100,805 research outputs found
Fisher Hartwig determinants, conformal field theory and universality in generalised XX models
We discuss certain quadratic models of spinless fermions on a 1D lattice, and
their corresponding spin chains. These were studied by Keating and Mezzadri in
the context of their relation to the Haar measures of the classical compact
groups. We show how these models correspond to translation invariant models on
an infinite or semi-infinite chain, which in the simplest case reduce to the
familiar XX model. We give physical context to mathematical results for the
entanglement entropy, and calculate the spin-spin correlation functions using
the Fisher-Hartwig conjecture. These calculations rigorously demonstrate
universality in classes of these models. We show that these are in agreement
with field theoretic and renormalization group arguments that we provide
Implications of an r-mode in XTE J1751-305: Mass, radius and spin evolution
Recently Strohmayer and Mahmoodifar presented evidence for a coherent
oscillation in the X-ray light curve of the accreting millisecond pulsar XTE
J1751-305, using data taken by RXTE during the 2002 outburst of this source.
They noted that a possible explanation includes the excitation of a non-radial
oscillation mode of the neutron star, either in the form of a g-mode or an
r-mode. The r-mode interpretation has connections with proposed spin-evolution
scenarios for systems such as XTE J1751-305. Here we examine in detail this
interesting possible interpretation. Using the ratio of the observed
oscillation frequency to the star's spin frequency, we derive an approximate
neutron star mass-radius relation which yields reasonable values for the mass
over the range of expected stellar radius (as constrained by observations of
radius-expansion burst sources). However, we argue that the large mode
amplitude suggested by the Strohmayer and Mahmoodifar analysis would inevitably
lead to a large spin-down of the star, inconsistent with its observed spin
evolution, regardless of whether the r-mode itself is in a stable or unstable
regime. We therefore conclude that the r-mode interpretation of the observed
oscillation is not consistent with our current understanding of neutron star
dynamics and must be considered unlikely. Finally we note that, subject to the
availability of a sufficiently accurate timing model, a direct
gravitational-wave search may be able to confirm or reject an r-mode
interpretation unambiguously, should such an event, with a similar inferred
mode amplitude, recur during the Advanced detector era.Comment: 8 pages, 3 figures; submitted to MNRA
Constrained LQR Using Online Decomposition Techniques
This paper presents an algorithm to solve the infinite horizon constrained
linear quadratic regulator (CLQR) problem using operator splitting methods.
First, the CLQR problem is reformulated as a (finite-time) model predictive
control (MPC) problem without terminal constraints. Second, the MPC problem is
decomposed into smaller subproblems of fixed dimension independent of the
horizon length. Third, using the fast alternating minimization algorithm to
solve the subproblems, the horizon length is estimated online, by adding or
removing subproblems based on a periodic check on the state of the last
subproblem to determine whether it belongs to a given control invariant set. We
show that the estimated horizon length is bounded and that the control sequence
computed using the proposed algorithm is an optimal solution of the CLQR
problem. Compared to state-of-the-art algorithms proposed to solve the CLQR
problem, our design solves at each iteration only unconstrained least-squares
problems and simple gradient calculations. Furthermore, our technique allows
the horizon length to decrease online (a useful feature if the initial guess on
the horizon is too conservative). Numerical results on a planar system show the
potential of our algorithm.Comment: This technical report is an extended version of the paper titled
"Constrained LQR Using Online Decomposition Techniques" submitted to the 2016
Conference on Decision and Contro
Vortex Splitting in Subcritical Nonlinear Schrodinger Equation
Vortices and axisymmetric vortex rings are considered in the framework of the
subcritical nonlinear Schrodinger equations. The higher order nonlinearity
present in such systems models many-body interactions in superfluid systems and
allows one to study the effects of negative pressure on vortex dynamics. We
find the critical pressure for which the straight-line vortex becomes unstable
to radial expansion of the core. The energy of the straight-line vortices and
energy, impulse and velocity of vortex rings are calculated. The effect of a
varying pressure on the vortex core is studied. It is shown that under the
action of the periodically varying pressure field a vortex ring may split into
many vortex rings and the conditions for which this happens are elucidated.
These processes are also relevant to experiments in Bose-Einstein condensates
where the strength and the sign of two-body interactions can be changed via
Feshbach resonance.Comment: Invited submission to the special issue on Vortex Rings, Journal of
Fluid Dynamics Researc
Oral Health Advice for People With Serious Mental Illness
People with serious mental illness experience an erosion of functioning in day-to-day life over a protracted period of time. There is also evidence to suggest that people with serious mental illness have a greater risk of experiencing oral disease and have greater oral treatment needs than the general population. However, oral health has never been seen as a priority in people suffering with serious mental illness
The molecular structure of isocyanic acid from microwave and infra-red absorption spectra
Experimental investigations of the infra-red and microwave spectra of the slightly asymmetric rotor, HNCO, have been made, and the structure of the molecule has been determined
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