Capillary wave dynamics on supported viscoelastic films: Single and double layers

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu {\em et al.}, Phys. Rev. E {\bf 74}, 010602 (R) (2006)].Comment: 14 pages, 9 figure

Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt

C-Cl Bond Fission, Hcl Elimination, And Secondary Radical Decomposition In The 193 Nm Photodissociation Of Allyl Chloride

The primary photodissociation dynamics of allyl chloride upon excitation at 193 nm is investigated in a crossed laser-molecular beam scattering apparatus. Tunable vacuum ultraviolet (VUV) photoionization of the products provides a unique ability to learn about the secondary reaction products of the nascent photoproducts formed. The data show evidence for four significant primary reaction channels: a previously unidentified low kinetic energy C-Cl bond fission channel producing unstable allyl radicals, an excited state C-Cl bond fission channel producing Cl atoms with high translational energy, an HCl elimination pathway releasing significant energy to product translation to HCl and its momentum-matched mass 40 partner, and an HCl elimination channel producing low kinetic energy HCl products and predominantly unstable mass 40 products. The measured branching of these primary reaction channels of [all C-Cl] : [fast C-Cl] : [slow C-Cl] : [fast HCl] : [slow HCl] : [all HCl] is 1.00: 0.971: 0.029: 0.291: 0.167: 0.458 (where fast refers to the high recoil kinetic energy channels). The high internal energy allyl radicals formed in the slow C-Cl fission pathway of allyl chloride further dissociate/isomerize, as do the unstable mass 40 products formed in the HCl elimination pathways, and these products are investigated. Photoionization efficiency (PIE) curves of the HCl product suggest that a three-centered elimination mechanism contributes significantly to an observed HCl elimination reaction. (C) 2002 American Institute of Physics

How Big is the Tax Advantage to Debt?

This paper uses an option valuation model of the firm to answer the question, "What magnitude tax advantage to debt is consistent with the range of observed corporate debt ratios?" We incorporate into the model differential personal tax rates on capital gains and ordinary income. We conclude that variations in the magnitude of bankruptcy costs across firms can not by itself account for the simultaneous existence of levered and unlevered firms. When it is possible for the value of the underlying assets to junip discretely to zero, differences across firms in the probability of this jump can account for the simultaneous existence of levered and unlevered firms. Moreover, if the tax advantage to debt is small, the annual rate of return advantage offered by optimal leverage may be so small as to make the firm indifferent about debt policy over a wide range of debt-to-firm value ratios.

The Turbulent Warm Ionized Medium: Emission Measure Distribution and MHD Simulations

We present an analysis of the distribution of H-alpha emission measures for the warm ionized medium (WIM) of the Galaxy using data from the Wisconsin H-Alpha Mapper (WHAM) Northern Sky Survey. Our sample is restricted to Galactic latitudes |b| > 10. We removed sightlines intersecting nineteen high-latititude classical H II regions, leaving only sightlines that sample the diffuse WIM. The distribution of EM sin |b| for the full sample is poorly characterized by a single normal distribution, but is extraordinarily well fit by a lognormal distribution, with = 0.146 +/- 0.001 and standard deviation 0.190 +/- 0.001. drops from 0.260 +/- 0.002 at Galactic latitude 10<|b|<30 to 0.038 +/- 0.002 at Galactic latitude 60<|b|<90. The distribution may widen slightly at low Galactic latitude. We compare the observed EM distribution function to the predictions of three-dimensional magnetohydrodynamic simulations of isothermal turbulence within a non-stratified interstellar medium. We find that the distribution of EM sin |b| is well described by models of mildy supersonic turbulence with a sonic Mach number of ~1.4-2.4. The distribution is weakly sensitive to the magnetic field strength. The model also successfully predicts the distribution of dispersion measures of pulsars and H-alpha line profiles. In the best fitting model, the turbulent WIM occupies a vertical path length of 400-500 pc within the 1.0-1.8 kpc scale height of the layer. The WIM gas has a lognormal distribution of densities with a most probable electron density n_{pk} = 0.03 cm^{-3}. We also discuss the implications of these results for interpreting the filling factor, the power requirement, and the magnetic field of the WIM.Comment: 16 pages, 13 figures, ApJ in press. Replacement reflects version accepted for publicatio

Debt Policy and the Rate of Return Premium to Leverage

Equilibrium in the market for real assets requires that the price of those assets be bid up to reflect the tax shields they can offer to levered firms.Thus there must be an equality between the market values of real assets and the values of optimally levered firms. The standard measure of the advantage to leverage compares the values of levered and unlevered assets, and can be misleading and difficult to interpret. We show that a meaningful measure of the advantage to debt is the extra rate of return, net of a market premium for bankruptcy risk, earned by a levered firm relative to an otherwise-identical unlevered firm. We construct an option valuation model to calculate such a measure and present extensive simulation results. We use this model to compute optimal debt maturities, show how this approach can be used for capital budgeting, and discuss its implications for the comparison of bankruptcy costs versus tax shields.

Photoionisation and Heating of a Supernova Driven, Turbulent, Interstellar Medium

The Diffuse Ionised Gas (DIG) in galaxies traces photoionisation feedback from massive stars. Through three dimensional photoionisation simulations, we study the propagation of ionising photons, photoionisation heating and the resulting distribution of ionised and neutral gas within snapshots of magnetohydrodynamic simulations of a supernova driven turbulent interstellar medium. We also investigate the impact of non-photoionisation heating on observed optical emission line ratios. Inclusion of a heating term which scales less steeply with electron density than photoionisation is required to produce diagnostic emission line ratios similar to those observed with the Wisconsin H{\alpha} Mapper. Once such heating terms have been included, we are also able to produce temperatures similar to those inferred from observations of the DIG, with temperatures increasing to above 15000 K at heights |z| > 1 kpc. We find that ionising photons travel through low density regions close to the midplane of the simulations, while travelling through diffuse low density regions at large heights. The majority of photons travel small distances (< 100pc); however some travel kiloparsecs and ionise the DIG.Comment: 10 pages, 13 figures, accepted to MNRA