408 research outputs found
A theoretical and numerical approach to "magic angle" of stone skipping
We investigate oblique impacts of a circular disk and water surface. An
experiment [ Clanet, C., Hersen, F. and Bocquet, L., Nature 427, 29 (2004) ]
revealed that there exists a "magic angle" of 20 [deg.] between a disk face and
water surface which minimize the required speed for ricochet. We perform
3-dimensional simulation of the water impacts using the Smoothed Particle
Hydrodynamics (SPH) and analyze the results with an ordinal differential
equation (ODE) model. Our simulation is in good agreement with the experiment.
The analysis with the ODE model give us a theoretical insight for the ``magic
angle" of stone skipping.Comment: 4 pages, 4figure
Vacuum field energy and spontaneous emission in anomalously dispersive cavities
Anomalously dispersive cavities, particularly white light cavities, may have
larger bandwidth to finesse ratios than their normally dispersive counterparts.
Partly for this reason, their use has been proposed for use in LIGO-like
gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze
the quantum noise associated with anomalously dispersive cavity modes. The
vacuum field energy associated with a particular cavity mode is proportional to
the cavity-averaged group velocity of that mode. For anomalously dispersive
cavities with group index values between 1 and 0, this means that the total
vacuum field energy associated with a particular cavity mode must exceed . For white light cavities in particular, the group index approaches
zero and the vacuum field energy of a particular spatial mode may be
significantly enhanced. We predict enhanced spontaneous emission rates into
anomalously dispersive cavity modes and broadened laser linewidths when the
linewidth of intracavity emitters is broader than the cavity linewidth.Comment: 9 pages, 4 figure
On the relation between Unruh and Sokolov--Ternov effects
We show that the Sokolov--Ternov effect -- the depolarization of particles in
storage rings coming from synchrotron radiation due to spin flip transitions --
is physically equivalent to the Unruh effect for circular acceleration if one
uses a spin 1/2 particle as the Unruh--DeWitt detector. It is shown that for
the electron, with gyromagnetic number , the exponential
contribution to the polarization, which usually characterizes the Unruh effect,
is "hidden" in the standard Sokolov-Ternov effect making it hard to observe.
Thus, our conclusions are different in detail from previous work.Comment: 23 pages, no figure
Thermal radiation of various gravitational backgrounds
We present a simple and general procedure for calculating the thermal
radiation coming from any stationary metric. The physical picture is that the
radiation arises as the quasi--classical tunneling of particles through a
gravitational barrier. We show that our procedure can reproduce the results of
Hawking and Unruh radiation. We also show that under certain kinds of
coordinate transformations the temperature of the thermal radiation will change
in the case of the Schwarzschild black holes. In addition we apply our
procedure to a rotating/orbiting system and show that in this case there is no
radiation, which has experimental implications for the polarization of
particles in circular accelerators.Comment: 6 pages revtex, added references, publication version. To be
published IJMP
Electrons as quasi-bosons in magnetic white dwarfs
A white dwarf star achieves its equilibrium from the balancing of the
gravitational compression against the Fermi degeneracy pressure of the electron
gas. In field theory there are examples (e.g. the monopole-charge system) where
a strong magnetic field can transform a boson into a fermion or a fermion into
a boson. In some condensed matter systems (e.g. fractional quantum Hall
systems) a strong magnetic field can transform electrons into effective
fermions, or effective anyons. Based on these examples we investigate the
possibility that the strong magnetic fields of some white dwarfs may transform
some fraction of the electrons into effective bosons. This could have
consequences for the structure of highly magnetized white dwarfs. It would
alter the mass-radius relationship, and in certain instances one could envision
a scenario where a white dwarf below the Chandrasekhar limit could nevertheless
collapse into a neutron star due to a weakening of the electron degeneracy
pressure. In addition the transformation of electrons into effective bosons
could result in the electrons Bose condensing, which could speed up the cooling
rate of white dwarfs.Comment: 10 pages. To be published IJMP
Blocking a wave: Frequency band gaps in ice shelves with periodic crevasses
We assess how the propagation of high-frequency elastic-flexural waves
