Fission of Halving Edges Graphs

In this paper we discuss an operation on halving edges graph that we call fission. Fission replaces each point in a given configuration with a small cluster of k points. The operation interacts nicely with halving edges, so we examine its properties in detail.Comment: 17 pages, 10 figure

Critical Thickness Ratio for Buckled and Wrinkled Fruits and Vegetables

Fruits and vegetables are usually composed of exocarp and sarcocarp and they take a variety of shapes when they are ripe. Buckled and wrinkled fruits and vegetables are often observed. This work aims at establishing the geometrical constraint for buckled and wrinkled shapes based on a mechanical model. The mismatch of expansion rate between the exocarp and sarcocarp can produce a compressive stress on the exocarp. We model a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. The derived bifurcation condition contains both geometrical and material constants. However, a careful analysis on this condition leads to the finding of a critical thickness ratio which separates the buckling and wrinkling modes, and remarkably, which is independent of the material stiffnesses. More specifically, it is found that if the thickness ratio is smaller than this critical value a fruit/vegetable should be in a buckling mode (under a sufficient stress); if a fruit/vegetable in a wrinkled shape the thickness ratio is always larger than this critical value. To verify the theoretical prediction, we consider four types of buckled fruits/vegetables and four types of wrinkled fruits/vegetables with three samples in each type. The geometrical parameters for the 24 samples are measured and it is found that indeed all the data fall into the theoretically predicted buckling or wrinkling domains. Some practical applications based on this critical thickness ratio are briefly discussed.Comment: 11 pages 9 figures 2 table

A practical approach to compensate for diodic effects of PS converted waves

In inhomogeneous media, PS converted waves often suffer from severe diodic effects. The traveltime and amplitude of PS converted waves may be different in the forward and reverse shooting directions, giving rise to different stacking velocities of PS converted waves and velocity ratios. These effects, compounded with the asymmetric raypath of PS converted waves, will further increase the difficulties and costs in processing PS converted-wave data. One common method to solve this problem is to separate a data set into two volumes with different shooting directions (e.g., negative or positive offset directions). Different values of the PS converted-wave velocities are used to process the two data sets separately and the two results are combined in the final stage. The problem with this method is that sometimes it is difficult to correlate the data sets and the final combined result may be degraded. In this paper, we propose a method to overcome this problem and apply this method to a 2D data set for improving the PS converted-wave imaging

Review of the Structural Stability, Electronic and Magnetic Properties of Nonmetal-Doped TiO2_2 from First-Principles Calculations

This paper reviews and summarizes the recent first-principles theoretical studies of the structural stability, electronic structure, optical and magnetic properties of nonmetal-doped TiO$_2$. The first section presents a comparison study of the structural stability for X-anion and X-cation doped TiO$_2$ (X=B, C, Si, Ge, N, P, As, Sb, S, Se, Te, F, Cl, Br, and I), which reveals that the sites of nonmetal dopants (i.e., at O sites or at Ti sites) in TiO$_2$ are determined by the growth condition of doped TiO$_2$ and the dopants' electronegativities. The next section reviews the electronic structure, optical absorption and mechanism of the visible-light photocatalytic activity for nonmetal-doped TiO$_2$. The third section summarizes the origin of the spin-polarization and the magnetic coupling character in C- (N- and B-) doped TiO$_2$.Comment: 21 pages, 24 figures, 3 table