Explore the vast range of titles available.

The entropy of rough neutrosophic multisets is introduced to measure the fuzziness degree of rough multisets information. The entropy is defined in two ways, which is the entropy of rough neutrosophic multisets generalize from existing entropy of single value neutrosophic set and the rough neutrosophic multisets entropy based on roughness approximation. The definition is derived from being satisfied in the following conditions required for rough neutrosophic multisets entropy. Note that the entropy will be null when the set is crisp, while maximum if the set is a completely rough neutrosophic multiset. Moreover, the rough neutrosophic multisets entropy and its complement are equal. Also, if the degree of lower and upper approximation for truth membership, indeterminacy membership, and falsity membership of each element decrease, then the sum will decrease. Therefore, this set becomes fuzzier, causing the entropy to increase.

Our aim of writing this manuscript is to found novel rough-approximation operators inspired by an abstract structure called “supra-topology”. This approach is more relaxed than topological ones and extends the scope of applications because an intersection condition of topology is dispensed. Firstly, we generate eight types of supra-topologies using Nk-neighborhood systems induced from any arbitrary relation. We elucidate the relationships between them and investigate the conditions under which some of them are identical. Then, we create new rough sets models from these supra-topologies and present the main characterizations of their lower and upper approximations. We apply these approximations to classify the regions of the subset and compute its accuracy measures. The master merits of the current approach are to produce the highest accuracy values compared with all approaches given in the published literature under a reflexive relation as well as preserve the monotonicity property of accuracy and roughness measures. Moreover, we demonstrate the good performance of the followed technique through analysis of some data of dengue fever disease. Ultimately, we debate the advantages and disadvantages of the followed approach and make a plan for some upcoming work.

A data set of 2890 field measurements was used to test the ability of several conventional flow resistance equations to predict mean flow velocity in gravel bed rivers when used with no calibration. The tests were performed using both flow depth and discharge as input since discharge may be a more reliable measure of flow conditions in shallow flows. Generally better predictions are obtained when using flow discharge as input. The results indicate that the Manning‐Strickler and the Keulegan equations show considerable disagreement with observed flow velocities for flow depths smaller than 10 times the characteristic grain diameter. Most equations show some systematic deviation for small relative flow depth. The use of new definitions for dimensionless variables in terms of nondimensional hydraulic geometry equations allows the development of a new flow resistance equation. The best overall performance is obtained by the Ferguson approach, which combines two power law flow resistance equations that are different for deep and shallow flows. To use this approach with flow discharge as input, a logarithmic matching equation in terms of the new dimensionless variables is proposed. For the domains of intermediate and large‐scale roughness, the field data indicate a considerable increase in flow resistance as compared with the domain of small‐scale roughness. The Ferguson approach is used to discuss the importance of flow resistance partitioning for bed load transport calculations at flow conditions with intermediate‐ and large‐scale roughness in natural gravel, cobble, and boulder bed streams. Key Points Some conventional flow resistance equations should not be used in shallow flows Between‐site and at‐a‐site variation of flow resistance show similarities Flow resistance partitioning can improve bedload transport predictions

The constant phase element (CPE) is a capacitive element with a frequency-independent negative phase between current and voltage which interpolates between a capacitor and a resistor. It is used extensively to model the complexity of the physics in e.g. the bioimpedance and electrochemistry fields. There is also a similar element with a positive phase angle, and both the capacitive and inductive CPEs are members of the family of fractional circuit elements or fractance. The physical meaning of the CPE is only partially understood and many consider it an idealized circuit element. The goal here is to provide alternative equivalent circuits, which may give rise to better interpretations of the fractance. Both the capacitive and the inductive CPEs can be interpreted in the time-domain, where the impulse and step responses are temporal power laws. Here we show that the current impulse responses of the capacitive CPE is the same as that of a simple time-varying series RL-circuit where the inductor’s value increases linearly with time. Similarly, the voltage response of the inductive CPE corresponds to that of a simple parallel RC circuit where the capacitor’s value increases linearly with time. We use the Micro-Cap circuit simulation program, which can handle time-varying circuits, for independent verification. The simulation corresponds exactly to the expected response from the proposed equivalents within 0.1% error. The realization with time-varying components correlates with known time-varying properties in applications, and may lead to a better understanding of the link between CPE and applications.

Superhydrophobicity is closely linked to the chemical composition and geometric characteristics of surface roughness. Building on our structural studies on water and air–water interfaces, this work aims to elucidate the mechanism underlying the wetting transition from the Wenzel to the Cassie state on a hydrophobic surface. In the Wenzel state, the grooves are filled with water, meaning that the surface roughness becomes embedded in the liquid. To evaluate the effects of surface roughness on water structure, a wetting parameter (WRoughness) is proposed, which is closely related to the geometric characteristics of roughness, such as pillar size, width, and height. During the wetting transition from Wenzel to Cassie states, the critical wetting parameter (WRoughness,c) may be expected, which corresponds to the critical pillar size (ac), width (wc), and height (hc). The Cassie state is expected when the WRoughness is less than WRoughness,c (ac), decreasing width (hc). Additionally, molecular dynamic (MD) simulations are conducted to demonstrate the effects of surface roughness on superhydrophobicity.

