Sisyphus and his rock: Quasi-random walk inspired by the motion of a ball transported by a dung beetle on combined terrain.

The majority of biologically inspired dynamic problems are essentially defined by the complexity of the contact surface where such motion takes place. From a statistical point of view, such a surface in many biological problems is typically a combination of a universal scale invariant (fractal) component and a well-defined component having a characteristic scale. If the biological object, here a dung ball, or its parts have a size comparable to the dimensions of the surface peculiarities, one can expect a strong influence on the motion. To avoid competition for the same food resource, some dung-feeding insect species form a dung ball and roll it away from the dung pile. In order to quickly escape competition, dung beetles seem to strictly follow an initial bearing. On flat terrain, they manage to roll a dung ball along a nearly perfect straight path. However, on a more realistic terrain, which normally includes both components mentioned above, the motion is more complex. In this study, we numerically model the ball transportation on terrain with different scales of surface profile. A strong correlation is observed between effective ball transportation (time, distance, work) and the ratio of the size of the ball relative to the size of the terrain roughness. Surface irregularities, with a characteristic size comparable to the ball diameter, are negatively correlated to the efficiency of ball transportation. In addition a strong correlation is found between the quasi random noise, numerically simulating the activity of a dung beetle trying to escape from a valley in which it is trapped, and the success in ball transportation.

Deriving the Characteristic Scale for Effectively Monitoring Heavy Metal Stress in Rice by Assimilation of GF-1 Data with the WOFOST Model.

Accurate monitoring of heavy metal stress in crops is of great importance to assure agricultural productivity and food security, and remote sensing is an effective tool to address this problem. However, given that Earth observation instruments provide data at multiple scales, the choice of scale for use in such monitoring is challenging. This study focused on identifying the characteristic scale for effectively monitoring heavy metal stress in rice using the dry weight of roots (WRT) as the representative characteristic, which was obtained by assimilation of GF-1 data with the World Food Studies (WOFOST) model. We explored and quantified the effect of the important state variable LAI (leaf area index) at various spatial scales on the simulated rice WRT to find the critical scale for heavy metal stress monitoring using the statistical characteristics. Furthermore, a ratio analysis based on the varied heavy metal stress levels was conducted to identify the characteristic scale. Results indicated that the critical threshold for investigating the rice WRT in monitoring studies of heavy metal stress was larger than 64 m but smaller than 256 m. This finding represents a useful guideline for choosing the most appropriate imagery.

Wavelet analysis of the atmospheric flows over real urban morphology.

Winds are the basic forces for atmospheric transport such as pollutant removal and pedestrian thermal comfort. The transport capability is commonly measured in terms of length and velocity scales. In this connection, the flows in the atmospheric surface layer (ASL) over the Kowloon Peninsula, Hong Kong (HK) are scrutinized by the large-eddy simulation (LES) to characterize the motion scales over real urban morphology. Apart from statistical analysis, the streamwise fluctuating velocity u' is examined by both wavelet and energy spectrum in which a primary peak is consistently shown at streamwise wavelength 70 m ≤ λx ≤ 300 m. A secondary peak at a longer wavelength 800 m ≤ λx ≤ 3000 m, however, is unveiled by wavelet only. It denotes the existence of intermittent turbulence structures whose sizes are much larger than those of buildings. Further wavelet analysis reveals that majority energy-carrying eddies are enlarging (tens to hundreds of meters) from the roughness sublayer (RSL) to the inertial sublayer (ISL). Analogous to its smooth-wall and schematic rough-wall counterparts, the turbulence kinetic energy (TKE) over urban areas is peaked in the ISL which is carried by eddies of size 50 m ≤ λx ≤ 1000 m. The (horizontal) spatial distribution of energy-carrying eddies is further visualized to compare the crucial motion scales in the RSL and ISL. Finally, conditional sampling is used to demystify the contribution to vertical momentum flux u'w' in terms of streamwise wavelength and quadrants. The results advance our fundamental understanding of ASL transport processes, fostering sustainable environmental policy.

Theoretical analysis of pollutant mixing zone considering lateral distribution of flow velocity and diffusion coefficient.

Theoretical formulae have shown significant advantages in describing the characteristic geometric scales of the pollutant mixing zone (PMZ) formed by offshore pollutant discharged by a single general form. They, however, fail to predict the influence of the lateral inhomogeneity of the river flow because constant flow velocity and the lateral diffusion coefficient are assumed during the derivation. The realistic flow velocity in a river is fitted by an exponential law in this study and the lateral diffusion coefficient is proposed to have the same form. Similar idea has been used in previous studies on the vertical dispersion of scalar in the lower atmosphere. Pollutant discharged from a steady onshore point source into a wide straight open channel is examined to characterize the concentration taking into consideration of these lateral variations. Theoretical formulae describing the maximum length, maximum width and its corresponding longitudinal position, as well as the area of the PMZ are derived. A non-dimensional standard curve equation for the isoconcentration boundary of PMZ is also obtained. The results show that the shape of the dimensionless standard curve of PMZ depends only on the exponential constants in the exponential laws. The exponential profiles that fit the near-shore velocity give good prediction, while the ones that match the entire lateral range up to the center of the river underpredict the PMZ significantly. These findings are of great importance for practitioners to characterize the geometry of the PMZ in rivers and for water quality modeling.

[Spatial scale effect of land use landscape pattern in Yongdeng County, Gansu Province, China.] / ç”˜è‚ƒæ°¸ç™»åŽ¿åœŸåœ°åˆ©ç”¨æ™¯è§‚æ ¼å±€çš„ç©ºé—´å°ºåº¦æ•ˆåº”.

Based on "patch-corridor-matrix" pattern, spatial scale effect of landscape pattern was studied in Yongdeng County of Lanzhou City, Gansu Province, China. The results showed that the grassland was the matrix of landscape structure in the studied area, road and river played the corridor role, and the other landscape elements (cultivated land, forest land, garden land, residential land, industrial and mineral land, public management and service land, and the other land) acted as patches. The patch level index and the landscape level index all showed obvious dependence on spatial extent. The scale effect of patch index of different landscape elements existed differently in different extent intervals, so did the scale effect of the landscape level index. Within the extent of 1-20 km, the scale effect showed the most obvious difference between the element types and the index types, while it became smaller in 21-90 km, and disappeared beyond 90 km. 90 km×90 km might be the effective extent to study the dependence of spatial extent of landscape structure.