Velocity, energy and helicity of vortex knots and unknots

In this paper we determine the velocity, the energy and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number $w$, given by the ratio of the number of meridian wraps to that of the longitudinal wraps. We find that for $w<1$ vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for $w>1$ knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by the writhe contribution. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, that are found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid $^4$He.Comment: 17 pages, 8 figures, 2 table

Model-independent constraints on contact interactions from LEP2 data analysis

We derive model-independent constraints on four-fermion contact interaction-type dynamics from the published preliminary LEP2 experimental data on e^+e^- annihilation into \mu^+\mu^- and \tau^+\tau^- pairs, measured at different energies between 130 and 207 GeV. The basic observables are chosen to be the total cross section and the forward-backward asymmetry, and the analysis realistically takes into account data uncertainties and correlations among measurements at the various energies. The combination of data from different energy points plays an important role in the determination of regions allowed for the contact interaction coupling constants. In contrast to the more common one-parameter analyses, we only obtain constraints on pairs of parameters rather than limits on individual ones.Comment: 13 pages, LaTeX, including figures. v2: Included discussion of tau data, version to appear in EPJ

Kelvin Wave Cascade and Decay of Superfluid Turbulence

Kelvin waves (kelvons)--the distortion waves on vortex lines--play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that non-trivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; corresponding kinetic equation is derived. On the basis of the kinetic equation, we prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.Comment: 4 pages, RevTe

Targeting Social Connection in the Context of Trauma: Functional Outcomes and Mechanisms of Change

The current study presents and preliminarily tests a brief, theory driven intervention designed to target social connectivity as a transdiagnostic mechanism of health. We tested four hypotheses to examine whether and how explicitly targeting social behavior engagement (activating values-led behaviors towards specific network members) may improve other downstream aspects of social connectivity (i.e., social cognitions measured as loneliness, interpersonal closeness, perceived social support) and functioning (quality of life [QOL] and posttraumatic stress symptoms [PTS]). Methods. Participants included 15 patients (10 veterans, 5 firefighters) who completed the six-session intervention. Demographics: age (M = 46, SD = 17), 87% male, race (80% Caucasian, 20% Hispanic), 60% married/partnered, 47% living alone. Our multi-analytic approach included parametric and non-parametric tests: (a) significance testing and effect sizes to examine whether variables of interest changed, and (b) Granger causality analysis of repeated measures to examine the mechanistic theory of change (does social behavior engagement lead to improved social cognition and functioning?). Results. Statistically significant, medium-large effect size improvements were shown for QOL (Cohens d = 1.05), PTS (d = 1.05), social behavior engagement (d = 0.78), and several social cognitions (loneliness, d = 0.80, interpersonal closeness, d = 0.53). Models accounted for medium-large variance explained in improved QOL (R2 = 0.47, 95% CI [0.00,0.66]) and PTS (R2 = 0.56, 95% CI[0.07,0.72]). The theory of change was supported, with increase in social behaviors preceding improvement in social cognitions (not vice-versa). Conclusions. Improving social connectivity is a mechanism for improving QOL and mental health. Focus on initiating values-driven social behaviors may be an efficient and effective entry point to stimulate change

The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra

We investigate closed ideals in the Grassmann algebra serving as bases of Lie-invariant geometric objects studied before by E. Cartan. Especially, the E. Cartan theory is enlarged for Lax integrable nonlinear dynamical systems to be treated in the frame work of the Wahlquist Estabrook prolongation structures on jet-manifolds and Cartan-Ehresmann connection theory on fibered spaces. General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra is studied in great detail. An effective Maurer-Cartan one-forms construction is suggested that is very useful for applications. As an example of application the developed Lie-invariant geometric object theory for the Burgers nonlinear dynamical system is considered having given rise to finding an explicit form of the associated Lax type representation

Localized induction equation and pseudospherical surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A: Mathematical and Genera

Recent Advances in Laboratory Infrared Spectroscopy of Polycyclic Aromatic Hydrocarbons: PAHs in the Far Infrared

Over 25 years of observations and laboratory work have shown that the mid-IR spectra of a majority of astronomical sources are dominated by emission features near 3.3, 6.2, 7.7, and 11.2 microns, which originate in free polycyclic aromatic hydrocarbon (PAH) molecules. PAHs dominate the mid-IR emission from many galactic and extragalactic objects. As such, this material tracks a wide variety of astronomical processes, making this spectrum a powerful probe of the cosmos Apart from bands in the mid-IR, PAHs have bands spanning the Far-IR (FIR) and emission from these FIR features should be present in astronomical sources showing the Mid-IR PAH bands. However, with one exception, the FIR spectral characteristics are known only for a few neutral small PAHs trapped in salt pellets or oils at room temperature, data which is not relevant to astrophysics. Furthermore, since most emitting PAHs responsible for the mid-IR astronomical features are ionized, the absence of any experimental or theoretical PAH ion FIR spectra will make it impossible to correctly interpret the FIR data from these objects. In view of the upcoming Herschel space telescope mission and SOFIA's FIR airborne instrumentation, which will pioneer the FIR region, it is now urgent to obtain PAH FIR spectra. This talk will present an overview recent advances in the laboratory spectroscopy of PAHs, Highlighting the FIR spectroscopy along with some quantum calculations

Is baryon number violated when electroweak strings intercommute?

We reexamine the self-helicity and the intercommutation of electroweak strings. A plausible argument for baryon number conservation when electroweak strings intercommute is presented. The connection between a segment of electroweak strings and a sphaleron is also discussed.Comment: CALT-68-1948, 11 pages, 5 figures available upon request. Replaced with revised version. (Request should be sent to [email protected]