formation. These companions provide insight into the extreme case of companion formation (either binary or planetary), and due to their relative ease of observation when compared to close companions, they offer a useful template for our expectations of more typical planets. We present the results from an adaptive optics imaging survey for wide (~50–500 AU) companions to solar-type stars in Upper Scorpius. We report one new discovery of a ~14 M_J companion around GSC 06214−00210and confirm that the candidate planetary-mass companion 1RXS J160929.1−210524 detected by Lafrenière et al. is in fact comoving with its primary star. In our survey, these two detections correspond to ~4% of solar-type stars having companions in the 6–20 M_J mass and ~200–500 AU separation range. This figure is higher than would be expected if brown dwarfs and planetary-mass companions were drawn from an extrapolation of the binary mass function. Finally, we discuss implications for the formation of these objects

The Angular Diameter and Fundamental Parameters of Sirius A

The Sydney University Stellar Interferometer (SUSI) has been used to make a new determination of the angular diameter of Sirius A. The observations were made at an effective wavelength of 694.1 nm and the new value for the limb-darkened angular diameter is 6.048 +/- 0.040mas (+/-0.66%). This new result is compared with previous measurements and is found to be in excellent agreement with a conventionally calibrated measurement made with the European Southern Observatory's Very Large Telescope Interferometer (VLTI) at 2.176 microns (but not with a second globally calibrated VLTI measurement). A weighted mean of the SUSI and first VLTI results gives the limb-darkened angular diameter of Sirius A as 6.041 +/- 0.017mas (+/-0.28%). Combination with the Hipparcos parallax gives the radius equal to 1.713 +/- 0.009R_sun. The bolometric flux has been determined from published photometry and spectrophotometry and, combined with the angular diameter, yields the emergent flux at the stellar surface equal to (5.32+/- 0.14)x10^8 Wm^-2 and the effective temperature equal to 9845 +/- 64 K. The luminosity is 24.7 +/- 0.7 L_sun.Comment: Accepted for publication in PAS

Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces

We use spatial light modulators (SLMs) to measure correlations between arbitrary superpositions of orbital angular momentum (OAM) states generated by spontaneous parametric down-conversion. Our technique allows us to fully access a two-dimensional OAM subspace described by a Bloch sphere, within the higher-dimensional OAM Hilbert space. We quantify the entanglement through violations of a Bell-type inequality for pairs of modal superpositions that lie on equatorial, polar, and arbitrary great circles of the Bloch sphere. Our work shows that SLMs can be used to measure arbitrary spatial states with a fidelity sufficient for appropriate quantum information processing systems