49,046 research outputs found
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 TiO 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. The first section presents a comparison
study of the structural stability for X-anion and X-cation doped TiO (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 are
determined by the growth condition of doped TiO 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. The third section summarizes the origin of the
spin-polarization and the magnetic coupling character in C- (N- and B-) doped
TiO.Comment: 21 pages, 24 figures, 3 table
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