Vibrational Transportation on a Platform Subjected to Sinusoidal Displacement Cycles Employing Dry Friction Control

Currently used vibrational transportation methods are usually based on asymmetries of geometric, kinematic, wave, or time types. This paper investigates the vibrational transportation of objects on a platform that is subjected to sinusoidal displacement cycles, employing periodic dynamic dry friction control. This manner of dry friction control creates an asymmetry, which is necessary to move the object. The theoretical investigation on functional capabilities and transportation regimes was carried out using a developed parametric mathematical model, and the control parameters that determine the transportation characteristics such as velocity and direction were defined. To test the functional capabilities of the proposed method, an experimental setup was developed, and experiments were carried out. The results of the presented research indicate that the proposed method ensures smooth control of the transportation velocity in a wide range and allows it to change the direction of motion. Moreover, the proposed method offers other new functional capabilities, such as a capability to move individual objects on the same platform in opposite directions and at different velocities at the same time by imposing different friction control parameters on different regions of the platform or on different objects. In addition, objects can be subjected to translation and rotation at the same time by imposing different friction control parameters on different regions of the platform. The presented research extends the classical theory of vibrational transportation and has a practical value for industries that operate manufacturing systems performing tasks such as handling and transportation, positioning, feeding, sorting, aligning, or assembling.

Bedrock river erosion through dipping layered rocks: quantifying erodibility through kinematic wave speed

Landscape morphology reflects drivers such as tectonics and climate but is also modulated by underlying rock properties. While geomorphologists may attempt to quantify the influence of rock strength through direct comparisons of landscape morphology and rock strength metrics, recent work has shown that the contact migration resulting from the presence of mixed lithologies may hinder such an approach. Indeed, this work counterintuitively suggests that channel slopes within weaker units can sometimes be higher than channel slopes within stronger units. Here, we expand upon previous work with 1-D stream power numerical models in which we have created a system for quantifying contact migration over time. Although previous studies have developed theories for bedrock rivers incising through layered stratigraphy, we can now scrutinize these theories with contact migration rates measured in our models. Our results show that previously developed theory is generally robust and that contact migration rates reflect the pattern of kinematic wave speed across the profile. Furthermore, we have developed and tested a new approach for estimating kinematic wave speeds. This approach utilizes channel steepness, a known base-level fall rate, and contact dips. Importantly, we demonstrate how this new approach can be combined with previous work to estimate erodibility values. We demonstrate this approach by accurately estimating the erodibility values used in our numerical models. After this demonstration, we use our approach to estimate erodibility values for a stream near Hanksville, UT. Because we show in our numerical models that one can estimate the erodibility of the unit with lower steepness, the erodibilities we estimate for this stream in Utah are likely representative of mudstone and/or siltstone. The methods we have developed can be applied to streams with temporally constant base-level fall, opening new avenues of research within the field of geomorphology.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

Historical soil maps with a reference to redoximorphic features as basis for ecohydrological modelling.

<p>Historical soil maps with a reference to profile redoximorphic features have obvious utility for ecohydrological modelling. That is particularly pertinent in areas with shallow water tables where catchments have both dry and moist parts, latter due to moisture source from either upper or low boundary. However, there is no convenient method for converting maps to hydrological model state variables. Here we propose that the steady state continuity equation in kinematic wave form can be parameterized using expert knowledge of the typical water table depth (WTD) for soils with different hydromorphy degrees based on redoximorphic features. To test the approach, six hillslope-based computational units (catenas) were obtained, for use in simulations, by automated of the Samovetc and Izberdey catchments in the Tambov region (Russia) using lumpR software. Five of the six catenas began at poorly drained flat upslope positions with soils with various degrees of saturation by shallow groundwater and one began at a well-drained upslope position. We guided parameterization of the kinematic wave model by critical range of the WTD known to correspond to each soil group on historical soil map of hydromorphy degree. Application of expert knowledge in this manner alone yielded a broad range of possible WTD values (e.g. 1.5-5 m for a semi-hydromorphic soil) for each soil entity, but linking a catena by the fundamental physical constraint of flow continuity enabled narrowing of the range to 0.2-1 m thereby reducing it by ca. 80%. We further tested the shallow water table approximation in the WASA-SED ecohydrological model based on catenary approach to simulate soil moisture profiles referring explicitly to soil groups of different hydromorphy degree and distinguish stagnic and gleyic regimes of waterlogging. The results show that the approach could substantially improve crop and water management precision.</p>

A Diffusion-Based Analysis of a Multiclass Road Traffic Network

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows based on conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under natural scaling, fluid, and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles’ travel time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results.

Bedrock River Erosion through Dipping Layered Rocks: Quantifying Erodibility through Kinematic Wave Speed

Landscape morphology reflects drivers such as tectonics and climate but is also modulated by underlying rock properties. While geomorphologists may attempt to quantify the influence of rock strength through direct comparisons of landscape morphology and rock strength metrics, recent work has shown that the contact migration resulting from the presence of mixed lithologies may hinder such an approach. Indeed, this work counterintuitively suggests channel slopes within weaker units can sometimes be higher than channel slopes within stronger units. Here, we expand upon previous work with 1-D stream power numerical models in which we have created a system for quantifying contact migration over time. Although previous studies have developed theory for bedrock rivers incising through layered stratigraphy, we can now scrutinize this theory with contact migration rates measured in our models. Our results show that previously developed theory is generally robust and that contact migration rates reflect the pattern of kinematic wave speed across the profile. Furthermore, we have developed and tested a new approach for estimating kinematic wave speeds. This approach utilizes stream steepness, a known base level fall rate, and contact dips. Importantly, we demonstrate how this new approach can be combined with previous work to estimate erodibility values. We demonstrate this approach by accurately estimating the erodibility values used in our numerical models. After this demonstration, we use our approach to estimate erodibility values for a stream near Hanksville, UT. Because we show in our numerical models that one can estimate the erodibility of the unit with lower steepness, the erodibilities we estimate for this stream in Utah are likely representative of mudstone and/or siltstone. The methods we have developed can be applied to streams with temporally constant base level fall, opening new avenues of research within the field of geomorphology.