121,267 research outputs found
Soliton Resonances for MKP-II
Using the second flow - the Derivative Reaction-Diffusion system, and the
third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the
product of two functions, satisfying those systems is a solution of the
modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative
dispersion (MKP-II). We construct Hirota's bilinear representation for both
flows and combine them together as the bilinear system for MKP-II. Using this
bilinear form we find one and two soliton solutions for the MKP-II. For special
values of parameters our solution shows resonance behaviour with creation of
four virtual solitons. Our approach allows one to interpret the resonance
soliton as a composite object of two dissipative solitons in 1+1 dimensions.Comment: 11 pages, 2 figures, Talk on International Conference "Nonlinear
Physics. Theory and Experiment. III", 24 June-3 July, 2004, Gallipoli(Lecce),
Ital
Phase diagram of the three band half-filled Cu-O two-leg ladder
We determine the phase diagram of the half-filled two-leg ladder both at weak
and strong coupling, taking into account the Cu d_{x^2-y^2} and the O p_x and
p_y orbitals. At weak coupling, renormalization group flows are interpreted
with the use of bosonization. Two different models with and without outer
oxygen orbitals are examined. For physical parameters, and in the absence of
the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears
when the outer oxygen atoms are included. We show that the circulating current
phase that preserves translational symmetry does not appear at weak coupling.
In the opposite strong-coupling atomic limit the model is purely electrostatic
and the ground states may be found by simple energy minimization. The phase
diagram so obtained is compared to the weak-coupling one.Comment: 10 pages, 5 figures, Version accepted for publication in PR
Stability of Noisy Metropolis-Hastings
Pseudo-marginal Markov chain Monte Carlo methods for sampling from
intractable distributions have gained recent interest and have been
theoretically studied in considerable depth. Their main appeal is that they are
exact, in the sense that they target marginally the correct invariant
distribution. However, the pseudo-marginal Markov chain can exhibit poor mixing
and slow convergence towards its target. As an alternative, a subtly different
Markov chain can be simulated, where better mixing is possible but the
exactness property is sacrificed. This is the noisy algorithm, initially
conceptualised as Monte Carlo within Metropolis (MCWM), which has also been
studied but to a lesser extent. The present article provides a further
characterisation of the noisy algorithm, with a focus on fundamental stability
properties like positive recurrence and geometric ergodicity. Sufficient
conditions for inheriting geometric ergodicity from a standard
Metropolis-Hastings chain are given, as well as convergence of the invariant
distribution towards the true target distribution
When is an error not a prediction error? An electrophysiological investigation
A recent theory holds that the anterior cingulate cortex (ACC) uses reinforcement learning signals conveyed by the midbrain dopamine system to facilitate flexible action selection. According to this position, the impact of reward prediction error signals on ACC modulates the amplitude of a component of the event-related brain potential called the error-related negativity (ERN). The theory predicts that ERN amplitude is monotonically related to the expectedness of the event: It is larger for unexpected outcomes than for expected outcomes. However, a recent failure to confirm this prediction has called the theory into question. In the present article, we investigated this discrepancy in three trial-and-error learning experiments. All three experiments provided support for the theory, but the effect sizes were largest when an optimal response strategy could actually be learned. This observation suggests that ACC utilizes dopamine reward prediction error signals for adaptive decision making when the optimal behavior is, in fact, learnable
Lyman alpha line formation in starbursting galaxies II. Extremely Thick, Dustless, and Static HI Media
The Lya line transfer in an extremely thick medium of neutral hydrogen is
investigated by adopting an accelerating scheme in our Monte Carlo code to skip
a large number of core or resonant scatterings. This scheme reduces computing
time significantly with no sacrifice in the accuracy of the results. We applied
this numerical method to the Lya transfer in a static, uniform, dustless, and
plane-parallel medium. Two types of photon sources have been considered, the
midplane source and the uniformly distributed sources. The emergent profiles
show double peaks and absorption trough at the line-center. We compared our
results with the analytic solutions derived by previous researchers, and
confirmed that both solutions are in good agreement with each other. We
investigated the directionality of the emergent Lya photons and found that limb
brightening is observed in slightly thick media while limb darkening appears in
extremely thick media. The behavior of the directionality is noted to follow
that of the Thomson scattered radiation in electron clouds, because both Lya
wing scattering and Thomson scattering share the same Rayleigh scattering phase
function. The mean number of wing scatterings just before escape is in exact
agreement with the prediction of the diffusion approximation. The Lya photons
