17,676 research outputs found
Transit Node Routing Reconsidered
Transit Node Routing (TNR) is a fast and exact distance oracle for road
networks. We show several new results for TNR. First, we give a surprisingly
simple implementation fully based on Contraction Hierarchies that speeds up
preprocessing by an order of magnitude approaching the time for just finding a
CH (which alone has two orders of magnitude larger query time). We also develop
a very effective purely graph theoretical locality filter without any
compromise in query times. Finally, we show that a specialization to the online
many-to-one (or one-to-many) shortest path further speeds up query time by an
order of magnitude. This variant even has better query time than the fastest
known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201
Optical properties of current carrying molecular wires
We consider several fundamental optical phenomena involving single molecules
in biased metal-molecule-metal junctions. The molecule is represented by its
highest occupied and lowest unoccupied molecular orbitals, and the analysis
involves the simultaneous consideration of three coupled fluxes: the electronic
current through the molecule, energy flow between the molecule and
electron-hole excitations in the leads and the incident and/or emitted photon
flux. Using a unified theoretical approach based on the non-equilibrium Green
function method we derive expressions for the absorption lineshape (not an
observable but a ueful reference for considering yields of other optical
processes) and for the current induced molecular emission in such junctions. We
also consider conditions under which resonance radiation can induce electronic
current in an unbiased junction. We find that current driven molecular emission
and resonant light induced electronic currents in single molecule junctions can
be of observable magnitude under appropriate realizable conditions. In
particular, light induced current should be observed in junctions involving
molecular bridges that are characterized by strong charge transfer optical
transitions. For observing current induced molecular emission we find that in
addition to the familiar need to control the damping of molecular excitations
into the metal substrate the phenomenon is also sensitive to the way in which
the potential bias si distributed on the junction.Comment: 56 pages, 8 figures; submitted to JC
Emergent Geometry and Quantum Gravity
We explain how quantum gravity can be defined by quantizing spacetime itself.
A pinpoint is that the gravitational constant G = L_P^2 whose physical
dimension is of (length)^2 in natural unit introduces a symplectic structure of
spacetime which causes a noncommutative spacetime at the Planck scale L_P. The
symplectic structure of spacetime M leads to an isomorphism between symplectic
geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of
symplectic structure \omega in terms of electromagnetic fields F=dA are
transformed into those of Riemannian metric g. This approach for quantum
gravity allows a background independent formulation where spacetime as well as
matter fields is equally emergent from a universal vacuum of quantum gravity
which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page
Identifying the Environment and Redshift of GRB Afterglows from the Time-Dependence of Their Absorption Spectra
The discovery of Gamma-Ray Burst (GRB) afterglows revealed a new class of
variable sources at optical and radio wavelengths. At present, the environment
and precise redshift of the detected afterglows are still unknown. We show that
if a GRB source resides in a compact (<100pc) gas-rich environment, the
afterglow spectrum will show time-dependent absorption features due to the
gradual ionization of the surrounding medium by the afterglow radiation.
Detection of this time-dependence can be used to constrain the size and density
of the surrounding gaseous system. For example, the MgII absorption line
detected in GRB970508 should have weakened considerably during the first month
if the absorption occurred in a gas cloud of size <100pc around the source. The
time-dependent HI or metal absorption features provide a precise determination
of the GRB redshift.Comment: 13 pages, 4 figures, submitted to ApJ
Observation of a push force on the end face of a nm fiber taper exerted by outgoing light
There are two different proposals for the momentum of light in a transparent
dielectric of refractive index n: Minkowski's version nE/c and Abrahm's version
E/(nc), where E and c are the energy and vacuum speed of light, respectively.
