We study wave propagation in two-dimensional granular crystals under the Hertzian contact law consisting of hexagonal packings of spheres under various basin geometries including hexagonal, triangular, and circular basins which can be tiled with hexagons. We find that the basin geometry will influence wave reflection at the boundaries, as expected, and also may result in bottlenecks forming. While exterior strikers the size of a single sphere have been considered in the literature, it is also possible to consider strikers which impact multiple spheres along a boundary, or to have multiple sides being struck simultaneously. It is also possible to consider obstructions or even strikers in the interior of the hexagonally packed granular crystal, as previously considered in the case of square packings, resulting in the basin geometry no longer forming a convex set. We consider various configurations of either boundary or interior strikers. We shall also consider the case where a granular crystal is composed of two separate crystals of differing material, with a single interface between the two distinct materials. Depending on the relative material properties of each type of sphere, this can result in a trapping of most of the wave energy within one of the two regions. While repeated reflections from the boundaries will cause the systems we study to fall into disorder for large time, there are a number of interesting wave structures and patters that emerge as transients at intermediate timescales.

BackgroundFetal deformity is a disease caused by abnormal chromosome structure, which may be influenced by genetic factors as well as the maternal and external environment. Magnetic resonance imaging (MRI) may be used to effectively diagnose fetus deformities. However it has been reported that gene analysis is a more accurate diagnostic method. The aim of the present study was to investigate the effectiveness of MRI in combination with gene analysis for the diagnosis of fetal congenital heart disease, a form of fetus deformity.MethodsMRI, array comparative genome hybridization analysis and fluorescence in situ hybridization were used to analyze the effectiveness of the two methods in a total of 78 pregnant women with suspected fetal congenital heart disease.ResultsOur findings demonstrated that the combination of MRI and gene analysis resulted in significantly improved diagnostic accuracy, sensitivity and specificity for fetal congenital heart disease compared with either method alone. MRI combined with gene analysis confirmed 42 fetuses with pulmonary stenosis, 24 with aortic stenosis and 12 healthy fetuses, which was significantly improved compared with MRI or gene analysis alone. It was also observed that gene analysis was a more efficient method of diagnosis compared with MRI; however, the combination of the two methods was the most effective.ConclusionIn conclusion, the results of the present study suggest that MRI combined with gene analysis may be a more effective diagnostic method for fetal congenital heart disease compared with the current protocol.

Background: To investigate the correlation between hypertriglyceridemic waist circumference (HTWC) phenotype and gestational diabetes mellitus (GDM). Methods: A total of 1083 patients with gestational age ≤8 weeks were divided into four groups: normal triglyceride and waist circumference group (group A, n=575), simple abdominal obesity group (group B, n=317), simple high triglyceride group (group C, n=125), and HTWC group (group D, n=66). General information and serum biochemical indicators were measured and recorded. Analysis of variance (ANOVA) and logistic regression analysis were used to evaluate the relationship between HTWC with GDM.Results: The prevalence of GDM in the HTWC group was signi cantly greater than in the other three groups. After adjustment by multivariate logistic regression analysis, the proportion of GDM in the HTWC group was 1.753 times higher than in group A.Conclusion: These ndings suggest that there is a signi cant correlation between HTWC phenotype and GDM, indicating that the HTWC phenotype could be applied as a simple marker for identifying GDM risk factors.

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