constituting the inner part of the emergent profiles follow the relationship
derived from the diffusion approximation. We present a brief discussion on the
application of our results to the formation of Lya broad absorption troughs and
P-Cygni type Lya profiles seen in the UV spectra of starburst galaxies.Comment: 24 papges, 12 figures, The revised version submitted to Ap
Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns
An exhaustive classification of certain class of static solutions for the
five-dimensional Einstein-Gauss-Bonnet theory in vacuum is presented. The class
of metrics under consideration is such that the spacelike section is a warped
product of the real line with a nontrivial base manifold. It is shown that for
generic values of the coupling constants the base manifold must be necessarily
of constant curvature, and the solution reduces to the topological extension of
the Boulware-Deser metric. It is also shown that the base manifold admits a
wider class of geometries for the special case when the Gauss-Bonnet coupling
is properly tuned in terms of the cosmological and Newton constants. This
freedom in the metric at the boundary, which determines the base manifold,
allows the existence of three main branches of geometries in the bulk. For
negative cosmological constant, if the boundary metric is such that the base
manifold is arbitrary, but fixed, the solution describes black holes whose
horizon geometry inherits the metric of the base manifold. If the base manifold
possesses a negative constant Ricci scalar, two different kinds of wormholes in
vacuum are obtained. For base manifolds with vanishing Ricci scalar, a
different class of solutions appears resembling "spacetime horns". There is
also a special case for which, if the base manifold is of constant curvature,
due to certain class of degeneration of the field equations, the metric admits
an arbitrary redshift function. For wormholes and spacetime horns, there are
regions for which the gravitational and centrifugal forces point towards the
same direction. All these solutions have finite Euclidean action, which reduces
to the free energy in the case of black holes, and vanishes in the other cases.
Their mass is also obtained from a surface integral.Comment: 31 pages, 1 figure, minor changes and references added. Final version
to be published in PR
Spin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells
We investigate the intrinsic spin Hall effect in two-dimensional electron
gases in quantum wells with two subbands, where a new intersubband-induced
spin-orbit coupling is operative. The bulk spin Hall conductivity
is calculated in the ballistic limit within the standard Kubo
formalism in the presence of a magnetic field and is found to remain finite
in the B=0 limit, as long as only the lowest subband is occupied. Our
calculated exhibits a nonmonotonic behavior and can change its
sign as the Fermi energy (the carrier areal density ) is varied between
the subband edges. We determine the magnitude of for realistic
InSb quantum wells by performing a self-consistent calculation of the
intersubband-induced spin-orbit coupling.Comment: 7 pages, 3 figure
Optical Spatial integration methods for ambiguity function generation
A coherent optical spatial integration approach to ambiguity function generation is described. It uses one dimensional acousto-optic Bragg cells as input tranducers in conjunction with a space variant linear phase shifter, a passive optical element, to generate the two dimensional ambiguity function in one exposure. Results of a real time implementation of this system are shown
Reconstructing Three-dimensional Structure of Underlying Triaxial Dark Halos From Xray and Sunyaev-Zel'dovich Effect Observations of Galaxy Clusters
While the use of galaxy clusters as {\it tools} to probe cosmology is
established, their conventional description still relies on the spherical
and/or isothermal models that were proposed more than 20 years ago. We present,
instead, a deprojection method to extract their intrinsic properties from X-ray
and Sunyaev--Zel'dovich effect observations in order to improve our
understanding of cluster physics. First we develop a theoretical model for the
intra-cluster gas in hydrostatic equilibrium in a triaxial dark matter halo
with a constant axis ratio. In this theoretical model, the gas density profiles
are expressed in terms of the intrinsic properties of the dark matter halos.
Then, we incorporate the projection effect into the gas profiles, and show that
the gas surface brightness profiles are expressed in terms of the
eccentricities and the orientation angles of the dark halos. For the practical
purpose of our theoretical model, we provide several empirical fitting formulae
for the gas density and temperature profiles, and also for the surface
brightness profiles relevant to X-ray and Sunyaev--Zel'dovich effect
observations. Finally, we construct a numerical algorithm to determine the halo
eccentricities and orientation angles using our model, and demonstrate that it
is possible in principle to reconstruct the 3D structures of the dark halos
from the X-ray and/or Sunyaev-Zel'dovich effect cluster data alone without
requiring priors such as weak lensing informations and without relying on such
restrictive assumptions as the halo axial symmetry about the line-of-sight.Comment: Accepted version, new discussions added, typos and minor mistakes
corrected, ApJ in press (2004, Feb. 1 scheduled, Vol. 601, No. 2 issue),26
pages, 7 postscript figure
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