Market Entry and Foreign Direct Investment

This paper discusses the impact of foreign direct investment (FDI) on market entry and welfare. It assumes that firms may enter markets in the first period as national firms only. In the second period, however, FDI is possible. The paper demonstrates that FDI reduces market entry because equilibrium profits in the second period decline with a decrease in the fixed cost of FDI. Therefore, compared to a trade regime without any FDI, prices rise in the first period but decline in the second period. The paper shows, however, that FDI will unambiguously improve the discounted sum of consumer surplus.foreign direct investment, multinational enterprises, imperfect competition, free entry

Cluster Formation in Contracting Molecular Clouds

We explore, through a simplified, semi-analytic model, the formation of dense clusters containing massive stars. The parent cloud spawning the cluster is represented as an isothermal sphere. This sphere is in near force balance between self-gravity and turbulent pressure. Self-gravity, mediated by turbulent dissipation, drives slow contraction of the cloud, eventually leading to a sharp central spike in density and the onset of dynamical instability. We suggest that, in a real cloud, this transition marks the late and rapid production of massive stars. We also offer an empirical prescription, akin to the Schmidt law, for low-mass star formation in our contracting cloud. Applying this prescription to the Orion Nebula Cluster, we are able to reproduce the accelerating star formation previously inferred from the distribution of member stars in the HR diagram. The cloud turns about 10 percent of its mass into low-mass stars before becoming dynamically unstable. Over a cloud free-fall time, this figure drops to 1 percent, consistent with the overall star formation efficiency of molecular clouds in the Galaxy.Comment: To appear in ApJ Vol. 667, September 2

Analyzation, design, fabrication and testing of a foil bearing rotor support system quarterly technical report, period ending 21 aug. 1965

High speed rotor support system with foil bearin

Dynamical Friction in a Gas: The Supersonic Case

Any gravitating mass traversing a relatively sparse gas experiences a retarding force created by its disturbance of the surrounding medium. In a previous contribution (Lee & Stahler 2011), we determined this dynamical friction force when the object's velocity was subsonic. We now extend our analysis to the supersonic regime. As before, we consider small perturbations created in the gas far from the gravitating object, and thereby obtain the net influx of linear momentum over a large, bounding surface. Various terms in the perturbation series formally diverge, necessitating an approximate treatment of the flow streamlines. Nevertheless, we are able to derive exactly the force itself. As in the subsonic case, we find that F=Mdot*V, where Mdot is the rate of mass accretion onto the object and V its instantaneous velocity with respect to distant background gas. Our force law holds even when the object is porous (e.g., a galaxy) or is actually expelling mass in a wind. Quantitatively, the force in the supersonic regime is less than that derived analytically by previous researchers, and is also less than was found in numerical simulations through the mid 1990s. We urge simulators to revisit the problem using modern numerical techniques. Assuming our result to be correct, it is applicable to many fields of astrophysics, ranging from exoplanet studies to galactic dynamics.Comment: Accepted to A&A. Comments from the community welcomed. 21 pages, 12 figure

The Ages of Pre-main-sequence Stars

The position of pre-main-sequence or protostars in the Hertzsprung--Russell diagram is often used to determine their mass and age by comparison with pre-main-sequence evolution tracks. On the assumption that the stellar models are accurate, we demonstrate that, if the metallicity is known, the mass obtained is a good estimate. However, the age determination can be very misleading because it is significantly (generally different by a factor of two to five) dependent on the accretion rate and, for ages less than about one million years, the initial state of the star. We present a number of accreting protostellar tracks that can be used to determine age if the initial conditions can be determined and the underlying accretion rate has been constant in the past. Because of the balance established between the Kelvin-Helmholtz, contraction timescale and the accretion timescale a pre-main-sequence star remembers its accretion history. Knowledge of the current accretion rate, together with an H--R-diagram position gives information about the rate of accretion in the past but does not necessarily improve any age estimate. We do not claim that ages obtained by comparison with these particular accreting tracks are likely to be any more reliable than those from comparisons with non-accreting tracks. Instead we stress the unreliability of any such comparisons and use the disparities between various tracks to estimate the likely errors in age and mass estimates. We also show how a set of coeval accreting objects do not appear coeval when compared with non-accreting tracks. Instead accreting pre-main-sequence stars of around a solar mass are likely to appear older than those of either smaller or larger mass.Comment: Accepted by MNRA