A Primal-Dual Augmented Lagrangian

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual $\ell$1 linearly constrained Lagrangian (pd$\ell$1-LCL) method

Foreign Bank Entry and Business Volatility: Evidence from U.S. States and Other Countries

The first-order effects of relaxed bank entry restrictions have been favorable, both within the U.S. and across countries. Internationally, the benefits of foreign entry seem to depend on the level of development, but at least for developing nations entrants are more efficient than incumbent banks and the stiffer competition seems to improve overall bank efficiency. In contrast to these first-order effects, the stability implications of increased entry are less obvious. This paper investigates whether greater integration resulting from foreign bank entry has been associated with more or less business cycle volatility. We approach the topic with mix of theory and evidence from both the U.S. states and countries. While theoretical effects are mixed, the empirical effect of relaxation of restrictions of cross-state banking has been to stabilize state-level fluctuations in the U.S. Applying a related set of tests to a panel of about 100 countries, however, we find no evidence that expansion of foreign banking has reduced business fluctuations. If anything, the evidence points tentatively in the other direction.

Contingent Claims Valuation of Corporate Liabilities: Theory and Empirical Tests

Although the Contingent Claims Analysis model has become the premier theory of how value is allocated among claimants on firms,its empirical validity remains an open question. In addition to being of academic interest, a test of the model would have significant practical implications. If it can be established that the model predicts actual market prices, then the model can be used to price new and untraded claims, to infer firm values from prices of traded claims like equity and to price covenants separately. In this paper evidence is presented on how well a model which makes the usual assumptions in the literature does in predicting market prices for claims in standard capital structures. The results suggest that the usual assumption list requires modification before it can serve as a basis for valuing corporate claims.

The interplay between X-ray photoevaporation and planet formation

We assess the potential of planet formation instigating the early formation of a photoevaporation driven gap, up to radii larger than typical for photoevaporation alone. For our investigation we make use of hydrodynamics models of photoevaporating discs with a giant planet embedded. We find that, by reducing the mass accretion flow onto the star, discs that form giant planets will be dispersed at earlier times than discs without planets by X-ray photoevaporation. By clearing the portion of the disc inner of the planet orbital radius, planet formation induced photoevaporation (PIPE) is able to produce transition disc that for a given mass accretion rate have larger holes when compared to standard X-ray photoevaporation. This constitutes a possible route for the formation of the observed class of accreting transition discs with large holes, which are otherwise difficult to explain by planet formation or photoevaporation alone. Moreover, assuming that a planet is able to filter dust completely, PIPE produces a transition disc with a large hole and may provide a mechanism to quickly shut down accretion. This process appears to be too slow however to explain the observed desert in the population of transition disc with large holes and low mass accretion rates.Comment: 11 pages, 10 figures, accepted by MNRAS on 31/12/201

S5 0836+710: An FRII jet disrupted by the growth of a helical instability?

The remarkable stability of extragalactic jets is surprising, given the reasonable possibility of the growth of instabilities. In addition, much work in the literature has invoked this possibility in order to explain observed jet structures and obtain information from these structures. For example, it was recently shown that the observed helical structures in the jet in S5 0836+710 could be associated with helical pressure waves generated by Kelvin-Helmholtz instability. Our aim is to resolve the arc-second structure of the jet in the quasar S5 0836+710 and confirm the lack of a hot-spot (reverse jet-shock) found by present observing arrays, as this lack implies a loss of jet collimation before interaction with the intergalactic medium. In this work, we use an observation performed in 2008 using EVN and MERLIN. The combined data reduction has provided a complete image of the object at arc-second scales. The lack of a hot-spot in the arc-second radio structure is taken as evidence that the jet losses its collimation between the VLBI region and the region of interaction with the ambient medium. This result, together with the previous identification of the helical structures in the jet with helical pressure waves that grow in amplitude with distance, allow us to conclude that the jet is probably disrupted by the growth of Kelvin-Helmholtz instability. This observational evidence confirms that the physical parameters of jets can be extracted using the assumption that instability is present in jets and can be the reason for many observed structures. Interestingly, the observed jet is classified as a FRII object in terms of its luminosity, but its large-scale morphology does not correspond to this classification. The implications of this fact are discussed.Comment: Accepted for publication in Astronomy & Astrophysic

