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Anisotropic and dispersive wave propagation within strain-gradient framework
In this paper anisotropic and dispersive wave propagation within linear
strain-gradient elasticity is investigated. This analysis reveals significant
features of this extended theory of continuum elasticity. First, and contrarily
to classical elasticity, wave propagation in hexagonal (chiral or achiral)
lattices becomes anisotropic as the frequency increases. Second, since
strain-gradient elasticity is dispersive, group and energy velocities have to
be treated as different quantities. These points are first theoretically
derived, and then numerically experienced on hexagonal chiral and achiral
lattices. The use of a continuum model for the description of the high
frequency behavior of these microstructured materials can be of great interest
in engineering applications, allowing problems with complex geometries to be
more easily treated
Uniform line fillings
Deterministic fabrication of random metamaterials requires filling of a space
with randomly oriented and randomly positioned chords with an on-average
homogenous density and orientation, which is a nontrivial task. We describe a
method to generate fillings with such chords, lines that run from edge to edge
of the space, in any dimension. We prove that the method leads to random but
on-average homogeneous and rotationally invariant fillings of circles, balls
and arbitrary-dimensional hyperballs from which other shapes such as rectangles
and cuboids can be cut. We briefly sketch the historic context of Bertrand's
paradox and Jaynes' solution by the principle of maximum ignorance. We analyse
the statistical properties of the produced fillings, mapping out the density
profile and the line-length distribution and comparing them to analytic
expressions. We study the characteristic dimensions of the space in between the
chords by determining the largest enclosed circles and balls in this pore
space, finding a lognormal distribution of the pore sizes. We apply the
algorithm to the direct-laser-writing fabrication design of optical
multiple-scattering samples as three-dimensional cubes of random but
homogeneously positioned and oriented chords.Comment: 10 pages, 12 figures; v3: restructured paper, more references, more
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