10,043 research outputs found
Algebraic Description of Shape Invariance Revisited
We revisit the algebraic description of shape invariance method in
one-dimensional quantum mechanics. In this note we focus on four particular
examples: the Kepler problem in flat space, the Kepler problem in spherical
space, the Kepler problem in hyperbolic space, and the Rosen-Morse potential
problem. Following the prescription given by Gangopadhyaya et al., we first
introduce certain nonlinear algebraic systems. We then show that, if the model
parameters are appropriately quantized, the bound-state problems can be solved
solely by means of representation theory.Comment: 12 pages, 8 eepic figures; minor correction
Reversible Vortex Ratchet Effects and Ordering in Superconductors with Simple Asymmetric Potential Arrays
We demonstrate using computer simulations that the simplest vortex ratchet
system for type-II superconductors with artificial pinning arrays, an
asymmetric one-dimensional (1D) potential array, exhibits the same features as
more complicated two-dimensional vortex ratchets that have been studied in
recent experiments. We show that the 1D geometry, originally proposed by Lee et
al. [Nature 400, 337 (1999)], undergoes multiple reversals in the sign of the
ratchet effect as a function of vortex density, substrate strength, and ac
drive amplitude, and that the sign of the ratchet effect is related to the type
of vortex lattice structure present. When the vortex lattice is highly ordered,
an ordinary vortex ratchet effect occurs which is similar to the response of an
isolated particle in the same ratchet geometry. In regimes where the vortices
form a smectic or disordered phase, the vortex-vortex interactions are relevant
and we show with force balance arguments that the ratchet effect can reverse in
sign. The dc response of this system features a reversible diode effect and a
variety of vortex states including triangular, smectic, disordered and square.Comment: 10 pages, 12 postscript figures. Version to appear in Phys. Rev.
Self-propulsion against a moving membrane: enhanced accumulation and drag force
Self-propulsion (SP) is a main feature of active particles (AP), such as
bacteria or biological micromotors, distinguishing them from passive colloids.
A renowned consequence of SP is accumulation at static interfaces, even in the
absence of hydrodynamic interactions. Here we address the role of SP in the
interaction between AP and a moving semipermeable membrane. In particular, we
implement a model of noninteracting AP in a channel crossed by a partially
penetrable wall, moving at a constant velocity . With respect to both the
cases of passive colloids with and AP with , the AP with finite
show enhancement of accumulation in front of the obstacle and experience a
largely increased drag force. This effect is understood in terms of an
effective potential localised at the interface between particles and membrane,
of height proportional to , where is the AP's re-orientation
time and the width characterising the surface's smoothness (
for hard core obstacles). An approximate analytical scheme is able to reproduce
the observed density profiles and the measured drag force, in very good
agreement with numerical simulations. The effects discussed here can be
exploited for automatic selection and filtering of AP with desired parameters.Comment: 13 pages, 3 figure
Thermally induced directed currents in hard rod systems
We study the non equilibrium statistical properties of a one dimensional
hard-rod fluid undergoing collisions and subject to a spatially non uniform
Gaussian heat-bath and periodic potential. The system is able to sustain finite
currents when the spatially inhomogeneous heat-bath and the periodic potential
profile display an appropriate relative phase shift, . By comparison with
the collisionless limit, we determine the conditions for the most efficient
transport among inelastic, elastic and non interacting rods. We show that the
situation is complex as, depending on shape of the temperature profile, the
current of one system may outperform the others.Comment: 5 pages, 2 figure
Which is the temperature of granular systems? A mean field model of free cooling inelastic mixtures
We consider a mean field model describing the free cooling process of a two
component granular mixture, a generalization of so called Maxwell model. The
cooling is viewed as an ordering process and the scaling behavior is attributed
to the presence of an attractive fixed point at for the dynamics. By
means of asymptotic analysis of the Boltzmann equation and of numerical
simulations we get the following results: 1)we establish the existence of two
different partial granular temperatures, one for each component, which violates
the Zeroth Law of Thermodynamics; 2) we obtain the scaling form of the two
distribution functions; 3) we prove the existence of a continuous spectrum of
exponents characterizing the inverse-power law decay of the tails of the
velocity, which generalizes the previously reported value 4 for the pure model;
4) we find that the exponents depend on the composition, masses and restitution
coefficients of the mixture; 5) we also remark that the reported distributions
represent a dynamical realization of those predicted by the Non Extensive
Statistical Mechanics, in spite of the fact that ours stem from a purely
dynamical approach.Comment: 23 pages, 9 figures. submitted for publicatio
Production of TeV gamma-radiation in the vicinity of the supermassive black hole in the giant radiogalaxy M87
Although the giant radiogalaxy M 87 harbors many distinct regions of
broad-band nonthermal emission, the recently reported fast variability of TeV
gamma rays from M 87 on a timescale of days strongly constrains the range of
speculations concerning the possible sites and scenarios of particle
acceleration responsible for the observed TeV emission. A natural production
site of this radiation is the immediate vicinity of the central supermassive
mass black hole (BH). Because of the low bolometric luminosity, the nucleus of
M 87 is effectively transparent for gamma rays up to energy of 10 TeV, which
makes this source an ideal laboratory for study of particle acceleration
processes close to the BH event horizon. We critically analyse different
possible radiation mechanisms in this region, and argue that the observed very
high-energy gamma ray emission can be explained by the inverse Compton emission
of ultrarelativistic electron-positron pairs produced through the development
of an electromagnetic cascade in the BH magnetosphere. We demonstrate, through
detailed numerical calculations of acceleration and radiation of electrons in
the magnetospheric vacuum gap, that this ``pulsar magnetosphere like'' scenario
can satisfactorily explain the main properties of TeV gamma-ray emission of M
87.Comment: 11 pages, ApJ, in prin
Driven low density granular mixtures
We study the steady state properties of a 2D granular mixture in the presence
of energy driving by employing simple analytical estimates and Direct
Simulation Monte Carlo. We adopt two different driving mechanisms: a) a
homogeneous heat bath with friction and b) a vibrating boundary (thermal or
harmonic) in the presence of gravity. The main findings are: the appearance of
two different granular temperatures, one for each species; the existence of
overpopulated tails in the velocity distribution functions and of non trivial
spatial correlations indicating the spontaneous formation of cluster
aggregates. In the case of a fluid subject to gravity and to a vibrating
boundary, both densities and temperatures display non uniform profiles along
the direction normal to the wall, in particular the temperature profiles are
different for the two species while the temperature ratio is almost constant
with the height. Finally, we obtained the velocity distributions at different
heights and verified the non gaussianity of the resulting distributions.Comment: 19 pages, 12 figures, submitted for publicatio
Period-Color and Amplitude-Color Relations in Classical Cepheid Variables - VI. New Challenges for Pulsation Models
We present multiphase Period-Color/Amplitude-Color/Period-Luminosity
relations using OGLE III and Galactic Cepheid data and compare with state of
the art theoretical pulsation models. Using this new way to compare models and
observations, we find convincing evidence that both Period-Color and
Period-Luminosity Relations as a function of phase are dynamic and highly
nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit
function and find the same result. Hence our results cannot be due to reddening
errors. We present statistical tests and the urls of movies depicting the
Period-Color/Period Luminosity and Wesenheit relations as a function of phase
for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate
nonlinearity as a function of phase and offer a new window toward a deeper
understanding of stellar pulsation. When comparing with models, we find that
the models also predict this nonlinearity in both Period-Color and
Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in
mimicking the LMC Cepheid relations, particularly at longer periods, though the
models predict systematically higher amplitudes than the observations
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