Estuary Classification Revisited

This paper presents the governing equations of a tidally-averaged, width-averaged, rectangular estuary in completely nondimensionalized forms. Subsequently, we discover that the dynamics of an estuary is entirely controlled by only two variables: (i) the Estuarine Froude number, and (ii) a nondimensional number related to the Estuarine Aspect ratio and the Tidal Froude number. Motivated by this new observation, the problem of estuary classification is re-investigated. Our analysis shows that the two control variables are capable of completely determining the stratification at the estuary mouth, and therefore can specify the estuary type. The theoretical estuary classification scheme proposed in this paper is validated against real estuarine data collected from existing literature. Our classification scheme on comparison with the state-of-the-art theory shows significant improvement.Comment: 6 pages, 4 figure

Structural RFV: Recovery Form and Defaultable Debt Analysis

Receiving the same fractional recovery of par at default for bonds of the same issuer and seniority, regardless of remaining maturity, has been labelled in the academic literature as a Recovery of Face Value at Default (RFV).Such a recovery form results from language found in typical bond indentures and is supported by empirical evidence from defaulted bond values.We incorporate RFV into an exogenous boundary structural credit risk model and compare its e ect to more typical recovery forms found in such models.We find that the chosen recovery form can significantly a ect valuation and the sensitivities produced by these models, thus having important implications for empirical studies attempting to validate structural credit risk models.We show that some features of existing structural models are a result of the recovery form assumed in the model and do not necessarily hold under an RFV recovery form.Some of our results complement those found in the literature which examines the endogeneity of the default boundary.We find that some features that may have been solely attributed to modelling the boundary as an optimal decision by the firm can be obtained in an exogenous boundary framework with RFV.This has direct implications for studies which attempt to determine whether endogenous or exogenous models are better supported empirically.We extend our results to incorporate a multifactor default-free term structure model and examine the impact of the recovery form in estimating the cost of debt capital within a structural model framework.bonds;credit;risk;capital costs;debt

On the stability of plane Couette-Poiseuille flow with uniform cross-flow

We present a detailed study of the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, $R_{inj}$ and the dimensionless wall velocity, $k$. Squire's transformation may be applied to the linear stability equations and we therefore consider 2D (spanwise-independent) perturbations. Corresponding to each dimensionless wall velocity, $k\in[0,1]$, two ranges of $R_{inj}$ exist where unconditional stability is observed. In the lower range of $R_{inj}$, for modest $k$ we have a stabilisation of long wavelengths leading to a cut-off $R_{inj}$. This lower cut-off results from skewing of the velocity profile away from a Poiseuille profile, shifting of the critical layers and the gradual decrease of energy production. Cross-flow stabilisation and Couette stabilisation appear to act via very similar mechanisms in this range, leading to the potential for robust compensatory design of flow stabilisation using either mechanism. As $R_{inj}$ is increased, we see first destabilisation and then stabilisation at very large $R_{inj}$. The instability is again a long wavelength mechanism. Analysis of the eigenspectrum suggests the cause of instability is due to resonant interactions of Tollmien-Schlichting waves. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality. The stabilisation at very large $R_{inj}$ appears to be due to decay in energy production, which diminishes like $R_{inj}^{-1}$. Our study is limited to two dimensional, spanwise independent perturbations.Comment: Accepted for publication in Journal of Fluid Mechanic

Low frequency random telegraphic noise (RTN) and 1/f noise in the rare-earth manganite Pr0.63_{0.63}Ca0.37_{0.37}MnO3_3 near the charge-ordering transition

We have studied low frequency resistance fluctuations (noise) in a single crystal of the rare earth perovskite manganite Pr$_{0.63}$Ca$_{0.37}$MnO$_3$ which shows a charge ordering transition at a temperature $T_{CO}$ ~ 245K. The noise measurements were made using an ac bias with and without a dc bias current imposed on it. We find that the spectral power $S_V(f)$ contains two components - one broad band 1/f part that exists for all frequency and temperature ranges and a single frequency Lorentzian of frequency $f_c$ which is strongly temperature dependent. The Lorentzian in $S_V(f)$ which appears due to Random telegraphic noise (RTN) as seen in the time series of the fluctuation, is seen in a very narrow temperature window around $T_{CO}$ where it makes the dominating contribution to the fluctuation. When the applied dc bias is increased beyond a certain threshold current density $J_{th}$, the electrical conduction becomes non-linear and one sees appearance of a significant Lorentzian contribution in the spectral power due to RTN. We explain the appearance of the RTN as due to coexisting Charge ordered (CO) and reverse orbitally ordered (ROO) phases which are in dynamical equilibrium over a mesoscopic length scale ($\approx 30nm$) and the kinetics being controlled by an activation barrier $E_{a} ~ 0.45eV. The 1/f noise is low for$T>>T_{CO}$but increases by nearly two orders in a narrow temperature range as$T_{CO}$ is approached from above and the probability distribution function (PDF) deviates strongly from a Gaussian. We explain this behavior as due to approach of charge localization with correlated fluctuators which make the PDF non-Gaussian.Comment: 23 pages, 14 figure

Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last Multiplier

We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Lienard type, viz \ddot{x} + f(x)x^2 + g(x) = 0 using Jacobi's last multiplier. The JM metric allows us to reformulate the Newtonian equation of motion for a variable mass as a geodesic equation for a Riemannian metric. We illustrate the procedure with examples of Painleve-Gambier XXI, the Jacobi equation and the Henon-Heiles system

Magnetic Field resulting from non-linear electrical transport in single crystals of charge-ordered Pr0.63_{0.63} Ca0.37_{0.37} MnO3_{3}}

In this letter we report that the current induced destabilization of the charge ordered (CO) state in a rare-earth manganite gives rise to regions with ferromagnetic correlation. We did this experiment by measurement of the I-V curves in single crystal of the CO system Pr$_{0.63}$Ca$_{0.37}$MnO$_{3}$ and simultanously measuring the magnetization of the current carrying conductor using a high T$_c$ SQUID working at T = 77K. We have found that the current induced destabilization of the CO state leads to a regime of negative differential resistance which leads to a small enhancement of the magnetization of the sample, indicating ferromagnetically aligned moments.Comment: 4 pages LateX, 4 eps figure