Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type

We describe the topological behavior of typical orbits of complex quadratic polynomials P_alpha(z)=e^{2\pi i alpha} z+z^2, with alpha of high return type. Here we prove that for such Brjuno values of alpha the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then combining with Part I of this work, we show that the limit set of the orbit of a typical point in the Julia set is equal to the closure of the critical orbit.Comment: 38 pages, 5 figures; fixed the issues with processing the figure

Social Media and the Fear of Missing Out: Scale Development and Assessment

For many, viewing social media causes them to relate their own lives to what they are seeing or reading, resulting in feelings that they are somehow missing out.  It is suggested that the fear of missing out influences decision making and behavior. The current research explores the measurement of FOMO, focusing on scale development and validation. Using extant scales for inadequacy, irritability, anxiety, and self- esteem, a list of items (n=37), postulated to measure FOMO, was created. In addition to the scale items, questions to assess behavioral and demographic characteristic were included.  A pre-test of the survey instrument was conducted (n=30).  The final survey was administered electronically, resulting in a useable sample of n=202. Principal components analysis resulted in a 10 item, 3-factor solution explaining 71% of the overall variance. The three factors performed reasonably well all with Cronbach’s alpha above or near Nunnally’s suggested .70 (Nunnally, 1978). Using the newly created scale, FOMO scores were calculated for each respondent. Results suggest significant differences in social media consumption across levels of FOMO.  Results also suggest significant differences in the use of particular social media based on ones level of FOMO.  Limitations include the sample and it is suggested that future research, including confirmatory factor analysis, should be conducted

Thurston's pullback map on the augmented Teichm\"uller space and applications

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page

Classification of Complex Polynomial Vector Fields in One Complex Variable

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.Comment: 57 pages, 35 figures, submitted to the Journal of Difference Equations and Application

Nest site selection by sea turtles

The distribution of 38 nests of loggerhead turtles (Caretta caretta) on beaches on Sanibel and Captiva islands, south-western Florida (26°26\u27N 82°16\u27W), and of 70 first digging attempts by green turtles (Chelonia mydas) on Ascension Island (7°57\u27S 14°22\u27W), was quantified. For loggerhead turtles on Sanibel and Captiva, nests were clumped close to the border between the open sand and the supra-littoral vegetation that backed the beaches. This spatial pattern of nests was closely reproduced by assuming simply that turtles crawled a random distance above the most recent high water line prior to digging. In contrast, green turtles on Ascension Island clumped their first digging attempts on the uneven beach above the springs high water line, crawling up to 80 m to reach this beach zone

Pre-dewetting transition on a hydrophobic wall: Statics and dynamics

For one-component fluids, we predict a pre-dewetting phase transition between a thin and thick low-density layer in liquid on a wall repelling the fluid. This is the case of a hydrophobic wall for water. A pre-dewetting line starts from the coexistence curve and ends at a surface critical point in the phase diagram. We calculate this line numerically using the van der Waals model and analytically using the free energy expansion up to the quartic order. We also examine the pre-dewetting dynamics of a layer created on a hydrophobic spot on a heterogeneous wall. It is from a thin to thick layer during decompression and from a thick to thin layer during compression. Upon the transition, a liquid region above the film is cooled for decompression and heated for compression due to latent heat convection and a small pressure pulse is emitted from the film into the liquid.Comment: 14 pages, 17 figure

Molecular Dynamics Study of the Nematic-Isotropic Interface

We present large-scale molecular dynamics simulations of a nematic-isotropic interface in a system of repulsive ellipsoidal molecules, focusing in particular on the capillary wave fluctuations of the interfacial position. The interface anchors the nematic phase in a planar way, i.e., the director aligns parallel to the interface. Capillary waves in the direction parallel and perpendicular to the director are considered separately. We find that the spectrum is anisotropic, the amplitudes of capillary waves being larger in the direction perpendicular to the director. In the long wavelength limit, however, the spectrum becomes isotropic and compares well with the predictions of a simple capillary wave theory.Comment: to appear in Phys. Rev.

In vivo measurements of muscle specific tension in adults and children

This article is available open access through the publisher’s website at the link below. Copyright @ 2009 The Authors.To better understand the effects of pubertal maturation on the contractile properties of skeletal muscle in vivo, the present study investigated whether there are any differences in the specific tension of the quadriceps muscle in 20 adults and 20 prepubertal children of both sexes. Specific tension was calculated as the ratio between the quadriceps tendon force and the sum of the physiological cross-sectional area (PCSA) multiplied by the cosine of the angle of pennation of each head within the quadriceps muscle. The maximal quadriceps tendon force was calculated from the knee extension maximal voluntary contraction (MVC) by accounting for EMG-based estimates of antagonist co-activation, incomplete quadriceps activation using the interpolation twitch technique and magnetic resonance imaging (MRI)-based measurements of the patellar tendon moment arm. The PCSA was calculated as the muscle volume, measured from MRI scans, divided by optimal fascicle length, measured from ultrasound images during MVC at the estimated angle of peak quadriceps muscle force. It was found that the quadriceps tendon force and PCSA of men (11.4 kN, 214 cm2) were significantly greater than those of the women (8.7 kN, 152 cm2; P 0.05) between groups: men, 55 ± 11 N cm−2; women, 57.3 ± 13 N cm−2; boys, 54 ± 14 N cm−2; and girls, 59.8 ± 15 N cm−2. These findings indicate that the increased muscle strength with maturation is not due to an increase in the specific tension of muscle; instead, it can be attributed to increases in muscle size, moment arm length and voluntary activation level

Surface layering of liquids: The role of surface tension

Recent measurements show that the free surfaces of liquid metals and alloys are always layered, regardless of composition and surface tension; a result supported by three decades of simulations and theory. Recent theoretical work claims, however, that at low enough temperatures the free surfaces of all liquids should become layered, unless preempted by bulk freezing. Using x-ray reflectivity and diffuse scattering measurements we show that there is no observable surface-induced layering in water at T=298 K, thus highlighting a fundamental difference between dielectric and metallic liquids. The implications of this result for the question in the title are discussed.Comment: 5 pages, 4 figures, to appear in Phys. Rev. B. 69 (2004