6,736 research outputs found
Strongly separated pairs of core electrons in computed ground states of small molecules
We have performed full configuration interaction computations of the ground
states of the molecules Be, BeH_2, Li, LiH, B, and BH and verified that the
core electrons constitute "separated electron pairs." These separated pairs of
core electrons have nontrivial structure; the core pair does not simply occupy
a single spatial orbital.
Our method of establishing the presence of separated electron pairs is direct
and conclusive. We do not fit a separated pair model; we work with the
wavefunctions of interest directly. To establish that a given group of
spin-orbitals contains a quasi-separated pair, we verify by direct computation
that the quantum state of the electrons that occupy those spin-orbitals is
nearly a pure 2-electron state.Comment: To appear in Computational and Theoretical Chemistr
Multiple steady states for characteristic initial value problems
The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results
Solar flux and its variations
Data are presented on the solar irradiance as derived from a number of sources. An attempt was made to bring these data onto a uniform scale. Summation of fluxes at all wavelengths yields a figure of 1357.826 for the solar constant. Estimates are made of the solar flux variations due to flares, active regions (slowly varying component), 27-day period, and the 11-yr cycle. Solar activity does not produce a significant variation in the value of the solar constant. Variations in the X-ray and EUV portions of the solar flux may be several orders of magnitude during solar activity, especially at times of major flares. It is established that these short wavelength flux enhancements cause significant changes in the terrestrial ionosphere
An adaptive pseudo-spectral method for reaction diffusion problems
The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions
Stability analysis of intermediate boundary conditions in approximate factorization schemes
The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method
Applications of spectral methods to turbulent magnetofluids in space and fusion research
Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas
Scaling of Pseudo-Critical Couplings in Two-Flavour QCD
We study the scaling behaviour of the pseudo-critical couplings for the
chiral phase transition in two-flavour QCD. We show that all existing results
from lattice simulations on lattices with temporal extent , 6 and 8
can be mapped onto a universal scaling curve. The relevant combination of
critical exponents, , is consistent with the scaling behaviour
expected for a second order phase transition with exponents. At present,
scaling according to the symmetry group can, however, not be ruled out.Comment: 8 pages, NSF-ITP 93-12
All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms
A standing-wave control field applied to a three-level atomic medium in a
planar hollow-core photonic crystal waveguide creates periodic variations of
linear and nonlinear refractive indexes of the medium. This property can be
used for efficient steering of light. In this work we study, both analytically
and numerically, the dynamics of probe optical beams in such structures. By
properly designing the spatial dependence of the nonlinearity it is possible to
induce long-living Bloch oscillations of spatial gap solitons, thus providing
desirable change in direction of the beam propagation without inducing
appreciable diffraction. Due to the significant enhancement of the
nonlinearity, such self-focusing of the probe beam can be reached at extremely
weak light intensities.Comment: 8 pages, 4 figure
The beta function and equation of state for QCD with two flavors of quarks
We measure the pressure and energy density of two flavor QCD in a wide range
of quark masses and temperatures. The pressure is obtained from an integral
over the average plaquette or psi-bar-psi. We measure the QCD beta function,
including the anomalous dimension of the quark mass, in new Monte Carlo
simulations and from results in the literature. We use it to find the
interaction measure, E-3p, yielding non-perturbative values for both the energy
density E and the pressure p. uuencoded compressed PostScript file Revised
version should work on more PostScript printers.Comment: 24 page
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