The Escape of Ionizing Photons from the Galaxy

The Magellanic Stream and several high velocity clouds have now been detected in optical line emission. The observed emission measures and kinematics are most plausibly explained by photoionization due to hot, young stars in the Galactic disk. The highly favorable orientation of the Stream allows an unambiguous determination of the fraction of ionizing photons, F_esc, which escape the disk. We have modelled the production and transport of ionizing photons through an opaque interstellar medium. Normalization to the Stream detections requires F_esc = 6%, in reasonable agreement with the flux required to ionize the Reynolds layer. Neither shock heating nor emission within a hot Galactic corona can be important in producing the observed H-alpha emission. If such a large escape fraction is typical of L_* galaxies, star-forming systems dominate the extragalactic ionizing background. Within the context of this model, both the three-dimensional orientation of the Stream and the distances to high-velocity clouds can be determined by sensitive H-alpha observations.Comment: 4 pages; LaTeX2e, emulateapj.sty, apjfonts.sty; 4 encapsulated PS figures. For correct labels, may need to print Fig. 3 separately due to psfig limitation. Astrophysical Journal (Letters), accepte

Confined compression of collagen hydrogels

Reconstituted collagen hydrogels are often used for in vitro studies of cell-matrix interaction and as scaffolds for tissue engineering. Understanding the mechanical and transport behaviours of collagen hydrogels is therefore extremely important, albeit difficult due to their very high water content (typically > 99.5%). In the present study the mechanical behaviour of collagen hydrogels in confined compression was investigated using biphasic theory (J. Biomech. Eng. 102 (1980) 73), to ascertain whether the technique is sufficiently sensitive to determine differences in the characteristics of hydrogels of between 0.2% and 0.4% collagen. Peak stress, equilibrium stress, aggregate modulus and hydraulic permeability of the hydrogels exhibited sensitivity to collagen content, demonstrating that the technique is clearly able to discriminate between hydrogels with small differences in collagen content and may also be sensitive to factors that affect matrix remodelling. The results also offer additional insight into the deformation-dependent permeability of collagen hydrogels. This study suggests that confined compression, together with biphasic theory, is a suitable technique for assessing the mechanical properties of collagen hydrogels

The Effect of Expansion on Mass Entrainment and Stability of Super-Alfv\'enic Jets

We extend investigations of mass entrainment by jets, which previously have focused on cylindrical supermagnetosonic jets and expanding trans-Alfv\'enic jets, to a set of expanding supermagnetosonic jets. We precess these jets at the origin to excite the helical mode of the Kelvin-Helmholtz (or KH) instability, in order to compare the results with predictions from linear stability analysis. We analyze this simulation set for the spatial development of magnetized mass, which we interpret as jet plus entrained, initially unmagnetized external mass. As with the previous simulation sets, we find that the growth of magnetized mass is associated with the growth of the KH instability through linear, nonlinear, and saturated stages and with the expansion of magnetized material in simulated observations of the jet. From comparison of measured wavelengths and wave speeds with the predictions from linear stability analysis, we see evidence that the KH instability is the primary cause for mass entrainment in these simulations, and that the expansion reduces the rate of mass entrainment. This reduced rate can be observed as a somewhat greater distance between the two transition points separating the three stages of expansion.Comment: 18 pages, 6 figures, AASTeX, to appear in Nov 1 issue of ApJ (vol 543), postscript versions of Figures 3 and 5 are available at http://crux.astr.ua.edu/~rosen/supcon/rh.htm