In this work, our target point is to focus on rough approximation operators generated from infra-topology spaces and examine their features. First, we show how infra-topology spaces are constructed from N j -neighborhood systems under an arbitrary relation. Then, we exploit these infra-topology spaces to form new rough set models and scrutinize their master characterizations. The main advantages of these models are to preserve all properties of Pawlak approximation operators and produce accuracy values higher than those given in several methods published in the literature. One of the unique characterizations of the current approach is that all the approximation operators and accuracy measures produced by the current approach are identical under a symmetric relation. Finally, we present two medical applications of the current methods regarding Dengue fever and COVID-19 pandemic. Some debates regarding the pros and cons of the followed technique are given as well as some upcoming work are proposed.

The flow over arbitrary roughness changes is investigated, revisiting the analysis of Belcher et al. (Q J R Meteorol Soc 116:611–635, 1990) regarding surface-roughness heterogeneity. The proposed theory is restricted to steady neutral boundary layers over flat regions with changes of roughness sufficiently slow and mild to inhibit the growth of nonlinear terms. The approach is based on a triple-deck decomposition of the flow above the roughness, although only the first two layers are interactive at leading order. Two experimental datasets (one with a smooth-to-rough and the other with a rough-to-smooth transition) are used to validate the theory. The latter is further compared against two large-eddy simulations featuring chessboard patterns of alternating surface roughness with relatively short and long length scales, respectively. All the comparisons show that the proposed theory is able to reasonably assess the wind-field perturbation due to the roughness heterogeneity, supporting the use of the model to quickly assess the effect of roughness changes in the flow field.

SmartRoadSense is a crowdsensing project aimed at monitoring the conditions of the road surface. Using the sensors of a smartphone, SmartRoadSense monitors the vertical accelerations inside a vehicle traveling the road and extracts a roughness index conveying information about the road conditions. The roughness index and the smartphone GPS data are periodically sent to a central server where they are processed, associated with the specific road, and aggregated with data measured by other smartphones. This paper studies how the smartphone vertical accelerations and the roughness index are related to the vehicle speed. It is shown that the dependence can be locally approximated with a gamma (power) law. Extensive experimental results using data extracted from SmartRoadSense database confirm the gamma law relationship between the roughness index and the vehicle speed. The gamma law is then used for improving the SmartRoadSense data aggregation accounting for the effect of vehicle speed.

Hydrodynamic modeling has been increasingly used to simulate water surface elevation which is important for flood prediction and risk assessment. Scarcity and inaccessibility of in situ bathymetric information have hindered hydrodynamic model development at continental-to-global scales. Therefore, river cross-section geometry is commonly approximated by highly simplified generic shapes. Hydrodynamic river models require both bed geometry and roughness as input parameters. Simultaneous calibration of shape parameters and roughness is difficult, because often there are trade-offs between them. Instead of parameterizing cross-section geometry and hydraulic roughness separately, this study introduces a parameterization of 1D hydrodynamic models by combining cross-section geometry and roughness into one conveyance parameter. Flow area and conveyance are expressed as power laws of flow depth, and they are found to be linearly related in log–log space at reach scale. Data from a wide range of river systems show that the linearity approximation is globally applicable. Because the two are expressed as power laws of flow depth, no further assumptions about channel geometry are needed. Therefore, the hydraulic inversion approach allows for calibrating flow area and conveyance curves in the absence of direct observations of bathymetry and hydraulic roughness. The feasibility and performance of the hydraulic inversion workflow are illustrated using satellite observations of river width and water surface elevation in the Songhua river, China. Results show that this approach is able to reproduce water level dynamics with root-mean-square error values of 0.44 and 0.50 m at two gauging stations, which is comparable to that achieved using a standard calibration approach. In summary, this study puts forward an alternative method to parameterize and calibrate river models using satellite observations of river width and water surface elevation.

Analysis of rock fracture deformation by normal stress is important for quantifying hydromechanical properties of fractured rocks that are related to a large number of geophysical problems and geoengineering applications. Experimental and numerical results for the closure of crystalline rock fractures subject to normal stress are presented in this study. An efficient high-resolution, half-space elastic–plastic contact model for analyzing the closure of crystalline rock fractures based on the Boussinesq’s solution is validated by high-precision and high-resolution experimental data. Using the validated elastic–plastic model, we investigate the correlation between fracture-specific stiffness and multi-scale surface roughness. The wavelet analysis method and the extended averaged slope magnitude for asperity heights (referred to as Z23D) are introduced to characterize the multi-scale surface roughness. The results show that the elastic–plastic contact model is effective and precise in modeling the closure of crystalline rock fractures, which matches better with the test results than the elastic model. The multi-scale features of surface roughness can be well characterized by the wavelet analysis and the extended roughness parameter Z23D. The specific stiffness is nonlinearly correlated with the multi-scale surface roughness that possibly follows a power law. The validated elastic–plastic contact model and the multi-scale surface roughness characterization methods, as well as the nonlinear correlation between the specific stiffness and the multi-scale surface roughness presented in this study, are helpful for evaluating the dependence of mechanical behaviors of rock fractures on its multi-scale surface roughness.