Topological Singularities in Periodic Media: Ginzburg–Landau and Core-Radius Approaches

We describe the emergence of topological singularities in periodic media within the Ginzburg–Landau model and the core-radius approach. The energy functionals of both models are denoted by $$E_{\varepsilon ,\delta }$$ E ε , δ , where $$\varepsilon $$ ε represent the coherence length (in the Ginzburg–Landau model) or the core-radius size (in the core-radius approach) and $$\delta $$ δ denotes the periodicity scale. We carry out the $$\Gamma $$ Γ -convergence analysis of $$E_{\varepsilon ,\delta }$$ E ε , δ as $$\varepsilon \rightarrow 0$$ ε → 0 and $$\delta =\delta _\varepsilon \rightarrow 0$$ δ = δ ε → 0 in the $$|\log \varepsilon |$$ | log ε | scaling regime, showing that the $$\Gamma $$ Γ -limit consists in the energy cost of finitely many vortex-like point singularities of integer degree. After introducing the scale parameter $$\begin{aligned} \lambda =\min \Bigl \{1,\lim _{\varepsilon \rightarrow 0} {|\log \delta _\varepsilon |\over |\log \varepsilon |}\Bigr \} \end{aligned}$$ λ = min { 1 , lim ε → 0 | log δ ε | | log ε | } (upon extraction of subsequences), we show that in a sense we always have a separation-of-scale effect: at scales smaller than $$\varepsilon ^\lambda $$ ε λ we first have a concentration process around some vortices whose location is subsequently optimized, while for scales larger than $$\varepsilon ^\lambda $$ ε λ the concentration process takes place “after” homogenization.

The Physical Metric in General Relativity, Size and Gravitational Lensing of Black Holes and Neutron Stars

The physical metric in general relativity has been introduced by the author as the exact solution of Einstein equation that fits the observation of time delay of the solar system. The necessary and sufficient condition for the physical metric is that the speed of light on the angular direction is unchanged from that of vacuum. A striking result is that the radius size of a black hole and a neutron star (summarized as compact object hereafter) is found to be 2.60 times greater than predicted by the Schwarzschild metric. In this article, the gravitational lensing of the compact object at long distance is absent. In other words, it is a feature result of the physical metric that the effect of the gravitational lensing for compact object by itself disappears at long distance. It will be shown that the recent observations are consistent with the prediction of the physical metric.

Abrupt Change Effect of Bandgap Energy on Quantum System of Silicon Nanowire

In the quantum system of Si nanowire (NW), the energy bandgap obviously increases with decreasing radius size of NW, in which the quantum confinement (QC) effect plays a main role. Furthermore, the simulation result demonstrated that the direct bandgap can be obtained as the NW diameter is smaller than 3 nm in Si NW with (001) direction. However, it is discovered in the simulating calculation that the QC effect disappears as the NW diameter arrives at size of monoatomic line, in which its bandgap sharply deceases where the abrupt change effect in bandgap energy occurs near the idea quantum wire. In the experiment, we fabricated the Si NW structure by using annealing and pulsed laser deposition methods, in which a novel way was used to control the radius size of Si NW by confining cylinder space of NW in nanolayer. It should have a good application on optic-electronic waveguide of silicon chip.

Unsteady state fluid structure of two-sided nonfacing lid-driven cavity induced by a semicircle at different radii sizes and velocity ratios

This paper aims in analyzing the effect of velocity ratio [Formula: see text] and Radius size of an inner semicircle inserted at the bottom wall of two-sided nonfacing lid-driven cavity on the bifurcation occurrence phenomena. The study has been performed by using finite volume method (FVM) and multigrid acceleration for certain pertinent parameters; Reynolds number, velocity ratios ([Formula: see text]) by step of 0.25 and Radius size of the inner semicircle ([Formula: see text]) by step of 0.05. An analysis of the flow evolution shows that, when increasing Re beyond a certain critical value, the flow becomes unstable then bifurcates for various velocity ratios and radius size of the semicircle. Therefore, critical Reynolds numbers are determined for each case. It is worth to mention that the transition to unsteadiness follows the classical scheme of a Hopf bifurcation. Results show also that in the standard case of a single lid-driven cavity ([Formula: see text]), the highest critical Reynolds number corresponds to the lowest radius of the semicircle and the same for ([Formula: see text]). Conversely, from ([Formula: see text]) where the left moving lid take effect, the opposite phenomenon occurs. In harmony with this, it has been found that elongating the cylinder radius accelerates the appearance of the unsteady regime and delays it in the opposite case. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. The numerical results are correlated in a sophisticated correlation of the critical Reynolds number with other parameters.

Females Are Not Proportionally Smaller Males: Relationships Between Radius Anthropometrics and Their Sex Differences

Background: Distal radius fracture reduction by internal fixation is most commonly achieved using volar locking plates (VLPs). Many standard VLP designs make little point contact with radius anatomy, and most postsurgical complications following fixation are attributed to poor implant fit. Sex differences may require consideration in implant design, as females more commonly require VLP removal. Therefore, the purpose of this research was to determine whether the relationships between measures of radius shape are proportional between the sexes. Methods: Three-dimensional radius bone geometries were created from 40 male and 34 female (mean age = 72.04 years) forearm computed tomographic scans in Mimics (Materialise NV, Leuven, Belgium). Eleven measures of radius shape were collected from each scan. Principal components analysis was performed on these measures to determine which shape variables account for the greatest differences in radius shape among individuals and between the sexes. Results: Principal component scores representing isometric radius size separated the sexes. Six anthropometric measures significantly correlated with isometric radius size for all specimens, whereas 3 and 1 measures significantly correlated with isometric radius size in males and females, respectively. Conclusions: Anthropometrics of male and female radii vary by different proportions. Using anthropometrics from both sexes to create a single implant system may not result in optimal patient fit for either sex.

An Adaptive Approach for the Calculation of Ensemble Gridpoint Probabilities

Traditional ensemble probabilities are computed based on the number of members that exceed a threshold at a given point divided by the total number of members. This approach has been employed for many years in coarse-resolution models. However, convection-permitting ensembles of less than ~20 members are generally underdispersive, and spatial displacement at the gridpoint scale is often large. These issues have motivated the development of spatial filtering and neighborhood postprocessing methods, such as fractional coverage and neighborhood maximum value, which address this spatial uncertainty. Two different fractional coverage approaches for the generation of gridpoint probabilities were evaluated. The first method expands the traditional point probability calculation to cover a 100-km radius around a given point. The second method applies the idea that a uniform radius is not appropriate when there is strong agreement between members. In such cases, the traditional fractional coverage approach can reduce the probabilities for these potentially well-handled events. Therefore, a variable radius approach has been developed based upon ensemble agreement scale similarity criteria. In this method, the radius size ranges from 10 km for member forecasts that are in good agreement (e.g., lake-effect snow, orographic precipitation, very short-term forecasts, etc.) to 100 km when the members are more dissimilar. Results from the application of this adaptive technique for the calculation of point probabilities for precipitation forecasts are presented based upon several months of objective verification and subjective feedback from the 2017 Flash Flood and Intense Rainfall Experiment.