Despite many tests and debates over nearly a century, momentum of light in a
transparent dielectric remains controversial. In this Letter, we report a
direct observation of the inward push force on the end face of a free nm fiber
taper exerted by the outgoing light. Our results clearly support Abraham
momentum. Our experiment also indicates an inward surface pressure on a
dielectric exerted by the incident light, different from the commonly
recognized pressure due to the specular reflection. Such an inward surface
pressure by the incident light may be useful for precise design of the
laser-induced inertially-confined fusion.Comment: 9 pages, 3 figures;Accepted for publication as a Letter in Physical
Review Letters(CODE: LP11093
Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars
The observed number counts of quasars may be explained either by long-lived
activity within rare massive hosts, or by short-lived activity within smaller,
more common hosts. It has been argued that quasar lifetimes may therefore be
inferred from their clustering length, which determines the typical mass of the
quasar host. Here we point out that the relationship between the mass of the
black-hole and the circular velocity of its host dark-matter halo is more
fundamental to the determination of the clustering length. In particular, the
clustering length observed in the 2dF quasar redshift survey is consistent with
the galactic halo - black-hole relation observed in local galaxies, provided
that quasars shine at ~10-100% of their Eddington luminosity. The slow
evolution of the clustering length with redshift inferred in the 2dF quasar
survey favors a black-hole mass whose redshift-independent scaling is with halo
circular velocity, rather than halo mass. These results are independent from
observations of the number counts of bright quasars which may be used to
determine the quasar lifetime and its dependence on redshift. We show that if
quasar activity results from galaxy mergers, then the number counts of quasars
imply an episodic quasar lifetime that is set by the dynamical time of the host
galaxy rather than by the Salpeter time. Our results imply that as the redshift
increases, the central black-holes comprise a larger fraction of their host
galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap
A Rigorous Derivation of Electromagnetic Self-force
During the past century, there has been considerable discussion and analysis
of the motion of a point charge, taking into account "self-force" effects due
to the particle's own electromagnetic field. We analyze the issue of "particle
motion" in classical electromagnetism in a rigorous and systematic way by
considering a one-parameter family of solutions to the coupled Maxwell and
matter equations corresponding to having a body whose charge-current density
and stress-energy tensor scale to zero size
in an asymptotically self-similar manner about a worldline as . In this limit, the charge, , and total mass, , of the body go to
zero, and goes to a well defined limit. The Maxwell field
is assumed to be the retarded solution associated with
plus a homogeneous solution (the "external field") that varies
smoothly with . We prove that the worldline must be a
solution to the Lorentz force equations of motion in the external field
. We then obtain self-force, dipole forces, and spin force
as first order perturbative corrections to the center of mass motion of the
body. We believe that this is the first rigorous derivation of the complete
first order correction to Lorentz force motion. We also address the issue of
obtaining a self-consistent perturbative equation of motion associated with our
perturbative result, and argue that the self-force equations of motion that
have previously been written down in conjunction with the "reduction of order"
procedure should provide accurate equations of motion for a sufficiently small
charged body with negligible dipole moments and spin. There is no corresponding
justification for the non-reduced-order equations.Comment: 52 pages, minor correction
Emission from Bow Shocks of Beamed Gamma-Ray Bursts
Beamed gamma-ray burst (GRB) sources produce a bow shock in their gaseous
environment. The emitted flux from this bow shock may dominate over the direct
emission from the jet for lines of sight which are outside the angular radius
of the jet emission, theta. The event rate for these lines of sight is
increased by a factor of 260*(theta/5_degrees)^{-2}. For typical GRB
parameters, we find that the bow shock emission from a jet with half-angle of
about 5 degrees is visible out to tens of Mpc in the radio and hundreds of Mpc
in the X-rays. If GRBs are linked to supernovae, studies of peculiar supernovae
in the local universe should reveal this non-thermal bow shock emission for
weeks to months following the explosion.Comment: ApJ, submitted, 15 pages, 3 figure
Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints
The Einstein constraint equations have been the subject of study for more
than fifty years. The introduction of the conformal method in the 1970's as a
parameterization of initial data for the Einstein equations led to increased
interest in the development of a complete solution theory for the constraints,
with the theory for constant mean curvature (CMC) spatial slices and closed
manifolds completely developed by 1995. The first general non-CMC existence
result was establish by Holst et al. in 2008, with extensions to rough data by
Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC
theory remains mostly open; moreover, recent work of Maxwell on specific
symmetry models sheds light on fundamental non-uniqueness problems with the
conformal method as a parameterization in non-CMC settings. In parallel with
these mathematical developments, computational physicists have uncovered
surprising behavior in numerical solutions to the extended conformal thin
sandwich formulation of the Einstein constraints. In particular, numerical
evidence suggests the existence of multiple solutions with a quadratic fold,
and a recent analysis of a simplified model supports this conclusion. In this
article, we examine this apparent bifurcation phenomena in a methodical way,
using modern techniques in bifurcation theory and in numerical homotopy
methods. We first review the evidence for the presence of bifurcation in the
Hamiltonian constraint in the time-symmetric case. We give a brief introduction
to the mathematical framework for analyzing bifurcation phenomena, and then
develop the main ideas behind the construction of numerical homotopy, or
path-following, methods in the analysis of bifurcation phenomena. We then apply
the continuation software package AUTO to this problem, and verify the presence
of the fold with homotopy-based numerical methods.Comment: 13 pages, 4 figures. Final revision for publication, added material
on physical implication
Quantum Vacuum Contribution to the Momentum of the Dielectric Media
Momentum transfer between matter and electromagnetic field is analyzed. The
related equations of motion and conservation laws are derived using
relativistic formalism. Their correspondence to various, at first sight
self-contradicting, experimental data (the so called Abraham-Minkowski
controversy) is demonstrated. A new, Casimir like, quantum phenomenon is
predicted: contribution of vacuum fluctuations to the motion of dielectric
liquids in crossed electric and magnetic fields. Velocities about can
be expected due to the contribution of high frequency vacuum modes
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