Length Of Rectangles Research Articles

Liouville metric of star-scale invariant fields: tails and Weyl scaling

We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter $$\gamma _c >0$$, the left–right length of rectangles for the Riemannian metric $$e^{\gamma \phi _{0,n}} ds^2$$ with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when $$\gamma < \min ( \gamma _c, 0.4)$$ and that subsequential limits are consistent with the Weyl scaling.

Particle-Size Analysis of Wood Fiber and Powder Based on Image Processing and Recognition

This article describes how to realize a wood fiber and powder automatic production and detection, using a mesh detection method based on image processing and particle-size analysis. With this method, the image will be transformed into an HSV color space, segmented based on S component with OSTU; calculated and analyzed with shape factor F, then rectangle fit, and finally the rectangle's length is converted into mesh. During wood flour mesh recognition, this article proposes the use of a rectangle fitting algorithm. In accordance with the actual demand for mesh recognition, a micro-nano wood flour mesh recognition system based on a modular approach has been designed and developed. This is as well as a mesh recognition design program based on wood flour features. The experiments and particle-size analysis results demonstrate that compared with traditional methods, the proposed approach is of higher accuracy and appropriate for extension.

Transmission Control Property of a Nano-optical System Made by an Antenna over a Bowtie Aperture

In this paper, we report a characteristic transmission control property of a nano-optical system by introducing an antenna over the input opening of a bowtie aperture. The transmission process through the system is investigated quantitatively by the coupling and transmission efficiencies, and an optical switch effect is found as the antenna length varies. To understand the physical mechanism, we then investigate the electrical field distribution of the antenna over a rectangle aperture as a simplified model. It is discovered that the "on" state of the system is due to Fabry–Perot resonances in the horizontal cavity formed by antenna, dielectric layer, and metal film. On the other hand, a cutoff occurs for the characteristic rectangle length shorter than the diffraction limit to turn the device to the "off" state. Such a phenomenon can thus provide a promising candidate for application in manipulating light in large-scale optoelectronic device integration.

Jamming transition of kinetically constrained models in rectangular systems

We theoretically calculate the average fraction of frozen particles in rectangular systems of arbitrary dimensions for the Kob-Andersen and Fredrickson-Andersen kinetically constrained models. We find the aspect ratio of the rectangle's length to width, which distinguishes short, square-like rectangles from long, tunnel-like rectangles, and show how changing it can effect the jamming transition. We find how the critical vacancy density converges to zero in infinite systems for different aspect ratios: For long and wide channels it decreases algebraically v(c) ~ W(-1/2) with the system's width W, while in square systems it decreases logarithmically vc) ~ 1/lnL with length L. Although derived for asymptotically wide rectangles, our analytical results agree with numerical data for systems as small as W ≈ 10.

Cavity mode waves during terahertz radiation from rectangularBi2Sr2CaCu2O8 + δ mesas

We re-examined the angular dependence of the radiation from the intrinsic Josephson junctions in rectangularmesas of Bi2Sr2CaCu2O8 + δ, in order to determine if the cavity mode part of the radiation arises from waves across the widthw or along the length of the mesas, associated with ‘hot spots’ (Wang et al 2010 Phys. Rev. Lett. 105 057002).We derived analytical forms for the angular dependence expected in both cases for ageneral cavity mode in which the width of the mesa corresponds to an integer multiple ofone-half the wavelength of the radiation. Assuming the coherent radiation from the acJosephson current source and the cavity magnetic surface current density source combineincoherently, fits to the data of Kadowaki et al (2010 J. Phys. Soc. Japan 79 023703) on amesa with mean for both wave directions using two models for the incoherent combination were made,which correspond to standing and traveling waves, respectively. The results suggest thatthe combined output from the uniform ac Josephson current source plus a cavity waveforming along the rectangle length is equally probable as that of the combined output fromthe uniform ac Josephson current plus a cavity wave across the width. However, for mesasin which is integral, where n is theindex of the rectangular TMzn, 0 mode, it is shown that standing cavity mode waves along the length of the mesa do not radiate in thexz plane perpendicular to the length of the mesa, suggesting experiments on such mesas couldhelp to resolve the question.

Achieving a new dimension: Children integrate three stimulus dimensions in volume estimations.

Although J. Piaget (1968) assumed that children up to 7 years old are unable to consider more than 1 stimulus dimension in their judgments, subsequent research has demonstrated that preschoolers can consider 2 dimensions, such as the width and length of rectangles to estimate their area (F. Wilkening, 1979). The present study addressed the question of whether children can also take 3 stimulus dimensions into account. Kindergartners, 1st and 3rd graders, and adults (N = 73) estimated the volume of cuboids that required the consideration of 3 dimensions: width, height, and length. The results showed that the majority of kindergartners already based their volume estimations on all 3 dimensions. A considerable proportion of kindergartners even integrated width, height, and length multiplicatively. There was no dramatic improvement with age, implying the implicit understanding of volume to develop relatively early in childhood. The results are discussed in light of children's cognitive competencies concerning multidimensional reasoning.

Effect of Rectangle Length on Velocity Thresholds for Real Movement

New data are reported on the influence of size on the velocity threshold for real movement. As the length of a narrow stimulus object increases, width remaining constant, the velocity threshold also increases. These findings are discussed in relation to some psychophysical experiments on contrast and some physiological experiments on motion.