33,447 research outputs found
Extended Hylleraas three-electron integral
A closed form expression for the three-electron Hylleraas integral involving
the inverse quadratic power of one inter-particle coordinate is obtained, and
recursion relations are derived for positive powers of other coordinates. This
result is suited for high precision calculations of relativistic effects in
lithium and light lithium-like ions.Comment: Submited to Phys. Rev.
On the rooted Tutte polynomial
The Tutte polynomial is a generalization of the chromatic polynomial of graph
colorings. Here we present an extension called the rooted Tutte polynomial,
which is defined on a graph where one or more vertices are colored with
prescribed colors. We establish a number of results pertaining to the rooted
Tutte polynomial, including a duality relation in the case that all roots
reside around a single face of a planar graph. The connection with the Potts
model is also reviewed.Comment: plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut
Fourier (1999
Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions
Formulas are presented for the recursive generation of four-body integrals in
which the integrand consists of arbitrary integer powers (>= -1) of all the
interparticle distances r_ij, multiplied by an exponential containing an
arbitrary linear combination of all the r_ij. These integrals are
generalizations of those encountered using Hylleraas basis functions, and
include all that are needed to make energy computations on the Li atom and
other four-body systems with a fully exponentially correlated Slater-type basis
of arbitrary quantum numbers. The only quantities needed to start the recursion
are the basic four-body integral first evaluated by Fromm and Hill, plus some
easily evaluated three-body "boundary" integrals. The computational labor in
constructing integral sets for practical computations is less than when the
integrals are generated using explicit formulas obtained by differentiating the
basic integral with respect to its parameters. Computations are facilitated by
using a symbolic algebra program (MAPLE) to compute array index pointers and
present syntactically correct FORTRAN source code as output; in this way it is
possible to obtain error-free high-speed evaluations with minimal effort. The
work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009
Master/slave manipulator system
System capabilities are equivalent to mobility, dexterity, and strength of human arm. Arrangement of torque motor, harmonic drive, and potentiometer combination allows all power and control leads to pass through center of slave with position-transducer arrangement of master, and "stovepipe joint" is incorporated for manipulator applications
Anthropomorphic master/slave manipulator system
An anthropomorphic master/slave manipulator system including master arm apparatus with a plurality of master tubular articulated portions is outlined. Objectives of this investion were to provide a system that accurately and smoothly simulates human limb movement at a remote location. The system has a high frequency response, a high structural stiffness and a design that protects the components of the slave mechanism. Simulation of human movements is possible in outer space, underwater, and in a hazardous environment such as in a high radiation area. The equivalent ability, dexterity, and strength of a human arm are simulated
Turbulent mixing of a slightly supercritical Van der Waals fluid at Low-Mach number
Supercritical fluids near the critical point are characterized by liquid-like
densities and gas-like transport properties. These features are purposely
exploited in different contexts ranging from natural products
extraction/fractionation to aerospace propulsion. Large part of studies
concerns this last context, focusing on the dynamics of supercritical fluids at
high Mach number where compressibility and thermodynamics strictly interact.
Despite the widespread use also at low Mach number, the turbulent mixing
properties of slightly supercritical fluids have still not investigated in
detail in this regime. This topic is addressed here by dealing with Direct
Numerical Simulations (DNS) of a coaxial jet of a slightly supercritical Van
der Waals fluid. Since acoustic effects are irrelevant in the Low Mach number
conditions found in many industrial applications, the numerical model is based
on a suitable low-Mach number expansion of the governing equation. According to
experimental observations, the weakly supercritical regime is characterized by
the formation of finger-like structures-- the so-called ligaments --in the
shear layers separating the two streams. The mechanism of ligament formation at
vanishing Mach number is extracted from the simulations and a detailed
statistical characterization is provided. Ligaments always form whenever a high
density contrast occurs, independently of real or perfect gas behaviors. The
difference between real and perfect gas conditions is found in the ligament
small-scale structure. More intense density gradients and thinner interfaces
characterize the near critical fluid in comparison with the smoother behavior
of the perfect gas. A phenomenological interpretation is here provided on the
basis of the real gas thermodynamics properties.Comment: Published on Physics of Fluid
Recursion relations for Hylleraas three-electron integral
Recursion relations for Hylleraas three-electron integral are obtained in a
closed form by using integration by parts identities. Numerically fast and well
stable algorithm for the calculation of the integral with high powers of
inter-electronic coordinates is presented.Comment: 12 pages, requires RevTeX4, submitted to Phys. Rev.
Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be
Accurate results for nonrelativistic energy, relativistic, QED, and finite
nuclear mass corrections are obtained for , and
states of the Li atom and Be ion. Our computational approach
uses the Hylleraas basis set with the analytic integration and recursion
relations. From comparison of experimental results for the isotope shifts to
theoretical predictions including nuclear polarizabilities, we obtain nuclear
charge radii for Li and Be isotopes.Comment: 19 pages, 8 tables, Phys. Rev. A in prin
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