Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system

Starting from the classical Saltzman two-dimensional convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system which includes a decoupled generalized Lorenz system. The consideration of this process breaks an important symmetry and couples the dynamics of fast and slow variables, with the ensuing modifications to the structural properties of the attractor and of the spectral features. When the relevant nondimensional number (Eckert number Ec) is different from zero, an additional time scale of O(Ec−1) is introduced in the system, as shown with standard multiscale analysis and made clear by several numerical evidences. Moreover, the system is ergodic and hyperbolic, the slow variables feature long-term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation. Increasing the strength of the thermal-viscous feedback has a stabilizing effect, as both the metric entropy and the Kaplan-Yorke attractor dimension decrease monotonically with Ec. The analyzed system features very rich dynamics: it overcomes some of the limitations of the Lorenz system and might have prototypical value in relevant processes in complex systems dynamics, such as the interaction between slow and fast variables, the presence of long-term memory, and the associated extreme value statistics. This analysis shows how neglecting the coupling of slow and fast variables only on the basis of scale analysis can be catastrophic. In fact, this leads to spurious invariances that affect essential dynamical properties (ergodicity, hyperbolicity) and that cause the model losing ability in describing intrinsically multiscale processes.

Rapid Keck Spectroscopy of Cataclysmic Variables

We present an analysis of Rapid Keck Spectroscopy of the CVs AM Her (polar) and SS Cyg (dwarf nova). We decompose the spectra into constant and variable components and identify different types of variability in AM Her with different characteristic timescales. The variable flickering component of the accretion disc flux and the observational characteristics of a small flare in SS Cyg are isolated.

The projected hand illusion: component structure in a community sample, and association with demographics, cognition and psychotic-like experiences

The projected hand illusion (PHI) is a variant of the rubber hand illusion (RHI), and both are commonly used to study mechanisms of self-perception. A questionnaire was developed by Longo et al. (2008) to measure qualitative changes in the RHI. Such psychometric analyses have not yet been conducted on the questionnaire for the PHI. The present study is an attempt to validate minor modifications of the questionnaire of Longo et al. to assess the PHI in a community sample (n = 48) and to determine the association with selected demographic (age, sex, years of education), cognitive (Digit Span), and clinical (psychotic-like experiences) variables. Principal components analysis on the questionnaire data extracted four components: Embodiment of “Other” Hand, Disembodiment of Own Hand, Deafference, and Agency—in both synchronous and asynchronous PHI conditions. Questions assessing “Embodiment” and “Agency” loaded onto orthogonal components. Greater illusion ratings were positively associated with being female, being younger, and having higher scores on psychotic-like experiences. There was no association with cognitive performance. Overall, this study confirmed that self-perception as measured with PHI is a multicomponent construct, similar in many respects to the RHI. The main difference lies in the separation of Embodiment and Agency into separate constructs, and this likely reflects the fact that the “live” image of the PHI presents a more realistic picture of the hand and of the stroking movements of the experimenter compared with the RHI.