Matter and dynamics in closed cosmologies

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about ``homoclinic phenomena and chaos'' highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results.Comment: 23 pages, 24 figures (compressed), LaTe

Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey

We test and reject the claim of Segal et al. (1993) that the correlation of redshifts and flux densities in a complete sample of IRAS galaxies favors a quadratic redshift-distance relation over the linear Hubble law. This is done, in effect, by treating the entire galaxy luminosity function as derived from the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance indicator; equivalently, we compare the flux density distribution of galaxies as a function of redshift with predictions under different redshift-distance cosmologies, under the assumption of a universal luminosity function. This method does not assume a uniform distribution of galaxies in space. We find that this test has rather weak discriminatory power, as argued by Petrosian (1993), and the differences between models are not as stark as one might expect a priori. Even so, we find that the Hubble law is indeed more strongly supported by the analysis than is the quadratic redshift-distance relation. We identify a bias in the the Segal et al. determination of the luminosity function, which could lead one to mistakenly favor the quadratic redshift-distance law. We also present several complementary analyses of the density field of the sample; the galaxy density field is found to be close to homogeneous on large scales if the Hubble law is assumed, while this is not the case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros, postscript also available at http://www.astro.princeton.edu/~library/preprints/pop682.ps.g

Rotation and activity of pre-main-sequence stars

We present a study of rotation (vsini) and chromospheric activity (Halpha EW) based on an extensive set of high-resolution optical spectra obtained with MIKE on the 6.5m Magellan Clay telescope. Our targets are 74 F-M dwarfs in the young stellar associations Eta Cha, TW Hydrae, Beta Pic, and Tuc-Hor, spanning ages from 6 to 30 Myr. While the Halpha EW for most F and G stars are consistent with pure photospheric absorption, most K and M stars show chromospheric emission. By comparing Halpha EW in our sample to results in the literature, we see a clear evolutionary sequence: Chromospheric activity declines steadily from the T Tauri phase to the main sequence. Using activity as an age indicator, we find a plausible age range for the Tuc-Hor association of 10-40 Myr. Between 5 and 30 Myr, we do not see evidence for rotational braking in the total sample, thus angular momentum is conserved, in contrast to younger stars. This difference indicates a change in the rotational regulation at 5-10 Myr, possibly because disk braking cannot operate longer than typical disk lifetimes, allowing the objects to spin up. The rotation-activity relation is flat in our sample; in contrast to main-sequence stars, there is no linear correlation for slow rotators. We argue that this is because young stars generate their magnetic fields in a fundamentally different way from main-sequence stars, and not just the result of a saturated solar-type dynamo. By comparing our rotational velocities with published rotation periods for a subset of stars, we determine ages of 13 (7-20) Myr and 9 (7-17} Myr for the Eta Cha and TWA associations, respectively, consistent with previous estimates. Thus we conclude that stellar radii from evolutionary models by Baraffe et al. (1998) are in agreement with the observed radii within +-15%. (abridged)Comment: 40 pages, 8 figures, ApJ, in pres

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Excitation Thresholds for Nonlinear Localized Modes on Lattices

Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, $\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit

Participatory Militias: An Analysis of an Armed Movement's Online Audience

Armed groups of civilians known as "self-defense forces" have ousted the powerful Knights Templar drug cartel from several towns in Michoacan. This militia uprising has unfolded on social media, particularly in the "VXM" ("Valor por Michoacan," Spanish for "Courage for Michoacan") Facebook page, gathering more than 170,000 fans. Previous work on the Drug War has documented the use of social media for real-time reports of violent clashes. However, VXM goes one step further by taking on a pro-militia propagandist role, engaging in two-way communication with its audience. This paper presents a descriptive analysis of VXM and its audience. We examined nine months of posts, from VXM's inception until May 2014, totaling 6,000 posts by VXM administrators and more than 108,000 comments from its audience. We describe the main conversation themes, post frequency and relationships with offline events and public figures. We also characterize the behavior of VXM's most active audience members. Our work illustrates VXM's online mobilization strategies, and how its audience takes part in defining the narrative of this armed conflict. We conclude by discussing possible applications of our findings for the design of future communication technologies.Comment: Participatory Militias: An Analysis of an Armed Movement's Online Audience. Saiph Savage, Andres Monroy-Hernandez. CSCW: ACM Conference on Computer-Supported Cooperative Work 201

The 157 nm Photodissociation of OCS

The photodissociation of OCS at 157 nm has been investigated by using tunable vacuum ultraviolet radiation to probe the CO and S photoproducts. Sulfur is produced almost entirely in the 1S state, while CO is produced in its ground electronic state and in vibrational levels from v=0-3 in the appropriate ratio (v=0):(v=1):(v=2):(v=3) = (1.0):(1.0):(0.5):(0.3). The rotational distribution for each vibrational level is found to be near Boltzmann, with temperatures that decrease from 1350 K for v=0 to 780 K for v=3. Measurements of the CO Doppler profiles demonstrate that the dissociation takes place from a transition of predominantly parallel character (β=1.8±0.2) and that the CO velocity and angular momentum vectors are perpendicular to one another

Control-volume representation of molecular dynamics

A Molecular Dynamics (MD) parallel to the Control Volume (CV) formulation of fluid mechanics is developed by integrating the formulas of Irving and Kirkwood, J. Chem. Phys. 18, 817 (1950) over a finite cubic volume of molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, which yields an equivalent to Reynolds' Transport Theorem for the discrete system. This approach casts the dynamics of the molecular system into a form that can be readily compared to the continuum equations. The MD equations of motion are reinterpreted in terms of a Lagrangian-to-Control-Volume (\CV) conversion function $\vartheta_{i}$, for each molecule $i$. The \CV function and its spatial derivatives are used to express fluxes and relevant forces across the control surfaces. The relationship between the local pressures computed using the Volume Average (VA, Lutsko, J. Appl. Phys 64, 1152 (1988)) techniques and the Method of Planes (MOP, Todd et al, Phys. Rev. E 52, 1627 (1995)) emerges naturally from the treatment. Numerical experiments using the MD CV method are reported for equilibrium and non-equilibrium (start-up Couette flow) model liquids, which demonstrate the advantages of the formulation. The CV formulation of the MD is shown to be exactly conservative, and is therefore ideally suited to obtain macroscopic properties from a discrete system.Comment: 19 pages, 15 figure

Cognitive and attitudinal impacts of a university AIDS course: interdisciplinary education as a public health intervention.

This paper describes an interdisciplinary, variable credit-bearing university course on acquired immunodeficiency syndrome (AIDS) that enrolled 429 students. Pre- and post-course questionnaries were used to assess knowledge and attitudes relative to AIDS and these were compared to National Health Interview Survey findings. Considerable cognitive and attitudinal changes occurred over the course period. University courses, taught annually, were found to be an efficient mechanism for educating large numbers of future community leaders and professionals about AID

Quantum Interaction ϕ44\phi^4_4: the Construction of Quantum Field defined as a Bilinear Form

We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation $\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can be expanded over Wick polynomials of the free $in$-field, and where $:\!\phi^3(t,{\bf x})\!:$ is defined as the normal ordered product with respect to the free $in$-field. The constructed solution is correctly defined as a bilinear form on $D_{\theta}\times D_{\theta}$, where $D_{\theta}$ is a dense linear subspace in the Fock space of the free $in$-field. On $D_{\theta}\times D_{\theta}$ the diagonal Wick symbol of this bilinear form satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe