731 research outputs found
The role of unusual conscious experiences in mental illness : an exploration guided by process models of symptom formation and by a hierarchical theory of personal illness : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Psychology at Massey University
The relationship between non-clinical unusual conscious experiences and mental illness was explored cross-sectionally in 104 users of community mental health services. Morris (1997) organised unusual conscious experiences and psychiatric symptoms according to the cognitive process errors believed to underlie them, and highlighted the role in the formation of symptoms of difficulties in determining the intentions of the self and others. Foulds's (1976) hierarchical theory of personal illness predicted that progressively more serious layers of symptoms would be experienced, in addition to those already present, as the ability to discern intentionalily diminished. Participants completed the Delusions-Symptoms-States Inventory and the Conscious Experiences Questionnaire, and their primary clinicians provided Global Assessment of Functioning ratings. Foulds's hierarchical theory was found to be valid, and the frequency of unusual conscious experiences and deficits in determining intentionality increased the higher participants were placed on his hierarchy. Global functioning, although unrelated to position on the hierarchy or symptom related distress (findings attributed to the failure to assess negative symptoms) was weakly associated with the frequency of unusual conscious experiences. Cognitive process errors were positively correlated with each other, consistent with the errors occurring in the course of a single underlying process. Predicted associations were found between: delusions of persecution and difficulties in determining the intentions of others; hallucinations and the attribution of imagined percepts to external sources; grandiose delusions and the attribution of the actions of others to the self; conversion symptoms and the attribution of actions of the self to external sources; dissociative symptoms and the attribution of percepts with an external origin to the imagination; and delusions (of grandiosity, persecution, contrition, and passivity) and the attribution of events to an unseen power or force. Predicted associations were not found for passivity delusions or delusions of contrition. The implications for dimensional conceptions of mental illness are discussed, and research recommended to isolate the trait component of unusual conscious experiences. The utility of the cognitive process and intentionality findings are discussed in terms of generating hypotheses for future research, and guiding cognitive behaviour therapy and clinical management
Radiation from structured-ring resonators
We investigate the scalar-wave resonances of systems composed of identical Neumann-type inclusions arranged periodically around a circular ring. Drawing on natural similarities with the undamped Rayleigh-Bloch waves supported by infinite linear arrays, we deduce asymptotically the exponentially small radiative damping in the limit where the ring radius is large relative to the periodicity. In our asymptotic approach, locally linear Rayleigh-Bloch waves that attenuate exponentially away from the ring are matched to a ring-scale WKB-type wave field. The latter provides a descriptive physical picture of how the mode energy is transferred via tunnelling to a circular evanescent-to-propagating transition region a finite distance away from the ring, from where radiative grazing rays emanate to the far field. Excluding the zeroth-order standing-wave modes, the position of the transition circle bifurcates with respect to clockwise and anti-clockwise contributions, resulting in striking spiral wavefronts
High-frequency homogenization of zero frequency stop band photonic and phononic crystals
We present an accurate methodology for representing the physics of waves, for
periodic structures, through effective properties for a replacement bulk
medium: This is valid even for media with zero frequency stop-bands and where
high frequency phenomena dominate. Since the work of Lord Rayleigh in 1892, low
frequency (or quasi-static) behaviour has been neatly encapsulated in effective
anisotropic media. However such classical homogenization theories break down in
the high-frequency or stop band regime.
Higher frequency phenomena are of significant importance in photonics
(transverse magnetic waves propagating in infinite conducting parallel fibers),
phononics (anti-plane shear waves propagating in isotropic elastic materials
with inclusions), and platonics (flexural waves propagating in thin-elastic
plates with holes). Fortunately, the recently proposed high-frequency
homogenization (HFH) theory is only constrained by the knowledge of standing
waves in order to asymptotically reconstruct dispersion curves and associated
Floquet-Bloch eigenfields: It is capable of accurately representing
zero-frequency stop band structures. The homogenized equations are partial
differential equations with a dispersive anisotropic homogenized tensor that
characterizes the effective medium.
