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Green-Kubo formula valid for systems with long-range or nonstationary correlations for which the standard approach is no longer valid.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

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure

You Got It in Your Hands: Stop-Signal Modality Influences on Reactive Response Inhibition with Gaming Controls

Mastering the art of stopping initiated actions is vital when playing video games. However, what characteristics make up the perfect warning or stop-signal remains unclear. In the present study we compared performance in a basic and a gamified stop-signal task depending on different stop-signal modalities: auditory, haptic and audio-haptic. Data from a complete within-subjects design (N = 24), revealed an advantage of haptic or audio-haptic stop-signals as compared to purely auditory ones. Further, results show an overall slower performance in the game-version compared to the basic version. With regards to the subjective experience, the results revealed higher motivation to perform in the gamified task, but a somewhat deeper flow experience in the basic task. In sum, these results confirm that stop-signal modality influences reactive response inhibition in both basic and gamified tasks. Future research may extend and generalize these findings to other cross-modal and more complicated gaming setups. Game developers may draw on these findings to optimize the communication of stop signals via vibrations in a handheld controller

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

A touching advantage: cross-modal stop-signals improve reactive response inhibition

The ability to inhibit an already initiated response is crucial for navigating the environment. However, it is unclear which characteristics make stop-signals more likely to be processed efficiently. In three consecutive studies, we demonstrate that stop-signal modality and location are key factors that influence reactive response inhibition. Study 1 shows that tactile stop-signals lead to better performance compared to visual stop-signals in an otherwise visual choice-reaction task. Results of Study 2 reveal that the location of the stop-signal matters. Specifically, if a visual stop-signal is presented at a different location compared to the visual go-signal, then stopping performance is enhanced. Extending these results, study 3 suggests that tactile stop-signals and location-distinct visual stop-signals retain their performance enhancing effect when visual distractors are presented at the location of the go-signal. In sum, these results confirm that stop-signal modality and location influence reactive response inhibition, even in the face of concurrent distractors. Future research may extend and generalize these findings to other cross-modal setups

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

A touching advantage:cross-modal stop-signals improve reactive response inhibition

The ability to inhibit an already initiated response is crucial for navigating the environment. However, it is unclear which characteristics make stop-signals more likely to be processed efficiently. In three consecutive studies, we demonstrate that stop-signal modality and location are key factors that influence reactive response inhibition. Study 1 shows that tactile stop-signals lead to better performance compared to visual stop-signals in an otherwise visual choice-reaction task. Results of Study 2 reveal that the location of the stop-signal matters. Specifically, if a visual stop-signal is presented at a different location compared to the visual go-signal, then stopping performance is enhanced. Extending these results, study 3 suggests that tactile stop-signals and location-distinct visual stop-signals retain their performance enhancing effect when visual distractors are presented at the location of the go-signal. In sum, these results confirm that stop-signal modality and location influence reactive response inhibition, even in the face of concurrent distractors. Future research may extend and generalize these findings to other cross-modal setups.</p