18,341 research outputs found
Optimal control of the state statistics for a linear stochastic system
We consider a variant of the classical linear quadratic Gaussian regulator
(LQG) in which penalties on the endpoint state are replaced by the
specification of the terminal state distribution. The resulting theory
considerably differs from LQG as well as from formulations that bound the
probability of violating state constraints. We develop results for optimal
state-feedback control in the two cases where i) steering of the state
distribution is to take place over a finite window of time with minimum energy,
and ii) the goal is to maintain the state at a stationary distribution over an
infinite horizon with minimum power. For both problems the distribution of
noise and state are Gaussian. In the first case, we show that provided the
system is controllable, the state can be steered to any terminal Gaussian
distribution over any specified finite time-interval. In the second case, we
characterize explicitly the covariance of admissible stationary state
distributions that can be maintained with constant state-feedback control. The
conditions for optimality are expressed in terms of a system of dynamically
coupled Riccati equations in the finite horizon case and in terms of algebraic
conditions for the stationary case. In the case where the noise and control
share identical input channels, the Riccati equations for finite-horizon
steering become homogeneous and can be solved in closed form. The present paper
is largely based on our recent work in arxiv.org/abs/1408.2222,
arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:1410.344
The large core limit of spiral waves in excitable media: A numerical approach
We modify the freezing method introduced by Beyn & Thuemmler, 2004, for
analyzing rigidly rotating spiral waves in excitable media. The proposed method
is designed to stably determine the rotation frequency and the core radius of
rotating spirals, as well as the approximate shape of spiral waves in unbounded
domains. In particular, we introduce spiral wave boundary conditions based on
geometric approximations of spiral wave solutions by Archimedean spirals and by
involutes of circles. We further propose a simple implementation of boundary
conditions for the case when the inhibitor is non-diffusive, a case which had
previously caused spurious oscillations.
We then utilize the method to numerically analyze the large core limit. The
proposed method allows us to investigate the case close to criticality where
spiral waves acquire infinite core radius and zero rotation frequency, before
they begin to develop into retracting fingers. We confirm the linear scaling
regime of a drift bifurcation for the rotation frequency and the core radius of
spiral wave solutions close to criticality. This regime is unattainable with
conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied
Dynamical Systems on 20/03/1
Energy eigenfunctions of the 1D Gross-Pitaevskii equation
We developed a new and powerful algorithm by which numerical solutions for
excited states in a gravito optical surface trap have been obtained. They
represent solutions in the regime of strong nonlinearities of the
Gross--Pitaevskii equation. In this context we also shortly review several
approaches which allow, in principle, for calculating excited state solutions.
It turns out that without modifications these are not applicable to strongly
nonlinear Gross-Pitaevskii equations. The importance of studying excited states
of Bose-Einstein condensates is also underlined by a recent experiment of
B\"ucker et al in which vibrational state inversion of a Bose-Einstein
condensate has been achieved by transferring the entire population of the
condensate to the first excited state. Here, we focus on demonstrating the
applicability of our algorithm for three different potentials by means of
numerical results for the energy eigenstates and eigenvalues of the 1D
Grosss-Pitaevskii-equation. We compare the numerically found solutions and find
out that they completely agree with the case of known analytical solutions.Comment: 18 pages, 11 figure
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
Ultrasound Tomography has seen a revival of interest in the past decade,
especially for breast imaging, due to improvements in both ultrasound and
computing hardware. In particular, three-dimensional ultrasound tomography, a
fully tomographic method in which the medium to be imaged is surrounded by
ultrasound transducers, has become feasible. In this paper, a comprehensive
derivation and study of a robust framework for large-scale bent-ray ultrasound
tomography in 3D for a hemispherical detector array is presented. Two
ray-tracing approaches are derived and compared. More significantly, the
problem of linking the rays between emitters and receivers, which is
challenging in 3D due to the high number of degrees of freedom for the
trajectory of rays, is analysed both as a minimisation and as a root-finding
problem. The ray-linking problem is parameterised for a convex detection
surface and three robust, accurate, and efficient ray-linking algorithms are
formulated and demonstrated. To stabilise these methods, novel
adaptive-smoothing approaches are proposed that control the conditioning of the
update matrices to ensure accurate linking. The nonlinear UST problem of
estimating the sound speed was recast as a series of linearised subproblems,
each solved using the above algorithms and within a steepest descent scheme.
The whole imaging algorithm was demonstrated to be robust and accurate on
realistic data simulated using a full-wave acoustic model and an anatomical
breast phantom, and incorporating the errors due to time-of-flight picking that
would be present with measured data. This method can used to provide a
low-artefact, quantitatively accurate, 3D sound speed maps. In addition to
being useful in their own right, such 3D sound speed maps can be used to
initialise full-wave inversion methods, or as an input to photoacoustic
tomography reconstructions
A dissipative scheme to approach the boundary of two-qubit entangled mixed states
We discuss the generation of states close to the boundary-family of maximally
entangled mixed states as defined by the use of concurrence and linear entropy.
The coupling of two qubits to a dissipation-affected bosonic mode is able to
produce a bipartite state having, for all practical purposes, the entanglement
and purity properties of one of such boundary states. We thoroughly study the
effects that thermal and squeezed character of the bosonic mode have in such a
process and we discuss tolerance to qubit phase-damping mechanisms. The
non-demanding nature of the scheme makes it realizable in a matter-light based
physical set-up, which we address in some details.Comment: 9 pages, 7 figures, RevTeX4, Accepted for publication by Physics
Review
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