through an ice shelf is modified by the presence of spatially periodic
crevasses. Analysis of the normal modes supported by the ice shelf with and
without crevasses reveals that a periodic crevasse distribution qualitatively
changes the mechanical response. The normal modes of an ice shelf free of
crevasses are evenly distributed as a function of frequency. In contrast, the
normal modes of a crevasse-ridden ice shelf are distributed unevenly. There are
"band gaps", frequency ranges over which no eigenmodes exist. A model ice shelf
that is 50 km in lateral extent and 300 m thick with crevasses spaced 500 m
apart has a band gap from 0.2 to 0.38 Hz. This is a frequency range relevant
for ocean wave/ice-shelf interactions. When the outermost edge of the crevassed
ice shelf is oscillated at a frequency within the band gap, the ice shelf
responds very differently from a crevasse-free ice shelf. The flexural motion
of the crevassed ice shelf is confined to a small region near the outermost
edge of the ice shelf and effectively "blocked" from reaching the interior.Comment: 6 pages, 4 figures, accepted to Annals of Glaciolog
Electromagnetic Momentum in Dispersive Dielectric Media
When the effects of dispersion are included, neither the Abraham nor the
Minkowski expression for electromagnetic momentum in a dielectric medium gives
the correct recoil momentum for absorbers or emitters of radiation. The total
momentum density associated with a field in a dielectric medium has three
contributions: (i) the Abraham momentum density of the field, (ii) the momentum
density associated with the Abraham force, and (iii) a momentum density arising
from the dispersive part of the response of the medium to the field, the latter
having a form evidently first derived by D.F. Nelson [Phys. Rev. A 44, 3985
(1991)]. All three contributions are required for momentum conservation in the
recoil of an absorber or emitter in a dielectric medium. We consider the
momentum exchanged and the force on a polarizable particle (e.g., an atom or a
small dielectric sphere) in a host dielectric when a pulse of light is incident
upon it, including the dispersion of the dielectric medium as well as a
dispersive component in the response of the particle to the field. The force
can be greatly increased in slow-light dielectric media.Comment: 9 pages. To be published by Optics Communication
Simulating Self-gravitating Hydrodynamic Flows
An efficient algorithm for solving Poisson's equation in two and three
spatial dimensions is discussed. The algorithm, which is described in detail,
is based on the integral form of Poisson's equation and utilizes spherical
coordinates and an expansion into spherical harmonics. The solver can be
applied to and works well for all problems for which the use of spherical
coordinates is appropriate. We also briefly discuss the implementation of the
algorithm into hydrodynamic codes which are based on a conservative
finite--difference scheme.Comment: 15 pages, compressed uu-encoded postscript file (232kB), to appear in
Computer Physics Communications, special issue Computational Hydrodynamics in
Astrophysic
Gauge theories and non-commutative geometry
It is shown that a -dimensional classical SU(N) Yang-Mills theory can be
formulated in a -dimensional space, with the extra two dimensions forming
a surface with non-commutative geometry. In this paper we present an explicit
proof for the case of the torus and the sphere.Comment: 12 page
Coherent Radio Pulses From GEANT Generated Electromagnetic Showers In Ice
Radio Cherenkov radiation is arguably the most efficient mechanism for
detecting showers from ultra-high energy particles of 1 PeV and above. Showers
occuring in Antarctic ice should be detectable at distances up to 1 km. We
report on electromagnetic shower development in ice using a GEANT Monte Carlo
simulation. We have studied energy deposition by shower particles and
determined shower parameters for several different media, finding agreement
with published results where available. We also report on radio pulse emission
from the charged particles in the shower, focusing on coherent emission at the
Cherenkov angle. Previous work has focused on frequencies in the 100 MHz to 1
GHz range. Surprisingly, we find that the coherence regime extends up to tens
of Ghz. This may have substantial impact on future radio-based neutrino
detection experiments as well as any test beam experiment which seeks to
measure coherent Cherenkov radiation from an electromagnetic shower. Our study
is particularly important for the RICE experiment at the South Pole.Comment: 44 pages, 29 figures. Minor changes made, reference added, accepted
for publication in Phys. Rev.
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