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## Full-Text Articles in Physics

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

#### Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

*All HMC Faculty Publications and Research*

A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant ...

Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski

#### Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski

*All HMC Faculty Publications and Research*

The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which ...

A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Mixed Alkali Halide Dimers, Robert J. Cave, Ian Ono '94

#### A Theoretical Investigation Of The Geometries, Vibrational Frequencies, And Binding Energies Of Several Mixed Alkali Halide Dimers, Robert J. Cave, Ian Ono '94

*All HMC Faculty Publications and Research*

Results are presented from ab initio calculations on several mixed alkali halide dimers made up of Li, Na, F, and Cl. All of the dimers are investigated at the restricted Hartree–Fock level to provide ab initio estimates of geometries, vibrational frequencies, and binding energies. The dimer LiNaF2 is then treated using a variety of basis sets at the Hartree–Fock level, as well as at correlated levels (second‐order Møller–Plesset and coupled‐cluster singles and doubles) to examine the sensitivity of the calculations to use of higher levels of theory. The results are then compared to the experimental ...

Quasidegenerate Variational Perturbation Theory And The Calculation Of First‐Order Properties From Variational Perturbation Theory Wave Functions, Robert J. Cave, Ernest R. Davidson

#### Quasidegenerate Variational Perturbation Theory And The Calculation Of First‐Order Properties From Variational Perturbation Theory Wave Functions, Robert J. Cave, Ernest R. Davidson

*All HMC Faculty Publications and Research*

In previous work on the treatment of correlation in molecular systems we have applied a multireference version of second‐order Hylleraas variational perturbation theory. The choice made for the partitioning of H treated the interactions between the correlating functions to infinite order and gave the corrections to the wave function to first order. The method was shown to be accurate in many cases, but became less so when near degeneracies occurred between the reference energy and other eigenvalues of H0. In this article we introduce an effective Hamiltonian method that is analogous to variational perturbation theory, but which is significantly ...

Hylleraas Variational Perturbation Theory: Application To Correlation Problems In Molecular Systems, Robert J. Cave, Ernest R. Davidson

#### Hylleraas Variational Perturbation Theory: Application To Correlation Problems In Molecular Systems, Robert J. Cave, Ernest R. Davidson

*All HMC Faculty Publications and Research*

Hylleraas variational perturbation theory is applied through second order in energy to estimate the correlation energy in several molecular systems. The specific choices for *H*_{0} and *V* which are made lead to equations nearly identical to the multireference linearized coupled‐cluster method of Laidig and Bartlett. The results obtained are in virtually exact agreement where comparisons have been made. Results from test calculations are presented for BeH_{2}, CH_{2}, and C_{2}H_{4}. In addition, the utility of perturbation theory for selecting correlating configurations is examined. This procedure is found to be quite accurate while significantly reducing ...