Scaling Green-Kubo relation and application to three aging systems

The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula valid for systems with long-range or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function $\langle v(t+\tau) v(t) \rangle$ asymptotically exhibits a certain scaling behavior and the diffusion is anomalous $\langle x^2(t) \rangle \simeq 2 D_\nu t^{\nu}$. We show how both the anomalous diffusion coefficient $D_\nu$ and exponent $\nu$ can be extracted from this scaling form. Our scaling Green-Kubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale invariant dynamics. This includes stationary systems with slowly decaying power law correlations as well as aging systems, whose properties depend on the the age of the system. Even for systems that are stationary in the long time limit, we find that the long time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity $D_{\nu}$ is not unique and we determine its values for a stationary respectively nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: Free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells and the L\'evy walk with numerous applications, in particular blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.Comment: 16 pages, 6 figures, 1 tabl

Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence

The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963-67. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to ITISE 2016 meeting in Granada, Spai

Fluctuations of time averages for Langevin dynamics in a binding force field

We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function.Comment: 5 pages, 3 figure

Experimental Impacts into Strength-Layered Targets: Crater Morphology and Morphometry

Impact cratering is a fundamental physical process that has dominated the evolution and modification of nearly every planetary surface in the Solar System. Impact craters serve as a means to probe the subsurface structure of a planetary body and provide hints about target surface properties. By examining small craters on the lunar maria and comparing these to experimental impacts in the laboratory, Oberbeck and Quaide first suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat-floored and concentric craters as crater diameter increases for a given regolith thickness. This quantitative relationship is commonly used to estimate regolith thicknesses on the lunar surface and has also been explored via numerical and experimental studies. Here we report on a series of experimental impact craters formed in targets com-posed of a thin layer of loose sand on top of a stronger substrate at the Experimental Impact Laboratory at NASA Johnson Space Center

Experimental Impacts into Strength-Layered Targets: Ejecta Kinematics

AImpact cratering has dominated the evolution and modification of planetary surfaces through-out the history of the solar system. Impact craters can serve as probes to understanding the details of a planetary subsurface; for example, Oberbeck and Quaide, suggested that crater morphology can be used to estimate the thickness of a regolith layer on top of a more competent unit. Lunar craters show a morphological progression from a simple bowl shape to flat-floored and concentric craters as crater diameter in-creases for a given regolith thickness. The final shape of the impact crater is a result of the subsurface flow-field initiated as the projectile transfers its energy and momentum to the target surface at the moment of impact. Therefore, when a regolith layer is present over a stronger substrate, such as is the case on the lunar surface, the substrate modifies the flow-field and thereby the excavation flow of the crater, which is reflected in the morphology of the final crater. Here we report on a series of experimental impacts into targets composed of a thin layer of loose sand on top of a stronger substrate. We use the Ejection-Velocity Measurement System developed to examine the ejecta kinematics during the formation of these craters

Effects of Management Practices on Grassland Birds: Burrowing Owl

Burrowing Owl ( Speotyto cunicularia hypugaea): Breeding range Suitable habitat Prey habitat Area requirements Brown-headed Cowbird brood parasitism Breeding-season phenology and site fidelity Species’ response to management Management Recommendations Characteristic

EFFECTS OF MANAGEMENT PRACTICES ON GRASSLAND BIRDS: LESSER PRAIRIE-CHICKEN

Information on the habitat requirements and effects of habitat management on grassland birds were summarized from information in more than 4,000 published and unpublished papers. A range map is provided to indicate the breeding distribution of Lesser Prairie-Chicken in the United States and southern Canada. Although birds frequently are observed outside the breeding range indicated, the maps are intended to show areas where managers might concentrate their attention. It may be ineffectual to manage habitat at a site for a species that rarely occurs in an area. The species account begins with a brief capsule statement, which provides the fundamental components or keys to management for the species. A section on breeding range outlines the current breeding distribution of the species in North America. The suitable habitat section describes the breeding habitat and occasionally microhabitat characteristics of the species, especially those habitats that occur in the Great Plains. Details on habitat and microhabitat requirements often provide clues to how a species will respond to a particular management practice. A table near the end of the account complements the section on suitable habitat, and lists the specific habitat characteristics for the species by individual studies. A special section on prey habitat is included for those predatory species that have more specific prey requirements. The area requirements section provides details on territory and home range sizes, minimum area requirements, and the effects of patch size, edges, and other landscape and habitat features on abundance and productivity. It may be futile to manage a small block of suitable habitat for a species that has minimum area requirements that are larger than the area being managed. The Brown-headed Cowbird (Molothrus ater) is an obligate brood parasite of many grassland birds. The section on cowbird brood parasitism summarizes rates of cowbird parasitism, host responses to parasitism, and factors that influence parasitism, such as nest concealment and host density. The impact of management depends, in part, upon a species’ nesting phenology and biology. The section on breeding-season phenology and site fidelity includes details on spring arrival and fall departure for migratory populations in the Great Plains, peak breeding periods, the tendency to renest after nest failure or success, and the propensity to return to a previous breeding site. The duration and timing of breeding varies among regions and years. Species’ response to management summarizes the current knowledge and major findings in the literature on the effects of different management practices on the species. The section on management recommendations complements the previous section and summarizes specific recommendations for habitat management provided in the literature. If management recommendations differ in different portions of the species’ breeding range, recommendations are given separately by region. The literature cited contains references to published and unpublished literature on the management effects and habitat requirements of the species. This section is not meant to be a complete bibliography; a searchable, annotated bibliography of published and unpublished papers dealing with habitat needs of grassland birds and their responses to habitat management is posted at the Web site mentioned below

Long-Term Effect of Therapeutic Horseback Riding in Youth With Autism Spectrum Disorder: A Randomized Trial

This paper presents 6-month follow-up data of 44% (N = 64/116) of participants (ages 6–16 years) with a diagnosis of autism spectrum disorder, who participated in a previously-published randomized controlled trial of therapeutic horseback riding (THR) compared to a no-horse contact active control. The objective of this study was to examine whether significant improvements of irritability, hyperactivity, social, and communication behaviors observed in participants randomized to receive a 10-week manual-based THR intervention were sustained 6 months after the intervention conclusion. Participants' caregivers from both the THR (n = 36) and active control (n = 28) groups completed a measure of irritability and hyperactivity behaviors (primary outcome variables). Additionally, only the THR group participants completed the full battery of study outcomes assessments. Between group comparisons examining the extended interval from baseline (1-month pre-intervention assessment) to 6-months after the intervention revealed that the THR group maintained reductions in irritability behavior at a 0.1 level (effect size = 0.32, p = 0.07). (Effect size = 0.32, p = 0.07), which was 73% of efficacy preserved from the primary post-intervention endpoint (within 1-month post-intervention). Hyperactivity behaviors did not sustain this same trend. Comparisons from baseline and 6-months after the intervention revealed that the THR group sustained significant initial improvements made in social and communication behaviors, along with number of words and different words spoken during a standard language sample. This is the first known study to examine and demonstrate the longer-term effects of THR for individuals with ASD and warrants a more thorough evaluation of whether the effects of THR are maintained for at least 6-months after the intervention compared to a control.Clinical Trial Registration Information: Trial of Therapeutic Horseback Riding in Children and Adolescents with Autism Spectrum Disorder; http://clinicaltrials.gov; NCT02301195