Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems

Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on which the system is not smooth. Much of our understanding of these cases relies on a reduction to piecewise linearity near the border-collision. We also review a number of codimension-two bifurcations in which nonlinearity is important.Comment: pdfLaTeX, 9 figure

Andronov-Hopf Bifurcations in Planar, Piecewise-Smooth, Continuous Flows

An equilibrium of a planar, piecewise-$C^1$, continuous system of differential equations that crosses a curve of discontinuity of the Jacobian of its vector field can undergo a number of discontinuous or border-crossing bifurcations. Here we prove that if the eigenvalues of the Jacobian limit to $\lambda_L \pm {\rm i} \omega_L$ on one side of the discontinuity and $-\lambda_R \pm {\rm i} \omega_R$ on the other, with $\lambda_L, \lambda_R >0$, and the quantity $\Lambda = \lambda_L / \omega_L -\lambda_R / \omega_R$ is nonzero, then a periodic orbit is created or destroyed as the equilibrium crosses the discontinuity. This bifurcation is analogous to the classical Andronov-Hopf bifurcation, and is supercritical if $\Lambda < 0$ and subcritical if $\Lambda >0$.Comment: laTex, 18 pages, 8 figure

Holography and Eternal Inflation

We show that eternal inflation is compatible with holography. In particular, we emphasize that if a region is asymptotically de Sitter in the future, holographic arguments by themselves place no bound on the number of past e-foldings. We also comment briefly on holographic restrictions on the production of baby universes.Comment: 14 pages, 3 figures, revtex4, (v2 relation with work of Banks and Fischler clarified, references added

Gravity wave analogs of black holes

It is demonstrated that gravity waves of a flowing fluid in a shallow basin can be used to simulate phenomena around black holes in the laboratory. Since the speed of the gravity waves as well as their high-wavenumber dispersion (subluminal vs. superluminal) can be adjusted easily by varying the height of the fluid (and its surface tension) this scenario has certain advantages over the sonic and dielectric black hole analogs, for example, although its use in testing quantum effects is dubious. It can be used to investigate the various classical instabilities associated with black (and white) holes experimentally, including positive and negative norm mode mixing at horizons. PACS: 04.70.-s, 47.90.+a, 92.60.Dj, 04.80.-y.Comment: 14 pages RevTeX, 5 figures, section VI modifie

Discontinuity Induced Bifurcations in a Model of Saccharomyces cerevisiae

We perform a bifurcation analysis of the mathematical model of Jones and Kompala [K.D. Jones and D.S. Kompala, Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures, J. Biotech., 71:105-131, 1999]. Stable oscillations arise via Andronov-Hopf bifurcations and exist for intermediate values of the dilution rate as has been noted from experiments previously. A variety of discontinuity induced bifurcations arise from a lack of global differentiability. We identify and classify discontinuous bifurcations including several codimension-two scenarios. Bifurcation diagrams are explained by a general unfolding of these singularities.Comment: 23 pages, 7 figure

The influence of anxiety on the progression of disability

OBJECTIVES: To determine the influence of anxiety on the progression of disability and examine possible mediators of the relationship. DESIGN: Community-based observational study. SETTING: Women's Health and Aging Study I, a prospective observational study with assessments every 6 months for 3 years. PARTICIPANTS: One thousand two functionally limited women aged 65 and older. MEASUREMENTS: Anxiety symptoms were assessed using four questions from the Hopkins Symptom Checklist (nervous or shaky, avoidance of certain things, tense or keyed up, fearful). Participants who reported experiencing two or more of these symptoms at baseline were considered anxious. Anxiety as a predictor of the onset of four types of disability was examined using Cox proportional hazards models. Three models were tested: an unadjusted model, a model adjusted for confounding variables (age, race, vision, number of diseases, physical performance, depressive symptoms), and a mediational model (benzodiazepine and psychotropic medication use, physical activity, emotional support). RESULTS: Nineteen percent of women reported two or more symptoms of anxiety at baseline. Unadjusted models indicate that anxiety was associated with a greater risk of worsening disability: activity of daily living (ADL) disability (relative risk (RR)=1.40, 95% confidence interval (CI)=1.10-1.79), mobility disability (RR=1.41, 95% CI=1.06-1.86), lifting disability (RR=1.54, 95% CI=1.20-1.97), and light housework disability (RR=1.77, 95% CI=1.32-2.37). After adjusting for confounding variables, anxiety continued to predict the development of two types of disability: ADL disability (RR=1.41, 95% CI=1.08-1.84) and light housework disability (RR=1.56, 95% CI=1.14-2.14). Finally, benzodiazepine and psychotropic medication use, physical activity, and emotional support were not significant mediators of the effect of anxiety on the development of a disability. CONCLUSION: Anxiety is a significant risk factor for the progression of disability in older women. Studies are needed to determine whether treatment of anxiety delays or prevents disabilit

Interior Structure of a Charged Spinning Black Hole in (2+1)(2+1)-Dimensions

The phenomenon of mass inflation is shown to occur for a rotating black hole. We demonstrate this feature in $(2+1)$ dimensions by extending the charged spinning BTZ black hole to Vaidya form. We find that the mass function diverges in a manner quantitatively similar to its static counterparts in $(3+1)$, $(2+1)$ and $(1+1)$ dimensions.Comment: 5 pages, 2 figures (appended as postscript files), WATPHYS-TH94/0

Bibbia, cristianesimo e letteratura italiana: uno sguardo d'assieme.

L'A. ripercorre la presenza della Bibbia nella letteratura italiana dalle origini ai giorni nostri, sottolineando la persistenza della ripresa del Sacro testo sia nella poesia che nella prosa