435,990 research outputs found
Efficient description of Bose-Einstein condensates in time-dependent rotating traps
Quantum sensors based on matter-wave interferometry are promising candidates
for high-precision gravimetry and inertial sensing in space. The favorable
source for the coherent matter waves in these devices are Bose-Einstein
condensates. A reliable prediction of their dynamics, which is governed by the
Gross-Pitaevskii equation, requires suitable analytical and numerical methods
which take into account the center-of-mass motion of the condensate, its
rotation and its spatial expansion by many orders of magnitude. In this
chapter, we present an efficient way to study their dynamics in time-dependent
rotating traps that meet this objective. Both, an approximate analytical
solution for condensates in the Thomas-Fermi regime and dedicated numerical
simulations on a variable adapted grid are discussed. We contrast and relate
our approach to previous alternative methods and provide further results, such
as analytical expressions for the one- and two-dimensional spatial density
distributions and the momentum distribution in the long-time limit that are of
immediate interest to experimentalists working in this field of research.Comment: 49 pages, 7 figures, preprint submitted to Advances in Atomic,
Molecular, and Optical Physics Volume 6
Sequential decoupling of negative-energy states in Douglas-Kroll-Hess theory
Here, we review the historical development, current status, and prospects of
Douglas--Kroll--Hess theory as a quantum chemical relativistic electrons-only
theory.Comment: 15 page
Freed by interaction kinetic states in the Harper model
We study the problem of two interacting particles in a one-dimensional
quasiperiodic lattice of the Harper model. We show that a short or long range
interaction between particles leads to emergence of delocalized pairs in the
non-interacting localized phase. The properties of these Freed by Interaction
Kinetic States (FIKS) are analyzed numerically including the advanced Arnoldi
method. We find that the number of sites populated by FIKS pairs grows
algebraically with the system size with the maximal exponent , up to a
largest lattice size reached in our numerical simulations, thus
corresponding to a complete delocalization of pairs. For delocalized FIKS pairs
the spectral properties of such quasiperiodic operators represent a deep
mathematical problem. We argue that FIKS pairs can be detected in the framework
of recent cold atom experiments [M.~Schreiber {\it et al.} Science {\bf 349},
842 (2015)] by a simple setup modification. We also discuss possible
implications of FIKS pairs for electron transport in the regime of
charge-density wave and high superconductivity.Comment: 26 pages, 21 pdf and png figures, additional data and high quality
figures are available at http://www.quantware.ups-tlse.fr/QWLIB/fikspairs/ ,
parts of sections 2 and 3 moved to appendices, manuscript accepted for EPJ
Numerical method for evolving the Projected Gross-Pitaevskii equation
In this paper we describe a method for evolving the projected
Gross-Pitaevskii equation (PGPE) for a Bose gas in a harmonic oscillator
potential. The central difficulty in solving this equation is the requirement
that the classical field is restricted to a small set of prescribed modes that
constitute the low energy classical region of the system. We present a scheme,
using a Hermite-polynomial based spectral representation, that precisely
implements this mode restriction and allows an efficient and accurate solution
of the PGPE. We show equilibrium and non-equilibrium results from the
application of the PGPE to an anisotropic trapped three-dimensional Bose gas.Comment: 12 pages, 5 figures. To appear in Phys. Rev. E. Convergence results
added, a few minor changes made and typos fixe
Finite Element Based Tracking of Deforming Surfaces
We present an approach to robustly track the geometry of an object that
deforms over time from a set of input point clouds captured from a single
viewpoint. The deformations we consider are caused by applying forces to known
locations on the object's surface. Our method combines the use of prior
information on the geometry of the object modeled by a smooth template and the
use of a linear finite element method to predict the deformation. This allows
the accurate reconstruction of both the observed and the unobserved sides of
the object. We present tracking results for noisy low-quality point clouds
acquired by either a stereo camera or a depth camera, and simulations with
point clouds corrupted by different error terms. We show that our method is
also applicable to large non-linear deformations.Comment: additional experiment
A Homotopy-Based Method for Optimization of Hybrid High-Low Thrust Trajectories
Space missions require increasingly more efficient trajectories to provide payload transport and mission goals by means of lowest fuel consumption, a strategic mission design key-point. Recent works demonstrated that the combined (or hybrid) use of chemical and electrical propulsion can give important advantages in terms of fuel consumption, without losing the ability to reach other mission objectives: as an example the Hohmann Spiral Transfer, applied in the case of a transfer to GEO orbit, demonstrated a fuel mass saving between 5-10% of the spacecraft wet mass, whilst satisfying a pre-set boundary constraint for the time of flight. Nevertheless, methods specifically developed for optimizing space trajectories considering the use of hybrid high-low thrust propulsion systems have not been extensively developed, basically because of the intrinsic complexity in the solution of optimal problem equations with existent numerical methods. The study undertaken and presented in this paper develops a numerical strategy for the optimization of hybrid high-low thrust space trajectories. An indirect optimization method has been developed, which makes use of a homotopic approach for numerical convergence improvement. The adoption of a homotopic approach provides a relaxation to the optimal problem, transforming it into a simplest problem to solve in which the optimal problem presents smoother equations and the shooting function acquires an increased convergence radius: the original optimal problem is then reached through a homotopy parameter continuation. Moreover, the use of homotopy can make possible to include a high thrust impulse (treated as velocity discontinuity) to the low thrust optimal control obtained from the indirect method. The impulse magnitude, location and direction are obtained following from a numerical continuation in order to minimize the problem cost function. The initial study carried out in this paper is finally correlated with particular test cases, in order to validate the work developed and to start investigating in which cases the effectiveness of hybrid-thrust propulsion subsists
Filterscape: energy recycling in a creative ecosystem
This paper extends previous work in evolutionary ecosystemic approaches to generative art. Filterscape, adopts the implicit fitness specification that is fundamental to this approach and explores the use of resource recycling as a means of generating coherent sonic diversity in a generative sound work. Filterscape agents consume and deposit energy that is manifest in the simulation as sound. Resource recycling is shown to support cooperative as well as competitive survival strategies. In the context of our simulation, these strategies are recognised by their characteristic audible signatures. The model provides a novel means to generate sonic diversity through de-centralised agent interactions
Nonparametric Infinite Horizon Kullback-Leibler Stochastic Control
We present two nonparametric approaches to Kullback-Leibler (KL) control, or
linearly-solvable Markov decision problem (LMDP) based on Gaussian processes
(GP) and Nystr\"{o}m approximation. Compared to recently developed parametric
methods, the proposed data-driven frameworks feature accurate function
approximation and efficient on-line operations. Theoretically, we derive the
mathematical connection of KL control based on dynamic programming with earlier
work in control theory which relies on information theoretic dualities for the
infinite time horizon case. Algorithmically, we give explicit optimal control
policies in nonparametric forms, and propose on-line update schemes with
budgeted computational costs. Numerical results demonstrate the effectiveness
and usefulness of the proposed frameworks
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