Figure 1: Snapshots of the optimization procedure to construct a boundary aligned 3D cross-frame field. The top row shows the internal streamlines. The next row contains another visualization with cubes spread by a parameterization along the current cross-frame field and rotated by the current local frame R(Φ). The corresponding number of iteration is shown at the bottom.
AbstractIn this paper, we present a method for constructing a 3D crossframe field, a 3D extension of the 2D cross-frame field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface cross-frame field (equivalent to a 4-Way Rotational-Symmetry vector field), symmetry for 3D crossframe fields cannot be formulated by simple one-parameter 2D rotations in the tangent planes. To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, we can formulate an efficient smoothness measure of the cross-frame field. Through minimization of this measure under certain boundary conditions, we can construct a smooth 3D cross-frame field that is aligned with the surface normal at the boundary. We visualize the resulting cross-frame field through restrictions to the boundary surface, streamline tracing in the volume, and singularities. We also demonstrate the application of the 3D cross-frame field to producing hexahedron-dominant meshes for given volumes, and discuss its potential in high-quality hexahedralization, much as its 2D counterpart has shown in quadrangulation.
Lightweight nitrogen-doped
ordered mesoporous carbon (NOMC) with
high specific surface area and pore volume have been prepared through
self-assembly and subsequent heat treatment route. The spherical NOMC
particles are decorated with CoFe2O4 nanoparticles
via coprecipitation method to enhance their microwave absorption property.
The electromagnetic parameters of the NOMC and CoFe2O4/NOMC composites are measured and the microwave reflection
loss properties are evaluated in the frequency range of 0.5–18
GHz. The results show that both the real part and imaginary part of
permittivity of NOMC totally decline and the real part of permeability
increases with the introduction of ferrite. However, the negative
values of the imaginary part of the complex permeability appear for
the CoFe2O4/NOMC composites, which may be caused
by enhanced eddy current effect due to the introduction of ferrite.
The reflection loss results exhibit that the CoFe2O4/NOMC composites have excellent microwave absorption performances.
The absorption bandwidth less than −10 dB reaches 5.0 GHz (11.9–16.9
GHz) for 40-F/NOMC composite (40 wt % ferrite) with 1.5 mm of thickness
and the minimum reflection loss value is up to −38.3 dB at
3.9 GHz for 30-F/NOMC composite with 4.0 mm of thickness. The excellent
absorption properties derive from the synergistic effect between dielectric
loss of NOMC and magnetic loss of ferrite and better impendence matching
at air and ferrite/NOMC composite interface. Thus, the lightweight
ferrite/NOMC composites exhibit their great potential as microwave
absorbing materials.
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