43,143 research outputs found
The Weighted Mean Curvature Derivative of a Space-Filling Diagram
Representing an atom by a solid sphere in -dimensional Euclidean space, we
get the space-filling diagram of a molecule by taking the union. Molecular
dynamics simulates its motion subject to bonds and other forces, including the
solvation free energy. The morphometric approach [HRC13,RHK06] writes the
latter as a linear combination of weighted versions of the volume, area, mean
curvature, and Gaussian curvature of the space-filling diagram. We give a
formula for the derivative of the weighted mean curvature. Together with the
derivatives of the weighted volume in [EdKo03], the weighted area in [BEKL04],
and the weighted Gaussian curvature [AkEd19], this yields the derivative of the
morphometric expression of the solvation free energy.Comment: 20 pages, 4 figure
The weighted Gaussian curvature derivative of a space-filling diagram
The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy
The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram
The morphometric approach [HRC13,RHK06] writes the solvation free energy as a
linear combination of weighted versions of the volume, area, mean curvature,
and Gaussian curvature of the space-filling diagram. We give a formula for the
derivative of the weighted Gaussian curvature. Together with the derivatives of
the weighted volume in [EdKo03], the weighted area in [BEKL04], and the
weighted mean curvature in [AkEd19], this yields the derivative of the
morphometric expression of solvation free energy.Comment: 16 pages, 2 figure
From rubber bands to rational maps: A research report
This research report outlines work, partially joint with Jeremy Kahn and
Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal
surfaces with boundary. One one hand, this lets us tell when one rubber band
network is looser than another, and on the other hand tell when one conformal
surface embeds in another.
We apply this to give a new characterization of hyperbolic critically finite
rational maps among branched self-coverings of the sphere, by a positive
criterion: a branched covering is equivalent to a hyperbolic rational map if
and only if there is an elastic graph with a particular "self-embedding"
property. This complements the earlier negative criterion of W. Thurston.Comment: 52 pages, numerous figures. v2: New example
Thermodynamic Relations in Correlated Systems
Several useful thermodynamic relations are derived for metal-insulator
transitions, as generalizations of the Clausius-Clapeyron and Eherenfest
theorems. These relations hold in any spatial dimensions and at any
temperatures. First, they relate several thermodynamic quantities to the slope
of the metal-insulator phase boundary drawn in the plane of the chemical
potential and the Coulomb interaction in the phase diagram of the Hubbard
model. The relations impose constraints on the critical properties of the Mott
transition. These thermodynamic relations are indeed confirmed to be satisfied
in the cases of the one- and two-dimensional Hubbard models. One of these
relations yields that at the continuous Mott transition with a diverging charge
compressibility, the doublon susceptibility also diverges. The constraints on
the shapes of the phase boundary containing a first-order metal-insulator
transition at finite temperatures are clarified based on the thermodynamic
relations. For example, the first-order phase boundary is parallel to the
temperature axis asymptotically in the zero temperature limit. The
applicability of the thermodynamic relations are not restricted only to the
metal-insulator transition of the Hubbard model, but also hold in correlated
systems with any types of phases in general. We demonstrate such examples in an
extended Hubbard model with intersite Coulomb repulsion containing the charge
order phase.Comment: 10 pages, 9 figure
Induced Chern-Simons term of a paired electron state in the quantum Hall system
The induced Chern-Simons term for a paired electron state is calculated in
the quantum Hall system by using a field theory on the von Neumann lattice. The
coefficient of the Chern-Simons term, which is the Hall conductance, has not
only the usual term proportional to a filling factor due to P (parity) & T
(time reversal) symmetry breaking but also correction terms due to P & T & U(1)
symmetry breaking. The correction term essentially comes from the
Nambu-Goldstone mode and depends on an infrared limit. It is shown that the
correction term is related to a topological number of a gap function in the
momentum space.Comment: 26 pages, 6 figure
Chaotic saddles in nonlinear modulational interactions in a plasma
A nonlinear model of modulational processes in the subsonic regime involving
a linearly unstable wave and two linearly damped waves with different damping
rates in a plasma is studied numerically. We compute the maximum Lyapunov
exponent as a function of the damping rates in a two-parameter space, and
identify shrimp-shaped self-similar structures in the parameter space. By
varying the damping rate of the low-frequency wave, we construct bifurcation
diagrams and focus on a saddle-node bifurcation and an interior crisis
associated with a periodic window. We detect chaotic saddles and their stable
and unstable manifolds, and demonstrate how the connection between two chaotic
saddles via coupling unstable periodic orbits can result in a crisis-induced
intermittency. The relevance of this work for the understanding of modulational
processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres
The Optical Counterpart to the Accreting Millisecond X-ray Pulsar SAX J1748.9-2021 in the Globular Cluster NGC 6440
We used a combination of deep optical and Halpha images of the Galactic
globular cluster NGC 6440, acquired with the Hubble Space Telescope, to
identify the optical counterpart to the accreting millisecond X-ray pulsar SAX
J1748.9-2021during quiescence. A strong Halpha emission has been detected from
a main sequence star (hereafter COM-SAX J1748.9-2021) located at only 0.15"
from the nominal position of the X-ray source. The position of the star also
agrees with the optical counterpart found by Verbunt et al. (2000) during an
outburst. We propose this star as the most likely optical counterpart to the
binary system. By direct comparison with isochrones, we estimated that COM-SAX
J1748.9-2021 has a mass of 0.70 Msun - 0.83 Msun, a radius of 0.88 pm 0.02 Rsun
and a superficial temperature of 5250pm80 K. These parameters combined with the
orbital characteristics of the binary suggest that the system is observed at a
very low inclination angle (~8 deg -14 deg) and that the star is filling or
even overflowing its Roche Lobe. This, together with the equivalent width of
the Halpha emission (~20 Ang), suggest possible on-going mass transfer. The
possibile presence of such a on-going mass transfer during a quiescence state
also suggests that the radio pulsar is not active yet and thus this system,
despite its similarity with the class of redback millisecond pulsars, is not a
transitional millisecond pulsar.Comment: 8 pages, 6 figures. Accepted for publication in Ap
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