51,909 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
Orbital Kondo effect in Cobalt-Benzene sandwich molecules
We study a Co-benzene sandwich molecule bridging the tips of a Cu nanocontact
as a realistic model of correlated molecular transport. To this end we employ a
recently developed method for calculating the correlated electronic structure
and transport properties of nanoscopic conductors. When the molecule is
slightly compressed by the tips of the nanocontact the dynamic correlations
originating from the strongly interacting Co 3d shell give rise to an orbital
Kondo effect while the usual spin Kondo effect is suppressed due to Hund's rule
coupling. This non-trivial Kondo effect produces a sharp and
temperature-dependent Abrikosov-Suhl resonance in the spectral function at the
Fermi level and a corresponding Fano line shape in the low bias conductance
Mix and match: a strategyproof mechanism for multi-hospital kidney exchange
As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor–patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal
A new chiral electro-optic effect: Sum-frequency generation from optically active liquids in the presence of a dc electric field
We report the observation of sum-frequency signals that depend linearly on an
applied electrostatic field and that change sign with the handedness of an
optically active solution. This recently predicted chiral electro-optic effect
exists in the electric-dipole approximation. The static electric field gives
rise to an electric-field-induced sum-frequency signal (an achiral third-order
process) that interferes with the chirality-specific sum-frequency at
second-order. The cross-terms linear in the electrostatic field constitute the
effect and may be used to determine the absolute sign of second- and
third-order nonlinear optical susceptibilities in isotropic media.Comment: Submitted to Physical Revie
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