Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Increased plasticity of the bodily self in eating disorders

Background: The rubber hand illusion (RHI) has been widely used to investigate the bodily self in healthy individuals. The aim of the present study was to extend the use of the RHI to examine the bodily self in eating disorders. Methods: The RHI and self-report measures of eating disorder psychopathology (EDI-3 subscales of Drive for Thinness, Bulimia, Body Dissatisfaction, Interoceptive Deficits, and Emotional Dysregulation; DASS-21; and the Self-Objectification Questionnaire) were administered to 78 individuals with an eating disorder and 61 healthy controls. Results: Individuals with an eating disorder experienced the RHI significantly more strongly than healthy controls on both perceptual (i.e., proprioceptive drift) and subjective (self-report questionnaire) measures. Furthermore, both the subjective experience of the RHI and associated proprioceptive biases were correlated with eating disorder psychopathology. Approximately 20% of the variance for embodiment of the fake hand was accounted for by eating disorder psychopathology, with interoceptive deficits and self-objectification significant predictors of embodiment. Conclusions: These results indicate that the bodily self is more plastic in people with an eating disorder. These findings may shed light on both aetiological and maintenance factors involved in eating disorders, particularly visual processing of the body, interoceptive deficits, and self-objectification

On the symmetry breaking phenomenon

We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases

Polarization of Astronomical Maser Radiation. IV. Circular Polarization Profiles

Profile comparison of the Stokes parameters $V$ and $I$ is a powerful tool for maser data analysis, providing the first direct methods for unambiguous determination of (1) the maser saturation stage, (2) the amplification optical depth and intrinsic Doppler width of unsaturated masers, and (3) the comparative magnitudes of Zeeman splitting and Doppler linewidth. Circular polarization recently detected in OH 1720 MHz emission from the Galactic center appears to provide the first direct evidence for maser saturation.Comment: 14 pages, 1 Postscript figures (included), uses aaspp4.sty. To appear in Astrophysical Journa

Cross-Correlation Studies between CMB Temperature Anisotropies and 21 cm Fluctuations

During the transition from a neutral to a fully reionized universe, scattering of cosmic microwave background (CMB) photons via free-electrons leads to a new anisotropy contribution to the temperature distribution. If the reionization process is inhomogeneous and patchy, the era of reionization is also visible via brightness temperature fluctuations in the redshifted 21 cm line emission from neutral Hydrogen. Since regions containing electrons and neutral Hydrogen are expected to trace the same underlying density field, the two are (anti) correlated and this is expected to be reflected in the anisotropy maps via a correlation between arcminute-scale CMB temperature and the 21 cm background. In terms of the angular cross-power spectrum, unfortunately, this correlation is insignificant due to a geometric cancellation associated with second order CMB anisotropies. The same cross-correlation between ionized and neutral regions, however, can be studied using a bispectrum involving large scale velocity field of ionized regions from the Doppler effect, arcminute scale CMB anisotropies during reionization, and the 21 cm background. While the geometric cancellation is partly avoided, the signal-to-noise ratio related to this bispectrum is reduced due to the large cosmic variance related to velocity fluctuations traced by the Doppler effect. Unless the velocity field during reionization can be independently established, it is unlikely that the correlation information related to the relative distribution of ionized electrons and regions containing neutral Hydrogen can be obtained with a combined study involving CMB and 21 cm fluctuations.Comment: 10 pages, 3 figure

Calculation of The Lifetimes of Thin Stripper Targets Under Bombardment of Intense Pulsed Ions

The problems of stripper target behavior in the nonstationary intense particle beams are considered. The historical sketch of studying of radiation damage failure of carbon targets under ion bombardment is presented. The simple model of evaporation of a target by an intensive pulsing beam is supposed. Stripper foils lifetimes in the nonstationary intense particle can be described by two failure mechanisms: radiation damage accumulation and evaporation of target. At the maximal temperatures less than 2500K the radiation damage are dominated; at temperatures above 2500K the mechanism of evaporation of a foil prevails. The proposed approach has been applied to the discription of behaviour of stripper foils in the BNL linac and SNS conditions.Comment: 12 pages, 5 figure

Persistent junk solutions in time-domain modeling of extreme mass ratio binaries

In the context of metric perturbation theory for non-spinning black holes, extreme mass ratio binary (EMRB) systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a "burst" of junk radiation which eventually propagates off the computational domain. We observe another unintended consequence of trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation. Our concluding section discusses the applicability of these observations to other numerical schemes and techniques used to solve distributionally forced master wave equations.Comment: Uses revtex4, 16 pages, 9 figures, 3 tables. Document reformatted and modified based on referee's report. Commentary added which addresses the possible presence of persistent junk solutions in other approaches for solving master wave equation