A New Method to Determine the Spatial Sensitivity of Time Domain Reflectometry Probes Based on Three-Dimensional Weighting Theory

The time domain reflectometry (TDR) method has been widely used to measure soil water content for agriculture and engineering applications. Quick design and optimization of the probe is crucial to achieving practical utilization. Generally, the two-dimensional weighting theory, calculation of the spatial sensitivity of TDR probes in the plane transverse to the direction of electromagnetic wave propagation, and relevant numerical simulation techniques can be used to solve any issues. However, it is difficult to tackle specific problems such as complex probe shape, end effect, and so forth. In order to solve these issues, a method including a three-dimensional weighting theory and the relevant numerical simulation technique was proposed and verified to confirm the feasibility of this method by means of comparing the existing experimental results and the computational values. First, a shaft probe was used to determine the impact of the shaft on the effective dielectric constant of the probe. Then, three-rod probes were calibrated by a sample with a special shape and water-level variations around the probe using the proposed method to determine the values of the apparent dielectric constant. Besides, model boundary size and end effect were also considered in the computation of dielectric constants. Results showed that compared with the experimental and computational data, the newly proposed method calculated the measurement sensitivity of the shaft probes well. In addition, it was observed that experiment dielectric constant values were slightly different from computational ones, not only using a vertical probe but also horizonal probe. Moreover, it was also found that there was a slight influence of sample shape and end effect on the apparent dielectric constant, but model boundary size has a certain impact on the values. Overall, the new method can provide benefits in the design and optimization of the probe.

Accounting for graded structure in adjective categories with valence-based opposition relationships

In contrast to noun categories, little is known about the graded structure of adjective categories. In this study, we investigated whether adjective categories show a similar graded structure and what determines this structure. The results show that adjective categories like nouns exhibit a reliable graded structure. Similar to nouns, we investigated whether similarity is the main determinant of the graded structure. We derived a low-dimensional similarity representation for adjective categories and found that valence differences in adjectives constitute an important organising principle in this similarity space. Valence was not implicated in the categories' graded structure, however. A formal similarity-based model using exemplars accounted for the graded structure by effectively discarding the valence differences between adjectives in the similarity representation through dimensional weighting. Our results generalise similarity-based accounts of graded structure and highlight a closely knit relationship between adjectives and nouns on a representational level.