We apply HFH to metamaterials, exploiting the subtle features of Bloch
dispersion curves such as Dirac-like cones, as well as zero and negative group
velocity near stop bands in order to achieve exciting physical phenomena such
as cloaking, lensing and endoscope effects. These are simulated numerically
using finite elements and compared to predictions from HFH. An extension of HFH
to periodic supercells enabling complete reconstruction of dispersion curves
through an unfolding technique is also introduced
Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings
A two-scale asymptotic theory is developed to generate continuum equations that model the macroscopic be- haviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The resulting equations include tensors that represent effective refractive indices near band edge frequencies along all principal axes directions, and these govern scalar functions providing long-scale mod- ulation of short-scale Bloch eigenstates, which can be used to predict the propagation of waves at frequencies outside of the long wavelength regime; these results are outside of the remit of typical homogenisation schemes. The theory we develop is applied to two topical examples, the first being the case of aligned dielectric cylin- ders, which has great importance in modelling photonic crystal fibres. Results of the asymptotic theory are veri- fied against numerical simulations by comparing photonic band diagrams and evanescent decay rates for guided modes. The second example is the propagation of electromagnetic waves localised within a planar array of di- electric spheres; at certain frequencies strongly directional propagation is observed, commonly described as dy- namic anisotropy. Computationally this is a challenging three-dimensional calculation, which we perform, and then demonstrate that the asymptotic theory captures the effect, giving highly accurate qualitative and quantitative comparisons as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour
Cloaking via mapping for the heat equation
This paper explores the concept of near-cloaking in the context of
time-dependent heat propagation. We show that after the lapse of a certain
threshold time instance, the boundary measurements for the homogeneous heat
equation are close to the cloaked heat problem in a certain Sobolev space norm
irrespective of the density-conductivity pair in the cloaked region. A
regularised transformation media theory is employed to arrive at our results.
Our proof relies on the study of the long time behaviour of solutions to the
parabolic problems with high contrast in density and conductivity coefficients.
It further relies on the study of boundary measurement estimates in the
presence of small defects in the context of steady conduction problem. We then
present some numerical examples to illustrate our theoretical results.Comment: 31 pages, 7 figures, 1 tabl
High frequency homogenization for travelling waves in periodic media
We consider high frequency homogenization in periodic media for travelling
waves of several different equations: the wave equation for scalar-valued waves
such as acoustics; the wave equation for vector-valued waves such as
electromagnetism and elasticity; and a system that encompasses the
Schr{\"o}dinger equation. This homogenization applies when the wavelength is of
the order of the size of the medium periodicity cell. The travelling wave is
assumed to be the sum of two waves: a modulated Bloch carrier wave having
crystal wave vector \Bk and frequency plus a modulated Bloch
carrier wave having crystal wave vector \Bm and frequency . We
derive effective equations for the modulating functions, and then prove that
there is no coupling in the effective equations between the two different waves
both in the scalar and the system cases. To be precise, we prove that there is
no coupling unless and (\Bk-\Bm)\odot\Lambda \in 2\pi
\mathbb Z^d, where is the
periodicity cell of the medium and for any two vectors the product is defined to be
the vector This last condition forces the
carrier waves to be equivalent Bloch waves meaning that the coupling constants
in the system of effective equations vanish.
We use two-scale analysis and some new weak-convergence type lemmas. The
analysis is not at the same level of rigor as that of Allaire and coworkers who
use two-scale convergence theory to treat the problem, but has the advantage of
simplicity which will allow it to be easily extended to the case where there is
degeneracy of the Bloch eigenvalue.Comment: 30 pages, Proceedings of the Royal Society A, 201
Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals
We demonstrate that photonic and phononic crystals consisting of closely
spaced inclusions constitute a versatile class of subwavelength metamaterials.
Intuitively, the voids and narrow gaps that characterise the crystal form an
interconnected network of Helmholtz-like resonators. We use this intuition to
argue that these continuous photonic (phononic) crystals are in fact
asymptotically equivalent, at low frequencies, to discrete capacitor-inductor
(mass-spring) networks whose lumped parameters we derive explicitly. The
crystals are tantamount to metamaterials as their entire acoustic branch, or
branches when the discrete analogue is polyatomic, is squeezed into a
subwavelength regime where the ratio of wavelength to period scales like the
ratio of period to gap width raised to the power 1/4; at yet larger wavelengths
we accordingly find a comparably large effective refractive index. The fully
analytical dispersion relations predicted by the discrete models yield
dispersion curves that agree with those from finite-element simulations of the
continuous crystals. The insight gained from the network approach is used to
show that, surprisingly, the continuum created by a closely packed hexagonal
lattice of cylinders is represented by a discrete honeycomb lattice. The
analogy is utilised to show that the hexagonal continuum lattice has a
Dirac-point degeneracy that is lifted in a controlled manner by specifying the
area of a symmetry-breaking defect
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