12,715 research outputs found
Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines
Solving nesting problems or irregular strip packing problems is to position
polygons in a fixed width and unlimited length strip, obeying polygon integrity
containment constraints and non-overlapping constraints, in order to minimize
the used length of the strip. To ensure non-overlapping, we used separation
lines. A straight line is a separation line if given two polygons, all vertices
of one of the polygons are on one side of the line or on the line, and all
vertices of the other polygon are on the other side of the line or on the line.
Since we are considering free rotations of the polygons and separation lines,
the mathematical model of the studied problem is nonlinear. Therefore, we use
the nonlinear programming solver IPOPT (an algorithm of interior points type),
which is part of COIN-OR. Computational tests were run using established
benchmark instances and the results were compared with the ones obtained with
other methodologies in the literature that use free rotation
Packing-limited growth of irregular objects
We study growth limited by packing for irregular objects in two dimensions.
We generate packings by seeding objects randomly in time and space and allowing
each object to grow until it collides with another object. The objects we
consider allow us to investigate the separate effects of anisotropy and
non-unit aspect ratio. By means of a connection to the decay of pore-space
volume, we measure power law exponents for the object size distribution. We
carry out a scaling analysis, showing that it provides an upper bound for the
size distribution exponent. We find that while the details of the growth
mechanism are irrelevant, the exponent is strongly shape dependent. Potential
applications lie in ecological and biological environments where sessile
organisms compete for limited space as they grow.Comment: 6 pages, 4 figures, 1 table, revtex
Dense Regular Packings of Irregular Non-Convex Particles
We present a new numerical scheme to study systems of non-convex, irregular,
and punctured particles in an efficient manner. We employ this method to
analyze regular packings of odd-shaped bodies, not only from a nanoparticle but
also both from a computational geometry perspective. Besides determining
close-packed structures for many shapes, we also discover a new denser
configuration for Truncated Tetrahedra. Moreover, we consider recently
synthesized nanoparticles and colloids, where we focus on the excluded volume
interactions, to show the applicability of our method in the investigation of
their crystal structures and phase behavior. Extensions to the presented scheme
include the incorporation of soft particle-particle interactions, the study of
quasicrystalline systems, and random packings.Comment: 4 pages, 3 figure
Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra
The determination of the densest packings of regular tetrahedra (one of the
five Platonic solids) is attracting great attention as evidenced by the rapid
pace at which packing records are being broken and the fascinating packing
structures that have emerged. Here we provide the most general analytical
formulation to date to construct dense periodic packings of tetrahedra with
four particles per fundamental cell. This analysis results in six-parameter
family of dense tetrahedron packings that includes as special cases recently
discovered "dimer" packings of tetrahedra, including the densest known packings
with density . This study strongly suggests that
the latter set of packings are the densest among all packings with a
four-particle basis. Whether they are the densest packings of tetrahedra among
all packings is an open question, but we offer remarks about this issue.
Moreover, we describe a procedure that provides estimates of upper bounds on
the maximal density of tetrahedron packings, which could aid in assessing the
packing efficiency of candidate dense packings.Comment: It contains 25 pages, 5 figures
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