Optimal monopoly investment and capacity utilization under random demand

Unique value-maximizing programs of irreversible capacity investment and capacity utilization are described and shown to exist under general conditions for monopolist exhibiting capital adjustment costs and serving random consumer demand for a nondurable good over an infinite horizon. Stationary properties of these programs are then fully characterized under the assumption of serially independent demand disturbances. Optimal monopoly behavior in this case includes acquisition of a constant and positive level of capacity, the maintenance of a positive expected value of excess capacity in each period, and an asymmetrical response of price to unanticipated fluctuations in consumer demand. Under a general form of Markovian demand, the effect of uncertainty on irreversible capacity investment is also described in terms of the discounted flow of expected revenue accruing to the marginal unit of existing capacity and the option value of deferring the acquisition of additional capital. The option value of deferring such acquisition, created by the irreversibility of capacity investment, is characterized directly in terms of the value function of the firm, and is then shown to be zero in a stationary equilibrium with serially independent demand disturbances. The response of investment to increase demand uncertainty depends, as a result, directly on the properties of the marginal revenue product of capital. A non-negative response of optimal capacity to increased uncertainty in market demand is demonstrated for a general class of aggregate consumer preferences.Industrial capacity

Shocked Molecular Hydrogen in the 3C 326 Radio Galaxy System

The Spitzer spectrum of the giant FR II radio galaxy 3C 326 is dominated by very strong molecular hydrogen emission lines on a faint IR continuum. The H2 emission originates in the northern component of a double-galaxy system associated with 3C 326. The integrated luminosity in H2 pure-rotational lines is 8.0E41 erg/s, which corresponds to 17% of the 8-70 micron luminosity of the galaxy. A wide range of temperatures (125-1000 K) is measured from the H2 0-0 S(0)-S(7) transitions, leading to a warm H2 mass of 1.1E9 Msun. Low-excitation ionic forbidden emission lines are consistent with an optical LINER classification for the active nucleus, which is not luminous enough to power the observed H2 emission. The H2 could be shock-heated by the radio jets, but there is no direct indication of this. More likely, the H2 is shock-heated in a tidal accretion flow induced by interaction with the southern companion galaxy. The latter scenario is supported by an irregular morphology, tidal bridge, and possible tidal tail imaged with IRAC at 3-9 micron. Unlike ULIRGs, which in some cases exhibit H2 line luminosities of comparable strength, 3C 326 shows little star-formation activity (~0.1 Msun/yr). This may represent an important stage in galaxy evolution. Starburst activity and efficient accretion onto the central supermassive black hole may be delayed until the shock-heated H2 can kinematically settle and coolComment: 27 pages, 7 figures, accepted for publication in the Astrophysical Journa

Trapping of magnetic flux by the plunge region of a black hole accretion disk

The existence of the radius of marginal stability means that accretion flows around black holes invariably undergo a transition from a MHD turbulent disk-like flow to an inward plunging flow. We argue that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole, and therefore may increase the importance of the Blandford-Znajek (BZ) effect relative to previous estimates that ignore the plunge region. We support this hypothesis by constructing and analyzing a toy-model of the dragging and trapping of a large scale field by a black hole disk, revealing a strong dependence of this effect on the effective magnetic Prandtl number of the MHD turbulent disk. Furthermore, we show that the enhancement of the BZ effect depends on the geometric thickness of the accretion disk. This may be, at least in part, the physical underpinnings of the empirical relation between the inferred geometric thickness of a black hole disk and the presence of a radio jet.Comment: 18 pages, 3 figures, accepted for publication in the Astrophysical Journal. See http://www.astro.umd.edu/~chris/publications/movies/flux_trapping.html for animation

Constraining the Nature of X-ray Cavities in Clusters and Galaxies

We present results from an extensive survey of 64 cavities in the X-ray halos of clusters, groups and normal elliptical galaxies. We show that the evolution of the size of the cavities as they rise in the X-ray atmosphere is inconsistent with the standard model of adiabatic expansion of purely hydrodynamic models. We also note that the majority of the observed bubbles should have already been shredded apart by Rayleigh-Taylor and Richtmyer-Meshkov instabilities if they were of purely hydrodynamic nature. Instead we find that the data agrees much better with a model where the cavities are magnetically dominated and inflated by a current-dominated magneto-hydrodynamic jet model, recently developed by Li et al. (2006) and Nakamura et al. (2006). We conduct complex Monte-Carlo simulations of the cavity detection process including incompleteness effects to reproduce the cavity sample's characteristics. We find that the current-dominated model agrees within 1sigma, whereas the other models can be excluded at >5sigma confidence. To bring hydrodynamic models into better agreement, cavities would have to be continuously inflated. However, these assessments are dependent on our correct understanding of the detectability of cavities in X-ray atmospheres, and will await confirmation when automated cavity detection tools become available in the future. Our results have considerable impact on the energy budget associated with active galactic nucleus feedback.Comment: 21 pages, 12 figures, emulateapj, accepted for publication in ApJ, responded to referee's comments and added a new model, conclusions unchange

Climate-induced changes in river flow regimes will alter future bird distributions

Anthropogenic forcing of the climate is causing an intensification of the global water cycle, leading to an increase in the frequency and magnitude of floods and droughts. River flow shapes the ecology of riverine ecosystems and climate-driven changes in river flows are predicted to have severe consequences for riverine species, across all levels of trophic organization. However, understanding species' responses to variation in flow is limited through a lack of quantitative modelling of hydroecological interactions. Here, we construct a Bioclimatic Envelope Model (BEM) ensemble based on a suite of plausible future flow scenarios to show how predicted alterations in flow regimes may alter the distribution of a predatory riverine species, the White-throated Dipper (Cinclus cinclus). Models predicted a gradual diminution of dipper probability of occurrence between present day and 2098. This decline was most rapid in western areas of Great Britain and was principally driven by a projected decrease in flow magnitude and variability around low flows. Climate-induced changes in river flow may, therefore, represent a previously unidentified mechanism by which climate change may mediate range shifts in birds and other riverine biota

Tributes to Professor Alan Hornstein

Tributes to Professor Alan Hornstein upon his retirement from the University of Maryland School of Law