A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts

We propose a phenomenological description for the effect of a weak noise on the position of a front described by the Fisher-Kolmogorov-Petrovsky-Piscounov equation or any other travelling wave equation in the same class. Our scenario is based on four hypotheses on the relevant mechanism for the diffusion of the front. Our parameter-free analytical predictions for the velocity of the front, its diffusion constant and higher cumulants of its position agree with numerical simulations.Comment: 10 pages, 3 figure

An Intrisic Topology for Orthomodular Lattices

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.Comment: Under submission to the International Journal of Theoretical Physic

An exactly soluble noisy traveling wave equation appearing in the problem of directed polymers in a random medium

We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of $N$ evolving particles which can be described by a noisy traveling wave equation with a noise of order $N^{-1/2}$. Our model can be viewed as the infinite range limit of a directed polymer in random medium with $N$ sites in the transverse direction. Despite some peculiarities of the traveling wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle.Comment: 5 page

Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era

The structural and dynamical properties of star clusters are generally derived by means of the comparison between steady-state analytic models and the available observables. With the aim of studying the biases of this approach, we fitted different analytic models to simulated observations obtained from a suite of direct N-body simulations of star clusters in different stages of their evolution and under different levels of tidal stress to derive mass, mass function and degree of anisotropy. We find that masses can be under/over-estimated up to 50% depending on the degree of relaxation reached by the cluster, the available range of observed masses and distances of radial velocity measures from the cluster center and the strength of the tidal field. The mass function slope appears to be better constrainable and less sensitive to model inadequacies unless strongly dynamically evolved clusters and a non-optimal location of the measured luminosity function are considered. The degree and the characteristics of the anisotropy developed in the N-body simulations are not adequately reproduced by popular analytic models and can be detected only if accurate proper motions are available. We show how to reduce the uncertainties in the mass, mass-function and anisotropy estimation and provide predictions for the improvements expected when Gaia proper motions will be available in the near future.Comment: 14 pages, 8 figures, accepted for publication by MNRA

Emergence of pulled fronts in fermionic microscopic particle models

We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A A$ on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. When internal fluctuations are suppressed, we explictly see the matching between the deterministic FKPP description and the microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a Rapid Communicatio

Butterfly gardening: using volunteers to provide data on flower use

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on August 22, 2007)Includes bibliographical references.Thesis (M.S.) University of Missouri-Columbia 2006.Dissertations, Academic -- University of Missouri--Columbia -- Fisheries and wildlife.Butterflies are considered to be good indicators of a healthy environment and reflect the environmental impact of urban development. The popularity of butterflies with the general public and declining butterfly populations, combined with the fact that lawns now occupy more than 12 million hectares in the United States, make a compelling case for a systematic survey of garden butterflies. This study looked at which species occur in Columbia, Missouri and which nectar sources they use. In addition, surveys examined the attitudes of people toward butterflies and other insects. We also looked at the impact of different lawn maintenance regimes on attracting butterflies to yards. We recruited volunteers to count butterflies in their yards once a week for 15 minutes from May through September 2002 and 2003. Volunteers observed most of the butterfly species expected in mid-Missouri. In addition to identifying and counting butterflies, they recorded the flowers on which any butterflies landed. Based on a literature search, flower genera were categorized as "recommended" or "not recommended" for use in butterfly gardens. Approximately 90% of the butterflies that were observed on flowers each year were on genera typically recommended for use in flower gardens. Genera most heavily used included Asclepias, Buddleja, Coreopsis, Echinacea, Eupatorium, Liatris, Rudbeckia, Salvia, Sedum, Tagetes, Trifolium / Melilotus / Medicago, Verbena, Zinnia. Yards in which homeowners tolerated a more "weedy" appearance had both more butterflies and more species per count

To grate a liquid into tiny droplets by its impact on a hydrophobic micro-grid

We report on experiments of drop impacting a hydrophobic micro-grid, of typical spacing a few tens of $\mu$m. Above a threshold in impact speed, liquid emerges to the other side, forming micro-droplets of size about that of the grid holes. We propose a method to produce either a mono-disperse spray or a single tiny droplet of volume as small as a few picoliters corresponding to a volume division of the liquid drop by a factor of up to 10$^5$. We also discuss the discrepancy of the measured thresholds with that predicted by a balance between inertia and capillarity.Comment: 3 pages, 5 figures, Accepted for publication in Applied Physics Letter

Genealogies of rapidly adapting populations

The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or infrequent evolutionary force. However, many species, particularly pathogens, are under continuous pressure to adapt in response to changing environments. A statistical framework for inference from diversity data of such populations is currently lacking. Toward this goal, we explore the properties of genealogies in a model of continual adaptation in asexual populations. We show that lineages trace back to a small pool of highly fit ancestors, in which almost simultaneous coalescence of more than two lineages frequently occurs. While such multiple mergers are unlikely under the neutral coalescent, they create a unique genetic footprint in adapting populations. The site frequency spectrum of derived neutral alleles, for example, is non-monotonic and has a peak at high frequencies, whereas Tajima's D becomes more and more negative with increasing sample size. Since multiple merger coalescents emerge in many models of rapid adaptation, we argue that they should be considered as a null-model for adapting populations.Comment: to appear in PNA

Deterministic reaction models with power-law forces

We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution function for the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker-Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished

From the stress response function (back) to the sandpile `dip'

We relate the pressure `dip' observed at the bottom of a sandpile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sandpile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing -- albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.Comment: 8 pages, 8 figures, accepted version to appear in Eur. Phys. J.