16,919 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
Quantum corrections to the Larmor radiation formula in scalar electrodynamics
We use the semi-classical approximation in perturbative scalar quantum
electrodynamics to calculate the quantum correction to the Larmor radiation
formula to first order in Planck's constant in the non-relativistic
approximation, choosing the initial state of the charged particle to be a
momentum eigenstate. We calculate this correction in two cases: in the first
case the charged particle is accelerated by a time-dependent but
space-independent vector potential whereas in the second case it is accelerated
by a time-independent vector potential which is a function of one spatial
coordinate. We find that the corrections in these two cases are different even
for a charged particle with the same classical motion. The correction in each
case turns out to be non-local in time in contrast to the classical
approximation.Comment: 19 page
A kinetic model of radiating electrons
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of phase space. The pathological solutions of the 1-particle theory may be removed by expanding the latter equation in powers of τ ≔ q 2/6πm. The radiation-induced change in entropy is explored and its physical origin is discussed. As a simple demonstration of the theory, the radiative damping rate of longitudinal plasma waves is calculated
A necklace of Wulff shapes
In a probabilistic model of a film over a disordered substrate, Monte-Carlo
simulations show that the film hangs from peaks of the substrate. The film
profile is well approximated by a necklace of Wulff shapes. Such a necklace can
be obtained as the infimum of a collection of Wulff shapes resting on the
substrate. When the random substrate is given by iid heights with exponential
distribution, we prove estimates on the probability density of the resulting
peaks, at small density
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
The free rigid body dynamics: generalized versus classic
In this paper we analyze the normal forms of a general quadratic Hamiltonian
system defined on the dual of the Lie algebra of real -
skew - symmetric matrices, where is an arbitrary real symmetric
matrix. A consequence of the main results is that any first-order autonomous
three-dimensional differential equation possessing two independent quadratic
constants of motion which admits a positive/negative definite linear
combination, is affinely equivalent to the classical "relaxed" free rigid body
dynamics with linear controls.Comment: 12 page
Magnetic mirror cavities as THz radiation sources and a means of quantifying radiation friction
We propose a radiation source based on a magnetic mirror cavity. Relativistic
electrons are simulated entering the cavity and their trajectories and
resulting emission spectra are calculated. The uniformity of the particle
orbits is found to result in a frequency comb in terahertz range, the precise
energies of which are tuneable by varying the electron's -factor. For
very high energy particles radiation friction causes the spectral harmonics to
broaden and we suggest this as a possible way to verify competing classical
equations of motion.Comment: 8 pages, 10 figure
Strong signatures of radiation reaction below the radiation dominated regime
The influence of radiation reaction (RR) on multiphoton Thomson scattering by
an electron colliding head-on with a strong laser beam is investigated in a new
regime, in which the momentum transferred on average to the electron by the
laser pulse approximately compensates the one initially prepared. This
equilibrium is shown to be far more sensitive to the influence of RR than
previously studied scenarios. As a consequence RR can be experimentally
investigated with currently available laser systems and the underlying widely
discussed theoretical equations become testable for the first time.Comment: 4 pages, 3 figure
Brane Gravitational Extension of Dirac's "Extensible Model of the Electron"
A gravitational extension of Dirac's "Extensible model of the electron" is
presented. The Dirac bubble, treated as a 3-dim electrically charged brane, is
dynamically embedded within a 4-dim -symmetric Reissner-Nordstrom bulk.
Crucial to our analysis is the gravitational extension of Dirac's brane
variation prescription; its major effect is to induce a novel geometrically
originated contribution to the energy-momentum tensor on the brane. In turn,
the effective potential which governs the evolution of the bubble exhibits a
global minimum, such that the size of the bubble stays finite (Planck scale)
even at the limit where the mass approaches zero. This way, without
fine-tuning, one avoids the problem so-called 'classical radius of the
electron'.Comment: 6 PRD pages, 4 figures; References adde
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