6,105 research outputs found
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, and the
dimensionless wall velocity, . 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, ,
two ranges of exist where unconditional stability is observed. In the
lower range of , for modest we have a stabilisation of long
wavelengths leading to a cut-off . 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 is increased,
we see first destabilisation and then stabilisation at very large .
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 appears to be due to decay in energy
production, which diminishes like . 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 PrCaMnO near the charge-ordering transition
We have studied low frequency resistance fluctuations (noise) in a single
crystal of the rare earth perovskite manganite PrCaMnO
which shows a charge ordering transition at a temperature ~ 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 contains two
components - one broad band 1/f part that exists for all frequency and
temperature ranges and a single frequency Lorentzian of frequency which
is strongly temperature dependent. The Lorentzian in 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 where
it makes the dominating contribution to the fluctuation. When the applied dc
bias is increased beyond a certain threshold current density , 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 () and the kinetics being controlled by
an activation barrier T>>T_{CO}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 Pr Ca MnO}
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
PrCaMnO and simultanously measuring the magnetization
of the current carrying conductor using a high T 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
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