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 $SO(2,1)$ 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

Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation, the $\lambda \phi^4$ model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating solutions is successful as a consequence of some powerful, recently discovered, cyclic identities satisfied by the Jacobi elliptic functions.Comment: 19 pages, 4 figure