Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called “change probabilities” for describing fracture roughness. In order to detect and visualize anisotropy of rock joint surfaces, the roughness of one-dimensional profiles taken in different directions is quantified. The central quantifiers, change probabilities, are based on counting monotonic changes in discretizations of a profile. These probabilities, which usually vary with the scale, can be reinterpreted as scale-dependent Hurst exponents. For a large class of Gaussian stochastic processes, change probabilities are shown to be directly related to the classical Hurst exponent, which generalizes a relationship known for fractional Brownian motion. While related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing the flexibility of modeling and investigating surface profiles. In particular, it allows a quick and efficient visualization and detection of roughness anisotropy and scale dependence of roughness.

Scale-space energy density for inhomogeneous turbulence based on filtered velocities

The energy spectrum is commonly used to describe the scale dependence of turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are mainly employed for inhomogeneous turbulence models. Attempts have been made to describe the scale dependence of inhomogeneous turbulence using the second-order structure function and two-point velocity correlation. However, unlike the energy spectrum, expressions for the energy density in the scale space fail to satisfy the requirement of being non-negative. In this study, a new expression for the scale-space energy density based on filtered velocities is proposed to clarify the reasons behind the negative values of the energy density and to obtain a better understanding of inhomogeneous turbulence. The new expression consists of homogeneous and inhomogeneous parts; the former is always non-negative, while the latter can be negative because of the turbulence inhomogeneity. Direct numerical simulation data of homogeneous isotropic turbulence and a turbulent channel flow are used to evaluate the two parts of the energy density and turbulent energy. It was found that the inhomogeneous part of the turbulent energy shows non-zero values near the wall and at the centre of a channel flow. In particular, the inhomogeneous part of the energy density changes its sign depending on the scale. A concave profile of the filtered-velocity variance at the wall accounts for the negative value of the energy density in the region very close to the wall.

The complete singlet contribution to the massless quark form factor at three loops in QCD

It is well known that the effect of top quark loop corrections in the axial part of quark form factors (FF) does not decouple in the large top mass or low energy limit due to the presence of the axial-anomaly type diagrams. The top-loop induced singlet-type contribution should be included in addition to the purely massless result for quark FFs when applied to physics in the low energy region, both for the non-decoupling mass logarithms and for an appropriate renormalization scale dependence. In this work, we have numerically computed the so-called singlet contribution to quark FFs with the exact top quark mass dependence over the full kinematic range. We discuss in detail the renormalization formulae of the individual subsets of the singlet contribution to an axial quark FF with a particular flavor, as well as the renormalization group equations that govern their individual scale dependence. Finally we have extracted the 3-loop Wilson coefficient in the low energy effective Lagrangian, renormalized in a $$ \mathrm{non}\hbox{-} \overline{\mathrm{MS}} $$ non ‐ MS ¯ scheme and constructed to encode the leading large mass approximation of our exact results for singlet quark FFs. We have also examined the accuracy of the approximation in the low energy region.

Kinematic distributions of the ηc leptoproduction in association with light hadrons

The ηc meson leptoproduction is calculated within the nonrelativistic QCD framework for the first time. It is found that the colour-singlet channel, although suppressed by a factor of αs relative to the colour-octet ones, provides important contribution for almost all the experimental conditions, which disagrees with some of the expectations before computation. We present the differential cross sections with respect to $$ {p}_t^2 $$ p t 2 , $$ {p}_t^{\bigstar 2} $$ p t ★ 2 , Q2, W, and z, for both HERA and EIC experimental conditions as a reference for future studies. The scale dependence and long-distance-matrix-element dependence are also investigated in this paper.

A cloud-based toolbox for the versatile environmental annotation of biodiversity data

A vast range of research applications in biodiversity sciences requires integrating primary species, genetic, or ecosystem data with other environmental data. This integration requires a consideration of the spatial and temporal scale appropriate for the data and processes in question. But a versatile and scale flexible environmental annotation of biodiversity data remains constrained by technical hurdles. Existing tools have streamlined the intersection of occurrence records with gridded environmental data but have remained limited in their ability to address a range of spatial and temporal grains, especially for large datasets. We present the Spatiotemporal Observation Annotation Tool (STOAT), a cloud-based toolbox for flexible biodiversity–environment annotations. STOAT is optimized for large biodiversity datasets and allows user-specified spatial and temporal resolution and buffering in support of environmental characterizations that account for the uncertainty and scale of data and of relevant processes. The tool offers these services for a growing set of near global, remotely sensed, or modeled environmental data, including Landsat, MODIS, EarthEnv, and CHELSA. STOAT includes a user-friendly, web-based dashboard that provides tools for annotation task management and result visualization, linked to Map of Life, and a dedicated R package (rstoat) for programmatic access. We demonstrate STOAT functionality with several examples that illustrate phenological variation and spatial and temporal scale dependence of environmental characteristics of birds at a continental scale. We expect STOAT to facilitate broader exploration and assessment of the scale dependence of observations and processes in ecology.