405 research outputs found
Heat transfer during film condensation of a liquid metal vapor
The object of this investigation is to resolve the discrepancy between theory and experiment for the case of heat transfer durirnfilm condensation of liquid metal vapors. Experiments by previous investigators have yielded data which are extremely scattered and markedly below the predictions of both the classical IUusselt theory and more recent modifications to it. All theoretical treatments so far have taken account only of the thermal resistance presented by the condensed film. However, calculations from kinetic theory show that with liquid metals a significant thermal resistance can exist at the liquid-vapor interface. This resistance increases with decreasing vapor pressure and is dependent on the value of the "condensation coefficient." Experimental work to back up this hypothesis of a liquid-vapor interfacial resistance is presented. The working fluid for the experiments is mercury condensing at low pressures in the absence of non-condensable gases on a vertical nickel surface. Data of previous investigators are analyzed, and possible reasons for being unable to interpret these results meaningfully are cited.Sponsored by the U. S. Atomic Energy Commissio
Algebraic Shape Invariant Models
Motivated by the shape invariance condition in supersymmetric quantum
mechanics, we develop an algebraic framework for shape invariant Hamiltonians
with a general change of parameters. This approach involves nonlinear
generalizations of Lie algebras. Our work extends previous results showing the
equivalence of shape invariant potentials involving translational change of
parameters with standard potential algebra for Natanzon type
potentials.Comment: 8 pages, 2 figure
Solar thermal power generation
The technologies and systems developed thus far for solar-thermal power generation and their approximate costs are described along with discussions for future prospects
Local Identities Involving Jacobi Elliptic Functions
We derive a number of local identities of arbitrary rank involving Jacobi
elliptic functions and use them to obtain several new results. First, we
present an alternative, simpler derivation of the cyclic identities discovered
by us recently, along with an extension to several new cyclic identities of
arbitrary rank. Second, we obtain a generalization to cyclic identities in
which successive terms have a multiplicative phase factor exp(2i\pi/s), where s
is any integer. Third, we systematize the local identities by deriving four
local ``master identities'' analogous to the master identities for the cyclic
sums discussed by us previously. Fourth, we point out that many of the local
identities can be thought of as exact discretizations of standard nonlinear
differential equations satisfied by the Jacobian elliptic functions. Finally,
we obtain explicit answers for a number of definite integrals and simpler forms
for several indefinite integrals involving Jacobi elliptic functions.Comment: 47 page
An improvement of Gribov's reggeon calculus
We derive an expression for Regge cuts and the associated enhancement of Regge poles, following Gribov's derivation of the reggeon calculus, but refraining from making an approximation made by Gribov. We show that Gribov's loop integrand should be multiplied by . This factor is identically unity for the Regge cut discontinuity, but is different from unity for enhanced singularities.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22146/1/0000575.pd
Unitarity bounds on diffraction dissociation
Using s-channel unitarity and the standard picture that diffraction dissociation and elastic scattering are the shadow of non-difractive particle production, we derive rigorous upper bounds for the diffraction dissociation cross section. The bounds are valid at each impact parameter, and are derived for an arbitrary number N of difractive channels. Our results are a generalization of previously derived bounds for the special simple case of N = 2 channels.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21751/1/0000145.pd
Baxter T-Q Equation for Shape Invariant Potentials. The Finite-Gap Potentials Case
The Darboux transformation applied recurrently on a Schroedinger operator
generates what is called a {\em dressing chain}, or from a different point of
view, a set of supersymmetric shape invariant potentials. The finite-gap
potential theory is a special case of the chain. For the finite-gap case, the
equations of the chain can be expressed as a time evolution of a Hamiltonian
system. We apply Sklyanin's method of separation of variables to the chain. We
show that the classical equation of the separation of variables is the Baxter
T-Q relation after quantization.Comment: 25 pages, no figures Extended section 10, one reference added.
Version accepted for publication in Jurnal of Mathematical Physic
Linear Superposition in Nonlinear Equations
Even though the KdV and modified KdV equations are nonlinear, we show that
suitable linear combinations of known periodic solutions involving Jacobi
elliptic functions yield a large class of additional solutions. This procedure
works by virtue of some remarkable new identities satisfied by the elliptic
functions.Comment: 7 pages, 1 figur
Slowly Rotating Homogeneous Stars and the Heun Equation
The scheme developed by Hartle for describing slowly rotating bodies in 1967
was applied to the simple model of constant density by Chandrasekhar and Miller
in 1974. The pivotal equation one has to solve turns out to be one of Heun's
equations. After a brief discussion of this equation and the chances of finding
a closed form solution, a quickly converging series solution of it is
presented. A comparison with numerical solutions of the full Einstein equations
allows one to truncate the series at an order appropriate to the slow rotation
approximation. The truncated solution is then used to provide explicit
expressions for the metric.Comment: 16 pages, uses document class iopart, v2: minor correction
Random sampling for estimating rice yield in Kolaba, Bombay
This article does not have an abstract
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