Finiteness and the falsification by fellow traveler property

We prove that groups enjoying the falsification by fellow traveler property are of type $F_3$, and have at most an exponential second order isoperimetric function.Comment: Appeared in 2002. I am putting all my past publications on arxi

A non-Hopfian almost convex group

In this article we prove that an "isometric multiple HNN-extension" of a group satisfying the falsification by fellow traveler property is almost convex. As a corollary, Wise's example of a CAT(0) non-Hopfian group is Almost convex.Comment: Appeared in 2004. I am putting all my past papers on arxi

Patterns theory and geodesic automatic structure for a class of groups

We introduce a theory of "patterns" in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain group presentations are almost convex.Comment: Appeared in 2003. I am putting all my past papers on arxi

On groups and counter automata

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.Comment: 18 page

Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.Comment: 17 pages in revtex. changes: 1 reference adde

Promoting Physical Activity in Middle School Girls: Trial of Activity for Adolescent Girls

Background - Physical activity is important for weight control and good health; however, activity levels decline in the adolescent years, particularly in girls. Design - Group randomized controlled trial. Setting/participants - Middle school girls with English-speaking skills and no conditions to prevent participation in physical activity in 36 schools in six geographically diverse areas of the United States. Random, cross-sectional samples were drawn within schools: 6th graders in 2003 (n=1721) and 8th graders in 2005 (n=3504) and 2006 (n=3502). Intervention - A 2-year study-directed intervention (fall 2003 to spring 2005) targeted schools, community agencies, and girls to increase opportunities, support, and incentives for increased physical activity. Components included programs linking schools and community agencies, physical education, health education, and social marketing. A third-year intervention used school and community personnel to direct intervention activities. Main outcome measures - The primary outcome, daily MET-weighted minutes of moderate-to-vigorous physical activity (MET-weighted MVPA), was assessed using accelerometry. Percent body fat was assessed using anthropometry. Results - After the staff-directed intervention (pre-stated primary outcome), there were no differences (mean=-0.4, 95% CI=-8.2 to 7.4) in adjusted MET-weighted MVPA between 8th-grade girls in schools assigned to intervention or control. Following the Program Champion-directed intervention, girls in intervention schools were more physically active than girls in control schools (mean difference 10.9 MET-weighted minutes of MVPA, 95% CI=0.52-21.2). This difference is about 1.6 minutes of daily MVPA or 80 kcal per week. There were no differences in fitness or percent body fat at either 8th-grade timepoint. Conclusion - A school-based, community-linked intervention modestly improved physical activity in girls

Design of the Trial of Activity in Adolescent Girls (TAAG)

The primary aim of the Trial of Activity in Adolescent Girls (TAAG) is to test an intervention to reduce by half the age-related decline in moderate to vigorous physical activity (MVPA) in middle school girls. The intervention will be evaluated using a group-randomized trial involving 36 middle schools. The primary endpoint is the mean difference in intensity-weighted minutes (i.e., MET-minutes) of MVPA between intervention and comparison schools assessed using accelerometry

Spatial and temporal spectra of noise driven stripe patterns

Spatial and temporal noise power spectra of stripe patterns are investigated, using as a model a Swift-Hohenberg equation with a stochastic term. In particular, the analytical and numerical investigations show: 1) the temporal noise spectra are of 1/f^alpha form, where alpha=1+(3-D)/4 with D the spatial dimension of the system; 2) that the stochastic fluctuations of the stripe position are sub-diffusive.Comment: Submitted to PR