25,667 research outputs found
Propagation of a Dark Soliton in a Disordered Bose-Einstein Condensate
We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein
condensate in presence of a random potential. This configuration involves
nonlinear effects and disorder, and we argue that, contrarily to the study of
stationary transmission coefficients through a nonlinear disordered slab, it is
a well defined problem. It is found that a dark soliton decays algebraically,
over a characteristic length which is independent of its initial velocity, and
much larger than both the healing length and the 1D scattering length of the
system. We also determine the characteristic decay time.Comment: 4 pages, 2 figure
Dark soliton past a finite-size obstacle
We consider the collision of a dark soliton with an obstacle in a
quasi-one-dimensional Bose condensate. We show that in many respects the
soliton behaves as an effective classical particle of mass twice the mass of a
bare particle, evolving in an effective potential which is a convolution of the
actual potential describing the obstacle. Radiative effects beyond this
approximation are also taken into account. The emitted waves are shown to form
two counterpropagating wave packets, both moving at the speed of sound. We
determine, at leading order, the total amount of radiation emitted during the
collision and compute the acceleration of the soliton due to the collisional
process. It is found that the radiative process is quenched when the velocity
of the soliton reaches the velocity of sound in the system
Solar prominence modelling and plasma diagnostics at ALMA wavelengths
Our aim is to test potential solar prominence plasma diagnostics as obtained
with the new solar capability of the Atacama Large Millimeter / submillimeter
Array (ALMA). We investigate the thermal and plasma diagnostic potential of
ALMA for solar prominences through the computation of brightness temperatures
at ALMA wavelengths. The brightness temperature, for a chosen line of sight, is
calculated using densities of hydrogen and helium obtained from a radiative
transfer code under non local thermodynamic equilibrium (NLTE) conditions, as
well as the input internal parameters of the prominence model in consideration.
Two distinct sets of prominence models were used: isothermal-isobaric
fine-structure threads, and large-scale structures with radially increasing
temperature distributions representing the prominence-to-corona transition
region. We compute brightness temperatures over the range of wavelengths in
which ALMA is capable of observing (0.32 - 9.6mm), however we particularly
focus on the bands available to solar observers in ALMA cycles 4 and 5, namely
2.6 - 3.6mm (Band 3) and 1.1 - 1.4mm (Band 6). We show how the computed
brightness temperatures and optical thicknesses in our models vary with the
plasma parameters (temperature and pressure) and the wavelength of observation.
We then study how ALMA observables such as the ratio of brightness temperatures
at two frequencies can be used to estimate the optical thickness and the
emission measure for isothermal and non-isothermal prominences. From this study
we conclude that, for both sets of models, ALMA presents a strong thermal
diagnostic capability, provided that the interpretation of observations is
supported by the use of non-LTE simulation results.Comment: Submitted to Solar Physic
The Space of Solutions of Coupled XORSAT Formulae
The XOR-satisfiability (XORSAT) problem deals with a system of Boolean
variables and clauses. Each clause is a linear Boolean equation (XOR) of a
subset of the variables. A -clause is a clause involving distinct
variables. In the random -XORSAT problem a formula is created by choosing
-clauses uniformly at random from the set of all possible clauses on
variables. The set of solutions of a random formula exhibits various
geometrical transitions as the ratio varies.
We consider a {\em coupled} -XORSAT ensemble, consisting of a chain of
random XORSAT models that are spatially coupled across a finite window along
the chain direction. We observe that the threshold saturation phenomenon takes
place for this ensemble and we characterize various properties of the space of
solutions of such coupled formulae.Comment: Submitted to ISIT 201
Finite Size Scaling of the Spin Stiffness of the Antiferromagnetic S=1/2 XXZ chain
We study the finite size scaling of the spin stiffness for the
one-dimensional s=1/2 quantum antiferromagnet as a function of the anisotropy
parameter Delta.Previous Bethe ansatz results allow a determination of the
stiffness in the thermodynamic limit. The Bethe ansatz equations for finite
systems are solvable even in the presence of twisted boundary conditions, a
fact we exploit to determine the stiffness exactly for finite systems allowing
for a complete determination of the finite size corrections. Relating the
stiffness to thermodynamic quantities we calculate the temperature dependence
of the susceptibility and its finite size corrections at T=0. A Luttinger
liquid approach is used to study the finite size corrections using
renormalization group techniques and the results are compared to the
numerically exact results obtained using the Bethe ansatz equations. Both
irrelevant and marginally irrelevant cases are considered
Bayesian learning of noisy Markov decision processes
We consider the inverse reinforcement learning problem, that is, the problem
of learning from, and then predicting or mimicking a controller based on
state/action data. We propose a statistical model for such data, derived from
the structure of a Markov decision process. Adopting a Bayesian approach to
inference, we show how latent variables of the model can be estimated, and how
predictions about actions can be made, in a unified framework. A new Markov
chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior
distribution. This step includes a parameter expansion step, which is shown to
be essential for good convergence properties of the MCMC sampler. As an
illustration, the method is applied to learning a human controller
Tightness of the maximum likelihood semidefinite relaxation for angular synchronization
Maximum likelihood estimation problems are, in general, intractable
optimization problems. As a result, it is common to approximate the maximum
likelihood estimator (MLE) using convex relaxations. In some cases, the
relaxation is tight: it recovers the true MLE. Most tightness proofs only apply
to situations where the MLE exactly recovers a planted solution (known to the
analyst). It is then sufficient to establish that the optimality conditions
hold at the planted signal. In this paper, we study an estimation problem
(angular synchronization) for which the MLE is not a simple function of the
planted solution, yet for which the convex relaxation is tight. To establish
tightness in this context, the proof is less direct because the point at which
to verify optimality conditions is not known explicitly.
Angular synchronization consists in estimating a collection of phases,
given noisy measurements of the pairwise relative phases. The MLE for angular
synchronization is the solution of a (hard) non-bipartite Grothendieck problem
over the complex numbers. We consider a stochastic model for the data: a
planted signal (that is, a ground truth set of phases) is corrupted with
non-adversarial random noise. Even though the MLE does not coincide with the
planted signal, we show that the classical semidefinite relaxation for it is
tight, with high probability. This holds even for high levels of noise.Comment: 2 figure
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