Leafwise Holomorphic Functions

It is a well-known and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the setting of holomorphically foliated spaces

Multiple scattering in random mechanical systems and diffusion approximation

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P_h, depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that (P_h -I)/h converges for small h to a second order elliptic differential operator L on compactly supported functions and that the Markov chain process associated to P_h converges to a diffusion with infinitesimal generator L. Both P_h and L are selfadjoint (densely) defined on the space L2(H,{\eta}) of square-integrable functions over the (lower) half-space H in R^m, where {\eta} is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator L respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.Comment: 34 pages, 13 figure

Random billiards with wall temperature and associated Markov chains

By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard domain, gives the probability distribution of the post-collision velocity for a given pre-collision velocity. A random billiard with microstructure (RBM) is a random billiard for which P is derived from a choice of geometric/mechanical structure on the boundary of the billiard domain. RBMs provide simple and explicit mechanical models of particle-surface interaction that can incorporate thermal effects and permit a detailed study of thermostatic action from the perspective of the standard theory of Markov chains on general state spaces. We focus on the operator P itself and how it relates to the mechanical/geometric features of the microstructure, such as mass ratios, curvatures, and potentials. The main results are as follows: (1) we characterize the stationary probabilities (equilibrium states) of P and show how standard equilibrium distributions studied in classical statistical mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine law, arise naturally as generalized invariant billiard measures; (2) we obtain some basic functional theoretic properties of P. Under very general conditions, we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert space. In a simple but illustrative example, we show that P is a compact (Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of eigenvalues of P to the features of the microstructure;(3) we explore the latter issue both analytically and numerically in a few representative examples;(4) we present a general algorithm for simulating these Markov chains based on a geometric description of the invariant volumes of classical statistical mechanics

Stability of periodic orbits in no-slip billiards

Rigid bodies collision maps in dimension-two, under a natural set of physical requirements, can be classified into two types: the standard specular reflection map and a second which we call, after Broomhead and Gutkin, no-slip. This leads to the study of no-slip billiards—planar billiard systems in which the moving particle is a disc (with rotationally symmetric mass distribution) whose translational and rotational velocities can both change after collisions with the boundary of the billiard domain. This paper, which continues the investigation initiated in Cox and Feres (2017 Dynamical Systems, Ergodic Theory, and Probability: in Memory of Chernov (Providence, RI: American Mathematical Society), is mainly focused on the issue of stability of periodic orbits in no-slip planar billiards. We prove Lyapunov stability of periodic orbits in polygonal billiards of this kind and, for general billiards domains, we obtain curvature thresholds for linear stability at commonly occurring period-2 orbits. More specifically, we prove that: (i) for billiard domains in the plane having piecewise smooth boundary and at least one corner of inner angle less than π, no-slip billiard maps admit elliptic period-2 orbits; (ii) polygonal no-slip billiards under this same corner angle condition always contain small invariant neighborhoods of the periodic point on which, up to smooth conjugacy, orbits of the return map lie on concentric circles; in particular the system cannot be ergodic with respect to the canonical invariant billiard measure; (iii) the no-slip version of the Sinai billiard must contain linearly stable periodic orbits of period 2 and, more generally, we obtain a curvature threshold at which the period-2 orbits go from being hyperbolic to being elliptic; (iv) finally, we make a number of observations concerning periodic orbits in wedge and triangular billiards. Our linear stability results extend those of Wojtkowski for the no-slip Sinai billiard

Family History of Alcohol Abuse Moderates Effectiveness of a Group Motivational Enhancement Intervention in College Women

This study examined whether a self-reported family history of alcohol abuse (FH+) moderated the effects of a female-specific group motivational enhancement intervention with first-year college women. First-year college women (N= 287) completed an initial questionnaire and attended an intervention (n=161) or control (n=126) group session, of which 118 reported FH+. Repeated measures ANCOVA models were estimated to investigate whether the effectiveness of the intervention varied as a function of one’s reported family history of alcohol abuse. Results revealed that family history of alcohol abuse moderated intervention efficacy. Although the intervention was effective in producing less risky drinking relative to controls, among those participants who received the intervention, FH+ women drank less across five weeks of follow-up than FH− women. The current findings provide preliminary support for the differential effectiveness of motivational enhancement interventions with FH+ women

Relationships Between Subgingival Microbiota and GCF Biomarkers in Generalized Aggressive Periodontitis

Aim To examine relationships between subgingival biofilm composition and levels of gingival crevicular fluid (GCF) cytokines in periodontal health and generalized aggressive periodontitis (GAP). Materials and methods Periodontal parameters were measured in 25 periodontally healthy and 31 GAP subjects. Subgingival plaque and GCF samples were obtained from 14 sites from each subject. 40 subgingival taxa were quantified using checkerboard DNA-DNA hybridization and the concentrations of 8 GCF cytokines measured using Luminex. Cluster analysis was used to define sites with similar subgingival microbiotas in each clinical group. Significance of differences in clinical, microbiological and immunological parameters among clusters was determined using the Kruskal-Wallis test. Results GAP subjects had statistically significantly higher GCF levels of interleukin-1β (IL-1β) (p\u3c0.001), granulocyte-macrophage colony-stimulating factor (GM-CSF) (p\u3c0.01), and IL-1β/IL-10 ratio (p\u3c0.001) and higher proportions of Red and Orange complex species than periodontally healthy subjects. There were no statistically significant differences in the mean proportion of cytokines among clusters in the periodontally healthy subjects, while the ratio IL-1β/IL-10 (p\u3c0.05) differed significantly among clusters in the aggressive periodontitis group. Conclusions Different subgingival biofilm profiles are associated with distinct patterns of GCF cytokine expression. Aggressive periodontitis subjects were characterized by a higher IL-1β/IL-10 ratio than periodontally healthy subjects, suggesting an imbalance between pro- and anti-inflammatory cytokines in aggressive periodontitis

Zone trapping/merging zones in flow analysis: A novel approach for rapid assays involving relatively slow chemical reactions

AbstractA novel strategy for accomplishing zone trapping in flow analysis is proposed. The sample and the reagent solutions are simultaneously inserted into convergent carrier streams and the established zones merge together before reaching the detector, where the most concentrated portion of the entire sample zone is trapped. The main characteristics, potentialities and limitations of the strategy were critically evaluated in relation to an analogous flow system with zone stopping. When applied to the spectrophotometric determination of nitrite in river waters, the main figures of merit were maintained, exception made for the sampling frequency which was calculated as 189h−1, about 32% higher relatively to the analogous system with zone stopping. The sample inserted volume can be increased up to 1.0mL without affecting sampling frequency and no problems with pump heating or malfunctions were noted after 8-h operation of the system. In contrast to zone stopping, only a small portion of the sample zone is halted with zone trapping, leading to these beneficial effects