Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection

The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity field. While the odd-order correlation functions of the active and passive fields differ, we propose that the even-order correlation functions are the same to leading order (up to a trivial multiplicative factor). The leading correlation functions are statistically preserved structures of the passive scalar decaying problem, and therefore universality of the scaling exponents of the even-order correlations of the active scalar is demonstrated.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Assessing Sexual Orientation Symptoms In Obsessive-Compulsive Disorder: Development And Validation Of The Sexual Orientation Obsessions And Reactions Test (SORT)

Obsessive-compulsive disorder (OCD) includes many symptom presentations, which creates unique diagnostic challenges. Fears surrounding one’s sexual orientation are common within OCD (also called SO-OCD), but SO-OCD is consistently misdiagnosed by physicians and psychologists. To address this issue, we describe the development of a self-report measure for assessing SO-OCD to help distinguish OCD from distress caused by a sexual orientation identity crisis. The current paper details two studies that established the psychometric properties and clinical utility of this measure. In Study 1, the factor structure, validity, and reliability were examined for the measure’s 12 items in a sample of 1,673 university students. The results revealed a two-factor solution for the measure (Factor 1: Transformation Fears; Factor 2: Somatic Checking) and preliminary evidence of validity and reliability. In Study 2, the measure was tested with LGBTQ and heterosexual community samples and clinical samples of individuals with SO-OCD and other types of OCD. The two-factor solution and evidence of validity and reliability were supported in these samples. Cut-off points were established to distinguish between community members and SO-OCD sufferers, as well as between those experiencing SO-OCD and other types of OCD. Limitations and future directions are discussed

Dynamics of Scalar Fields in the Background of Rotating Black Holes

A numerical study of the evolution of a massless scalar field in the background of rotating black holes is presented. First, solutions to the wave equation are obtained for slowly rotating black holes. In this approximation, the background geometry is treated as a perturbed Schwarzschild spacetime with the angular momentum per unit mass playing the role of a perturbative parameter. To first order in the angular momentum of the black hole, the scalar wave equation yields two coupled one-dimensional evolution equations for a function representing the scalar field in the Schwarzschild background and a second field that accounts for the rotation. Solutions to the wave equation are also obtained for rapidly rotating black holes. In this case, the wave equation does not admit complete separation of variables and yields a two-dimensional evolution equation. The study shows that, for rotating black holes, the late time dynamics of a massless scalar field exhibit the same power-law behavior as in the case of a Schwarzschild background independently of the angular momentum of the black hole.Comment: 14 pages, RevTex, 6 Figure

Opportunistic Uses of the Traditional School Day Through Student Examination of Fitbit Activity Tracker Data

In large part due to the highly prescribed nature of the typical school day for children, efforts to design new interactions with technology have often focused on less-structured after-school clubs and other out-of-school environments. We argue that while the school day imposes serious restrictions, school routines can and should be opportunistically leveraged by designers and by youth. Specifically, wearable activity tracking devices open some new avenues for opportunistic collection of and reflection on data from the school day. To demonstrate this, we present two cases from an elementary statistics classroom unit we designed that intentionally integrated wearable activity trackers and childcreated data visualizations. The first case involves a group of students comparing favored recess activities to determine which was more physically demanding. The second case is of a student who took advantage of her knowledge of teachers’ school day routines to test the reliability of a Fitbit activity tracker against a commercial mobile app

Non-Markovian Decay and Lasing Condition in an Optical Microcavity Coupled to a Structured Reservoir

The decay dynamics of the classical electromagnetic field in a leaky optical resonator supporting a single mode coupled to a structured continuum of modes (reservoir) is theoretically investigated, and the issue of threshold condition for lasing in presence of an inverted medium is comprehensively addressed. Specific analytical results are given for a single-mode microcavity resonantly coupled to a coupled resonator optical waveguide (CROW), which supports a band of continuous modes acting as decay channels. For weak coupling, the usual exponential Weisskopf-Wigner (Markovian) decay of the field in the bare resonator is found, and the threshold for lasing increases linearly with the coupling strength. As the coupling between the microcavity and the structured reservoir increases, the field decay in the passive cavity shows non exponential features, and correspondingly the threshold for lasing ceases to increase, reaching a maximum and then starting to decrease as the coupling strength is further increased. A singular behavior for the "laser phase transition", which is a clear signature of strong non-Markovian dynamics, is found at critical values of the coupling between the microcavity and the reservoir.Comment: to appear in Phys. Rev. A (December 2006 issue

Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the relation between the structure of the QNM's of the KG equation and the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in order for the QNM's to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM's do {\it not} form a complete set. For such systems, we show that a complete set of QNM's can often be obtained by introducing an infinitesimal change in the effective potential

Turbulent Drag Reduction by Flexible and Rodlike Polymers: Crossover Effects at Small Concentrations

Drag reduction by polymers is bounded between two universal asymptotes, the von-K\'arm\'an log-law of the law and the Maximum Drag Reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The cross-over behavior from the Newtonian von-K\'arm\'an log-law to the MDR is however not universal, showing different characteristics for flexible and rodlike polymers. In this paper we provide a theory for this cross-over phenomenology.Comment: 5 pages, 4 figures, submitted to Physical Review

Late Time Tail of Wave Propagation on Curved Spacetime

The late time behavior of waves propagating on a general curved spacetime is studied. The late time tail is not necessarily an inverse power of time. Our work extends, places in context, and provides understanding for the known results for the Schwarzschild spacetime. Analytic and numerical results are in excellent agreement.Comment: 11 pages, WUGRAV-94-1