3,188 research outputs found
Introduction to Principal Components Analysis
Understanding the inverse equivalent width - luminosity relationship (Baldwin
Effect), the topic of this meeting, requires extracting information on
continuum and emission line parameters from samples of AGN. We wish to discover
whether, and how, different subsets of measured parameters may correlate with
each other. This general problem is the domain of Principal Components Analysis
(PCA). We discuss the purpose, principles, and the interpretation of PCA, using
some examples from QSO spectroscopy. The hope is that identification of
relationships among subsets of correlated variables may lead to new physical
insight.Comment: Invited review to appear in ``Quasars and Cosmology'', A.S.P.
Conference Series 1999. eds. G. J. Ferland, J. A. Baldwin, (San Francisco:
ASP). 10 pages, 2 figure
A tale of two airfoils: resolvent-based modelling of an oscillator vs. an amplifier from an experimental mean
The flows around a NACA 0018 airfoil at a Reynolds number of 10250 and angles
of attack of alpha = 0 (A0) and alpha = 10 (A10) are modelled using resolvent
analysis and limited experimental measurements obtained from particle image
velocimetry. The experimental mean velocity profiles are data-assimilated so
that they are solutions of the incompressible Reynolds-averaged Navier-Stokes
equations forced by Reynolds stress terms which are derived from experimental
data. Spectral proper orthogonal decompositions (SPOD) of the velocity
fluctuations and nonlinear forcing find low-rank behaviour at the shedding
frequency and its higher harmonics for the A0 case. In the A10 case, low-rank
behaviour is observed for the velocity fluctuations in two bands of
frequencies. Resolvent analysis of the data-assimilated means identifies
low-rank behaviour only in the vicinity of the shedding frequency for A0 and
none of its harmonics. The resolvent operator for the A10 case, on the other
hand, identifies two linear mechanisms whose frequencies are a close match with
those identified by SPOD. It is also shown that the second linear mechanism,
corresponding to the Kelvin-Helmholtz instability in the shear layer, cannot be
identified just by considering the time-averaged experimental measurements as a
mean flow due to the fact that experimental data are missing near the leading
edge. The A0 case is classified as an oscillator where the flow is organised
around an intrinsic instability while the A10 case behaves like an amplifier
whose forcing is unstructured. For both cases, resolvent modes resemble those
from SPOD when the operator is low-rank. To model the higher harmonics where
this is not the case, we add parasitic resolvent modes, as opposed to classical
resolvent modes which are the most amplified, by approximating the nonlinear
forcing from limited triadic interactions of known resolvent modes.Comment: 32 pages, 23 figure
Phenomenon of ordinariness in nursing
This phenomenological research aimed to illuminate the nature and effects of ordinariness in nursing and to discover whether the phenomenon enhanced the nursing encounter. The researcher worked as a participant observer with six registered nurses in a Professorial Nursing Unit. Following each interaction, the researcher wrote her impressions in a personal-professional journal and audiotaped conversations with the respective nurses and patients to gain their impressions. Using a theoretical framework of the phenomenological concepts of lived experience, Dasein, Being-in-the-world and fusion of horizons as an underpinning methodology, an initial hermeneutical analysis and interpretation of the impressions generated qualities and activities indicative of the aspects of the phenomenon of ordinariness in nursing. The second phase of the analysis and interpretation sought to illuminate the nature of the phenomenon itself. Eight actualities of the nature of the phenomenon emerged: \u27allowingness,\u27 \u27straightforwardness,\u27 \u27self-likeness,\u27 \u27homeliness,\u27 \u27favourableness,\u27 \u27intuneness,\u27 \u27lightheartedness\u27 and \u27connectedness.\u27 These actualities were described in relation to the phenomenon of interest. The effects of the phenomenon were the creative potential to enhance the nursing encounter and included many and various effects of facilitation, fair play, familiarity, family, favouring, feelings, fun and friendship. The research found that nurses and patients shared a common sense of humanity, which enhanced the nursing encounter. Within the context of caring, the nurses were ordinary people, perceived as being extraordinarily effective, by the very ways in which their humanness shone through their knowledge and skills, to make their whole being with patients something more than just professional helping. The shared sense of ordinariness between nurses and patients made them as one in then- humanness and created a special place, in which the relative strangeness of the experience of being in a health care setting, could be made familiar and manageable
On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations
The relationship between Koopman mode decomposition, resolvent mode
decomposition and exact invariant solutions of the Navier-Stokes equations is
clarified. The correspondence rests upon the invariance of the system operators
under symmetry operations such as spatial translation. The usual interpretation
of the Koopman operator is generalised to permit combinations of such
operations, in addition to translation in time. This invariance is related to
the spectrum of a spatio-temporal Koopman operator, which has a travelling wave
interpretation. The relationship leads to a generalisation of dynamic mode
decomposition, in which symmetry operations are applied to restrict the dynamic
modes to span a subspace subject to those symmetries. The resolvent is
interpreted as the mapping between the Koopman modes of the Reynolds stress
divergence and the velocity field. It is shown that the singular vectors of the
resolvent (the resolvent modes) are the optimal basis in which to express the
velocity field Koopman modes where the latter are not a priori known
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