52,985 research outputs found
An Introduction to Conformal Ricci Flow
We introduce a variation of the classical Ricci flow equation that modifies
the unit volume constraint of that equation to a scalar curvature constraint.
The resulting equations are named the Conformal Ricci Flow Equations because of
the role that conformal geometry plays in constraining the scalar curvature.
These equations are analogous to the incompressible Navier-Stokes equations of
fluid mechanics inasmuch as a conformal pressure arises as a Lagrange
multiplier to conformally deform the metric flow so as to maintain the scalar
curvature constraint. The equilibrium points are Einstein metrics with a
negative Einstein constant and the conformal pressue is shown to be zero at an
equilibrium point and strictly positive otherwise. The geometry of the
conformal Ricci flow is discussed as well as the remarkable analytic fact that
the constraint force does not lose derivatives and thus analytically the
conformal Ricci equation is a bounded perturbation of the classical
unnormalized Ricci equation. That the constraint force does not lose
derivatives is exactly analogous to the fact that the real physical pressure
force that occurs in the Navier-Stokes equations is a bounded function of the
velocity. Using a nonlinear Trotter product formula, existence and uniqueness
of solutions to the conformal Ricci flow equations is proven. Lastly, we
discuss potential applications to Perelman's proposed implementation of
Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur
Statistics of some atmospheric turbulence records relevant to aircraft response calculations
Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included
RURAL ECONOMIC DEVELOPMENT: NEW OPPORTUNITIES AND CHALLENGES FOR COMMERCIAL BANKERS
The report discusses commercial banks' role in supporting economic development in rural America. It details demographic and economic trends in rural America. It discusses a number of economic development programs available to commercial bankers and to private sector/public sector partnerships. Finally, the report proposes a set of new tools for commercial bankers to further strengthen their participation in rural community economic development. Note: Figures are not included in the machine readable copy--contact the authors for more information.demographic trends, economic trends, rural America, role of commercial banks, economic development programs, new tools for bankers, Community/Rural/Urban Development, Financial Economics,
Anomalous magnetoresistance peak in (110) GaAs two-dimensional holes: Evidence for Landau-level spin-index anticrossings
We measure an anomalous magnetoresistance peak within the lowest Landau level
(nu = 1) minimum of a two-dimensional hole system on (110) GaAs.
Self-consistent calculations of the valence band mixing show that the two
lowest spin-index Landau levels anticross in a perpendicular magnetic field B
consistent with where the experimental peak is measured, Bp. The temperature
dependence of the anomalous peak height is interpreted as an activated behavior
across this anticrossing gap. Calculations of the spin polarization in the
lowest Landau levels predict a rapid switch from about -3/2 to +3/2 spin at the
anticrossing. The peak position Bp is shown to be affected by the confinement
electrostatics, and the utility of a tunable anticrossing position for
spintronics applications is discussed.Comment: 4 pages, 4 figure
Radiant heat exchange in a space environment Scientific technical report, 1 Feb. - 31 Jul. 1970
Spectral and directional surface property effects on radiant heat transfer in space environmen
Radiant heat exchange in a space environment Scientific technical report, 1 Aug. 1969 - 31 Jan. 1970
Spectral surface property effects on radiant heat transfer in aerospace environmen
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